Robust signal detection in colored noise with unknown covariance is essential in radar, cognitive radio, integrated sensing and communication (ISAC), and quantum sensing applications. This paper develops a unified analytical framework for the Standard Condition Number (SCN) detector, which employs the ratio of the largest to smallest eigenvalues of the whitened sample covariance matrix. The framework jointly covers both ideal conditions in which the training and sensing noise statistics are identical and disturbed conditions in which interference or jamming alters the sensing covariance. Despite the SCN's practical relevance, its finite-sample false-alarm and detection behavior has not been analytically characterized. Using random matrix theory (RMT), we derive general expressions for these probabilities, provide closed-form results for special cases, and show that the SCN preserves the Constant False Alarm Rate (CFAR) property under covariance mismatch. Analytical and simulation results confirm that the proposed unified framework delivers consistent detection performance and greater robustness than conventional eigenvalue- and LRT-based detectors.

Movable antennas have recently emerged as a promising paradigm to overcome the inherent inflexibility of conventional fixed antenna arrays. By enabling the physical movement of antenna elements, movable antennas introduce additional spatial degrees of freedom to wireless systems. Although the importance of the movement delay has been recognized, a critical yet unexplored problem is that the movement schemes used to transition from the initial to the target positions are overlooked. This paper presents a systematic investigation of two fundamental movement schemes: concurrent movement and cumulative movement, and addresses a key design question: Should we prioritize minimizing the total configuration time or maximizing the communication performance under a limited movement budget? Specifically, two different optimization problems are formulated to maximize the sum rate under different movement constraints, thereby introducing tighter coupling between antenna positions and beamforming design, increasing computational complexity in joint optimization, and necessitating efficient allocation of delay budgets across multiple antennas. To this end, we develop an alternating-optimization-based algorithm to obtain the corresponding suboptimal solutions. A theoretical degeneration analysis is further conducted to provide fundamental insights. The optimal strategy for a single antenna can surprisingly be to not move. While in multi-antenna systems, the performance gap scales with antenna displacement, movement budgets, and transmit power. Simulation results show that movable antennas substantially improve achievable rates over fixed antennas, with concurrent movement benefiting low-latency scenarios, while cumulative movement favoring high-rate or delay-tolerant scenarios.

Wideband near-field communication (NFC) systems are subject to the spatial-wideband effect arising from frequency-dependent array responses, leading to array-gain loss and inter-user interference leakage. To address this challenge, we propose a rate-splitting multiple access (RSMA)-enabled NFC transmit scheme that integrates true-time-delay (TTD)–based hybrid beamfocusing. RSMA enables flexible inter-user interference management, while TTD-based architectures effectively mitigate spatial-wideband effect and significantly reduce radio frequency chain requirements. As a proxy for the performance degradation induced by the spatial-wideband effect, we adopt the minimum user rate as the optimization metric. Specifically, we aim to maximize the minimum rate by jointly optimizing frequency-dependent analog beamfocusing, digital beamfocusing, and common rate allocation. The resulting problem is highly nonconvex. To solve it efficiently, we develop a penalty-based iterative algorithm that partitions the design variables into three blocks and applies block coordinate descent (BCD) to optimize each block in an alternating manner. The proposed framework is further extended to accommodate sub-connected TTD-based hybrid architectures. Comprehensive simulation results demonstrate that the proposed scheme: (i) effectively compensates for the spatial-wideband effect, addressing a critical wideband NFC bottleneck; (ii) achieves performance close to that of full-digital beamfocusing with substantially lower hardware complexity; and (iii) delivers significant performance gains compared to existing benchmark schemes.

Integrated sensing and communication (ISAC) systems enable communication and sensing functions via three protocols, including ($\text{TP}_{1}$) concurrently using the same time-frequency resources, ($\text{TP}_{2}$) scheduling them independently, or ($\text{TP}_{3}$) a hybrid technique that combines both. Nevertheless, all existing studies rely on the first approach, and none provide a comprehensive performance evaluation of all three protocols. Thus, this paper offers an extensive performance evaluation of these protocols, emphasizing their advantages, limitations, and trade-offs. Specifically, we maximize the sum communication and/or sensing rate for all protocols in a full-duplex ISAC system with multiple users and targets. Numerical results reveal that protocols ($\text{TP}_{1}$) and ($\text{TP}_{3}$) necessitate a sensing metric considering both transmit and receiver beams to ensure adequate sensing performance. In contrast, although protocol ($\text{TP}_{2}$) can utilize more straightforward sensing metrics and avoid communication-sensing interference, it may not achieve high communication performance.

Reconfigurable Intelligent Surfaces (RIS) have emerged as transformative technologies, enhancing spectral efficiency and improving interference management in multi-user cooperative communications. This paper investigates the integration of RIS with Flexible-Duplex (FlexD) communication, featuring dynamic scheduling capabilities, to mitigate unintended external interference in multi-user wireless networks. By leveraging the reconfigurability of RIS and dynamic scheduling, we propose a user-pair selection scheme to maximize system throughput when full channel state information (CSI) of interference is unavailable. We develop a mathematical framework to evaluate the throughput outage probability when RIS introduces spatial correlation. The derived analytical results are used for asymptotic analysis, providing insights into dynamic user scheduling under interference based on statistical channel knowledge. Finally, we compare FlexD with traditional Full Duplex (FD) and Half Duplex (HD) systems against RIS-assisted FlexD. Our results show FlexD’s superior throughput enhancement, energy efficiency and data management capability in interference-affected networks, typical in current and next-generation cooperative wireless applications like cellular and vehicular communications.

Cell-free (CF) integrated sensing and communication (ISAC) combines CF architecture with ISAC. CF employs distributed access points, eliminates cell boundaries, and enhances coverage, spectral efficiency, and reliability. ISAC unifies radar sensing and communication, enabling simultaneous data transmission and environmental sensing within shared spectral and hardware resources. CF-ISAC leverages these strengths to improve spectral and energy efficiency while enhancing sensing in wireless networks. As a promising candidate for next-generation wireless systems, CF-ISAC supports robust multi-user communication, distributed multi-static sensing, and seamless resource optimization. However, a comprehensive survey on CF-ISAC has been lacking. This paper fills that gap by first revisiting CF and ISAC principles, covering cooperative transmission, radar cross-section, target parameter estimation, ISAC integration levels, sensing metrics, and applications. It then explores CF-ISAC systems, emphasizing their unique features and the benefits of multi-static sensing. State-of-the-art developments are categorized into performance analysis, resource allocation, security, and user/target-centric designs, offering a thorough literature review and case studies. Finally, the paper identifies key challenges such as synchronization, multi-target detection, interference management, and fronthaul capacity and latency. Emerging trends, including next-generation antenna technologies, network-assisted systems, near-field CF-ISAC, integration with other technologies, and machine learning approaches, are highlighted to outline the future trajectory of CF-ISAC research.

Cell-free (CF) architectures and full-duplex (FD) communication are leading candidates for next-generation wireless networks. The CF framework removes cell boundaries in traditional cell-based systems, thereby mitigating the inter-cell interference and improving the coverage probability. In contrast, FD communication allows simultaneous transmission and reception on the same frequency-time resources, effectively doubling the spectral efficiency (SE). The integration of these technologies, known as CF FD communication, leverages the advantages of both approaches to enhance the spectral and energy efficiency in wireless networks. CF FD communication is particularly promising due to the low-power and cost-effective FD-enabled access points (APs), which are ideal for short-range transmissions between APs and users. Despite its potential, a comprehensive survey or tutorial on CF FD communication has been notably absent. This paper aims to address this gap in the literature. It begins with an overview of FD communication fundamentals, self-interference cancellation techniques, and CF technology principles, including their implications for current wireless networks. The discussion then moves to the integration and compatibility of CF and FD technologies, focusing on channel estimation, performance analysis, and resource allocation in CF FD massive multiple-input multiple-output (mMIMO) networks, supported by an extensive literature review and case studies. The potential of combining a sub-category of CF architecture—network-assisted CF technology—with FD technology is also explored, including a detailed case study on fundamentals, performance analysis, AP operation, and mode assignments. Finally, emerging CF FD paradigms, like millimeter-wave communications, unmanned aerial vehicles, and reconfigurable intelligent surfaces, are discussed, highlighting existing contributions and unresolved issues.

This paper introduces a universal optimization framework for integrated sensing and communication (ISAC) systems, which are expected to be fundamental aspects of sixth-generation networks. In particular, we develop an iterative augmented Lagrangian manifold optimization (IALMO) framework designed to maximize communication sum rate while satisfying sensing beampattern gain targets, users’ minimum rate requirements, and base station (BS) transmit power limits. IALMO applies the principles of Riemannian manifold optimization to navigate the complex, non-convex landscape of the resource allocation problem. It efficiently leverages the augmented Lagrangian method to ensure adherence to constraints. Comprehensive numerical results are presented to validate our framework, which illustrates the IALMO method’s superior capability to enhance the dual functionalities of communication and sensing in ISAC systems. For instance, with 12 antennas and 30 dBm BS transmit power, our proposed IALMO algorithm delivers a 4.2% sum rate gain over a benchmark optimization-based algorithm. Remarkably, the suggested method performs better in complexity and execution time. For instance, the proposed IALMO algorithm reduces average algorithm execution time by 89.5% with 20 BS transmit antennas compared to the standard optimization-based benchmark. This work demonstrates significant improvements in system performance and contributes a new algorithmic perspective to ISAC resource management.

Integrated sensing and communication (ISAC) networks leverage extremely large-scale antenna arrays and high frequencies. This inevitably extends the Rayleigh distance, making near-field (NF) spherical wave propagation dominant. This unlocks numerous spatial degrees of freedom, raising the challenge of optimizing them for communication and sensing tradeoffs. To this end, we propose a rate-splitting multiple access (RSMA)-based NF-ISAC transmit scheme utilizing hybrid analog-digital antennas. RSMA enhances interference management, while a variable number of dedicated sensing beams adds beamforming flexibility. The objective is to maximize the minimum communication rate while ensuring multi-target sensing performance by jointly optimizing receive filters, analog and digital beamformers, common rate allocation, and the sensing beam count. To address uncertainty in sensing beam allocation, a rank-zero solution reconstruction method demonstrates that dedicated sensing beams are unnecessary for NF multi-target detection. A penalty dual decomposition (PDD)-based double-loop algorithm is introduced, employing weighted minimum mean-squared error (WMMSE) and quadratic transforms to reformulate communication and sensing rates. Simulations reveal that the proposed scheme: 1) achieves performance comparable to fully digital beamforming with fewer RF chains, 2) maintains NF multi-target detection without compromising communication rates, and 3) significantly outperforms conventional multiple access schemes and far-field ISAC systems.

Autonomous aerial vehicle (AAV)-assisted mobile edge computing systems have high mobility and can be deployed in various rugged terrain and emergency scenarios for communication and monitoring. However, the malicious use of AAV swarms poses a potential threat to key areas. Therefore, accurate positioning of AAV swarms is crucial for the security of high-value civilian facilities and equipment. This article investigates angle estimation of coherent signals from AAV swarms in bistatic multiple-input multiple-output radar under nonuniform noise. The nonuniform noise powers are iteratively estimated based on the structural characteristics of the covariance matrix and subsequently removed from the observations. Transmission-reception diversity smoothing is then applied to the signal subspace, obtained through higher order singular value decomposition, to recover the rank deficiency. Furthermore, a block sparse reconstruction method is proposed, utilizing the reweighted smoothed$\ell _{0}$-norm, to obtain angle estimates. This method automatically pairs the direction-of-arrivals and direction-of-departures of AAVs. Experimental results demonstrate the superiority of our approach over existing solutions.

Cell-free integrated sensing and communication (CF-ISAC) systems are just emerging as an interesting technique for future communications. Such a system comprises several multiple-antenna access points (APs), serving multiple single-antenna communication users and sensing targets. However, efficient beamforming designs that achieve high precision and robust performance in densely populated networks are lacking. This paper proposes a new beamforming algorithm by exploiting the inherent Riemannian manifold structure. The aim is to maximize the communication sum rate while satisfying sensing beampattern gains and per AP transmit power constraints. To address this constrained optimization problem, a highly efficient augmented Lagrangian model-based iterative manifold optimization for the CF-ISAC (ALMCI) algorithm is developed. This algorithm exploits the geometry of the proposed problem and uses a complex oblique manifold. Conventional convex-concave procedure (CCPA) and multidimensional complex quadratic transform (MCQT)-SCA algorithms are also developed as comparative benchmarks. The ALMCI algorithm significantly outperforms both of these. For example, with 16 APs having 12 antennas and 30 dBm transmit power each, our proposed ALMCI algorithm yields 22.7 % and 6.7 % sum rate gains over the CCPA and MCQT-SCA algorithms, respectively. In addition to improvement in communication capacity, the ALMCI algorithm achieves superior beamforming gains and reduced complexity.

This paper presents a robust sparse direct position determination (DPD) method for multiple emitters using distributed sensor arrays in the presence of unknown gain-phase errors. The proposed method tackles the problem under a block sparse Bayesian learning (BSBL) framework, which incorporates perturbed steering vector factorization to separate the position parameter from the gain-phase errors, making dictionary completely known without learning. This paper devises a customized hyperparameter update rule for the proposed DPD model within the foundation of the BSBL-EM method, allowing for varying block parameters instead of constraining them to be consistent. The position estimates of emitters are determined by calculating the mean value of the posterior distribution of the reconstructed waveforms. Simulations demonstrate the superior performance of the developed BSBL direct localization method over its state-of-the-art rivals, which exhibits enhanced localization accuracy and robustness against gain-phase errors.

In a large area such as a warehouse, using a bistatic backscatter network of passive tags for coverage brings up the issue of insufficient energy harvested by the tags, resulting in poor communication performance. To overcome this problem, we propose a solution that involves the use of distributed radio frequency emitters in a cell-free architecture to deliver more power to the tags. Our approach optimizes the emitter power allocation coefficients while ensuring the tags' energy harvesting requirements are met. By doing so, we provide the same rate quality for all tags and mitigate the effect of the tags' spatial distribution. Compared to the equal-power benchmark, our algorithm yields significant improvements. For example, it achieves$\sim 51\%$and$\sim 16\%$gains in harvested power and tag rate, respectively, for 0 dBm and 20 dBm with 100 emitters, respectively.

This paper introduces an innovative multi-queue fog architecture coupled with an intelligent controller, aimed at enhancing the efficiency and adaptability of fog computing environments. Unlike conventional single-queue fog architectures that typically rely on basic first-in-first-out (FIFO) task execution models in fog servers, our approach offers heightened granularity and flexibility in task scheduling. This feature enables effective task management, catering specifically to Internet of Things (IoT) applications characterized by varying degrees of time-sensitivity and resource requirements. Our proposed deep weighted-fair fog servers (DeepWFFS) scheme comprises two key elements: the weighted-fair fog server (WFFS) framework and an intelligent deep controller (DC) leveraging deep reinforcement learning (DRL) for task prioritization. The WFFS framework adopts multiple queues within fog servers, each assigned a predefined weight representing task priority. This prevents task starvation and promotes equitable task execution. Meanwhile, the DC continuously monitors task workloads and priorities, ensuring optimal task allocation to the most suitable queues within fog and cloud servers. Through simulation, our results exhibit the superior performance of DeepWFFS compared to benchmark schemes. This advancement showcases the potential of our architecture to efficiently manage diverse tasks in fog computing environments.

The direct position determination (DPD) technique utilizes raw received signals to localize agents in a single step, eliminating the need for intermediary measurements. The DPD is recognized for its accuracy superiority over the two-step approach, especially under low signal-noise-ratio (SNR) condition. However, few existing DPD research has focused on scenarios involving moving or unsynchronized agents. In this article, we develop a novel and extended problem, direct localization and synchronization (DLAS) for highly mobile agents with unsynchronized frequency shifts in collocated multiple-input-multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems. The base stations (BSs) sequentially broadcast signals in a time-division multiple access (TDMA) manner, and both Doppler effect and oscillator’s nondeterminism lead to frequency shifts at the agent side. In order to compensate for the position variation of the fast-moving agent, we construct a motion model with uniform acceleration. Next, we propose a computationally efficient DLAS method based on the maximum-likelihood (ML) principle. Specifically, we first decouple the frequency shifts from other unknowns by exploiting the periodicity of block-type pilots and determine a nonlinear optimization problem. We then develop an iterative solution using the frequency shifts to optimally extract real DLAS parameters from complex signal observables. Moreover, we present the closed-form Cramér-Rao lower bound (CRLB) for our estimators determined from the derived general bounding result in complex field. We theoretically analyze the performance gain owing to prior information, and compare the computational complexity among different algorithms. Finally, we provide extensive numerical results to establish the superiority of our proposed method.

The Internet of Medical Things (IoMT) and fog computing facilitate the shift from hospital-based medical examinations to real-time electronic healthcare. A novel transmit scheme for fog computing-enabled IoMT is proposed in this article to address real-time monitoring needs, utilizing uplink and downlink rate splitting (RS) techniques. Fog computing enables offloading partial computation tasks to the edge server while processing the remaining tasks locally to reduce computing time. Uplink and downlink RS techniques offer flexible co-channel interference management to minimize offloading and feedback durations. The primary objective is to minimize the overall time cost encompassing task offloading, data processing, and result feedback. For this purpose, decisions on task offloading, computing resource allocation, uplink beamforming, downlink beamforming, and common rate allocation are jointly designed. However, this approach leads to a nonconvex optimization problem. Several auxiliary variables are introduced to handle this, and accurate surrogates are constructed to smooth the logarithmic transmit rate. Additionally, closed-form expressions are derived for optimal computing resource allocation per user. Based on these formulations, computing resource allocation and energy consumption are transformed into a convex constraint set. Finally, an alternating optimization algorithm is developed to update auxiliary and intrinsic variables iteratively. Simulation results demonstrate the effectiveness of the proposed transmit scheme and algorithm, showing substantial improvements over several baseline methods.

We propose an uplink rate splitting (RS) scheme for real-time health monitoring in the Internet of Medical Things (IoMT). To minimize total time cost, we jointly optimize biosensor grouping (BG), decoding order, power allocation, receiver beamforming, and computation resources allocation under the constraints of the transmit power and computation resources. This process results in a discrete nonconvex problem, which we decouple into three independent subproblems: 1) reduce co-channel interference to ease the transmit time cost. We solve this with a low-complexity BG algorithm; 2) optimize decoding order, power allocation, and receiver beamforming to reduce the forwarding time cost. We thus develop an alternating optimization algorithm. Specifically, we propose a decoding order update algorithm to optimize ordering, which can converge to the global optimum. We construct accurate surrogates via a quadratic transform approach and use surrogate optimization to attack other variables; and 3) allocate computation resources to minimize the processing time cost. Here, we derive the optimal solution with closed-form expressions. Simulation results indicate that the proposed overall scheme and algorithms present significant performance gains over several existing benchmarks.

In distributed computing systems, to mitigate the adverse effect of stragglers on the computation time, computation redundancy is used. The redundancy can be added proactively at the beginning, or reactively after some time based on the delay pattern of the workers. While most of the existing work with reactive mitigation strategy only considered task replication, we propose a coded reactive straggler mitigation with an uncoded and a coded phase for distributed matrix-matrix multiplications. Specifically, in the uncoded phase of the proposed strategy, the master distributes the computational job without redundancy among the workers. After a predetermined waiting time, the master cancels the remaining tasks. It then encodes the remaining tasks and distributes them among the workers. In the uncoded phase, in addition to the conventional erasure model, where workers can communicate only once, we consider multi-message communication (MMC) model to exploit the partial works done by workers. The optimum waiting time for the uncoded phase and the optimum code rate for the coded phase are also obtained. Our simulation results demonstrate that the proposed coded reactive mitigation significantly decreases the execution time in comparison with both the proactive mitigation strategy or the existing reactive mitigation strategy.

This study introduces and investigates the integration of a cell-free architecture with bistatic backscatter communication (BiBC), referred to as cell-free BiBC or distributed access point (AP)-assisted BiBC, which can enable potential applications in future (EH)-based Internet-of-Things (IoT) networks. To that purpose, we first present a pilot-based channel estimation scheme for estimating the direct, cascaded, and forward channels. Next, we utilize the channel estimates to design the optimal beamforming weights at the APs, reflection coefficients at the tags, and reception filters at the reader to maximize the tag sum rate while meeting the tags’ minimum energy requirements. Because the proposed maximization problem is non-convex, we propose a solution based on alternative optimization, fractional programming, and Rayleigh quotient techniques. We also quantify the computational complexity of the developed algorithms. Finally, we present extensive numerical results to validate the proposed channel estimation scheme and optimization framework, as well as the performance of the integration of these two technologies. Our algorithm yields impressive gains compared to the random beamforming/combining benchmark. For example, it achieves ~ 64.8% and ~ 253.5% gains in harvested power and tag sum rate, respectively, for 10dBm with 36 APs and 3 tags.

Current backscatter channel estimators employ an inefficient silent pilot transmission protocol, where tags alternate between silent and active states. To enhance performance, we propose a novel approach where tags remain active simultaneously throughout the entire training phase. This enables a one-shot estimation of both the direct and cascaded channels and accommodates various backscatter network configurations. We derive the conditions for optimal pilot sequences and also establish that the minimum variance unbiased (MVU) estimator attains the Cramér-Rao lower bound. Next, we propose new pilot designs to avoid pilot contamination. We then present several linear estimation methods, including least square (LS), scaled LS, and linear minimum mean square error (MMSE), to evaluate the performance of our proposed scheme. We also derive the analytical MMSE estimator using our proposed pilot designs. Furthermore, we adapt our method for cellular-based passive Internet-of-Things (IoT) networks with multiple tags and cellular users. Extensive numerical and simulation results are provided to validate the effectiveness of our approach. Notably, at least 10dBm and 12dBm power savings compared to the prior art are achieved when estimating the direct and cascaded channels. These findings underscore the practical benefits and superiority of our proposed approach.

The era of ubiquitous, affordable wireless connectivity has opened doors to countless practical applications. In this context, ambient backscatter communication (AmBC) stands out, utilizing passive tags to establish connections with readers by harnessing reflected ambient radio frequency (RF) signals. However, conventional data detectors face limitations due to their inadequate knowledge of channel and RF-source parameters. To address this challenge, we propose an innovative approach using a deep neural network (DNN) for channel state information (CSI) estimation and signal detection within AmBC systems. Unlike traditional methods that separate CSI estimation and data detection, our approach leverages a DNN to implicitly estimate CSI and simultaneously detect data. The DNN model, trained offline using simulated data derived from channel statistics, excels in online data recovery, ensuring robust performance in practical scenarios. Comprehensive evaluations validate the superiority of our proposed DNN method over traditional detectors, particularly in terms of bit error rate (BER). In high signal-to-noise ratio (SNR) conditions, our method exhibits an impressive approximately 20% improvement in BER performance compared to the maximum likelihood (ML) approach. These results underscore the effectiveness of our developed approach for AmBC channel estimation and signal detection. In summary, our method outperforms traditional detectors, bolstering the reliability and efficiency of AmBC systems, even in challenging channel conditions.

Backscatter communications (BCs), allowing passive devices to transmit information by reflecting incident RF signals, have emerged as an attractive solution for the green Internet of Things (IoT). In the practical implementation of BC systems, we observe two common and interesting phenomena: wavy backscatter signals and striped-shape constellation clusters. These phenomena differ significantly from the traditional point-to-point communication and the theoretical BC systems, substantially degrading the system performance. Unfortunately, their causes and potential solutions remain unexplored. Motivated by this, this paper investigates the origins and designs of the corresponding solving methods. Specifically, we first reveal the causes of these phenomena: the time-varying interference stemming from the phase-locked loop (PLL) non-ideality. Then, we introduce our solutions: the dynamic self-interference cancellation (DSIC) and the data-aided decision boundary (DDB) algorithms. Finally, we implement and evaluate our solutions on a practical BC platform. Experimental results show that our solutions can reduce the bit error rate (BER) by up to two orders of magnitude, extend the communication range by over three times, and maintain linear runtime complexity, demonstrating their effectiveness and applicability in practical BC systems.

In distributed computing systems, to mitigate the adverse effect of stragglers on the computation time, computation redundancy is used. The redundancy can be added proactively at the beginning, or reactively after some time based on the delay pattern of the workers. While most of the existing work with reactive mitigation strategy only considered task replication, we propose a coded reactive straggler mitigation with an uncoded and a coded phase for distributed matrix-matrix multiplication. Specifically, in the uncoded phase of the proposed reactive strategy, the master distributes the computational job without redundancy among workers and waits for some time. After the waiting time, the master cancels the remaining tasks. It then encodes the remaining tasks and distributes them among the workers that have already completed their computations. The expected execution time of the proposed method is analytically obtained. Furthermore, the optimal waiting time for the uncoded phase and the optimal code rate for the coded phase are investigated. Our simulation results demonstrate that the proposed coded reactive mitigation strategy significantly decreases the execution time in comparison with the proactive mitigation strategy or repetition-based reactive mitigation strategy.

Ambient internet-of-things networks are just emerging to support sixth-generation wireless goals. We thus investigate a symbiotic radio (SR) system for a single-user primary network and a backscatter communication network that supports non-orthogonal multiple access. The primary base station (BS) concurrently supports the primary user and multiple tags, which modulate and reflect their data using the primary BS signal. The user decodes its data and the tags’ data using the successive interference cancellation technique. We propose a novel optimization framework to accommodate the requirements of both the primary user and the tags while also improving SR network performance. By constructing the beamforming vectors to support both primary and backscatter networks, we develop a BS transmit power minimization problem. The problem formulation ensures the various quality-of-service demands of the user and the tags and the tag energy harvesting requirements. Because of the non-convexity of the problem, we employ semi-definite relaxation techniques to obtain a sub-optimal solution. We evaluate the computational complexity of the proposed algorithm. Finally, we present extensive numerical results and simulations that establish the validity and performance gains of the proposed optimization scheme without modifying the fundamental passive tag architecture.

In this paper, we introduce the DRJLRA algorithm, a load and resource allocation scheme based on deep reinforcement learning (DRL) for a generic multi-master, multi-worker coded distributed computing (CDC) system. Our aim is to minimize the combined delay of communication and computation for a set of matrix-vector multiplication tasks. The proposed DRL-based approach has several unique features that set it apart from existing literature. Firstly, it is applicable to general CDC systems with multiple masters and workers. Additionally, it considers multi-task CDC systems with stochastic task arrivals, takes into account the heterogeneity of workers with random computation and communication delays, and utilizes the state-of-the-art soft actor-critic (SAC) DRL algorithm, making it versatile and efficient in handling complex and dynamic CDC environments. Our results demonstrate that DRJLRA outperforms benchmark schemes significantly. It is thus well-suited for real-world CDC systems with diverse and dynamic workloads.

Optimal beamforming design is developed for a nonorthogonal multiple access (NOMA)-aided symbiotic radio (SR) system where a base station (BS) simultaneously serves multiple NOMA users and a secondary ambient tag. The nearest user of the tag decodes its own data and the tag data using the successive interference cancellation (SIC) technique. We design optimal transmit beamforming and power allocation at the BS to maximize the weighted sum rate of NOMA users and the tag, under the minimum rate requirements while satisfying the tag’s minimum energy requirement. Because the problem is nonconvex, we propose algorithms using alternative optimization and fractional programming techniques. Our results reveal that significant performance gains can be achieved while keeping the tag design intact. For example, the proposed beamforming can increase harvested power and data rate by 2.16×103% and 314.5% compared to random beamforming.

In ambient backscatter communications, backscatter devices (BDs) utilize ambient “legacy” radio signals as both a harvested energy source and a carrier on which to modulate data. Symbiotic radio, a subtype in which the legacy system assists both its own users and underlaid BDs, has attracted much research interest recently. Furthermore, cell-free massive multiple-input multiple-output (CF mMIMO) systems are promising for beyond-5G networks from both spectral and energy efficiency perspectives. To reap the benefits of both, we consider a primary CF mMIMO system where the access points (APs) aid an underlaid BD layer to both harvest energy and reflect information toward the primary receivers (PRs) (which receive data from both layers). To acquire separate channel state information (CSI) of the direct and backscattered channels at the APs, a two-phase uplink pilot training method is proposed, with the effects of pilot contamination and spatial correlation between antennas accounted for. However, the receivers are assumed to only have partial CSI (statistical knowledge plus instantaneous phase information for partially coherent reception). Assuming uplink/downlink radio channel reciprocity, the CSI is used to design downlink precoding vectors for the APs such that channel hardening is enhanced and both PRs and BDs benefit. We derive expressions for the average signal-to-interference-plus-noise ratios of both primary and backscatter signals, accounting for the effects of imperfect CSI, spatial correlation, pilot contamination, and channel hardening. Furthermore, the average power harvested in the BDs is derived. Simulation results demonstrate that the performance of the proposed scheme is much more uniform across all devices with CF mMIMO than with conventional co-located mMIMO. The use of CF mMIMO also largely removes the need for special consideration of the BD layer in the symbiotic system, which is not the case with co-located mMIMO.

This article studies the network lifetime optimization problem in a multiuser mobile-edge computing (MEC)-enabled Internet of Things (IoT) system comprising an access point (AP), a MEC server, and a set of$K$mobile devices (MDs) with limited battery capacity. Considering the residual battery energy at the MDs, stochastic task arrivals, and time-varying wireless fading channels, a soft actor–critic (SAC)-based deep reinforcement learning (DRL) lifetime maximization, called DeepLM, is proposed to jointly optimize the task splitting ratio, the local CPU-cycle frequencies at the MDs, the bandwidth allocation, and the CPU-cycle frequency allocation at the MEC server subject to the task queuing backlogs constraint, the bandwidth constraint, and maximum CPU-cycle frequency constraints at the MDs and the MEC server. Our results reveal that DeepLM enjoys a fast convergence rate and a small oscillation amplitude. We also compare the performance of DeepLM with three benchmark offloading schemes, namely, fully edge computing (FEC), fully local computing (FLC), and random computation offloading (RCO). DeepLM increases the network lifetime by 496% and 229% compared to the FLC and RCO schemes. Interestingly, it achieves such a colossal lifetime improvement when its nonbacklog probability is 0.99, while that of FEC, FLC, and RCO is 0.69, 0.53, and 0.25, respectively, showing a significant performance gain of 30%, 46%, and 74%.

With the development of next-generation wireless networks, the Internet of Things (IoT) is evolving towards the intelligent IoT (iIoT), where intelligent applications usually have stringent delay and jitter requirements. In order to provide low-latency services to heterogeneous users in the emerging iIoT, multi-tier computing was proposed by effectively combining edge computing and fog computing. More specifically, multi-tier computing systems compensate for cloud computing through task offloading and dispersing computing tasks to multi-tier nodes along the continuum from the cloud to things. In this paper, we investigate key techniques and directions for wireless communications and resource allocation approaches to enable task offloading in multi-tier computing systems. A multi-tier computing model, with its main functionality and optimization methods, is presented in detail. We hope that this paper will serve as a valuable reference and guide to the theoretical, algorithmic, and systematic opportunities of multi-tier computing towards next-generation wireless networks.

Multi-tier computing effectively enables flexible computation and communication resource sharing by offloading computation-intensive tasks to nearby servers along the cloud-to-thing continuum. In essence, multi-tier computing networks can distribute computing, storage, and communication functions anywhere between the cloud and the endpoint to take full advantage of the resources available along this continuum, thus extending the traditional cloud computing architecture to the edge of the network. With multi-tier computing, some application component processing, such as delay-sensitive components, can take place at the edge of the network, while other components, such as time-tolerant and computation-intensive components, can be performed in the cloud. To best meet user requirements, centralized cloud computing with extensive resources, secure environments, and powerful algorithms is still needed, but also must be complemented by distributed fog and edge computing with shared resources, accessible environments, and simple algorithms for real-time decision-making. Given heterogeneous computing resources and collaborative service architectures, future multi-tier computing networks will be capable of supporting a full range of computing and networking services for different environments and applications. This Special Issue aims to provide a forum for the latest advances in multi-tier computing for next-generation wireless network research, innovations, and applications. Multi-tier computing enables low-latency processing by allowing data to be processed at the network edge close to end devices. It also facilitates the distribution of fog/edge nodes to collect data from end devices. Therefore, multi-tier computing effectively complements the cloud computing architecture.

Multi-tier computing effectively enables flexible computation and communication resource sharing by offloading computation-intensive tasks to nearby servers along the cloud-to-thing continuum. In essence, multi-tier computing networks can distribute computing, storage, and communication functions anywhere between the cloud and the endpoint to take full advantage of the resources available along this continuum, thus extending the traditional cloud computing architecture to the edge of the network. With multi-tier computing, some application component processing, such as delay-sensitive components, can take place at the edge of the network, while other components, such as time-tolerant and computation-intensive components, can be performed in the cloud. To best meet user requirements, centralized cloud computing with extensive resources, secure environments, and powerful algorithms is still needed, but also must be complemented by distributed fog and edge computing with shared resources, accessible environments, and simple algorithms for real-time decision-making. Given heterogeneous computing resources and collaborative service architectures, future multi-tier computing networks will be capable of supporting a full range of computing and networking services for different environments and applications. Multi-tier computing enables low-latency processing by allowing data to be processed at the network edge close to end devices. It also facilitates the distribution of fog/edge nodes to collect data from end devices. Therefore, multi-tier computing effectively complements the cloud computing architecture.

Monostatic backscatter (MBS) networks provide connectivity for ultra-low power and low-cost tags for numerous applications. However, the reader operates in the full-duplex (FD) mode and experiences self-interference (SI) levels much higher (e.g., 160 dB) than the desired signal. However, hardware-based SI cancellation (SIC) techniques can remove SI partially only. Therefore, residual SI (RSI) dramatically degrades system performance. To remedy this problem, we develop a sum-rate maximization algorithm that suppresses the RSI and ensures that the tags harvest sufficient energy. It jointly optimizes the reader precoder and combiners and the tags reflection coefficients. Because of the non-convexity of this problem, we utilize alternating optimization (AO) to split it into three parts. They are then solved using successive convex approximation (SCA) and semidefinite relaxation (SDR) techniques to yield the precoder, a generalized Rayleigh quotient-based closed-form solution for the combiners, and geometric programming (GP) to get the reflection coefficients. Simulation results validate the fast convergence of the algorithm and show significant sum rate improvements (more than 21%) over the baselines.

We propose a new wireless paradigm for railways – transmissive metasurface (TMS) assisted communications. It compensates for the Doppler shift brought by high mobility and reduces signal degradation due to train carriages. Specifically, the elements of the TMS panel attached to train windows manipulate the links between the base station (BS) and the onboard users. One fundamental problem with it is: does the channel introduced by TMS outperform the traditional direct channel? To answer this, we compare the gains of direct and cascaded channels and introduce the cascaded-outperform-direct probability (CODP), which is the probability that the latter exceeds the former. We then derive two simplified closed-form CODP expressions by approximating the cascaded channel gain as mixed Gaussian and Gamma distributions. Moreover, BS-related parameters impact the CODP; we show that the CODP has (i) global maximum points concerning the azimuth angle of the path from the BS to the TMS, the distance from the BS to the railway, and the BS height, respectively, and (ii) a minimum point in terms of the azimuth angle of the path from the BS to the TMS. Finally, we provide numerical results to verify our analysis and derivations.

The emerging intelligent transparent surface (ITS), unlike the intelligent reflection surface (IRS), allows incident signals to penetrate it instead of being reflected, which enables the ITS to combat the severe signal penetration loss for high-speed railway (HSR) wireless communications. This paper thus investigates the channel estimation problem where the ITS is attached to the HSR carriage window. We first propose a new transmission scheme with two pilot blocks for each frame. Second, we formulate the channels as functions of physical parameters and thus transform the problem into a parameter recovery problem. Third, we develop a successive closed-form, maximum likelihood (ML) channel estimation algorithm. Specifically, each estimate is expressed as the sum of its perfectly known value and the estimation error. By leveraging the relationship between channels for the two pilot blocks, we eliminate the unknown parameters besides Doppler shifts, which can be thereby recovered. With the reconstructed Doppler-induced phase shifts, we acquire other channel parameters. Moreover, the Cramér-Rao lower bound (CRLB) for each parameter is derived as a performance benchmark. Finally, we provide numerical results to establish the effectiveness of our proposed estimators.

e investigate a wireless power transfer (WPT)-based backscatter-mobile edge computing (MEC) network with a reconfigurable intelligent surface (RIS).In this network, wireless devices (WDs) offload task bits and harvest energy, and they can switch between backscatter communication (BC) and active transmission (AT) modes. We exploit the RIS to maximize energy efficiency (EE). To this end, we optimize the time/power allocations, local computing frequencies, execution times, backscattering coefficients, and RIS phase shifts.e investigate a wireless power transfer (WPT)-based backscatter-mobile edge computing (MEC) network with a reconfigurable intelligent surface (RIS).In this network, wireless devices (WDs) offload task bits and harvest energy, and they can switch between backscatter communication (BC) and active transmission (AT) modes. We exploit the RIS to maximize energy efficiency (EE). To this end, we optimize the time/power allocations, local computing frequencies, execution times, backscattering coefficients, and RIS phase shifts.WThis goal results in a multi-objective optimization problem (MOOP) with conflicting objectives. Thus, we simultaneously maximize system throughput and minimize energy consumption via the Tchebycheff method, transforming into two single-objective optimization problems (SOOPs). For throughput maximization, we exploit alternating optimization (AO) to yield two sub-problems. For the first one, we derive closed-form resource allocations. For the second one, we design the RIS phase shifts via semi-definite relaxation, a difference of convex functions programming, majorization minimization techniques, and a penalty function for enforcing a rank-one solution. For energy minimization, we derive closed-form resource allocations. We demonstrate the gains over several benchmarks. For instance, with a 20-element RIS, EE can be as high as 3 (Mbits/Joule), a 150% improvement over the no-RIS case (achieving only 2 (Mbits/Joule)).

In this paper, we address the antenna selection (AS) problem in full-duplex (FD) cooperative non-orthogonal multiple access (NOMA) systems, where a multi-antenna FD relay bridges the connection between the multi-antenna base station and NOMA far user. Specifically, two AS schemes, namely max-U1 and max-U2, are proposed to maximize the end-to-end signal-to-interference-plus-noise ratio at either or both near and far users, respectively. Moreover, a two-stage AS scheme, namely quality-of-service (QoS) provisioning scheme, is designed to realize a specific rate at the far user while improving the near user’s rate. To enhance the performance of the QoS provisioning AS scheme, the idea of dynamic antenna clustering is applied at the relay to adaptively partition the relay’s antennas into transmit and receive subsets. The proposed AS schemes’ exact outage probability and achievable rate expressions are derived. To provide more insight, closed-form asymptotic outage probability expressions for the max-U1 and max-U2 AS schemes are obtained. Our results show that while the QoS provisioning AS scheme can deliver a near-optimal performance for static antenna setup at the relay, it provides up to 12% average sum rate gain over the optimum AS selection with fixed antenna setup.

We consider a generalized space shift keying (GSSK)-enabled multiple-input multiple-output (MIMO) ambient backscatter communication (ABC) system. We propose a scheme to exploit the multiple antenna structure of the system to achieve a lower error-rate performance than conventional ABC systems. Furthermore, we present a novel low complexity energy-based maximum likelihood (EML) GSSK detector, which does not require the perfect knowledge of the ambient source’s signal, unlike the conventional ABC receivers. To gain insights into the performance of the proposed scheme, we derive the exact pairwise error probability (PEP) of the EML detector and further obtain an upper bound on the probability of error. We also derive a simple asymptotic PEP expression as the number of antennas of the reader becomes large. Finally, we derive a simple, asymptotic PEP at the reader when the noise variance approaches zero, i.e., under the large signal-to-interference ratio regime. We validate our analysis through Monte Carlo simulations and show a small performance loss due to the approximations.

We study the performance of a network-coded cooperative (NCC) system in an underlay cognitive radio network (CRN). The primary network (PN) consists of a single transmitter-receiver pair, and the secondary network (SN) is an NCC system with$N$users,$M$relays, and a single destination. The relays employ decode-and-forward (DF) protocol and use network coding (NC). We study the performance of the SN under two types of power constraints: i) the combined peak interference power constraint on the PN and maximum transmit power constraint at the SN; and ii) the single peak interference power constraint on the PN. For the SN, an exact closed-form expression and an asymptotically tight end-to-end outage probability are derived, and the diversity order and coding gain are quantified. Compared to the existing literature, the proposed CRN NCC has four main distinguishable features: i) it applies to general CRN NCC network settings with an arbitrary number of users and relays; ii) it considers general relay selection mechanism and independent and non-identically distributed (i.n.i.d.)$Nakagami-m$fading channels; iii) it assumes secondary-to-primary and primary-to-secondary interference links; and iv) it provides a generalization of previous work and includes existing results in the literature as special cases.

This paper investigates the performance of a network-coded cooperative (NCC) system in an underlay cognitive radio network (CRN). The primary network (PN) consists of a single transmitter-receiver pair, while the secondary network (SN) is composed of N sources, a single destination, and M decode-and-forward (DF) relays, employing network coding (NC) over non-binary Galois field. For the SN, a closed-form expression and an asymptotically tight end-to-end (E2E) outage probability (OP) are derived and the diversity order is quantified. Compared to the existing literature, the proposed CRN NCC has four main distinguishable features: i) it is applicable to general CRN NCC network settings with arbitrary number of sources and relays; ii) it considers general relay selection and independent and non-identically distributed (i.n.i.d.) Nakagami-m fading channels; iii) it accounts for maximum transmit power at the SN and assumes secondary-to-primary (S2P) and primary-to-secondary (P2S) interference links; and iv) it provides a generalization of previous works and includes existing results in the literature as special cases. Simulation results are further provided to confirm the correctness of our analysis.

Non-binary kernels are used to improve the length flexibility of polar codes. Given the long decoding latency of the successive-cancellation (SC) decoder, devising fast decoding solutions for non-binary kernels is necessary. In this work, we identify a new node in the decoding tree of polar codes which are constructed by commonly used ternary kernels. We call this t-dimensional SPC (tD-SPC) node and propose a low-complexity decoder for it. Moreover, we adapt a node introduced for binary kernel to be used in the fast SC decoding of the 3×3 kernel polar codes. Simulation results show that implementing the proposed fast decoders can reduce the decoding latency by more than 40% if a performance loss of just 0.5 dB is tolerated.

We study the effect of outdated channel state information (CSI) and co-channel interference (CCI) on the performance of relay selection (RS) network-coded cooperative (NCC) multiple-input multiple-output (MIMO) systems. Specifically, we consider a RS MIMO-NCC system where N single-antenna sources communicate with one multiple-antenna destination using M decode-and-forward (DF) multiple-antenna relays. The destination selects K best relays according to the quality of relay-destination channels. The selected relays apply network coding (NC) on the received sources' symbols using network code coefficients based on maximum distance separable (MDS) codes. The exact closed-form outage probability (OP) of the system is derived. The asymptotic high signal-to-noise ratio (SNR) OP is also obtained, through which the diversity order and the coding gain are found. Numerical results are further presented to illustrate the adverse effect of outdated CSI and CCI on the system performance and to validate the accuracy of our analysis.

We investigate the achievable rate of a single-cell distributed massive multi-input multi-output (MIMO) system underlaid a licensed primary multi-user co-located Massive MIMO network. We propose an access point (AP) selection procedure and power allocation (PA) method to improve the performance of the secondary network and derive the closed-form sum rate expression for Rayleigh fading channels by considering the effects of pilot contamination, inter-user interference and statistical downlink channel state information (CSI) at secondary users (SUs). Our results reveal that, the joint use of AP selection procedure and PA method significantly improve the achieved sum rate of the SUs while preserving the performance of the primary network.

In this paper, we investigate the performance of a wireless-powered energy beamforming system with a multiple-antenna access point (AP) and a single-antenna user (SU). The SU first harvests radio frequency (RF) energy from the AP in the downlink (DL) and transmits the information to the AP in the uplink (UL). We consider imperfect estimates and derive the distribution of the received signal-to-noise ratio (SNR) at the AP. The average throughput performance of delay-limited and delay-tolerant modes are evaluated by the outage probability (OP) and ergodic capacity (EC). Finally, analytical and asymptotic results are validated by Monte Carlo simulations.

Performance analysis of energy beamforming with a multiple-antenna access point (AP) and a single-antenna user over line-of-sight (LOS) channels is not readily available. In this paper, we thus consider Rician channels between the AP and the user and derive the distribution of the received signal-to-noise ratio (SNR) via the distribution of the product of two independent non-central Chi-square variables. We also derive exact expressions for outage probability (OP), ergodic capacity (EC), throughput optimal energy harvesting time and bit error rates (BERs). Several approximate or asymptotic expressions are also derived. Finally, simulation results are presented to verify our analytical results.

This paper addresses a classical problem in random matrix theory-finding the distribution of the maximum eigen-value of the correlated Wishart unitary ensemble. In particular, we derive a new exact expression for the cumulative distribution function (c.d. f.) of the maximum eigen-value of a 2 × 2 correlated non-central Wishart matrix with rank-l mean. By using this new result, we derive the exact outage probability of 2 × 2 multiple-input multiple-output maximum-ratio-combining (MIMO-MRC) in Rician fading with transmit correlation and a strong line-of-sight (LoS) component (rank-l channel mean). We also show that the outage performance is affected by the relative alignment of the eigen-spaces of the mean and correlation matrices. In general, when the LoS path aligns with the least eigenvector of the correlation matrix, in the high transmit signal-to-noise ratio (SNR) regime, the outage gradually improves with the increasing correlation. Moreover, we show that as K (Rician factor) grows large, the outage event can be approximately characterized by the c.d.f. of a certain Gaussian random variable.

In this6study, the channel estimation problem is investigated for a wireless communication system assisted by a reconfigurable intelligent surface (RIS). The RIS thus creates an assistant channel, which has the features of positivity and dominance. Owing to these features, the channel estimation problem is formulated as a constrained residual sum of squares minimisation problem, which differs radically from the traditional channel estimation issue. An efficient Lagrange multiplier and dual ascent‐based estimation scheme is then designed to obtain an iterative solution for the estimator. Moreover, the Cramér–Rao lower bounds are deduced as a performance benchmark. Simulation results show that the authors' designed scheme improves the estimation accuracy up to 33%, compared with the conventional least‐square method in the low signal‐to‐noise ratio regime.

Fast time-varying channel parameters and large penetration losses for signals passing through train carriages are two well-known challenges for wireless communications on high speed rails (HSRs). In this paper, we introduce, for the first time, backscatter technology into HSR wireless communications, which can address these two challenges and yet have low complexity of signal processing and low cost of circuit implementation compared with traditional solutions such as relaying or beamforming. Specifically, we propose a backscatter aided wireless transmission (BAWT) scheme and demonstrate that it outperforms the existing direct wireless transmission (DWT) scheme. We derive the upper and lower bounds of channel capacity for BAWT and prove that it exceeds that of DWT on certain conditions. We also propose the transceiver design for both BAWT and DWT, including joint carrier frequency offset and channel estimator, and signal detector. We show that BAWT, rather than DWT, can obtain the channel statistical information in practical applications due to fixed train antennas and unchanged tracks, which can be utilized to facilitate channel estimation. Finally, simulation results are provided to corroborate the proposed solutions.

Ambient backscatter devices (tags and readers) use existing radio frequency (RF) signals to transmit data. Most prior works consider single-antenna tags, but this paper investigates the case of multiple-antenna tags, which are capable of simultaneous energy harvesting and data transmission. However, the multi-antenna channel between the tag and the reader, and the unpredictable nature of RF signals due to uncontrollable RF sources (e.g., location and transmit power), make signal detection highly challenging. Thus, the detection process becomes a hypothesis testing problem with unknown parameters. Consequently, we design a blind detector based on the generalized likelihood ratio test (GLRT) without using channel state information (CSI), signal power and noise variance. The decision threshold and detection probability of it are also analyzed in detail. Furthermore, to maximize its detection performance, we develop the optimal backscatter antenna selection scheme. Interestingly, we show that the detector performs best when only two backscatter antennas are selected. Finally, extensive simulation results validate the analysis and illustrate the effectiveness of the proposed detector.

This paper investigates the application of full-duplex (FD) multi-antenna transceivers in proactive eavesdropping systems. To this end, we jointly optimize the transmit and receive beamformers at the legitimate FD monitor to maximize the eavesdropping non-outage probability of the system. The resulting non-convex problem is solved using two-layer decomposition technique. The inner layer problem is formulated as a semidefinite relaxation problem, and the outer problem is solved by one-dimensional line search. We further propose sub-optimum beamforming designs, where the beamformers are obtained using zero-forcing, and maximum ratio transmission. To archive a low-complexity implementation, we study the antenna selection problem as an alternative for performance optimization. Particularly, based on the system's eavesdropping non-outage probability, several antenna selection schemes are proposed to choose single transmit and single receive antenna at the FD monitor. For each scheme, we derive closed-form expressions of the eavesdropping non-outage probability. Our findings reveal that proposed antenna selection schemes can achieve the performance close to that of the proposed optimum/sub-optimum beamforming design, but with much lower implementation complexity.

Although the hybrid of cell-free (CF) massive multiple-input multiple-output (MIMO) and non-orthogonal multiple access (NOMA) promises massive spectral efficiency gains, the type of precoders employed at the access points (APs) impacts the gains. In this paper, we thus comprehensively evaluate the system performance with maximum ratio transmission (MRT), full-pilot zero-forcing (fpZF) and modified regularized ZF (mRZF) precoders. We derive their closed-form sum rate expressions by considering Rayleigh fading channels, the effects of intra-cluster pilot contamination, inter-cluster interference, and imperfect successive interference cancellation (SIC). Our results reveal that this system supports significantly more users simultaneously at the same coherence interval compared to its OMA equivalent. However, intra-cluster pilot contamination and imperfect SIC degrade the system performance when the number of users is low. Moreover, with perfect SIC, mRZF and fpZF significantly outperform MRT. Also, we show that this system with either mRZF or fpZF precoding outperforms OMA systems with MRT. The analytical findings are verified by numerical results.

For a multi-way relay network (MWRN) with K users, K time slots are needed for full data exchange. Thus, the overall spectral efficiency, due to the 1/K pre-log factor, declines as number of users grows. It has recently been improved to roughly K/2 time slots, but even this improvement does not arrest the decline. Herein, we reduce this task to just two time slots regardless of K. To do this, we exploit the performance gains of non-orthogonal multiple-access (NOMA) and a massive multiple-input multiple-output (MIMO) relay. First, the users transmit their signals to the relay, which uses maximal ratio combining reception. Next, the relay transmits a superposition-coded signal for all users by using maximal ratio transmission. Each user then performs successive interference cancellation (SIC) decoding of data symbols of the other K - 1 user nodes. We use the so-called worst-case Gaussian approximation to derive the overall sum rate and demonstrate significant spectral-efficiency gains and energy-efficiency gains over the existing MWRN counterparts. We also design the relay power allocation matrix to maximize the minimum among the user rates, thus maximizing the user fairness. Furthermore, the effects of imperfect SIC and imperfect channel state information (CSI) on the sum rate are analyzed.

Signal detection in colored noise with an unknown covariance matrix has a myriad of applications in diverse scientific/engineering fields. The test statistic is the largest generalized eigenvalue (l.g.e.) of the whitened sample covariance matrix, which is constructed via m-dimensional p signal-plusnoise samples and m-dimensional n noise-only samples. A finite dimensional characterization of this statistic under the alternative hypothesis has hitherto been an open problem. We answer this problem by deriving cumulative distribution function (c.d.f.) of this l.g.e. via the powerful orthogonal polynomial approach, exploiting the deformed Jacobi unitary ensemble (JUE). Two special cases and an asymptotic version of the c.d.f. are also derived. With this new c.d.f., we comprehensively analyze the receiver operating characteristics (ROC) of the detector. Importantly, when the noise-only covariance matrix is nearly rank deficient (i.e., m = n), we show that (a) when m and p increase such that m/p is fixed, at each fixed signal-to-noise ratio (SNR), there exists an optimal ROC profile. We also establish a tight approximation of it; and (b) asymptotically, reliable signal detection is always possible if SNR scales with m.

Ambient backscatter technology utilizes ambient radio frequency (RF) signals to enable battery-free devices (tags and readers) to communicate. Most existing studies assume single-antenna tags. However, in this paper, we consider tags with multiple antennas, which are exploited to provide transmit diversity. Channel state information (CSI) estimation is then a fundamental challenge because the tags can transmit few or no training symbols. To overcome it, we require detectors that operate without CSI. Thus, we propose and design three detectors based on the chi-squared test, F-test and Bartlett's test. The latter two are blind detectors because they require neither CSI nor the knowledge of RF source power and noise variance. We derive the detection probability bounds for the first two detectors. We also propose optimal tag antenna selection schemes to maximize the detection probabilities. Finally, simulation results are provided to corroborate our theoretical studies.

We consider a network-coded cooperative (NCC) system that consists of N ≥ 2 sources, M ≥ 1 decode- and-forward (DF) relays, and a single destination. The relays perform network coding (NC) on the received sources' symbols using maximum distance separable (MDS) codes. For this system, we propose the most generalized user-relay selection (GURS) scheme in the literature that selects any arbitrary subsets of K users and any arbitrary subsets of L relays subject to practical constraints such as load balancing conditions and scheduling policy. Our analytical results and design guidelines generalize and subsume all existing results as special cases. To this end, we derive a new closed-form outage probability (OP) expression, assuming non-identically and independently distributed (n.i.i.d.) Rayleigh fading channels. The asymptotic outage expression at high signal-to-noise ratio (SNR) regime is further derived, based on which, the achievable diversity order and coding gain are quantified. The theoretical derivations are also validated through Monte-Carlo simulation.

This paper investigates the classical statistical signal processing problem of detecting a signal in the presence of colored noise with an unknown covariance matrix. In particular, we consider a scenario wherem-dimensionalppossible signal-plus-noise samples andm-dimensionalnnoise-only samples are available at the detector. Then the presence of a signal can be detected using the largest generalized eigenvalue (l.g.e.) of the so called whitened sample covariance matrix. This amounts to statistically characterizing the maximum eigenvalue of the deformed Jacobi unitary ensemble (JUE). To do this, we employ the powerful orthogonal polynomial approach to determine a new finite dimensional expression for the cumulative distribution function (c.d.f.) of the l.g.e. of the deformed JUE. This new c.d.f. expression facilitates the further analysis of the receiver operating characteristics (ROC) of the detector. It turns out that, form=n, when m andpincrease such thatm/pis fixed, there exists an optimal ROC profile for each fixed signal-to-noise ratio (SNR). In this respect, we have established a tight approximation for the corresponding optimal ROC profile.

We study the performance of generalized user-relay selection (GURS) scheme in network-coded cooperation systems. In particular, we propose the most general case of user-relay selection mechanism that selects any arbitrary subsets of users and relays subject to any practical constraints such as load balancing conditions, scheduling policy, and other factors. Our results thus can be applied to a large set of situations and include all existing results in the literature as special cases. We develop performance characterizations of the system under consideration in terms of outage probability over non-identically and independently distributed (n.i.i.d.) Rayleigh fading channels. The asymptotic outage expressions at high signal-to-noise ratio (SNR) regime are further derived and then, based on the derived expressions, we quantify the diversity order. The theoretical derivations are validated through Monte-Carlo simulations.

Device-to-device (D2D) where users communicate directly with each other with limited base station involvement can significantly improve spectral efficiency, energy efficiency, and throughput in future cellular networks. Moreover, RF (radio frequency) energy harvesting (EH) promises to prolong the battery life and improve energy efficiency of D2D communication. Mobility diversity refers to the gains accrued via user mobility. Is it possible to exploit the mobility of D2D terminals via user movements to enhance their ability to harvest RF energy? To this end, we analyze the performance of a mobile D2D device powered by EH from the transmissions of underlying cellular base stations (BSs), whose locations are modeled as a homogeneous Poisson point process. We model the movements of D2D nodes via a modified random waypoint model. Log-distance path loss is considered, and it is assumed that EH takes place solely within harvesting zones surrounding each BS and that each D2D user requires a fixed number of charging time slots before being able to transmit. We derive the probability of a D2D device being within an EH region surrounding BSs after multiple transitions, and the probability of being within the the fully charged state using a Markov-chain approach taking into account temporal effects. It is shown that the number of transitions required to be within a harvesting region increases significantly when the harvesting threshold power increases.

This paper addresses the performance of a full-duplex (FD) generalized frequency division multiplexing (GFDM) transceiver in the presence of radio frequency (RF) impairments including phase noise, carrier frequency offset (CFO) and in-phase (I) and quadrature (Q) imbalance. We study analog and digital self-interference (SI) cancellation and develop a complementary SI suppression method. Closed-form solutions for the residual SI power and the desired signal power and signal-to-interference ratio (SIR) are provided. Simulation results show that the RF impairments degrade SI cancellation and FD GFDM is more sensitive to them compares to FD orthogonal frequency division multiplexing (OFDM). Hence, we propose an FD GFDM receiver filter for maximizing the SIR. Significantly, it achieves 25 dB higher SIR than FD OFDM transceiver.

We propose a novel transmission protocol for multiway relay networks (MWRNs) in which the number of timeslots required for full mutual multi-way data exchange among K user nodes can be reduced to just two from Γ(K - 1)/21 + 1 in the current state-of-the-art. The proposed MWRN adopts superposition-coded transmission, successive interference cancellation (SIC) reception, power-domain non-orthogonal multipleaccess (NOMA) and linear detection/precoding facilitated by massive multiple-input multiple-output (MIMO). First, the user nodes transmit their signals to a massive MIMO-enabled relay, where a linear detector based on maximal ratio combining criterion is used for signal reception. Next, the relay composes a superposition-coded signal for each user node and transmits towards the user nodes by using a linear precoder based on maximal ratio transmission criterion. User nodes perform SICbased decoding for retrieving symbols sent by the remaining K user nodes. Thus, our proposed MWRN protocol completes the full mutual multi-way data exchange among all users within two time-slots. We derive the achievable sum rate of it via the so-called worst-case Gaussian approximation and show that a significant spectral efficiency gain can be achieved over the existing MWRN counterparts.

In this paper, we study the performance of opportunistic source selection (OSS) in multisource multirelay network-coded cooperative (NCC) systems. For this system, we derive the exact outage probability and asymptotic measures such as the diversity and coding gains. The derived analytical results provide an efficient means to evaluate the impact of different system parameters on the system performance. Our results reveal that the proposed NCC system greatly exploits the diversity gains in multisource multirelay NCC systems and thus provides a considerable performance improvement. From the derived closed-form diversity gains, we also evaluate the optimal number of selected relays that maximizes the achievable diversity gain. Numerical results are also presented to validate the theoretical analysis.

This paper investigates the problem of sum rate maximization for a full-duplex (FD) generalized frequency division multiplexing (GFDM) based secondary user (SU) link, operating in a spectrum hole. The right and left adjacent channels of the spectrum hole have two active primary users (PUs), and thus adjacent channel interference (ACI) on them must be below a threshold. For SU link, radio frequency (RF) impairments including phase noise, in-phase (I) and quadrature (Q) imbalance, and carrier frequency offset (CFO) are considered and analog domain and digital domain self-interference (SI) cancellation techniques are applied. We consider two cases: (1) two independent oscillators for local transmitter and receiver, (2) single shared oscillator between them. We derive the powers of residual SI, desired signal and noise and signal-to-interference-plus noise ratio (SINR). Furthermore, power spectral density (PSD) of FD transmitter is calculated and ACI is formulated. By using successive convex approximation, sum rate maximization problem subject to ACI limits on adjacent PUs is defined and solved. Finally, we show that FD GFDM for the SU link can achieve twice higher sum rate than FD orthogonal frequency division multiplexing (OFDM).

We investigate the optimal transmission policy for an energy-harvesting wireless sensor node. The node must decide whether an arrived packet should be transmitted or dropped, based on the packet's priority, wireless channel gain, and the energy status of the node. The problem is formulated under the Markov decision process (MDP) framework. For such a problem, the conventional method to get the optimal policy is by using a state value function, which is three-dimensional in the considered problem, leading to high complexity. Fortunately, to reduce complexity, we derive an equivalent solution for the optimal policy via a one-dimensional after-state value function. We show that the after-state value function is differentiable and nondecreasing. We also discover a threshold structure of the optimal policy that is derived by the after-state value function. Furthermore, to approximate the after-state value function, we propose a learning algorithm to train a three-layer monotone neural network. The trained network thus finds a near-optimal selective transmission policy of the node. Finally, through simulation, we demonstrate the learning efficiency of the algorithm and the performance of the learned policy.

The successive-cancellation list (SCL) and successive-cancellation flip (SCF) decoding can be used to improve the performance of polar codes, especially for short to moderate length codes. However, their serial decoding nature results in significant decoding latencies. Implementing some operations in parallel can reduce their decoding latencies. This paper presents fast implementations of the SCL and SCF decoders. In particular, we propose fast parallel list decoders for five newly identified types of nodes in the decoding tree of a polar code, which significantly improves the decoding latency. We also present novel fast SCF decoders that decode some special nodes in the decoding tree of a polar code without serially computing bit log-likelihood ratios. Using our proposed fast parallel SCF decoders, we observed an improvement up to 81% with respect to the original SCF decoder. This significant reduction in the decoding latency is observed without sacrificing the bit-error-rate performance of the code.

This paper investigates a user-fairness relay selection (RS) problem for decode-and-forward (DF) full-duplex (FD) relay networks, where multiple users cooperate with multiple relays in each coherence time. We consider two residual self-interference (RSI) models with or without direct links. We propose a sub-optimal relay selection (SRS) scheme which requires only the instantaneous channel state information (CSI) of source-to-relay and relay-to-destination links. To evaluate the performance, the outage probability of SRS is derived for different scenarios depending on RSI models and the availability of direct links. To further investigate, asymptotic expressions are derived for the high-transmit power regime. For comparison purposes, 1) the average throughputs of the FD and half-duplex (HD) modes are derived; 2) non-orthogonal transmission is considered and its performance is discussed with approximations; and 3) the impact of imperfect CSI is investigated with the aid of analysis. While simulation results are provided to verify the analytical results, they reveal interesting fundamental trends. It turns out that a significant throughput degradation occurs with FD mode over HD mode when self-interference is fully proportional to the transmit power. Since all users can communicate in the same coherence time with the FD mode, these joint RS schemes are useful for user-fairness low-latency applications.

Network-coded cooperation (NCC) has recently gained interest as it improves the network throughput in multi-source cooperative systems. NCC has been studied for single-antenna terminals only. Employing multiple-input multiple-output (MIMO) techniques can significantly improve the performance of NCC systems. Furthermore, the existing relay selection (RS) strategies for NCC utilize the “max-min” end-to-end (E2E) criterion. This selection strategy (called Strategy A) is complicated even for a network with single-antenna terminals as it requires global channel state information (CSI). This requirement makes it hard to implement RS-based NCC. To counter this issue, we introduce a new RS strategy (Strategy B), which utilizes only the local CSI (not global CSI), significantly reducing the signaling overhead without sacrificing the performance. The performance of MIMO-NCC under Strategies A and B is studied over independent and non-identically distributed (i.n.i.d.) Rayleigh fading channels. Relays and the destination are equipped with multiple antennas, whereas sources have a single antenna. The exact outage probability expressions of the system under consideration are derived. The asymptotic outage expressions are further provided to obtain valuable insights into the practical system-design parameters such as the diversity order and coding gain. Furthermore, numerical results are provided in support of the analytical results.

Device-to-device (D2D) networks underlaying a millimeter-wave cellular network have great potential for capacity growth. Thus, it is important to characterize the outage of such a D2D link incorporating millimeter-wave propagation effects, user association rules, power control, and spatial randomness. To this end, we model the locations of cellular transmitters and receivers as homogeneous Poisson point processes and those of the D2D nodes as a Matérn cluster process, and incorporate blockages due to random objects, sectored antenna patterns, log-distance path loss, and Nakagami-m fading. Furthermore, we consider antenna gain inversion-based power control, and peak power constraints for D2D devices along with distinct path loss exponents and distinct fading severities for line-of-sight (LOS) and non-LOS scenarios. With the aid of stochastic geometry tools, we derive closed-form expressions of the moment generating function of the aggregate interference on a D2D receiver node and its outage probability for two transmitter-receiver association schemes- nearest association and LOS association. We finally show that the feasibility of millimeter-wave D2D communication relies heavily on the D2D cluster radii, peak power thresholds, and node densities. Furthermore, these parameters affect the performance of the desired link more than the interference and noise.

Spectrum harvesting is needed for large-scale wireless networks to access underutilized spectrum and support multiple heterogeneous users. Cooperative spectrum harvesting (CSH) allows for improved co-channel existence and intra-/inter-cell interference mitigation, which dramatically improves spectral efficiency. However, good performance metrics to quantify CSH schemes are not available. For example, existing metrics such as data rate, error/outage probability, and multiplexing/diversity gains may not clearly distinguish large signal-to-interference-plus-noise ratio (SINR) scenarios and sum-rate performance for multiple links. To overcome these limitations, we propose two new metrics called spectrum access level (SAL) and user participation level (UPL). The advantages of these metrics are: 1) achieving distinct upper bounds for multiple links; 2) upper bounds being evaluated directly by basic CSH system model; and 3) determining the performance at any power level of CSH schemes even if they are not interference exempt. Moreover, a novel CSH system model is conceived to achieve satisfying spectrum access ability based on SAL and UPL, and an interference-exempt scheme is designed to achieve relevant upper bounds. Numerical results verify the efficiency of SAL and UPL, and the spectrum access ability of proposed system model with interference-exempt scheme.

Wireless energy harvesting, physical-layer security, and full-duplex wireless are important, emerging fifth generation (5G) technologies. In this paper, we thus investigate a source-destination link with an energy-harvesting full-duplex relay and a jammer (to degrade the eavesdropper channel) in the presence of an eavesdropper. Thus, to exploit energy harvesting and to improve security, we propose a full-duplex jammer (FDJ) protocol and its half-duplex version (HDJ). Two cases for availability of the eavesdropper channel state information (ECSI) are considered: complete ECSI and incomplete ECSI. For both FDJ and HDJ protocols and for complete ECSI, we derive the instantaneous and average secrecy rates and compute optimal time split for energy harvesting. To gain more insights, we consider a practical interference-limited scenario and derive closed-form cumulative distribution function of the signal-to-interference plus noise ratio at the destination and eavesdropper nodes. Comparatively, we show that FDJ improves instantaneous secrecy rate over HDJ. However, the degree of improvement is highly dependent on time split for energy harvesting, amount of self-interference, the channel gains, and locations of the nodes. Our findings reveal that FDJ increases the average secrecy rate 150% over HDJ and 260% over HD relaying without jammer. For incomplete ECSI scenario, we derive asymptotic secrecy outage and show that FDJ performs better for small-to-medium values of source powers; otherwise, HDJ yields a higher gain.

In this paper, we propose a novel successive two-way relaying (STWR) system that uses a pair of conventional half-duplex (HD) relays to mimic a full-duplex two-way relay (FD-TWR). Although classical FD-TWR is spectral efficient and expands cell coverage, the proposed STWR utilizes the existing HD infrastructure to boost the FD implementation and offers bi-directional data exchange and low-complexity residual self-interference (RSI) mitigation. To formulate STWR, we develop a unified signal model to facilitate the mitigation of the generalized self-interference (GSI). GSI consists of back-propagating interference due to two-way relaying, RSI of FD sources and inter-relay interference caused by the pairs of HD relays. Because the GSI channel matrix has a distinct row linearity, we propose an efficient digital approach to remove the GSI and design two low-complexity algorithms. These algorithms avoid RSI channel estimation, full-rank matrix, and complex matrix computation. Our analysis and simulations show that: 1) the proposed STWR achieves the multiplexing gain of the true FD-TWR; 2) the distance between the two HD relays should be optimized to achieve the highest spectral efficiency; and 3) the STWR system with two algorithms can achieve a diversity order of one or two, respectively. Therefore, the STWR concept achieves a flexible tradeoff between performance and complexity, potentially enabling large-scale relay deployments.

In this paper, we demonstrate the coverage probability improvement of a millimeter wave (mmWave) network due to the deployment of spatially random decode-and-forward (DF) relays. We assume the transmitter and receiver are located at a fixed distance and that the potential relay nodes are spatially distributed as a two dimensional homogeneous Poisson point process (PPP). We first derive the spatial distribution of decoding set of relays that meet the required signal-to-noise ratio (SNR) threshold. From this set, we select a relay that has minimum path- loss from the receiver and derive the coverage probability achievable due to this selection. The analysis is based on stochastic geometry and is verified via Monte-Carlo simulation. The coverage probabilities of (a) direct link without relaying and (b) relayed link are compared to show that relaying provides significant coverage improvements.

A novel opportunistic antenna selection aided spatial modulation, called opportunistic spatial modulation (OSM), is proposed, which exhibits an attractive system reliability enhancement with low complexity. Its unique features enable a comprehensive analytical framework, which is challenging to acquire with existing transmit-antenna-selection-aided spatial modulation (TASS-SM) schemes. Closed-form expression of improved union bound for the average symbol error probability (ASEP) of proposed OSM-MISO system is derived. Furthermore, we compare the proposed OSM with a prevalent existing TASS-SM scheme to confirm the feasibility and effectiveness of our scheme. Simulation results are provided to corroborate the analytical results.

This paper investigates the outage probability of the achievable secrecy rate in the presence of multiple eavesdroppers that employ energy harvesting (EH) and information decoding (ID). We derive the theoretical outage probability of the achievable secrecy rate between the legitimate transmitter and receiver pair when both the main channel and wiretap channel experience Rician fading. This work also considers both ideal and imperfect channel state information as well as different EH architectures (i.e. separated and integrated receiver architecture) in the secrecy analysis. Furthermore, the use of transmit antenna selection (TAS) for enhancing message confidentiality is also studied. Numerical and simulation results are provided to validate our analysis.

This paper proposes an opportunistic spatial modulation (OSM) scheme where the transmit antennas are divided into K ≥ 1 equal groups, and the best antenna from each group is selected to form a K transmit antenna subset for implementing spatial modulation (SM). Thus, the activation of one antenna from the subset to transmit one of the M-ary modulation symbols achieves a data rate of log2(K) + log2(M) bits per channel use. Notably, special cases of OSM include conventional SM and pure single transmit antenna selection. To characterize and comparatively evaluate OSM, we first consider phase-shift keying modulation and derive a closed-form, improved union-bound of symbol error probability (SEP) with a single-antenna receiver. Explicit expressions for the SEP in the high signal-to-noise ratio regime are also presented. Extensions to quadrature amplitude modulation analysis and simulations of multiple-antenna reception case are also provided. Simulation results corroborate the analytical results and reveal the interesting interplay between the signal and spatial constellation diagrams. For a given number of transmit antennas and targeted data rate, asymptotically, the SEP can be minimized by using only one antenna group and the largest size of signal constellation, as this configuration achieves the full-diversity order.

Soft iterative detection/decoding algorithms are fundamentally necessary for multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) adopted in the Third Generation Long Term Evolution (LTE)-Advanced in order to increase the capacity and achieve high data rates. However, their high performance critically requires log likelihood ratio computations with prohibitive complexity. This challenge will be addressed in this paper. We first use the assumption of Gaussian transmit symbols to show the equivalence among several existing algorithms. We next develop a non-Gaussian approximation for high-order constellations, which paves the way for interference cancellation-based detectors. Based on both Gaussian and non-Gaussian approximations, we thus develop several capacity-achieving iterative MIMO-OFDM demodulation and decoding algorithms. To this end, we adopt K-best algorithms to take advantage of both the types of approximations and the list decoder. Unlike existing algorithms, our proposed K-best algorithms make use of the a priori probabilities to generate the list. Simulations of standard-compliant LTE systems demonstrate that the proposed algorithms outperform the existing ones.

This paper considers a cloud radio access network, where full-duplex (FD) users communicate with remote radio heads (RRHs) that are spatially distributed. We consider all participate RRH association (ARA) and single nearest RRH association (SRA) policies with optimal, maximum ratio combining/maximal ratio transmission (MRT), and zero-forcing/MRT (ZF/MRT) processing schemes and derive analytical expressions useful to compare the average uplink/downlink (UL/DL) sum rate among association schemes as a function of the number of RRHs antennas and UL/DL RRH density. We also study a dense network setting with multiple FD users and derive exact expressions for the average UL/DL rates, where a user-centric clustering technique is adopted and each user is served by its nearest UL and DL RRHs. Furthermore, by maximizing the instantaneous sum rate, we develop an optimum power allocation scheme for the single-user case. We observe that ARA results in a rate region that is strongly biased toward the UL or DL, but using SRA results in a more balanced rate region. Moreover, SRA policy with ZF/MRT processing achieves up to 32% and 42% average sum rate gains as compared with the HD SRA and FD ARA counterparts, respectively.

We consider the detection of an integer vector x̂ ∈ ℤnfrom the linear observation y = Ax̂ + v, where A ∈ ℝm×nis a random matrix with independent and identically distributed (i.i.d.) standard Gaussian N (0, 1) entries, and ν ∈ ℝmis a noise vector with i.i.d. N (0, σ2) entries with given σ. In digital communications, x̂ is typically uniformly distributed over an n-dimensional box B. For this detection problem, successive interference cancellation decoders are popular due to their low complexity, and a detailed analysis of their word error rates (WERs) is highly useful. In this paper, we derive closed-form WER expressions for two cases: (1) x̂ ∈ℤnis fixed and (2) x̂ is uniformly distributed over B. We also investigate some of their properties in detail and show that they agree closely with simulated word error probabilities.

Millimeter wave communication is a promising concept for the fifth generation (5G) of cellular wireless networks due to the large available bandwidth while device to device (D2D) communication among nearby devices which saves network resources is also gaining attention. As such, D2D networks underlaying millimeter wave cellular systems hold massive potential. However, the performance of such a D2D network incorporating spatial randomness and power control has not yet been characterized. To fill this knowledge gap, we develop a comprehensive analysis of the performance of a D2D receiver. To this end, we model cellular transmitters and receivers as homogeneous Poisson point processes and the D2D network as a Matern cluster process, and incorporate blockages due to random objects, sectored antenna patterns, log-distance path loss, and Nakagami-m fading. Furthermore, we consider path loss and antenna gain inversion based power control, and peak power constraints for D2D devices along with distinct path loss exponents and fading severities for line-of-sight and non-line-of-sight scenarios. With the aid of stochastic geometry tools, we derive closed-form expressions of the moment generating function of the aggregate interference experienced by a D2D receiver and its outage probability. We finally show that the feasibility of millimeter wave D2D communication relies heavily on the D2D cluster radii, peak power thresholds, and node densities.

Energy harvesting underlay device-to-device (D2D) networks are a promising solution to increase spectral and energy efficiency of wireless systems. However, to what extent is the performance of such networks affected by spatial randomness, temporal correlations, power control procedures, and channel uncertainties? To answer this question, we consider an environment with a multi channel primary user network whose nodes and D2D transmitters are spatially distributed as a homogeneous Poisson point process and the wireless signals are subject to log-distance path loss, Rayleigh fading, and path loss inversion based power control. We derive expressions for the ambient radio frequency power available for harvesting at a D2D transmitter, and approximate it using a Gamma distribution. Furthermore, we use a Markov chain model to derive the probability of a successful energy harvest for single slot and multi slot harvesting schemes, and derive the coverage performance of a D2D receiver when a D2D transmitter gets assigned to a sub-band randomly. It is concluded that a D2D receiver sensitivity between -120 dBm and -100 dBm is optimum for both single and multi-slot harvests, and that a higher primary transmitter density is detrimental to multi slot harvesting when the D2D transmitter-receiver distance increases.

Spectrum and energy constraints are fundamental barriers to the future growth of wireless communication networks, and to break this gridlock is the promise of energy harvesting cognitive radio (CR) networks. To this end, this paper investigates the feasibility of energy harvesting underlay CR networks with the primary system employing power control. We consider primary and underlay nodes distributed randomly in R2as homogeneous Poisson point processes (PPP). Underlay transmitters scavenge power from primary transmitters, and are able to transmit as long as they are outside a guard region surrounding a primary receiver. The primary and underlay systems are assumed to perform power control based on path loss inversion, and that a underlay transmitter requires N charging slots to fully charge its batteries after depletion. We consider two cases of power depletion after a underlay transmission: 1) full power depletion, and 2) partial power depletion based on distances to the intended receivers. We derive the probability of a successful charge by mapping the PPP of primary transmitters to an equivalent PPP incorporating random transmit powers, and use a Markov chain to derive the probability of a successful transmission while incorporating temporal effects for the two aforementioned power depletion scenarios. We show that the probability of successful transmission is not greatly affected by the guard distance, and that it drops by approximately 10 fold for each 15 dB increase in the threshold received power level required for an energy harvest. We further show that energy harvesting is most feasible when the threshold power required for a harvest is lower than the receiver sensitivity of a primary receiver.

The integer-forcing (IF) linear multiple-input and multiple-output (MIMO) receiver is a recently proposed suboptimal receiver which nearly reaches the performance of the optimal maximum likelihood receiver for the entire signal-to-noise ratio (SNR) range and achieves the optimal diversity multiplexing tradeoff for the standard MIMO channel with no coding across transmit antennas in the high SNR regime. The optimal integer coefficient matrix A* ϵ ZNt×Ntfor IF maximizes the total achievable rate, where Nt is the column dimension of the channel matrix. To obtain A*, a successive minima problem (SMP) on an Nt-dimensional lattice that is suspected to be NP-hard needs to be solved. In this paper, an efficient exact algorithm for the SMP is proposed. For efficiency, our algorithm first uses the LLL reduction to reduce the SMP. Then, different from existing SMP algorithms which form the transformed A*column by column in Ntiterations, it first initializes with a suboptimal matrix which is the Nt× Ntidentity matrix with certain column permutations that guarantee this suboptimal matrix is a good initial solution of the reduced SMP. The suboptimal matrix is then updated, by utilizing the integer vectors obtained by employing an improved Schnorr-Euchner search algorithm to search the candidate integer vectors within a certain hyper-ellipsoid, via a novel and efficient algorithm until the transformed A*is obtained in only one iteration. Finally, the algorithm returns the matrix obtained by left multiplying the solution of the reduced SMP with the unimodular matrix that is generated by the LLL reduction. Simulation results show the optimality of our novel algorithm and indicates that the new one is much more efficient than existing optimal algorithms.

Wireless and digital communications applications require the detection of an integer vector x̂ from y = Ax̂ + v, where A ϵ ℝm×nis a random matrix whose entries are independent and identically distributed (i.i.d.) standard Gaussian N(0,1) entries, and v ϵ ℝmis a noise vector following the Gaussian distribution N(0,σ2) with given σ. The successive interference cancellation (SIC) decoders are frequently used to detect x̂ due to their high accuracy and low implementation complexity. However, to accurately characterize their performance, we need to analyze their symbol error rates (SER). In this paper, we derive a closed-form expression for the SER of the SIC decoders and investigate its properties. Simulated error probabilities of the SIC decoders agree closely with our theoretical expressions.

We consider a single channel energy harvesting cognitive radio system, where the joint optimization of spectrum sensing, channel probing and transmission power control is considered with the goal to maximize the throughput. We model this control problem as a two-stage continuous-state Markov decision process with one stage for sensing and probing control, and the other for transmission power control. By utilizing the stochastic structure of the two-stage Markov decision process, we simplify the model via the notion of after-state, which reduces the state space and facilitates decision makings. Finally, the performance of the generated strategy is investigated via simulation.

We consider an energy harvesting wireless communication link, where arriving data packets have different importance values. The wireless transmitter needs to decide whether each arriving data packet should be transmitted or not, based on the packet's importance value, channel condition, and energy status. Under certain conditions, we show this high dimensional control problem can be transformed to a one dimensional continuous value function estimation problem using the notion of after-state. Then, by analyzing the structure of the value function, we propose a polynomial approximation to effectively compress the continuous function space into a finite weight space. Furthermore, we develop a reinforcement learning algorithm for our after-state setting. Finally, the proposed function approximation and learning algorithm are investigated under various system parameter settings via simulation.

Distributed storage systems (DSSs) provide a scalable solution for reliably storing massive amounts of data coming from various sources. Heterogeneity of these data sources often means different data classes (types) exist in a DSS, each needing a different level of quality of service (QoS). As a result, efficient data storage and retrieval processes that satisfy various QoS requirements are needed. This paper studies storage allocation, meaning how the data of different classes is spread over storage nodes, for a multi-class DSS. More specifically, assuming a probabilistic access to the storage nodes, we aim at maximizing the weighted sum of the probability of successful data recovery of data classes, when for each class a minimum QoS (probability of successful recovery) is guaranteed. Solving this optimization problem for a general setup is intractable. Thus, we find the optimal storage allocation when the data of each class is spread minimally over the nodes, i.e. minimal spreading allocation (MSA). Then, by comparing the performance of the optimal MSA with the performance upper bound, we show that the optimal MSA is indeed the optimal storage allocation in many practical cases. Numerical examples are also presented for better illustration of the results.

In communications, one frequently needs to detect a parameter vector x in a box from a linear model. The box-constrained rounding detector xBRand Babai detector xBBare often used to detect x due to their high probability of correct detection, which is referred to as success probability, and their high efficiency of implimentation. It is generally believed that the success probability PBRof xBRis not larger than the success probability PBBof xBB. In this paper, we first present formulas for PBRand PBBfor two different situations: x is deterministic and x is uniformly distributed over the constraint box. Then, we give a simple example to show that PBRmay be strictly larger than PBBif x is deterministic, while we rigorously show that pBR≤ pBBalways holds if x is uniformly distributed over the constraint box.

In this paper, we investigate the performance of network coded cooperation (NCC) systems based on relay selection in the presence of imperfect channel state information (CSI). Specifically, we consider an uplink cellular scenario with N sources, M relays and a single destination. The relays adopt decode and forward (DF) relaying and use maximum distance separable (MDS) codes as their encoding vectors. We investigate the impact of imperfect CSI on outage probability and asymptotic and finite-SNR diversity-multiplexing tradeoff (DMT) of the system under consideration. Simulation results are further presented to corroborate the analytical findings and provide insight into the system design where imperfect CSI and finite SNR regime are taken into account.

In wireless channels, the received signal to noise ratio (SNR) can be represented as γ = βγ̅, where γ is the average SNR and β is a random variable with probability density function (PDF) f(β). In this paper, we analyze the high SNR performance of wireless channels with a logarithmic singularity. That is, f(β) = aβt+ bβμlog(β) + ··· near β = 0. This logarithmic singularity (LS) is critically important in determining the high SNR performance and appears to have been completely overlooked. Important special cases include Gamma-Gamma and Generalized-K channels. For instance, the GG has been used to model scattering, reflection, and diffraction and optical, navigation and relay channels [1]. This versatility highlights the importance of LS wireless channels. Classical asymptotic or high SNR analysis is developed by expanding f(β) = aβt+ · · · near β = 0 and expressing the diversity and coding gain as direct functions of a and t. However, as this monomial expansion does not hold for LS channels, we develop generalized asymptotic performance measures for outage and error rates. The results show significantly improved accuracy in the SNR range of 1025 dB. For this range, our new asymptotic expressions achieve much better accuracy than the conventional ones that ignore this singularity.

Caching popular multimedia content has the potential to take wireless networking to an unprecedented height in terms of user experience. Primary motif behind content caching is to give frequent access to popular content cached at local caches, such as femto access point with finite storage. Although content-caching was Initially limited to wired backbone networks, it now being developed for wireless networks. The main difference between these two cases is the potential mobility of the user. We thus investigate the impact of user mobility on the performance of content-caching wireless heterogeneous networks (HetNets). We describe the user mobility by the random waypoint model and characterize the spatial randomness of different types of nodes by using independent Poisson point processes. Using their stochastic properties, we analyze the handover probabilities and evaluate expected download delay as a function of handover probabilities.

We analyze relay selection for an underlay cognitive radio (CR) two-way relay network (TWRN) with zero-forcing (ZF) transmission and receiving. The source and the destination nodes are massive multiple-input multiple-output (MIMO) enabled. Relays will perform amplify and forwarding (AF) while the destination and source nodes perform self interference cancellation. We first obtain asymptotic signal-to-interference-plus-noise ratio (SINR) values under the power scaling at the relay and end nodes. Then, we derive optimal power allocation schemes for the end nodes to satisfy the interference constraints at the primary user (PU). Based on these optimal values, we analyze the effect of relay selection on the sum rate. With the use of massive MIMO, the SINR and the sum rate will only depend on the pathloss coefficients of the channels and average noise levels. Thus, the relay selection can be done at the deployment stages of the system and most of the time it simplifies to selection of the relay with the highest number of antennas. Our simulation results validate the analytical asymptotic results and qualify CR massive MIMO TWRNs as a possible candidate for future wireless systems.

This paper analyzes the problem of optimum user association and sum rate maximization for software defined radio access networks (SD-RANs) with access node diversity for fifth generation (5G) wireless networks. We consider four complementary types of access nodes namely, a massive multiple- input multiple-output (MIMO) base station (BS), MIMO BSs, small cells (SCs), and indoor and outdoor distributed antenna systems (DAS). The SDRAN user association problem is solved through a novel three-stage optimization scheme called the place coverage (TPC). TPC divides the user equipment (UEs) into two sets of indoor and outdoor UEs. Initially, TPC associates indoor UEs with the indoor DAS access nodes. Next, outdoor UEs are associated with the outdoor DAS access nodes, SCs, MIMO BSs, and the massive MIMO BS. Finally, the remaining resources of indoor and outdoor access nodes are used to serve the UEs that have not been served. The scope of TPC is multifold. First, TPC reflects the closest model to a real-world diverse 5G network. Secondly, servicing the indoor UEs with iDAS antennas results in lower power load per user for the access network resulting in better coverage, quality, and data speed. Thirdly, TPC provides reduced radiation levels for indoor UEs. Numerical results show that TPC provides significant sum rate and fairness gains over the received signals strength (RSS) based association schemes [1]. Moreover, TPC provides comparable performance levels as the optimum association scheme based on exhaustive search while bringing significant complexity reduction.

The authors study the transmit power allocation (PA) problem for a network of two multi‐antenna terminals (one of which is a massive multiple‐input and multiple‐output (MIMO) terminal) and a two‐way, amplify‐and‐forward relay. The relay is limited to a single antenna. Using perfect channel state information, the terminals employ beamforming with maximum‐ratio‐transmission and maximum‐ratio‐combining for transmission and reception, respectively. The authors investigate two practical problems, namely; (i) maximising the sum rate subject to a total power constraint (ii) maximising the sum rate when one of the terminals must exceed a target signal‐to‐noise ratio (SNR). For the first case, the authors derive the closed‐form optimal PA and for the second, the authors derive a sub‐optimal PA. In both cases, the resulting sum rates are a function of instantaneous channel gains. Thus by averaging over the Nakagami‐ m distribution and exploiting the weak law of large numbers, the authors derive the closed‐form ergodic sum rates. Finally, the simulation results validate the theoretical analysis and show the sum‐rate improvements over uniform PA. For example, to achieve 4 bit/s/Hz, a uniform allocation needs 1 dB more than the authors’ optimal allocation. When one of the SNRs must exceed a target value, the gap between the authors’ sub‐optimal PA and random PA increases to 2 dB.

We investigate the impact of small-macro cell cooperation (SMC) in improving the spectral efficiency and reliability of uplink transmission in a heterogeneous network. We consider a network of two user equipments (UEs), a macro-cell base station (BS) and a small-cell BS. Joint SMC involves macro-to-small quantized feedback and decode-forward relaying from small to macro cell. This cooperation utilizes full-duplex transmission and intra-network spectrum sharing. We first propose a transmission scheme based on superposition block Markov encoding at each UE, coherent decode-forward relaying and sliding window decoding at the small-cell BS, and quantize-forward relaying and backward decoding at the macro-cell BS. Second, we derive the optimal macro-cell quantization to maximize the whole spectral efficiency. Third, for a certain non-fading scenario, we prove that the proposed scheme asymptotically achieves the capacity (maximum spectral efficiency) by reaching the cut-set bound as macro-cell power approaches infinity. Fourth, we formulate the outage probability over block fading channels, considering the outage events at the small and macro-cell BSs and the channel variations over different blocks. Last, we generalize the proposed scheme to an N (>2)-UE case. As macro-cell power increases, the results show that the proposed scheme achieves a full diversity order of two and outperforms all existing non-SMC schemes. These strong results suggest the utility of the proposed scheme for potential deployment in 5G cellular networks.

The downlink performance of two-tier (macro/pico) multi-antenna cellular heterogeneous networks employing space division multiple access (SDMA) technique with zero-forcing precoding is analyzed in this paper. The number of users simultaneously served with SDMA by a base-station (BS) depends on the number of active users in its cell, with the maximum served users limited to Lmax. To protect the pico users from severe macro-interference, part of the antennas at each macro BS is proposed to be utilized toward interference nulling to pico users. The partitioning of macro antenna resources to serve macro-users and to null interference to pico users for optimal performance is investigated in this paper. Biased-nearest-distance-based user association scheme is proposed, where the bias value accounts for the natural bias due to the differences in multi-antenna transmission schemes across tiers, as well as the artificial bias for load balancing. The signal-to-interference-ratio coverage probability, rate distribution, and average rate of a typical user are then derived. Our results demonstrate that the proposed interference nulling scheme has strong potential for improving performance if the macro antennas partitioning is carefully done. The optimalL*maxfor both macro and pico-tier, which maximize the average data rate, is also investigated and it is found to outperform both single-user beamforming and fullSDMA. Finally, the impact of imperfect channel state information due to limited feedback is analyzed.

This paper proposes a new medium access control (MAC) protocol for low power sensor devices, suitable for IoT systems. IEEE 802.15.4 standard is suitable for low power wireless personal area network (WPAN) but it does not satisfy the data rate and reliability requirements for IoT systems in a 5G wireless network. We have observed that unnecessary packet drop takes place due to beacon superframe broadcasting during data transmission and it is the primary reason for the standard's data-rate and reliability shortfall. This problem represents a scenario where data transmission takes place with the lack of available time for data transmission in that superframe duration. To overcome this lacuna, we incorporate backoff freezing mechanism, where the backoff counter freezes whenever the available time for data transmission is insufficient in that superframe duration. A novel sleep protocol is designed to reduce power consumption in idle states too. The proposed MAC protocol is modeled using a 3- dimensional Markov chain for analytical performance evaluation. Analytical results are verified with the simulation run in ns-2.35. Proposed MAC with sleep protocol significantly outperforms the existing state-of-the-art protocols.

We investigate the outage and decoding-delay performances for full-duplex (FD) decode-forward (DF) relaying with backward and sliding window decoding. In our analysis, we consider a block fading channel with full channel state information (CSI) availability at receivers and with limited CSI at transmitters. For backward decoding where the destination starts decoding from the last transmission block, we derive the average block decoding delay. For sliding window decoding, we analyze both joint and sequential decoding where the destination utilizes two received blocks either simultaneously or sequentially to decode the source data. We then derive their average block decoding delays and outage performances by considering channel variation over two transmission blocks and outage events at both the relay and the destination. When comparing FD relaying with backward decoding and half-duplex (HD) transmission, numerical results show that joint sliding-window decoding is the preferred choice in terms of complexity, decoding delay and outage performances.

The downlink performance of two-tier (macro/pico) multi-antenna cellular heterogeneous networks (HetNets) employing space division multiple access (SDMA) technique is analyzed in this paper. The number of users simultaneously served with SDMA by each BS in a resource block depends on user distribution, unlike previous studies which assume the number to be any arbitrary value. By exploiting the feasibility of deploying larger number of antennas at macro BS, we propose to utilize the excess spatial degrees of freedom for interference nulling to pico users from their corresponding nearest (dominant) macro BSs. Biased-nearest-distance based user association scheme is proposed as those introduced in previous studies are unsuitable for analyzing the proposed multi-antenna scheme. Coverage probability and average data rate of a typical user are then evaluated. Our results demonstrate that the proposed interference nulling scheme has strong potential to improve performance. However, the system parameters such as association bias, and number of dedicated antennas at each macro BS for serving its own users must be carefully tuned.

We study the multiple access relay channel (MARC) with relay-destination cooperation (MARC-RDC). This channel resembles the uplink transmission in heterogeneous network where two user equipments (UEs) communicate with macro-cell base station (BS) through small-cell BS. We propose a coding scheme where the transmission is carried over B blocks and each UE performs superposition block Markov encoding. The relay (small-cell BS) first jointly decodes both UEs information using sliding window decoding over two transmission blocks and then forwards these information to the destination (macro-cell BS) coherently with UEs. The destination quantizes its received signal in each block and forwards the quantization index to the relay. The destination then decodes both UEs information using backward decoding. For this scheme, we derive the achievable rate region and compare it with existing schemes and the cut-set bound. Results show that relay-destination cooperation enlarges the rate region as the destination power increases. We further show that the proposed scheme asymptotically achieves the capacity by reaching the cut-set bound when the destination power approaches infinity and the ratio of one UE-destination to UE-relay link amplitudes is equal to that of the other UE. These results make the proposed scheme appealing for deployment in 5G cellular networks.

While massive MIMO based underlay cognitive radio (CR) networks are a promising concept in the next generation of wireless networks to increase spectral efficiency, reusing the same pilot sequences in both networks cause pilot contamination leading to residual interference. Thus, this paper investigates the affects of pilot contamination on a random CR network underlaid upon a random primary network where both networks employ path loss inversion based power control. A Matern cluster process is considered for the underlay system, while homogeneous Poisson point processes are considered for the primary transmitters and receivers. We derive the moment generating function of the normalized aggregate interference at an underlay receiver, its first two moments, and the outage probability. Finally, it is shown that the underlay cluster radius, ensured received power levels through power control and the different node densities have a significant effect on the outage of an underlay receiver.

This paper considers a cloud radio access network (C-RAN) where spatially distributed remote radio heads (RRHs) communicate with a full-duplex user. In order to reflect a realistic scenario, the uplink (UL) and downlink (DL) RRHs are assumed to be equipped with multiple antennas and distributed according to a Poisson point process. We consider all participate and nearest RRH association schemes with distributed beam-forming in the form of maximum ratio combining/maximal ratio transmission (MRC/MRT) and zero-forcing/MRT(ZF/MRT) processing. We derive analytical expressions useful to compare the average sum rate among association schemes as a function of the number of RRHs antennas and density of the UL and DL RRHs. Numerical results show that significant performance improvements can be achieved by using the full-duplex mode as compared to the half-duplex mode, while the choice of the beamforming design as well as the RRH association scheme plays a critical role in determining the full-duplex gains.

This paper investigates the impact of co-channel interference (CCI), imperfect channel state information (CSI) and pilot contamination for multi-pair massive multiple-input multiple-output (MIMO) two-way relay networks (TWRNs). We consider a multi-cell TWRN system consisting of single-antenna user nodes and amplify-and-forward (AF) relay nodes having very large antenna arrays. Under the aforementioned channel imperfections, the asymptotic signal-to-interference-noise ratio and asymptotic sum rate expressions are derived in closed-form whenever the number of relay antennas grows unbounded with respect to the number of user nodes. For perfect CSI case, the transmit power at the user nodes and the relay can be scaled down inversely proportional to the number of antennas at the relay. Moreover, for the imperfect CSI case, these transmit powers can only be scaled down inversely proportional to the square-root of the relay antenna count. Thus, even with imperfect CSI, the benefits of employing a massive MIMO-enabled relay on transmit power savings are significant. Moreover, our analysis shows that although the detrimental effect of CCI can be asymptotically negated completely, the residual interference due to pilot contamination cannot be mitigated even in the limit of infinitely many relay antennas.

Ambient backscatter, a new communication technology, can permit battery-free devices to communicate with other devices through reflecting the ambient radio frequency signals. One challenge for ambient backscatter communication system is to recover the backscattered information bits hidden in the received signals. Existing solutions are mainly based on energy detector and thus provide poor performance at low signal noise ratio (SNR). To solve this problem, a detection algorithm based on statistical covariances is suggested in this paper. Specifically, we calculate the distributions of two covariance-based statistics, design the detection rule, and then derive the closed- form expressions for detection probability and bit error rate (BER). It is found that our proposed algorithm outperforms the energy detector at low SNR regions. Finally, the simulation results are provided to corroborate our theoretical studies.

High reliability and low latency are critical performance targets in the fifth-generation cellular networks. How does a full-duplex decode-forward relay fare in this context? To answer this question, we analyze the outage and (average) decoding-delay for both joint and sequential sliding window decoding. For comparison, we also analyze decoding delay of backward decoding and consider its existing outage analysis. In our analysis, we consider a block fading channel with full channel state information (CSI) availability at receivers and with limited CSI at transmitters and outage events at both relay and destination and channel variation over different blocks in sliding window decoding. Moreover, by analyzing the asymptotic performance at high SNR, we prove that both joint and sequential decoding achieve a full diversity order of two and derive the coding gain gaps between backward decoding and joint and sequential sliding window decoding. To see the benefits of full-duplex relaying, we also include the performance of half-duplex schemes and conclude that the preferred scheme depends on the rate, outage, and delay requirements for a specific service.

Ambient backscatter technology that utilizes the ambient radio frequency signals to enable the communications of battery-free devices has attracted much attention recently. In this paper, we study the problem of signal detection for an ambient backscatter communication system that adopts the differential encoding to eliminate the necessity of channel estimation. Specifically, we formulate a new transmission model, design the data detection algorithm, and derive two closed-form detection thresholds. One threshold is used to approximately achieve the minimum sum bit error rate (BER), while the other yields balanced error probabilities for “0” bit and “1” bit. The corresponding BER expressions are derived to fully characterize the detection performance. In addition, the lower and the upper bounds of BER at high signal-to-noise ratio regions are also examined to simplify a performance analysis. Simulation results are then provided to corroborate the theoretical studies.

Cellular heterogeneous networks (HetNets) can improve capacity by offloading users from congested macro cells to lightly loaded small cells through biased association known as cell range expansion (CRE). However, the offloaded (range-expanded) users must be protected from macro interference through time/frequency resource partitioning. In this paper, we develop an analytical framework to evaluate the performance gain due to CRE further supported by resource partitioning in two-tier (macro-pico) networks with multichannel downlinks, e.g., those based on orthogonal frequency division multiple access (OFDMA). By exploiting the flexibility in subchannel allocation offered by OFDMA, frequency-domain resource partitioning is proposed in which the macro tier is muted on a fraction of total subchannels, which are allocated exclusively to range-expanded pico users. The load perceived by a base-station is a key factor in determining its interference contribution over the network and is directly affected by user offloading and resource partitioning. Thus, the analysis of such systems must incorporate cell load. While previous studies mostly rely on full-load assumption, in this paper, we properly characterize cell load as the function of user density, association bias and resource partitioning fraction. We then, evaluate the performance in terms of average user data rate over the entire network, and also investigate the optimal choice of association bias and resource partitioning fraction.

A cooperative network in which confidential messages are conveyed from a source to a legitimate destination with the help of decode-and-forward relays in the presence of a malicious eavesdropper is considered. Tight upper bounds on the ergodic secrecy rate are derived in the cases of i) cooperative beamforming and ii) multi-user selection. Further, a new concept of cooperative diversity gain, namely, adapted cooperative diversity gain (ACDG), is investigated. It is shown that the ACDG can be seen as an effective metric to evaluate the security level of a cooperative wireless network in the presence of eavesdroppers. Also, the ACDG obtained in the cooperative beamforming scenario is equal to the traditional cooperative diversity gain of traditional multiple-input single-output networks, while the ACDG obtained in the multiuser scenario is equal to that of traditional single-input multiple-output networks.

This paper investigates the effects of different cooperative sensing strategies on erroneous spectrum sensing for an interweave cognitive radio network. The setup is as follows. Primary receiver nodes and secondary nodes are randomly distributed in R2. We model them as two independent homogeneous Poisson point processes. Beacon (out-of-band) signals, periodically transmitted by primary receivers, indicate to the secondary nodes that spectrum is occupied. Whenever beacon detection fails, the transmissions of secondary nodes generate harmful interference. Thus, to alleviate this issue, the misdetection probability of secondary nodes must be reduced. To this end, we propose two strategies: 1) a secondary node cooperates with its closest neighbour, and 2) a secondary node cooperates with M random neighbours within a given radius. Furthermore, along with these co-operation strategies, we investigate three primary beacon detection methods for secondary nodes: 1) separately decoding each primary beacon, 2) detecting only the closest primary receiver?s beacon, and 3) detecting the aggregate beacon signal from all primary receivers. For the exponential path loss and Rayleigh fading considered, we derive the total misdetection probability for each scheme along with the resulting outage probability of a primary receiver. We finally show through numerical results that M co-operation works better for lower reception thresholds, and that for a reception threshold of -120 dBm, a 104fold decrease in the misdetection probability is achievable.

Ambient backscatter is a new communication technology that utilizes ambient radio frequency signals to enable battery-free devices to communicate with each other. In this paper, we study the problem of signal detection and bit error rate (BER) performance for this new communication system where the differential encoding is adopted to eliminate the necessity of channel estimation. We formulate a new transmission model, design the data detection approach, and derive the optimal/approximate closed-form detection thresholds. In addition, the performance at high signal-to-noise region (SNR) is also analyzed, where the lower and the upper bounds of BERs are found. Simulation results are then provided to corroborate our theoretical studies.

We consider a wireless energy harvesting (EH) relay network. Relays without embedded energy supply harvest energy from the source node. Considering a time switching protocol, performance measures such as average signal-to-noise ratio (SNR), outage and throughput are analyzed. Subsequently, optimal EH time is selected in order to maximize the throughput. Then, a multiple-relay network is considered with relay selection, which can achieve full diversity at any EH time. All theoretical results are validated by numerical simulations.

Spectrum sensing performance of a cognitive radio (CR) deploying the traditional energy detector (ED) degrades in the presence of random network interference where both the number and locations of the interferers are random, thus preventing correct detection of primary user (PU) in the band of interest. However, it is not clear how the ED performance in such random network interference can be improved. Moreover, the previous studies do not consider complete modeling of the wireless environment including the cumulative effects of path-loss, fading and random network interference. We thus take these effects into account and investigate the performance of the p-norm detector, which offers the flexibility of adapting p to the operating conditions (as against fixed p = 2 for ED). Such adaptability yields remarkable performance gains over ED (say, 15% gain even at 10 dB lower (than that for ED) PU signal powers). Further, cooperative spectrum sensing with multiple CRs yields additional performance gains (say, 30% better performance at optimal cooperative detection threshold) compared to single CR based sensing even under the cumulative effects of path-loss, fading and random network interference.

In this paper, we present mathematical frameworks for error performance analysis in interference limited networks such as cellular networks. Due to the increasing irregularity in the spatial deployment of nodes in the emerging heterogeneous cellular networks (HCNs), we employ stochastic geometry approach by abstracting the node locations as a homogeneous Poisson point process (PPP). First, we characterize the average error probability of an intended communication link with a given transmitter-receiver separation, which is subject to interference from these Poisson distributed nodes. More specifically, we develop uniform approximation (UA), which is highly accurate over the whole range of signal-to-interference ratio (SIR) and hence, serve as an alternative to existing complex analytical results. Error probability UAs for both single-antenna and maximal ratio combining (MRC) receivers are derived in this paper. Next, we evaluate the average error probability of any typical user in the network, which is served by the node providing the maximum received power. Mellin-transform based method is proposed in this case, which often yield closed-form solution. An example of BPSK modulation is given in the paper.

We consider a wireless system with a full-duplex (FD) access point (AP) that transmits to a scheduled user in the downlink (DL) channel, while receiving data from an user in the uplink (UL) channel at the same time on the same frequency. In this system, loopback interference (LI) at the AP and inter user interference between the uplink (UL) user and downlink (DL) user can cause performance degradation. In order to characterize the effects of LI and inter user interference, we derive closed-form expressions for the outage probability and achievable sum rate of the system. In addition an asymptotic analysis that reveals insights into the system behavior and performance degradation is presented. Our results indicate that under certain conditions, FD transmissions yield performance gains over half-duplex (HD) mode of operation.

Power control for uplink transmission in a randomly laid-out cellular network operating over an environment with path loss and composite Rayleigh-lognormal shadowing is investigated. Each mobile station (MS) adjusts its transmit power to completely remove shadowing and to partially invert the effect of path loss. Using stochastic geometry tools, we derive an approximate coverage probability expression and validate it via simulations. With the power control scheme considered, shadowing with lower standard deviation improves the coverage probability. Also the severity of shadowing of local and surrounding environments has the same effect on the coverage probability. It was also observed that at low signal-to-interference-plus-noise ratio (SINR) thresholds, complete compensation of shadowing and partial compensation of path loss improves coverage, while at high SINR thresholds inverting only the effect of shadowing gives a better coverage probability.

In an underlay cognitive radio network, the secondary (underlay) transmitters generate interference to a primary receiver, while an underlay receiver is subject to interference from both the primary transmitters and other underlay transmitters not associated with it. Although guard regions, maximum allowable underlay transmit powers, and contention distances help guarantee a minimum performance to the primary network, no such safeguard exists for the underlay network. To this end, this paper characterizes the aggregate interference on an underlay receiver while considering power control and receiver association schemes for both networks. Transmitters and receivers of both networks are assumed to be distributed as independent Poisson fields in the 2-D plane, and all links undergo exponential path loss and Rayleigh fading. We derive the moment generating function of the aggregate interference on an underlay receiver and its outage probability. We show that the interference from the primary network does not depend on any node density, and that it dominates the aggregate interference. Furthermore, it is shown that increasing primary and underlay receiver densities reduce the outage probability under lower required power thresholds for the primary receivers.

Missed-detection probability expressions for energy detectors often involve infinite series and do not provide quick insights into the effects of operating conditions. To overcome these limitations, we develop novel asymptotic analyses by proposing an approximate probability density function (PDF) of a random variable β, which, in general, can characterize fading channels in diverse operating conditions. The coefficients of the proposed approximate PDF of β are obtained by matching the coefficients of the approximate PDF's series expansion (or coefficients of the approximate PDF's moment generating function (MGF)) with those of the exact PDF (or MGF) of β. By using the proposed approximation, a unified closed-form asymptotic missed-detection probability is derived. Its usefulness is then demonstrated for fading channels without and with antenna diversity, for cooperative detection, and in co-channel interference. For each case, the sensing gain, which reveals the effect of the operating conditions on the detection performance, is determined explicitly. Furthermore, the asymptotic complementary area under the receiver operating characteristic curve, an alternative performance metric, is derived, and found to reveal the sensing gain. Numerical results verify the accuracy of our derived asymptotic expressions over a wider signal-to-noise ratio (SNR) range compared to the existing asymptotic solution, which is accurate only for high SNRs.

A relay network in which a source wishes to convey a confidential message to a legitimate destination with the assistance of trusted relays is considered. In particular, cooperative beamforming and user selection techniques are applied to protect the confidential message. The secrecy rate (SR) and secrecy outage probability (SOP) of the network are investigated first, and a tight upper bound for the SR and an exact formula for the SOP are derived. Next, asymptotic approximations for the SR and SOP in the high signal-to-noise ratio (SNR) regime are derived for two different schemes: 1) cooperative beamforming and 2) multiuser selection. Furthermore, a new concept of cooperative diversity gain, namely, adapted cooperative diversity gain (ACDG), which can be used to evaluate the security level of a cooperative relaying network, is investigated. It is shown that the ACDG of cooperative beamforming is equal to the conventional cooperative diversity gain of traditional multiple-input single-output networks, while the ACDG of the multiuser scenario is equal to that of traditional single-input multiple-output networks.

A full-duplex (FD) multiple antenna access point (AP) communicating with single antenna half-duplex (HD) spatially random users to support simultaneous uplink (UL)/downlink (DL) transmissions is investigated. Since FD nodes are inherently constrained by the loopback interference (LI), we study precoding schemes for the AP based on maximum ratio combining (MRC)/maximal ratio transmission (MRT), zero-forcing, and the optimal scheme for UL and DL sum rate maximization using tools from stochastic geometry. In order to shed insights into the systems performance, simple expressions for single antenna/perfect LI cancellation/negligible internode interference cases are also presented. We show that FD precoding at AP improves the UL/DL sum rate and hence a doubling of the performance of the HD mode is achievable. In particular, our results show that these impressive performance gains remain substantially intact even if the LI cancellation is imperfect. Furthermore, relative performance gap between FD and HD modes increases as the number of transmit/receive antennas becomes large, while with the MRC/MRT scheme, increasing the receive antenna number at FD AP, is more beneficial in terms of sum rate than increasing the transmit antenna number.

Relay selection strategies help to improve spectral and energy efficiencies, to enhance transmission robustness, or to reduce latency in multi-relay cooperative networks. Two novel relay selection strategies are proposed and analyzed here for multiple-input multiple-output (MIMO) amplify-and-forward (AF) two-way relay networks (TWRNs) with spatial multiplexing. Specifically, they are designed to maximize the effective end-to-end signal-to-noise ratio (SNR), and thereby minimize the overall outage probability or maximize the achievable sum rate. Interestingly, the first strategy amounts to maximizing the minimum of the eigenvalues of the Wishart matrices from the selected relay to the two user nodes. Counter-intuitively, the latter strategy amounts to maximizing the minimum of the determinant of the same Wishart matrices. The performance of these two strategies is investigated by deriving lower/upper bounds of the overall outage probability and the average sum rate approximations in closed form. Further, the asymptotic high-SNR approximations of the outage probability are derived, and thereby, the achievable diversity-multiplexing tradeoff is quantified. This tradeoff reveals that whenever the sum of relay antennas is fixed, the achievable diversity order is always a constant, and hence, the multiplexing gain can indeed be improved by equally distributing antennas among the available set of relays. Our results reveal that relay selection indeed significantly alleviates the inherent diversity-gain loss associated with the use of available degrees of freedom for spatial multiplexing.

Performance analysis of the energy detector (ED) in fading channels has received enormous attention recently. However, averaging the generalized Marcum-Q function over fading statistics often results in complicated special functions and/or infinite series based expressions. Motivated by the need for simple expressions without compromising the accuracy, we propose a new representation for the probability density function (PDF) of the fading channel gain. This representation is then used to derive simple, unified expression for asymptotic miss-detection probability in closed-form. The derived expression is evaluated for several fading channels and antenna diversity schemes. Numerical results reveal its high accuracy over a wide range of signal-to-noise-ratio (SNR) (as low as 0 dB) unlike the existing asymptotic expression which is accurate only for high SNR regime (say, SNR ≥ 20 dB).

We consider an underlay cognitive relay network coexisting with a primary multicast network (e.g. digital television (TV) broadcasting network), in which secondary user (SU) transmissions are power constrained to limit the interference on any primary receiver in the network. The primary receivers and SU relays are randomly located due to irregular deployments and/or mobility and thus, their spatial distributions are modeled by two independent Poisson point processes (PPPs). In this paper, we analyze an opportunistic relaying scenario and develop a relay-selection scheme by considering the interference constraints on all the primary receivers in the network. We then analytically evaluate the relaying performance in terms of outage probability by using tools from stochastic geometry and point process theory, and finally compare the performance against that of direct communication. Closed-form expressions are derived for the outage probabilities of both the relay and direct links, along with their high-signal-to-noise ratio (SNR) asymptotics.

This paper analyzes how transmit power control affects the aggregate interference arising from a Poisson field of underlay cognitive radio (CR) transmitter nodes distributed in a finite area. We consider three per-user, location dependent power control schemes, when each CR transmitter is associated with the nearest CR receiver, where the CR receivers form a Poisson field in the entire 2-dimensional space. The 3 schemes are based on: 1) CR transmitter-receiver distance rc2) rcand a constant cut-off power level 3) rcand a random cut-off power level, respectively. For each of these, the exact moment generating function (MGF) and mean of aggregate interference power are derived. We also investigate the primary system outage due to aggregate interference. Rayleigh fading and exponential path loss links are assumed. Monte-Carlo simulation results validate our analysis and also show that the CR power thresholds and node densities significantly affect the aggregate interference.

In this paper, we propose a cognitive transmission scheme for Amplify-and-Forward (AF) two-way relay networks (TWRNs) and investigate its joint sensing and transmission performance. Specifically, we derive the overall false alarm probability, the overall detection probability, the outage probability of the cognitive TWRN over Rayleigh fading channels. Furthermore, based on these probabilities, the spectrum hole utilization efficiency of the cognitive TWRN is defined and evaluated. It is shown that smaller individual or overall false alarm probability can result in less outage probability and thus larger spectrum hole utilization efficiency for cognitive TWRN, and also produce more interference to the primary users. Interestingly, it is found that given data rate, more transmission power for the cognitive TWRN does not necessarily obtain higher spectrum hole utilization efficiency. Moreover, our results show that a maximum spectrum hole utilization efficiency can be achieved through an optimal allocation of the time slots between the spectrum sensing and data transmission phases. Finally, simulation results are provided to corroborate our proposed studies.

We propose a novel base stations (BSs) - mobile stations (MSs) association policy for cellular networks. In this policy, the BS which provides the highest signal-to-interference ratio (SIR) among those located within a predetermined maximum association distance of the MS is selected as the serving BS. This policy encompasses the conventional highest-SIR association as a special case. Application of the new policy in 2- and 3- dimensional single-tier (homogeneous) and 2-dimensional two-tier (heterogeneous) networks is discussed. Coverage probability expressions are derived assuming BSs in each tier are distributed according to an independent homogeneous Poisson point process (PPP). Rayleigh fading and exponential path-loss radio channels are assumed. Analysis is validated by Monte-Carlo simulations. For single-tier networks, two methods are proposed for the selection of the maximum association distance. With such selection, the proposed association policy performs similarly to the highest-SIR association. It is shown that this policy can also be used to manage user offloading to small cells in two-tier heterogeneous networks.

This paper investigates the aggregate interference from interweave cognitive secondary nodes spatially distributed in a finite Poisson field. These secondary nodes sense an out-of-band beacon to initiate their transmissions, which can be concurrent with those of the primary system if a sensing error is made. The resulting aggregate interference is analyzed in this paper. For this purpose, general Nakagami-m fading and path-loss are assumed for all relevant channels. Moreover, we incorporate random secondary node transmit powers with any probability distribution. The analysis includes the exact moment generating function (MGF) of the aggregate interference along with the exact outage probability of the primary system. Furthermore, we develop a simple MGF approximation which is valid for severely fading channels and for lower beacon reception threshold to beacon transmit power ratios. Finally, we show that a lower fading severity significantly improves the diversity order of the PR due to more accurate spectrum sensing by the secondary nodes.

Erroneous beacon detection by interweave secondary nodes generates interference on the primary system. This paper analyzes how the aggregate interference behaves when secondary nodes use transmit power control and receiver association schemes. For this purpose, secondary transmitter nodes and receiver nodes are assumed to be distributed over a circular region and over the entire 2-D plane respectively. Two independent Poisson point processes model these distributions. We propose a receiver association scheme where each secondary transmitter attempts to connect to the closest available receiver. If it is not available, the transmitter attempts to connect with the next closest. This process continues until the M-th closest receivers are scanned. If no receiver is available, the transmitter remains silent. Moreover, a per-user transmit power control scheme is considered in which the transmit power is based on the distance between the transmitter and the associated receiver subject to a cut-off power level. All links are assumed to undergo path-loss and Rayleigh fading. The exact moment generating function (MGF) of the aggregate interference, the outage probability of the primary system, and the average probability of concurrent transmission are derived. Validated by simulations, our results show how the aggregate interference is affected by secondary power thresholds, receiver densities, and availability of the secondary receiver.

Cognitive relay technology has been envisioned as a promising transmission scheme to enhance the reliability and coverage of secondary networks. However, the performance of cognitive relay networks (CRNs) is limited by the lack of accurate channel state information (CSI). As such, this paper adequately addresses the impact of imperfect CSI on the performance of cognitive multihop networks by proposing a simple yet effective backoff control power method. In addition, novel exact and asymptotic expressions for outage probability and ergodic capacity over Rayleigh fading channels are also derived. These tractable analytical results reveal new insight into the design, e.g., the number of hops for secondary network, and optimization of cognitive multihop networks.

The performance of cognitive spectrum sharing systems with opportunistic relay selection over Nakagami-m fading is analyzed in the presence of multiple primary users (PUs). In particular, we derive an exact closed-form expression for the outage probability (OP) of the considered cognitive relay systems under the joint impact of maximal transmit power Ptat secondary transmitter and peak interference power Ipat the primary user. Our general formulas cover several specific practical scenarios, e.g., where the maximal transmit power can be neglected compared to the peak interference power. In addition, a tractable expression for the asymptotic OP is also derived and reveals important insights into the system performance. We show that the number of PUs only affects the coding gain but not the diversity gain.

Tone injection (TI) mitigates the high peak-to-average power ratio problem without incurring data rate loss or extra side information. However, optimal TI requires an exhaustive search over all possible constellations, which is a hard optimization problem. In this paper, a novel TI scheme that uses the clipping noise to find the optimal equivalent constellations is proposed. By minimizing the mean error of the clipping noise and possible constellation points, the proposed scheme easily determines the size and position of the optimal equivalent constellations. The proposed scheme achieves significant PAPR reduction while maintaining low complexity.

This paper investigates the relay selection (RS) problem in networks with multiple users and multiple common amplify-and-forward (AF) relays. We first give an optimality measure for RS in multiple-user relay networks. An optimal RS (ORS) algorithm is then provided, which is an extension of an RS scheme in the literature that maximizes the minimum end-to-end receive signal-to-noise ratio (SNR) of all users. The complexity of the ORS is quadratic in both the number of users and the number of relays. A suboptimal RS (SRS) scheme is also proposed, which has linear complexity in the number of relays and quadratic complexity in the number of users. Furthermore, diversity orders of both the ORS and the proposed SRS are derived and compared with those of a naive RS scheme and the single-user case. The ORS is shown to achieve full diversity, while the diversity order of the SRS decreases with the number of users. For two-user networks, the closed-form outage probabilities and array gains corresponding to the minimum SNR of the users in the RS schemes are derived. It is proved that the advantage of the SRS over the naive RS scheme increases as the number of relays in the network increases. Simulation results are provided to corroborate the analytical results.

Two transmission strategies, namely (i) pairwise zero-forcing transmission and (ii) non-pairwise zero-forcing transmission, for multiple-input multiple-output (MIMO) amplify-and-forward (AF) multi-way relay networks (MWRNs) are analytically studied. To this end, lower and upper bounds of the outage probability, the corresponding high signal-to-noise ratio outage probability approximations, the achievable sum rate, and the fundamental diversity-multiplexing trade-off are derived in closed-form. The proposed pairwise zero-forcing transmission strategy possesses a lower practical implementation complexity as each node requires only the instantaneous respective node-to-relay channel knowledge. Counter intuitively, the non-pairwise zero-forcing transmission strategy achieves higher spatial multiplexing gains over the pairwise counterpart at the expense of higher relay processing complexity and more stringent channel state information requirements. Moreover, numerical results are presented to further validate our analysis and thereby to obtain valuable insights into practical MIMO AF MWRN implementation.

This paper studies relay selection schemes for two-way amplify-and-forward (AF) relay networks. For a network with two users that exchange information via multiple AF relays, we first consider a single-relay selection (SRS) scheme based on the maximization of the worse signal-to-noise ratio (SNR) of the two end users. The cumulative distribution function (CDF) of the worse SNR of the two users and its approximations are obtained, based on which the block error rate (BLER), the diversity order, the outage probability, and the sum-rate of the two-way network are derived. Then, with the help of a relay ordering, a multiple-relay selection (MRS) scheme is developed. The training overhead and feedback requirement for the implementation of the relay selection schemes are discussed. Numerical and simulation results are provided to corroborate the analytical results.

This paper proposes and analyzes cognitive multihop decode-and-forward networks in the presence of interference due to channel estimation errors. To reduce interference on the primary network, a simple yet effective back-off control power method is applied for secondary multihop networks. For a given threshold of interference probability at the primary network, we derive the maximum back-off control power coefficient, which provides the best performance for secondary multihop networks. Moreover, it is shown that the number of hops for secondary network is upper-bounded under the fixed settings of the primary network. For secondary multihop networks, new exact and asymptotic expressions for outage probability (OP), bit error rate (BER) and ergodic capacity over Rayleigh fading channels are derived. Based on the asymptotic OP and BEP, a pivotal conclusion is reached that the secondary multihop network offers the same diversity order as compared with the network without back off. Finally, we verify the performance analysis through various numerical examples which confirm the correctness of our analysis for many channel and system settings and provide new insight into the design and optimization of cognitive multihop networks.

We derive uniform approximations (UAs) for typical performance measures such as error probability, outage probability and capacity of wireless transmissions over flat fading channels impaired by noise. Uniform refers to the fact that these approximations are accurate over the whole range (low to high) of signal-to-noise ratio (SNR) values. First, the high-SNR results of Wang and Giannakis are generalized and unified for an arbitrary performance measure. Second, we develop a Mellin-transform-based procedure to construct low- and high-SNR asymptotics of error probability or outage. Specifically, these asymptotics are related to the left- and right-sided poles of a Mellin product with respect to its fundamental strip. Third, by using multiple low-SNR terms and a single high-SNR term, UAs for the error probability of coherent modulation are constructed for Rayleigh fading, maximal-ratio-combining (MRC), selection-combining (SC), dual hop relaying, and co-channel interference. UAs are also developed for the error probability of single- and multi-channel differential modulation, the product of two Q functions, and the miss probability of energy detection. By using a single low-SNR term and multiple high-SNR terms, the outage probability UA is also developed. Finally, since the capacity measure is not an exponentially decaying function, we derive a UA for an intermediate function which is based on the moment-generating function (MGF) and ultimately, the resulting approximation for the capacity.

The sum rate of multiple-input multiple-output (MIMO) amplify-and-forward (AF) two-way relay networks (TWRNs) with zero-forcing (ZF) transmission is analyzed. Namely, (1) ZF at the two sources for transmission and reception and (2) ZF at the relay for transmission and reception, are treated. Specifically, the exact sum rate expressions and corresponding high signal-to-noise ratio (SNR) approximations are derived for uncorrelated and min-semi-correlated (i.e., correlation exists only at the minimum antenna terminal) Rayleigh fading cases in closed-form. Moreover, the closed-form upper and lower bounds of the sum rate are derived for max-semi-correlated (i.e., correlation exists only at the maximum antenna terminal) and doubly-correlated Rayleigh fading cases. Notably, these sum rate bounds and high SNR approximations provide valuable insights into practical MIMO AF TWRN system-design and the maximum achievable spatial multiplexing gain. All the analyses are verified by using Monte-Carlo simulations.

The sum rate of multiple-input multiple-output (MIMO) amplify-and-forward (AF) two-way relay networks (TWRNs) with transmit/receive zero-forcing (ZF) is analytically studied. Specifically, the exact sum rate expressions are derived for uncorrelated and semi-correlated Rayleigh fading cases in closed-form. Moreover, the closed-form upper and lower bounds of the sum rate are derived for doubly-correlated Rayleigh fading. In particular, these sum rate bounds are tight, and consequently, serve as benchmarks providing valuable insights into practical MIMO AF TWRN system-design. All the analyses are verified by using Monte-Carlo simulations.

A pair-wise transmit/receive zero-forcing (Tx/Rx ZF) transmission strategy is proposed and analyzed for multiple-input multiple-output (MIMO) amplify-and-forward (AF) multi-way relay networks (MWRNs). The performance of this system set-up is studied by deriving lower and upper bounds of the overall outage probability, the corresponding high signal-to-noise ratio outage approximations, and the achievable diversity-multiplexing trade-off. The proposed pair-wise Tx/Rx ZF transmission strategy possesses a lower implementation complexity as each source requires only the instantaneous respective source-to-relay channel knowledge. Moreover, our analysis provides valuable insights into practical MIMO AF MWRN implementation.

The main drawback of orthogonal frequency division multiplexing (OFDM) systems is the high peak-to-average power ratio (PAPR), which leads to performance degradation and power inefficiency. Tone injection (TI) is a distortionless technique that can reduce PAPR efficiently without incurring data rate loss or extra side information. However, optimal TI requires an exhaustive search over all combinations of possible constellations, which is an NP-hard problem. Suboptimal algorithms, achieving different tradeoffs between the PAPR reduction and complexity, have thus been developed. In this paper, we introduce a novel parallel tabu search algorithm for TI. Simulation results show that the proposed algorithm achieves significant PAPR reduction while maintaining low complexity.

A novel joint beamforming and antenna selection strategy is proposed and analyzed for two-way multiple-input multiple-output amplify-and-forward relay networks. Specifically, this strategy selects the optimal transmit precoding and receiver filtering vectors at the two source terminals, and an optimal transmit/receive antenna at the relay terminal based on minimizing the overall outage probability. The performance of this transmission strategy is quantified by first deriving the exact cumulative distribution function of the effective signal-to-noise ratio (SNR), and thereby, evaluating the overall outage probability, its asymptotically exact high SNR approximation and achievable diversity order. For a multiple relay scenario, a joint relay, beamforming, and antenna selection strategy is proposed and analyzed as well. Interestingly, our selection strategies are optimal in the sense of the overall outage probability, and hence, in the sense of achievable diversity order as well.

We derive simple uniform approximations (UAs) for the bit error rate (BER), the symbol error rate (SER), and the outage of wireless digital communication systems impaired by fading, noise, and interference. The striking feature of the UAs is their accuracy over the whole range of signal-to-noise ratio (SNR) values, whereas the existing high-SNR approximations break down as the SNR decreases. The UAs require slightly more information than that for high-SNR expressions. The additional information required in the case of error probabilities is the several moments (fractional) of channel gain, which can be extracted readily from the PDF, MGF or the Mellin transform of the PDF. The computation of the UA is simple and requires only the solution of a set of linear equations. Additionally, we also generalize the previous asymptotic results of Wang and Giannakis. The unified asymptotic results of the average of an arbitrary performance measure are thus derived. Various BER and SER expressions then become special cases of this unified approach.

In this paper, the estimation of doubly selective channel is considered for amplify-and-forward (AF) relay networks. The complex exponential basis expansion model (CE-BEM) is chosen to describe the time-varying channel, from which the infinite channel parameters are mapped onto finite ones. Since direct estimation of these coefficients encounters high computational complexity and large spectral cost, we develop an efficient estimator targeting at some specially defined channel parameters. The training sequence design that can minimize the channel estimation mean-square error is also proposed.

Two new transmit/receive (Tx/Rx) antenna selection strategies are proposed and analyzed for two-way multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay networks. These two strategies select the best transmit and receive antennas at the two sources and the relay based on (i) minimizing the overall outage probability and (ii) maximizing the sum-rate. The performance of these selection strategies is quantified by deriving the overall outage probability, its high SNR approximation and the diversity order providing valuable insights into practical system-designs. Importantly, multiple relay and multiple user two-way relay network set-ups are also treated by proposing and analyzing (i) joint relay and antenna selection strategies, and (ii) joint user, relay and antenna selection strategies, respectively. Interestingly, our outage probability results reveal that the joint relay and antenna selection strategies achieve significant diversity and array gains over those of their single relay counterparts. In fact, the diversity orders of individual relayed-branches accumulate to yield the overall diversity of the multi-relay networks. For example, at 10-2outage probability, the dual-antenna relay provides a 14 dB gain over a single-antenna relay, and having two dual-antenna relays improves the gain by another 5 dB. Moreover, the performance degradation due to practical transmission impairments (i) feedback delays, (ii) spatially-correlated fading and (iii) non-identically distributed fading is quantified. Impact of channel prediction to circumvent outdated channel state information for antenna selection due to feedback delay is also studied. All the derivations are validated through Monte-Carlo simulations.

A comprehensive performance analysis framework for dual-hop multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay networks with hop-by-hop beamforming (i.e. both source and relay perform beamforming) is presented. The system performance degradation due to practical transmission impairments (i) feedback delays, (ii) channel estimation errors and (iii) spatially-correlated fading is quantified. To this end, closed-form expressions for the cumulative distribution function of the end-to-end signal-to-noise ratio, its moment generating function, the outage probability, and the average bit error rate (BER) are derived. The asymptotic high SNR approximations of the outage probability and average BER are derived to obtain valuable system-design insights such as the diversity order and array gain. In order to illustrate the usefulness of our analysis, four applications, which employ dual-hop MIMO relaying with hop-by-hop beamforming, are also presented and analyzed. Furthermore, our analyses are validated through Monte-Carlo simulations.

Based on a new vision of the inactivation decoding process, we set a new degree distribution design criterion for the LT part of Raptor codes. Under an infinite block length assumption, a family of degree distributions that satisfy the new design criterion is analytically derived. The finite length performance of this family is investigated by using computer simulations and is shown to outperform the conventional design.

This paper investigates the impact of using outdated channel estimates for relay selection and signal amplification on the performance of amplify-and-forward (AF) relays under partial relay selection (PRS) and opportunistic relay selection (ORS). In practice, outdated channel state information (CSI) can occur due to feedback or scheduling delay. Both variable gain (VG) AF and fixed gain AF schemes are considered. Outage probability, the average bit error rate (BER) and simplified high signal-to-noise ratio approximations are derived. The effect of parameters such as the number of relays, the rank of chosen relay, and the correlation between the delayed and current channel state information are analyzed. Outdated CSI for computing relay gains in PRS causes about 2 dB loss. In ORS, a 3% reduction in correlation causes up to an order of magnitude increase in the outage probability.

This paper considers the analytical performance of primary users (PUs) subject to interference due to secondary users (SU) in an underlay cognitive radio system over Rayleigh fading. In particular, we focus on a more general spatial configuration where the interfered PU, not only located at the center of the cell, is having a protective region which is free of SUs and the SUs are distributed over a finite area in contrast to the commonly used infinite area assumption. We first characterize the statistical properties of the aggregate interference at the PU due to SUs, by deriving new exact closed form expressions for the moment generating function, cumulants, first, second and third moments and first order expansions of the cumulative distribution functions corresponding to propagation scenarios with path loss factors, two and four. We then investigate the PU performance by presenting new analytical expressions for the outage probability, amount of fading as well as the diversity order and coding gain. Our results indicate that the PU can achieve the full diversity gain given a non-zero protective region around the PU.

To evaluate the unitary integrals, such as the well-known Harish–Chandra–Itzykson–Zuber integral, character expansions were developed by Balantekin, where the matrix integrand is a group member; i.e., a square matrix with a nonzero determinant. Recently, this method has been exploited to derive the joint eigenvalue distributions of the Wishart matrices; i.e.,${\bf H}{\bf H}^{\ast}$where${\bf H}$is the complex Gaussian random channel matrix of a multiple-input multiple-output (MIMO) system. The joint eigenvalue distributions are used to calculate the moment generating function of the mutual information (ergodic capacity) of a MIMO channel. In this paper, we show that the previous integration framework presented in the literature is not correct, and results in incorrect joint eigenvalue distributions for the Ricean and full-correlated Rayleigh MIMO channels. We develop a new framework to apply the character expansions for integrations over the unitary group, involving general rectangular complex matrices in the integrand. We derive the correct distribution functions and use them to obtain the capacity of the Ricean and correlated Rayleigh MIMO systems in a unified and straightforward approach. The integration technique proposed in this paper is general enough to be used for other unitary integrals in engineering, mathematics, and physics.

Four joint relay and antenna selection strategies for dual-hop amplify-and-forward (AF) multiple-input multiple-output relay networks are studied. Two of them require full channel state information (CSI) whereas the other two require only partial CSI. The relays are either channel-assisted AF or fixed-gain AF type. The first joint selection strategy involves choosing the best relay and the best single transmit antennas at the source and the relay. The second strategy jointly involves choosing the best relay and the best single transmit/receive antenna pairs at the source-to-relay and relay-to-destination channels. Moreover, two partial selection strategies, which can be used when the global CSI is not available, are also proposed and analyzed. In order to quantify the system performance analytically, the exact outage probability of all selection strategies is derived in closed-form. Direct insights into the system-design are obtained by deriving the asymptotic outage probability, asymptotic average symbol error rate, diversity order and array gain.

The resource allocation problem for two sources communicating via an amplify-forward relay is studied from an outage perspective. Analog network coding is considered for half-duplex nodes with perfect receiver-side channel knowledge. Under a sum power constraint, an optimal power allocation that minimizes an approximate outage probability is derived and shown to improve the performance upto 4.77 dB. A cut-set bound is also optimized to serve as a comparison reference. When such a power allocation is not feasible, two novel resource- optimized schemes, which exploit conventional one-way relaying, are proposed to reduce the outage at low multiplexing gains1.

A novel transmit/receive (Tx/Rx) antenna selection strategy is proposed and analyzed for two-way multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay networks. This strategy involves choosing the best transmit and receive antennas at the two sources and the relay based on the minimization of the overall outage probability. The performance of the proposed selection strategy is quantified by deriving the overall outage probability and its high SNR approximation. Specifically, the diversity order is derived to obtain valuable insights into practical system designing. In particular, our results are extended to cater the multiple relay scenario, and thereby, a joint relay and Tx/Rx antenna selection strategy is proposed and analyzed. To this end, the overall outage probability, its high SNR approximation and diversity order are derived. Our numerical results show that the proposed selection strategies achieve the full diversity order. All the analyses are validated through Monte-Carlo simulations.

A problem of joint optimal bandwidth and power allocation in cognitive networks under fading channels is considered. It is assumed that multiple secondary users (SUs) share the spectrum of a primary user (PU) using frequency division multiple access. The bandwidth and power are allocated so as to maximize the sum ergodic capacity of all SUs under the total bandwidth constraint of the licensed spectrum as well as different combinations of the peak/average transmit power constraints at the SUs and the peak/average interference power constraint imposed by the PU. Although the optimization problem is convex, its dimension and, thus, complexity may be high. Therefore, computationally efficient ways of solving the problem are of importance and are investigated here by finding structures of the optimal solutions to the problem under different combinations of the constraints.

A comprehensive performance analysis of dual-hop multiple-input multiple-output amplify-forward relay networks with hop-by-hop beamforming is presented. The impact of practical transmission impairments; (i) feedback delays, (ii) channel estimation errors and (iii) spatially-correlated fading on the system performance is studied. Specifically, the amount of performance degradation due to these impairments are quantified analytically and illustrated through numerical results. Numerical results show that these impairments degrade the system performance significantly. The cumulative distribution function of the end-to-end signal-to-noise ratio is derived and used to obtain the moment generating function, the outage probability, and the average symbol error rate (SER) in closed-form. The asymptotic outage probability and average SER are derived to obtain valuable system-design insights such as the diversity order and array gain. Further, our analyses are validated through Monte-Carlo simulations.

A novel approximation for the end-to-end signal-to-noise ratio (e2e SNR) of multi-hop (N≥2) fixed-gain amplify-and-forward (FG-AF) relay networks over independent and non-identically distributed Nakagami-m fading channels is proposed. Two types of FG-AF relays; (i) blind-AF, and (ii) semi-blind-AF are treated. The cumulative distribution and the moment generating function of the proposed e2e SNR approximation are derived in closed-form and used to derive the outage probability, the average symbol error rate, and the generalized SNR moments. The resulting performance metrics for the blind-AF relay case are asymptotically exact and thus, the asymptotic outage probability, the asymptotic average SER, the diversity order, and the coding gain are derived. Numerical and simulation results are presented to verify the comparative performance against the exact performance metrics and existing bounds. Our results reveal that the proposed performance approximations outperform the existing bounds in most of the cases.

As required in the IEEE 802.22 proposal, spectrum sensing techniques should be capable enough to sense the primary signal with very low receiver sensitivity such as at -116 dBm. In this paper, the detection performance of an energy detector used for spectrum sensing in cognitive radio networks is investigated under such very low signal-to-noise ratio (SNR) levels. The analysis focuses on the derivation of a closed-form expression for the average missed-detection probability over Rayleigh fading and Nakagami-m fading channels. Subsequently, the detection threshold is optimized for minimizing the total error rate. The analysis is validated by numerical and simulation results. The sensing requirements defined in IEEE 802.22 are also discussed with numerical examples.

It is well known that although the conventional sphere decoder (SD) achieves optimal maximum likelihood (ML) performance at a reduced complexity compared to the naive ML detector, the SD computational complexity varies with signal noise ratio (SNR) and is high in the low SNR region. This paper proposes a new idea to overcome these drawback that reduces the complexity significantly at a negligible performance loss. The main idea is to scale the search radius of the original SD by a factor that depends on the SNR. This factor tends to unity for high SNR, which means there is no performance loss for high SNRs. The resulting SD performs nearly-optimal ML detection over the whole range of SNRs, while keeping its complexity roughly constant. We give simulation results and theoretical analysis to confirm the advantages of the proposed SD. It is suitable practical implementation because of its effectively-reduced and almost-fixed complexity.

This paper examines space division duplexing (SDD) in multiple-input multiple-output (MIMO) systems. The antennas each full-duplex node has are partitioned to form two antenna banks - one for transmission, the other for reception. Self-interference is avoided at each full-duplex node by utilizing the nullspace (or the left nullspace) of corresponding self-interference channel for transmission (or reception). Simulation results are provided on the error performance. Useful insights are obtained on the effects finite precision arithmetic, and quantization errors have on the feasibility of SDD.

In this paper, we consider the problem of channel estimation for two-way relay networks (TWRN) under time-selective environment. We first parameterize the time-varying channels by the basis expansion model (BEM) and then propose a novel pilot symbol aided modulation (PSAM) for TWRN. A linear approach to estimate the cascaded channels is designed and the optimal training sequences are derived based on minimizing the mean-square error (MSE) criterion. Moreover, we develop an algorithm to recover the individual channel knowledge with which both the channel estimation accuracy and the system performance can be improved. Various simulations are provided to corroborate the proposed studies.

In this paper, an extension of raptor codes is introduced which keeps all the desirable properties of raptor codes, including the linear complexity of encoding and decoding per information bit, unchanged. The new design, however, improves the performance in terms of the reception rate. Our simulations show a 10% reduction in the needed overhead at the benchmark block length of 64,520 bits and with the same complexity per information bit.

The power allocation problem corresponding to the communication of two sources via a relay with amplify-forward capability is studied from the outage probability perspective. Analog network coding is considered for half-duplex nodes with perfect channel state information at the receiver side. Under a sum-power constraint on the transmit powers of the nodes, an optimal power allocation strategy that minimizes the high signal-to-noise ratio approximation of the outage probability is derived and shown to improve the performance significantly. As a reference for comparison, a cut-set type bound is also optimized for the setup.

Interference management is a major issue in underlay cognitive radio networks. In this paper, we focus on characterizing the statistics of the aggregate interference experienced by a primary user and evaluate its performance through important metrics such as outage probability, bit error rate and amount of fading. In previous works, the infinite interferers area assumption prevailed since it mainly simplifies the analysis. In contrast, we investigate the more realistic finite area, and further consider various practical spatial configurations. Two of the possible applications the proposed finite reconfigurable model can advocate are the IEEE 802.22 (WRAN) digital TV scenario and the aggregate interference considering different path loss exponents. We first derive the exact moment generating function (MGF) of the interference, then quantify the mean, the variance, and the skewness. Subsequently, the primary system performances are evaluated leading to novel expressions based on the interference MGF.

A systematic scheme is proposed to facilitate arbitrary virtual channel (VC)-to-user mappings in space dimension, through multiple-input multiple-output physical layer multicasting. It is a divide-and-conquer strategy, which breaks down the VC-to-user mapping to manageable orthogonal sub-mappings, each represented in terms of a multicast antenna group (MAG). A generalized form of block diagonalization is proposed to make transmissions pertaining to distinct MAGs orthogonal. Known non-iterative coordinated beamforming techniques are investigated for intra-MAG beamforming. The approach enables physical layer multicasting with non-iterative beamforming techniques alone.

This paper evaluates the impact of using outdated channel estimates due to feedback delay for relay selection and signal amplification on the performance of partial relay selection with amplify-and-forward (AF) relays. Both variable and fixed gain AF schemes are considered. Expressions for the system's outage probability and the average bit error rate, and their high signal-to-noise ratio (SNR) approximations are derived. The effect of parameters such as the rank of relay chosen, SNR imbalance and the correlation between the delayed and current channel state information are studied and verified through simulations.

This paper evaluates the impact of using outdated channel estimates in a multiuser Amplify-and-Forward (AF) relay network, under Nakagami-m fading. Both variable gain AF and fixed gain AF schemes are considered. Expressions for the system's outage probability and the average bit error rate (BER) are derived. Since the expressions are barely tractable, we also present approximations for the high signal-to-noise ratio (SNR) regime. By doing so we characterize the impact of network parameters such as the number of relays, correlation between the delayed and current channel state information, chosen user rank and SNR imbalance on the performance degradation.

In this paper, we apply the data-dependent superimposed training (DDST) in amplify-and-forward (AF) relay networks with cyclic-prefix single carrier (CPSC) modulation. We consider various issues such as channel estimation, training design and data detection. A sub-optimal training sequence that can minimize the upper bound of the mean square error of the estimator is derived. Since the DDST estimator can only find the overall channel information, we further propose a doubly cooperative estimator (DCE) to track the individual channel knowledge at the cost of some performance loss. Simulations are then provided to corroborate the proposed studies.

A new class of upper bounds on the end-to-end signal-to-noise ratio (SNR) of channel-assisted amplify-and-forward (AF) multi-hop (N ≥ 2) relay networks is presented. It is the half-harmonic mean of the minimum of the first P ≥ 0 hop SNRs and the minimum of the remaining N-P hop SNRs. The parameter P varies between 0 to N and may be chosen to provide the tightest bound. The closed-form cumulative distribution function and moment generating function are derived for independent and non-identically distributed Rayleigh fading and for independent and identically distributed Nakagami-m fading, where m is an integer. The resulting outage probability and the average symbol error rate bounds are asymptotically-exact. The asymptotic-exactness holds for any 0 ≤ P ≤ N. As applications, two cases of multi-hop multi-branch relay networks (i) the best branch selection and (ii) maximal ratio combining reception are treated. Numerical results are provided to verify the comparative performance against the existing bounds.

Knowing accurate noise variance and signal power is crucial to most spectrum-sensing algorithms such as energy detection, matched filter detection, and cyclostationary detection. In this paper, we consider a practical scenario when these two parameters are unknown and are needed to be estimated before the spectrum sensing. This task is non-trivial without knowing the status of the primary user, and we categorize the related spectrum sensing as a blind one. We develop the estimation algorithms for unknown parameters by exploiting the signal constellation of the primary user. Three different parameter estimators that do not require any training are then proposed based on the moments of the received signals. Since the secondary user may not know the primary user's signal constellation, we develop a robust approach that approximates a finite quadrature amplitude modulation (QAM) constellation by a continuous uniform distribution. We also derive the modified Cramer-Rao bound (CRB) for noise variance estimation. Then the optimal moment pair is found from minimizing the mean squared error (MSE) of the signal-to-noise ratio (SNR). The method of choosing the spectrum sensing threshold by taking into consideration the estimation error is also discussed.

A comprehensive performance analysis of the energy detector over fading channels with single antenna reception or with antenna diversity reception is developed. For the no-diversity case and for the maximal ratio combining (MRC) diversity case, with either Nakagami-m or Rician fading, expressions for the probability of detection are derived by using the moment generating function (MGF) method and probability density function (PDF) method. The former, which avoids some difficulties of the latter, uses a contour integral representation of the Marcum-Q function. For the equal gain combining (EGC) diversity case, with Nakagami-m fading, expressions for the probability of detection are derived for the cases L =2,3,4 and L >; 4, where L is the number of diversity branches. For the selection combining (SC) diversity, with Nakagami-m fading, expressions for the probability of detection are derived for the cases L =2 and L >; 2. A discussion on the comparison between MGF and PDF methods is presented. We also derive several series truncation error bounds that allow series termination with a finite number of terms for a given figure of accuracy. These results help quantify and understand the achievable improvement in the energy detector's performance with diversity reception. Numerical and simulation results are also provided.

Detection performance of an energy detector used for cooperative spectrum sensing in a cognitive radio network is investigated over channels with both multipath fading and shadowing. The analysis focuses on two fusion strategies: data fusion and decision fusion. Under data fusion, upper bounds for average detection probabilities are derived for four scenarios: 1) single cognitive relay; 2) multiple cognitive relays; 3) multiple cognitive relays with direct link; and 4) multi-hop cognitive relays. Under decision fusion, the exact detection and false alarm probabilities are derived under the generalized "k-out-of-n" fusion rule at the fusion center with consideration of errors in the reporting channel due to fading. The results are extended to a multi-hop network as well. Our analysis is validated by numerical and simulation results. Although this research focuses on Rayleigh multipath fading and lognormal shadowing, the analytical framework can be extended to channels with Nakagami-m multipath fading and lognormal shadowing as well.

Composite fading (i.e., multipath fading and shadowing together) has increasingly been analyzed by means of the K channel and related models. Nevertheless, these models do have computational and analytical difficulties. Motivated by this context, we propose a mixture gamma (MG) distribution for the signal-to-noise ratio (SNR) of wireless channels. Not only is it a more accurate model for composite fading, but is also a versatile approximation for any fading SNR. As this distribution consists of N (≥ 1) component gamma distributions, we show how its parameters can be determined by using probability density function (PDF) or moment generating function (MGF) matching. We demonstrate the accuracy of the MG model by computing the mean square error (MSE) or the Kullback-Leibler (KL) divergence or by comparing the moments. With this model, performance metrics such as the average channel capacity, the outage probability, the symbol error rate (SER), and the detection capability of an energy detector are readily derived.

In this paper, channel estimation and training sequence design are considered for amplify-and-forward (AF)-based two-way relay networks (TWRNs) in a time-selective fading environment. A new complex-exponential basis expansion model (CE-BEM) is proposed to represent the mobile-to-mobile time-varying channels. To estimate such channels, a novel pilot symbol-aided transmission scheme is developed such that a low complex linear approach can estimate the BEM coefficients of the convoluted channels. More essentially, two algorithms are designed to extract the BEM coefficients of the individual channels. The optimal training parameters, including the number of the pilot symbols, the placement of the pilot symbols, and the power allocation to the pilot symbols, are derived by minimizing the channel mean-square error (MSE). The selections of the system parameters are thoroughly discussed in order to guide practical system design. Finally, extensive numerical results are provided to corroborate the proposed studies.

Joint estimation of the carrier frequency offset (CFO) and the channel is developed for a two-way relay network (TWRN) that comprises two source terminals and an amplify-and-forward (AF) relay. The terminals use orthogonal frequency division multiplexing (OFDM). New zero-padding (ZP) and cyclic-prefix (CP) transmission protocols, which maintain the carrier orthogonality and ensure low estimation and detection complexity, are proposed. Both protocols lead to the same estimation problem which can be solved by the nulling-based least square (LS) algorithm and perform identically when the block length is large. We present detailed performance analysis by proving the unbiasedness of the LS estimators at high signal-to-noise ratio (SNR) and by deriving the closed-form expression of the mean-square-error (MSE). Simulation results are provided to corroborate our findings.

In this paper, an analytical framework is developed for the performance analysis of three transmit antenna selection (TAS) strategies for dual-hop multiple-input multiple-output channel-assisted amplify-and-forward (CA-AF) relay networks over Rayleigh fading. The cumulative distribution function of a lower bound of the end-to-end signal-to-noise ratio (SNR) of the optimal TAS strategy is derived and used to obtain the upper bounds of the outage probability and the average symbol error rate (SER). The exact moment generating functions (MGFs) of the end-to-end SNR of two suboptimal TAS strategies are also derived for the ideal CA-AF MIMO relay networks. These MGFs are then used to present accurate and efficient closed-form approximations to evaluate the outage probability and average SER. Numerical and Monte-Carlo simulation results are provided to analyze the performance of the system and to verify the accuracy of our analytical framework.

In this paper, the effect of feedback delays on the performance of multiple-input multiple-output antenna amplify-and-forward relay networks with the best transmit/receive antenna pair selection over Rayleigh fading is studied. The cumulative distribution function and the moment generating function of the end-to-end signal-to-noise ratio (SNR) are derived. Closed-form expressions for the outage probability, average symbol error rate (SER), and the SNR moments are also derived. To gain further insights, the asymptotic outage probability, average SER, diversity order, and coding gain are presented. Numerical results and Monte-Carlo simulations are provided to illustrate the detrimental effects of feedback delays on the system performance and to verify the accuracy of our analysis.

This paper investigates detection capability of energy detectors. With the help of receiver operating characteristics (ROC) curve and area under the ROC curve (AUC), a new measure, Complementary AUC (CAUC), is introduced as a proxy for the overall detection capability. When relays are available to help forward the target signal, the upper bound of the CAUC under Rayleigh fading channels is derived without and with a direct path. In addition, the average CAUC is discussed for Nakagami-m fading channels without and with diversity combining. The analytical results are validated by numerical examples.

In this paper we examine the use of generalized singular value decomposition (GSVD) for coordinated beamforming in MIMO systems. GSVD facilitates joint decomposition of a class of matrices arising inherently in source-to-2 destination MIMO broadcast scenarios. GSVD allows two channels of suitable dimensionality to be jointly diagonalized, i.e. to be reduced to non-interfering virtual broadcast channels, through the use of jointly determined transmit precoding and receiver reconstruction matrices. Potential applications for GSVD-based beamforming can be found in MIMO broadcasting, as well as in MIMO relaying under all amplify-and-forward, decode-and-forward, and code-and-forward relay processing schemes. Several of them are highlighted here. We also present simulation-based performance analysis results to justify the use of GSVD for coordinated beamforming.

We examine the distribution of the per virtual-channel received signal-to-noise ratio over a multiple-input multiple-output channel modeled by a rank-2 non-central Wishart matrix. The exact probability density function is derived for all possible non-centrality matrices; and verified through simulation for selected systems. Identities for exact analytic results on the outage probability, the average symbol error rate, and the moment generating function are also derived.

In this paper, channel estimation for two-way relay networks (TWRNs) over time-varying channels is investigated. We consider the amplify-and-forward (AF) relaying scheme and adopt the complex-exponential basis expansion model (CE-BEM) that represents the time-varying channel by a finite number of parameters. We develop the estimation methods for both the cascaded channels and the individual channels and also apply the total least square (TLS) algorithm to improve the estimation accuracy. Moreover, the training design is discussed and a heuristic criterion is proposed to minimize the condition number of the estimation matrix. The simulation results verify the goodness of the criterion.

This paper proposes a superimposed training strategy to estimate the individual frequency and channel parameters in an amplify-and-forward (AF) two-way relay network (TWRN). Two efficient suboptimal estimation algorithms and an iterative process to further improve the performance are proposed. The estimation Cramér-Rao Bound (CRB) on the proposed estimation strategy is also derived. The simulations confirm that the iterative estimation process converges rapidly and that the resultant estimation mean square error (MSE) approaches the CRB, especially for the case when the carrier frequency offset between the two source terminals is small.

The resource allocation problem in wireless multi-user decode-and-forward (DF) relay networks is considered. The conventional resource allocation schemes based on the equal distribution of bandwidth and/or power may not be efficient for the networks with constrained/limited power and bandwidth resources at both sources and relays. Therefore, joint bandwidth and power allocation schemes are proposed based on (i) the maximization of the sum capacity of all users (source-destination pairs); (ii) the maximization of the worst user capacity; (iii) the minimization of the total power consumptions for all users. It is shown that the proposed problem formulations can be transformed to equivalent convex optimization problems. Therefore, the joint bandwidth and power allocation problems can be efficiently solved. The performance improvements offered by the proposed schemes are demonstrated by simulations.

In this paper, we study the problem of joint carrier frequency offset (CFO) and channel estimation for amplify-andforward (AF) two-way relay network (TWRN) that comprises two source terminals and one relay node. Both the system design and the estimation problem become more challenging when CFO is non-zero in a frequency-selective environment, as compared to the conventional point-to-point communication systems. By introducing some redundancy, we propose a cyclic prefix (CP) based OFDM modulation for TWRN that is capable of maintaining the advantage of using multi-carrier transmission and at the same time facilitates the system initialization, e.g., synchronization and channel estimation. We then apply a least square (LS) approach to solve the estimation problem. The approximated Cramér-Rao Bound (CRB) has been derived as the performance benchmark of the proposed estimator. Finally, simulations are provided to corroborate the theoretical studies. ©2010 IEEE.

The performance of a multi-hop amplify-and-forward relay network is analyzed. The source and destination terminals are equipped with multiple-antennas and the relays with single-antennas. The cumulative distribution function and the moment generating function of two tight upper bounds of the end-to-end signal-to-noise ratio are derived. The lower bounds for the outage probability and the average symbol error rate (SER) are also derived. The results take into account the source-relay and the relay-destination correlation matrices; the uncorrelated case is treated as well. The asymptotic outage probability, average SER, diversity order and coding gain are also derived. Numerical results and Monte-Carlo simulations are presented to analyze the system performance and show the tightness of the proposed bounds.

Existing works on joint carrier frequency offset (CFO) and channel estimation in two-way relay networks (TWRN) only deal with the composite channel parameters and the mixed CFO values. In this paper, we design a superimposed pilot based training strategy such that the individual frequency and channel parameters can be obtained at the source terminals. We consider the amplify-and-forward (AF) relaying scheme and discuss the zero-padding (ZP) based orthogonal frequency division multiplexing (OFDM) modulation in order to cope with the frequency selective fading channels. We build up the system model and propose the joint estimation method. An iterative process is also proposed to further improve the estimation accuracy. To make the study complete, we also derive the Cram\'er-Rao Bound (CRB) and compare with the mean square error of our algorithms. Finally, simulation results are provided to corroborate our studies.

In this paper, we propose an output-threshold multiple relay selection scheme for dual-hop multi-branch cooperative wireless networks. The proposed scheme selects the first Lcarbitrary ordered relays out of L relays such that the maximal ratio combined signal-to-noise-ratio (SNR) of the Lcrelayed paths and the direct path barely exceeds a preset threshold. Closed-form expressions are derived for the cumulative distribution function, the probability density function, and the moment generating function of an output SNR upper bound for independent and identically distributed Rayleigh fading. Lower bounds for the outage probability, the average symbol error rate, and the average number of selected relays are also derived. Moreover, upper bounds for the average output SNR and the ergodic capacity are also derived. The analytical results are verified via the Monte-Carlo simulation. The performance of our proposed scheme is compared to that of the existing relay selection schemes. The proposed schemes provide more flexibility in utilizing bandwidth and spatial diversity in cooperative wireless networks.

This paper presents a new upper bound on the end-to- end signal-to-noise ratio (SNR) of channel-assisted amplify-and-forward (AF) multi-hop relay networks. The harmonic mean of the minimum of the first P ≥ 0 hop SNRs and the minimum of the remaining hop SNRs forms the new bound. Closed-form expressions are derived for the cumulative distribution function and the moment generating function of this SNR upper bound for independent and non-identically distributed Rayleigh, and independent and identically distributed Nakagami-m fading, where m is an integer. The outage probability and the average symbol error rate bounds are also derived. Our proposed bounds are compared against the existing bounds.

The Nakagami-lognormal distribution is the commonly used composite distribution for modeling multipath fading and shadowing. In this paper, simple and new form of distribution which can accurately represent both the mutlipath fading and shadowing effects is introduced. The signal-to-noise ratio (SNR) of the Nakagami-lognormal distribution follows the gamma-lognormal distribution, which is accurately approximated by a weighted mixture of gamma distributions. We show how the weights and other parameters of the summands are obtained. Further, accuracy of the mixture distribution is compared with the KGdistribution - a popular approximation of the Nakagami-lognormal distribution.

In this paper, we consider an interesting and practical scenario for spectrum sensing in cognitive radio network, where both the signal power of the primary user and the noise variance are treated as unknowns before the detection. Knowing accurate noise variance and signal power is crucial in most sensing algorithms, e.g., energy detection. By exploiting the received signal structure, we propose blind spectrum sensing methods in the sense that both the signal power of the primary user and the noise variance are estimated, which is a non-trivial task before knowing the status of the primary user. Three different algorithms, direct estimator, approximate maximum likelihood (ML) estimator and pseudo linear minimum mean square error (MMSE) estimator, are proposed based on the moments of received signals. Simulation results confirm that the proposed algorithms can estimate the noise variance and the primary user's signal power with high accuracy.

The performance of a cooperative network with Cooperative Maximal Ratio Combining (C-MRC) is analyzed. To this end, we propose a heuristic approximation to the total received SNR (signal-to-noise ratio) at the destination. The approximation is not only an accurate representation of the received SNR, but also amenable to performance analysis. We then derive the probability density function (PDF) of the approximate SNR. The PDF is used to derive expressions of the parameters required for the performance analysis of rate adaptive transmission, based on the use of a discrete set of modes of square M-ary quadrature amplitude modulation (QAM), with a cooperative network employing C-MRC. Analytical expressions for mode selection probability, the outage probability, the average spectral efficiency, and the average bit error rate are derived. Results show that performance of the system under C-MRC is comparable with other cooperative networks.

In this paper, we study the problem of joint carrier frequency offset (CFO) and channel estimation for two-way relay network (TWRN). We consider the frequency selective fading channels and adopt the zero padding (ZP) based orthogonal frequency division multiplexing (OFDM) as the modulation of the transmission. Due to the mixture of the first and the second transmission phases, the joint estimation problem becomes much challenging than that in the traditional point-to-point communication systems. By introducing some redundancy, we modify the structure of ZP-OFDM to cope with non-zero frequency synchronization errors. We then propose a nulling-based least square (NLS) method for joint CFO and channel estimation. A detailed performance analysis of NLS has been conducted, where we prove that the unbiasedness of NLS and derive the closed-form estimation mean-square-error (MSE) at high signal-to-noise ratio (SNR). Finally, simulations are provided to corroborate the proposed studies.

We analyze the impact of outdated channel state information due to feedback delay on the performance of amplify-and-forward relays with the$k$th worst partial relay selection scheme. In our analysis, new expressions for the system's outage probability and the average bit error rate are derived. The effects of the rank of the relay chosen, the average SNR imbalance, and the correlation between the delayed and current signal-to-noise ratio (SNR) on the system performance are investigated. Additionally, simple and accurate outage and average BER approximations are also derived to quantify the performance at high SNR. We also give simulation results to support the theoretical study.

Receive antenna selection for unitary space-time modulation (USTM) over semi-correlated Ricean fading channels is analyzed (this work generalizes that of Ma and Tepedelenlio-glu for the independent and identically distributed (i.i.d.) Rayleigh fading case). The antenna selection rule is that the receive antennas with the largest signal powers are chosen. For single antenna selection, we derive the maximum likelihood decoding for the correlated Ricean case. We also derive the Chernoff bound on the pairwise error probability for the high signal to- noise ratio (SNR) region and obtain the coding gain and diversity order. Our results show that even when there are transmitter side correlations and a line of sight component, receive antenna selection with USTM preserves the full diversity order if the USTM constellation is of full rank. We also give an approximation to the distribution function of a quadratic form of non-zero mean complex Gaussian variates (from Nabar et al.) at the high SNR region. Based on this approximation, a closed-form expression for the coding gain is also obtained and compared with that of the i.i.d. Rayleigh case. We also analyze the case of multiple receive antenna selection and derive the coding gain and diversity order. We show that USTM constellations, which have been proposed for the i.i.d. Rayleigh channel, can be used with the correlated Ricean channel as well.

Sums of lognormal random variables (RVs) are of wide interest in wireless communications and other areas of science and engineering. Since the distribution of lognormal sums is not log-normal and does not have a closed-form analytical expression, many approximations and bounds have been developed. This paper develops two computational methods for the moment generating function (MGF) or the characteristic function (CHF) of a single lognormal RV. The first method uses classical complex integration techniques based on steepest-descent integration. The saddle point of the integrand is explicitly expressed by the Lambert function. The steepest-descent (optimal) contour and two closely-related closed-form contours are derived. A simple integration rule (e.g., the midpoint rule) along any of these contours computes the MGF/CHF with high accuracy. The second approach uses a variation on the trapezoidal rule due to Ooura and Mori. Importantly, the cumulative distribution function of lognormal sums is derived as an alternating series and convergence acceleration via the Epsilon algorithm is used to reduce, in some cases, the computational load by a factor of 106! Overall, accuracy levels of 13 to 15 significant digits are readily achievable.

In this paper, a new class of full-diversity, rate-one space–time block codes (STBCs) called semiorthogonal algebraic space–time block codes (SAST codes) is proposed. SAST codes are delay optimal when the number of transmit antennas is even. The SAST codeword matrix has a generalized Alamouti structure where the transmitted symbols are replaced by circulant matrices and the commutativity of circulant matrices simplifies the detection of transmit symbols. SAST codes with maximal coding gain are constructed by using rate-one linear threaded algebraic space–time (LTAST) codes. Compared with LTSAT codes, SAST codes not only reduce the complexity of maximum-likelihood detection, but also provide remarkable performance gain. They also outperform other STBC with rate one or less. SAST codes also perform well with suboptimal detectors such as the vertical-Bell Laboratories layered space–time (V-BLAST) nulling and cancellation receiver. Finally, SAST codes attain nearly 100% of the Shannon capacity of open-loop multiple-input–single-output (MISO) channels.

A simple figure of merit to describe the performance of an energy detector is desirable. The area under the receiver operating characteristic (ROC) curve, denoted (AUC), is such a measure, which varies between 1/2 and 1. If the detector's performance is no better than flipping a coin, then the AUC is 1/2 , and it increases to one as the detector performance improves. However, in the wireless literature, the AUC measure has gone unnoticed. In this paper, to address this gap, we comprehensively analyze the AUC of an energy detector with no-diversity reception and with several popular diversity schemes. The channel model is assumed to be Nakagami-m fading. First, the average AUC is derived for the case of no-diversity reception. Second, the average AUC is derived for diversity reception cases including maximal ratio combining (MRC), square-law combining (SLC) and selection combining (SC). Further, for Rayleigh fading channels, the impacts of channel estimation errors and fading correlations are analyzed. High SNR (signal-to-noise ratio) approximations and the detection diversity gain are also derived. The analytical results are verified by numerical computations and by Monte-Carlo simulations.

This paper analyzes the performance of an energy detector over wireless channels with composite multipath fading and shadowing effects. These effects are modeled by using the K and K_G channel models. Closed-form average detection probabilities are derived for both K and K_G channel models for the no-diversity reception case. A simple approximation is also derived for large values of energy threshold in the energy detector. The analysis is then extended to cases with diversity receptions including maximal ratio combining (MRC) and selection combining (SC). Analytical results are verified by Monte Carlo simulation and by numerical methods. Receiver operating characteristic (ROC) curves are presented for different degrees of multipath fading and shadowing. Finally, the Rayleigh-lognormal distribution and the K distribution are numerically compared, and the validity of the K channel model for representing the impact of shadowing on the performance of energy detection is affirmed.

One of the major drawbacks of orthogonal frequency division multiplexing (OFDM) signals is the high peak to average power ratio (PAPR) of the transmitted signal. Many PAPR reduction techniques have been proposed in the literature, among which, partial transmit sequence (PTS) technique has been taken considerable investigation. However, PTS technique requires an exhaustive search over all combinations of allowed phase factors, whose complexity increases exponentially with the number of sub-blocks. In this paper, a newly suboptimal method based on modified artificial bee colony (ABC-PTS) algorithm is proposed to search the better combination of phase factors. The ABC-PTS algorithm can significantly reduce the computational complexity for larger PTS subblocks and offers lower PAPR at the same time. Simulation results show that the ABC-PTS algorithm is an efficient method to achieve significant PAPR reduction.

A new exponential-type integral for the generalized M-th order Marcum Q-function QM(alpha, beta) is obtained when M is not necessarily an integer. This new representation includes a classical formula due to Helstrom for the special case of positive integer order M and an additional integral correction term that vanishes when M assumes an integer value. The new form has both computational utility (numerous existing computational algorithms for QM(alpha, beta) are limited to integer M) and analytical utility (e.g., performance evaluation of selection diversity receiver in correlated Nakagami-m fading with arbitrary fading severity index, unified analysis of binary and quaternary modulations over generalized fading channels, and development of a Markovian threshold model for block errors in correlated Nakagami-m fading channels). Tight upper and lower bounds for QM(alpha, beta) that holds for any arbitrary real order M ges 0.5 are also derived.

In this paper, we exploit cooperative spectrum sensing technique for applications in a relay based cognitive radio network. Relays are assigned in cognitive radio networks to transmit the primary user's signal to a cognitive coordinator. This research is focused on the detection of primary user in single or multiple cognitive relay scenarios. The performance of energy detector is analyzed for independent Rayleigh fading channels. False alarm and detection probabilities are derived theoretically with or without direct communication between the primary user and the cognitive coordinator. An upper bound is also given for detection probability. Our analysis is validated by numerical and simulation results.

This paper develops highly accurate numerical techniques for evaluating the mgf/ chf of a single lognormal variable and for computing the lognormal sum cdf. Complex integration techniques based on the steepest-descent integration are thus developed for evaluating the lognormal mgf/ chf. The saddlepoint of the integrand is explicitly expressed using the Lambert-W function. The optimal steepest-descent contour passing through the saddlepoint is then derived. Even a simple mid-point-rule-based integration technique can be used along this contour to evaluate the mgf/ chf at extremely high precision. A highly efficient, extremely accurate numerical method is then developed for evaluating the cdf of sum of independent lognormal variables. The cdf is expanded as an alternating series, on which the Epsilon algorithm for convergence acceleration is applied. This reduces the computational load significantly.

The distribution of the received signal power ¿ of a multiple-input multiple-output system, with the associated 2 × 2 complex Wishart matrix having n degrees of freedom, is investigated under the channel inversion power allocation scheme. Exact closed-form expressions are derived for the probability density function and the cumulative distribution function of ¿. The analysis covers systems with transmit-receive antennas {Nt,Nr| min(Nt, Nr) = 2, max(Nt, Nr) ¿ 2}, and independent and identically distributed Rayleigh fading links between each antenna pair. We derive (i) the distribution of Shannon capacity of the multiple-input multiple-output channel (ii) average symbol error rate for a class of modulation schemes that includes Binary Phase Shift Keying.

In this paper, we study the problem of joint carrier frequency offset (CFO) and channel estimation for two-way relay network (TWRN) that comprises two source terminals and one relay node. We build up the signal model, from which we identify the CFO and channels at the two source terminals. As the very first attempt to discuss the joint CFO and the channel estimation for TWRN, we consider relay node that purely amplifies and forwards, which is also known as the repeater. The new model is different from the traditional ones in that the unknown CFO is combined with only part of the channel parameters. We then propose two joint estimation methods, i.e., the approximate maximum-likelihood (ML) method and the nulling-based method. The Cramer-Rao Bounds (CRB) of both methods are derived in closed-form. Simulations are then provided to corroborate the proposed studies.

In cognitive radio networks with the coexistence of primary and secondary users, the problem of how to optimally allocate available resources (e.g., bandwidth and power) to multicast groups of secondary users that use orthogonal frequency division multiplexing (OFDM) is important. Taking the maximization of the weighted sum rate of such groups as the design objective, we propose a practically optimal subcarrier and power allocation scheme under constraints on the tolerable interference thresholds at individual primary user's frequency bands. Specifically, the optimization problem is solved via the dual method, where subcarriers are assigned in a per-tone basis and power is distributed in a water-filling fashion. As the number of subcarriers becomes large, the dual-domain solution becomes the global optimum of the primal problem with the duality gap vanishing to zero. The proposed design is valid for both unicast and multicast transmissions, and its computational complexity is only linear in the number of subcarriers. The effects of adjacent subcarrier nulling technique, which is to reduce mutual interference between primary and secondary frequency bands, on the proposed scheme are also examined. The superiority of the dual approach is confirmed by numerical results.

The outage probability is a fundamental performance metric, which has been widely investigated in the literature. In this paper, we develop a general method to compute the outage given the moment generating function (MGF). When computing the outage using the MGF, integration along the standard Bromwich contour suffers from a loss of accuracy due to oscillatory nature of the integrand. One can address this difficulty by using the Cauchy's theorem to replace the Bromwich contour by an appropriate equivalent contour. For highly-accurate numerical results, the steepest descent contour is the most suitable replacement. Unfortunately, this optimal contour can not be in general expressed in closed-form. The class of Talbot contours characterized by three parameters provides an alternative. However, it is not clear how these parameters need to be tuned for best results. We propose the use of linear regression to set the parameter values so as to minimize the mismatch between corresponding Talbot contour and the steepest-descent contour. The resulting integral has a smooth and rapidly decaying integrand, making it possible for the outage probability to be evaluated with high accuracy by using a simple numerical integration method. This approach is general in a sense that it works for any system where the MGF is known. Thus, it can handle a wide range of fading distributions and a variety of communication systems.

Super-imposed pilots can be used as an alternative to traditional pilots that are used for channel estimation. Superimposed pilots improve bandwidth efficiency. We apply it to the amplify and forward (AF) relay systems. In this paper we give the channel estimation (CE) results, analyze the system performance, study the power allocation methods and extend our result to multi-hop relay systems. Our main contribution is that we suggest and prove the existence of minimum bit error rate (BER) as a function of pilot signal power, find the best power allocation ratio value that can reach the minimum BER, analyze parameters' influence on the ratio value, and extend our result to multi-hop systems.

This work considers two-way relay channels (TWRC), where two terminals transmit simultaneously to each other with the help of a relay node. For single antenna systems, we propose several new transmission schemes for both amplify-and-forward (AF) protocol and decode-and-forward (DF) protocol where the channel state information is not required. These new schemes are the counterpart of the traditional noncoherent detection or differential detection in point-to-point communications. Differential modulation design for TWRC is challenging because the received signal is a mixture of the signals from both source terminals. We derive maximum likelihood (ML) detectors for both AF and DF protocols, where the latter can be considered as performing differential network coding at the physical layer. As the exact ML detector is prohibitively complex, we propose several suboptimal alternatives including decision feedback detectors and prediction-based detectors. All these strategies work well as evidenced by the simulation results. The proposed protocols are especially useful when the required average data rate is high. In addition, we extend the protocols to the multiple-antenna case and provide the design criterion of the differential unitary space time modulation (DUSTM) for TWRC.

This paper derives a new infinite series representation for the trivariate non-central chi-squared distribution when the underlying correlated Gaussian variables have a tridiagonal form of an inverse covariance matrix. The joint probability density function is derived using Miller's approach and Dougall's identity. Moreover, the trivariate cumulative distribution function (cdf) and characteristic function (chf) are also derived. Finally, the bivariate non-central chi-squared distribution and some known forms are shown to be special cases of the more general distribution. However, the derivation of non-central chi-squared distribution for an arbitrary covariance matrix seems intractable via Miller's approach. Two applications of the newly derived results are provided for performance analysis of multiple input multiple output (MIMO) systems with transmit antenna selection over a correlated Rician fading environment. Some numerical results are also presented to verify the accuracy of the analytical expressions.

Probability density functions (pdf's) are derived for the phase and amplitude (envelope) of the complex gain X +jY (j = radic-1), where X and Y are two correlated non zero-mean Gaussian random variables. The pdf of the amplitude is derived as an infinite series, but reduces to a closed-form expression when the means are zero. The classical Rayleigh and Rician pdf's turn out to be special cases of the derived pdf. This pdf is used to analyze the error performance of non-coherent binary frequency shift keying (BFSK) with in-phase/quadrature(I/Q) imbalance over an additive white Gaussian noise (AWGN) channel. The resulting bit error rate (BER) expression is derived as an infinite series. The analytical expressions are validated by simulation, and the I/Q imbalance related performance degradation is quantified. Convergence of the PDF series and the BER series is established.

In the uplink of Orthogonal Frequency-Division Multiple Access (OFDMA) systems, the user carrier frequency offsets result in inter-carrier-interference (ICI) and multipleuser-interference (MUI), leading to a degradation of the bit error rate (BER). This paper treats this uplink scenario and derives the average uplink capacity and the BER using the signal-to-interference-and-noise ratio (SINR) analysis. Adaptive power allocation is suggested to increase the capacity. When the frequency offsets are modeled as zero-mean Gaussian or Uniform random variables, the BER is derived as a closed-form infiniteseries. The series requires at least 50 terms to ensure sufficient accuracy.

In this letter, the use of adaptive source transmission with amplify-and-forward relaying is proposed. Three different adaptive techniques are considered: (i) optimal simultaneous power and rate adaptation; (ii) constant power with optimal rate adaptation; (iii) channel inversion with fixed rate. The capacity upper bounds of these adaptive protocols are derived for the amplify-and-forward cooperative system over both independent and identically distributed (i.i.d.) Rayleigh fading and non-i.i.d. Rayleigh fading environments. The capacity analysis is based on an upper bound on the effective received signal-to-noise ratio (SNR). The tightness of the upper bound is validated by the use of a lower bound and by Monte Carlo simulation. It is shown that at high SNR the optimal simultaneous power and rate adaptation and the optimal rate adaptation with constant power provide roughly the same capacity. Channel inversion is shown to suffer from a deterioration in capacity relative to the other adaptive techniques.

In this paper, we consider an amplify-and-forward wireless relay system where multiple source nodes communicate with their corresponding destination nodes with the help of relay nodes. Conventionally, each relay equally distributes the available resources to its relayed sources. This approach is clearly sub-optimal since each user experiences dissimilar channel conditions, and thus, demands different amount of allocated resources to meet its quality-of-service (QoS) request. Therefore, this paper presents novel power allocation schemes to i) maximize the minimum signal-to-noise ratio among all users; ii) minimize the maximum transmit power over all sources; iii) maximize the network throughput. Moreover, due to limited power, it may be impossible to satisfy the QoS requirement for every user. Consequently, an admission control algorithm should first be carried out to maximize the number of users possibly served. Then, optimal power allocation is performed. Although the joint optimal admission control and power allocation problem is combinatorially hard, we develop an effective heuristic algorithm with significantly reduced complexity. Even though theoretically sub-optimal, it performs remarkably well. The proposed power allocation problems are formulated using geometric programming (GP), a well-studied class of nonlinear and nonconvex optimization. Since a GP problem is readily transformed into an equivalent convex optimization problem, optimal solution can be obtained efficiently. Numerical results demonstrate the effectiveness of our proposed approach.

Frequency offset estimation for an orthogonal frequency-division multiple access (OFDMA) uplink for amplify-and-forward (AF) relays and a new type of relay (R) called decode-and-compensate-and-forward (DcF) relays are studied. Multiple relays are considered, and the relay with the best S rarr R channel is chosen to perform re-transmission, where S and R represent the source and relay nodes, respectively. Frequency offsets due to the mismatches between the transmitter and receiver oscillators are considered, and without considering the effect of Doppler shift, both S rarr D and S rarr R rarr D links have the same frequency offset, where D represents the destination. Thus, by using these two transmissions, D generates two frequency offset estimates, which are combined to minimize the mean square error (MSE). Power allocation between S and R can be adaptively adjusted to optimize the cooperative scheme in terms of frequency offset error variance. When channel state information (CSI) is available at each mobile node, a scheme where the relays adaptively switch between the cooperative and conventional (no relaying) transmissions is proposed to optimize the frequency offset estimation. Although the frequency offset estimation accuracy in the DcF mode is somewhat worse than the AF mode, both modes outperform the conventional transmission. However, DcF (or decode-and-forward (DF)) relays outperform AF relays in terms of channel capacity and bit error rate (BER).

In this work, we consider differential modulation in two-way relay channels (TWRC). In single antenna systems, we propose non-coherent schemes for both amplify-and forward (AF) and decode-and-forward (DF) where the channel state information is not required. These new schemes are counterparts of the traditional non-coherent detection in point to point communications. The difficulty with differential modulation design in TWRC is that the received signal is a mixture of the signals from both source terminals. We derive maximum likelihood (ML) detectors for both AF and DF. The DF protocol can be considered as performing differential network coding at the physical layer. In addition, we propose several suboptimal alternatives including decision feedback and prediction based detectors. All these strategies work well as evidenced by simulation results. We also extend the schemes to the multiple-antenna case and provide design criterion of differential unitary space time modulation.

Recently, a maximum likelihood (ML) detection rule for differential unitary space time modulation (DUSTM) under the existence of unknown carrier frequency offset (CFO) has been derived. However, the ML detection is based on the exhaustive search over all the unitary group codes. In this paper, we design an efficient detection algorithm for newly derived ML rule, by modifying the bound intersection detector (BID). Our proposed algorithm is seen as a generalization of the existing BID that is known to be an optimal detector for the conventional DUSTM. The simulation results show that the proposed algorithm can save a large portion of the computational complexity compared to the naive searching method.

Multiple-input multiple-output (MIMO) channels have been studied from various aspects including the average of the mutual information between the transmitter and receiver (ergodic capacity) when the channel gains are known to the receiver only. A common approach for capacity analysis is to find the moment generating function (MGF) of the mutual information and by direct differentiation, the mean of the mutual information (capacity) is calculated. Recently, character expansions of groups have been used for integration over unitary matrices to obtain the joint eigenvalue distribution of the correlated Wishart matrix i.e. HH* where H is the zero mean full correlated complex Gaussian random MIMO channel matrix. In this paper, we show that the previous attempt for capacity analysis of full correlated MIMO channels is correct for square channel matrices only. We modify the approach from square matrices to rectangular matrices to obtain the correct joint eigenvalue distribution of the correlated Wishart matrix. The result can be used to obtain the MGF and the capacity of full correlated MIMO channels.

In this paper, we consider an amplify-and-forward (AF) wireless relay system where multiple source nodes communicate with their corresponding destination nodes with the help of relay nodes. While each user is assisted by one relay, one relay can assist many users. Conventionally, each relay node is assumed to equally distribute the available bandwidth and power resources to all sources for which it helps to relay information. Realizing the sub-optimality of this approach, in this paper, we present efficient power allocation schemes to i) maximize the minimum end-to-end signal-to-noise ratio among all users; ii) minimize the total transmit power over all sources; iii) maximize the system throughput. Our approach is based on geometric programming (GP), a well-studied class of nonlinear and nonconvex optimization. Since a GP problem is readily transformed into an equivalent convex optimization problem, optimal power allocation can be obtained efficiently. Numerical results demonstrate the effectiveness of our proposed approach.

In this paper, we evaluate the performance improvement in an Orthogonal Frequency-Division Multiple Access (OFDMA) uplink achievable with cooperative relaying in the presence of frequency offsets. We consider both the amplify- and-forward (AF) and decode-and-forward (DF) relays. In each transmission, each node plays two roles i.e., the source node and relay, simultaneously, but at different subcarriers. The proposed scheme improves performance without sacrificing the transmission rate and power of the cooperative relays, and the total power used to transmit each symbol, including the power consumed in node the source node and the relays, is kept constant. The outage information rates of the proposed cooperative transmission scheme are derived, and the diversity gain of each forwarding mode in an interference-limited environment is analyzed in this paper. Numerical results illustrate the superior performance of the proposed scheme over the conventional transmission with regard to outage information rate.

Optimal pilots design and placement for the frequency offset and channel estimation in orthogonal frequency- division multiplexing access (OFDMA) uplink systems are proposed. The received pilots of multiple users can always be demodulated, even if they are totally overlapped due to the large frequency offsets. With the knowledge of channel state information (CSI) at the receiver, the performance of the proposed frequency offset estimation is robust to the channel estimation errors. The frequency offset and CSI can be jointly estimated by employing the proposed pilots.

This paper discusses channel estimation in a cooperative orthogonal frequency-division multiplexing (OFDM) network in the presence of frequency offsets. Both the amplify- and-forward (AF) and decode-and-forward (DF) relaying modes are analyzed. In order to eliminate the multiple access interference (MAI), the maximum number of active AF and DF relays are [N/2L-1] and [N/L], respectively, where N is the total number of subcarriers, L is the channel order and [a] is the maximum integer part of a. The pairwise error probability (PEP) of orthogonal space-time coding in cooperative OFDM due to both the frequency offset and channel estimation errors is also evaluated. The optimal power allocation ratio between the source and the set of the relays to minimize the PEP is derived for both the relay modes. When L-3, and this gap increases to about 11.3 dB when the variance increases to 10-2.

Joint eigenvalue distribution of the noncentral complex Wishart matrix, i.e. HH* where H is the nonzero-mean complex Gaussian random channel matrix of a multiple-input multiple-output (MIMO) system, is required for the analysis of Ricean MIMO channels from different aspects, including the average of mutual information between the transmitter and the receiver (ergodic capacity), when the channel gains are known to the receiver only. Previous works rely on the available results in mathematics for the joint eigenvalue distribution, obtained by integration over unitary matrices using classic integration methods. In this paper, we present a powerful integration method over unitary matrices which exploits the representation theory and characters of groups. The method was originally proposed for square matrices. We modify the approach from square matrices to rectangular matrices to solve a more general integral over unitary matrices and obtain the joint eigenvalue distribution of the noncentral Wishart matrix. Our result is the generalization of the previous classical integral over unitary matrices so that the result is not restricted to diagonal and/or real matrices, particularly.

In [1], antenna selection for multiple antenna systems that employ unitary space-time (ST) signaling has been studied under the assumption of an independent Rayleigh fading channel. In this paper, the performance of such a system is investigated for spatially correlated-fading channels. The channel state information (CSI) is not known at the receiver nor at the transmitter. Antenna selection is thus performed at the receiver based on the instantaneous received signal power. By deriving the Chernoff bound on the pairwise error probability (PEP), we quantify the effects of channel correlation on the diversity order and coding gain at high signal-to-noise ratio (SNR). Analytical results indicate that the full diversity order is preserved in such a channel as long as the unitary signals are full rank. However, spatial correlations result in a loss of the coding gain.

The use of constant-power, rate-adaptive M-QAM transmission with an amplify-and-forward cooperative system is proposed. The upper bound expressions are derived for the outage probability, achievable spectral efficiency, and error rate performance for the amplify-and-forward cooperative system over both independent and identically distributed (i.i.d.) and non-i.i.d. Rayleigh fading environments. The analysis is based on an accurate upper bound on the total effective signal-to- noise ratio SNR at the destination. Adaptive continuous rate M-QAM achieves a capacity that comes within a constant gap of the Shannon capacity of the channel, but adaptive discrete rate M-QAM suffers additional performance penalties.

This paper evaluates the performance improvement in orthogonal frequency-division multiplexing access (OFDMA) uplink frequency offset estimation achieved with cooperative relaying. The transmission of each source node (node S) can be improved by optimizing the diversity gain through exploiting the cooperation of the other nodes (cooperative relays), and the relays can operate in either the amplify-and-forward (AF) or decode-and-compensation-and-forward (DcF) mode. One or more than one geographically closely located mobile nodes comprise a cooperative group (CG), and the nodes of the same CG cooperate with each other. In each transmission, the role of the relay is to "help" the source node transmit its training sequence, or, in other words, the relay creates a parallel route between the source node and the destination terminal to improve the reliability of the transmission of S. In the proposed cooperative scheme, the total power used to transmit each training sequence, including that consumed in node S and the relay, is kept constant. Based on the interference analysis, the signal-to-interference-plus-noise ratio (SINR) in both the relay and the destination terminal are derived. The AF mode's cooperative scheme always outperforms that of the DcF mode in terms of frequency offset estimation accuracy due to the estimation error propagation in the latter.

This letter presents a new method to directly analyze and optimize symbol error rate (SER) performance of minimum decoding complexity (MDC) ABBA space-time block codes based on a tight union bound on SER. Additionally, a new signal transformation for rectangular quadrature amplitude modulation is proposed to provide better performance than the existing ones with lower encoding/decoding complexities. It is also shown that MDC-ABBA codes achieve full-diversity with antenna selection and limited feedback.

An exact expression for the joint density of three correlated Rician variables is not available in the open literature. In this letter, we derive new infinite series representations for the trivariate Rician probability density function (pdf) and the joint cumulative distribution function (cdf). Our results are limited to the case where the inverse covariance matrix is tridiagonal. This case seems the most general one that is tractable with Miller¿s approach and cannot be extended to more than three Rician variables. The outage probability of triple branch selective combining (SC) receiver over correlated Rician channels is presented as an application of the density function.

Recently, the advantages of the discrete cosine transform (DCT) based orthogonal frequency-division multiplexing (OFDM) have come to the light. We thus consider DCT- OFDM with non-circular transmission (our results cover circular transmission as well) and present two blind joint maximum- likelihood frequency offset and phase offset estimators. Both our theoretical analysis and numerical comparisons reveal new advantages of DCT-OFDM over the traditional discrete Fourier transform (DFT) based OFDM. These advantages, as well as those already uncovered in the early works on DCT-OFDM, support the belief that DCT-OFDM is a promising multi-carrier modulation scheme.

Can conventional differential unitary space time modulation (DUSTM) be applied when there is an unknown carrier frequency offset (CFO)? This paper answers this question affirmatively and derives the necessary maximum likelihood (ML) detection rule. The asymptotic performance of the proposed ML rule is analyzed, leading to a code design criterion for DUSTM by using the modified diversity product. The resulting proposed decision rule is a new differential modulation scheme in both the temporal and spatial domains. Two sub-optimal multiple-symbol decision rules with improved performance are also proposed. For the efficient implementation of these, we derive a modified bound intersection detector (BID), a generalization of the previously derived optimal BID for the conventional DUSTM. The simulation results show that the proposed differential modulation scheme is more robust against CFO drifting than the existing double temporal differential modulation.

The cumulative distribution function (cdf) of a sum of correlated or even independent lognormal random variables (RVs), which is of wide interest in wireless communications, remains unsolved despite long standing efforts. Several cdf approximations are thus widely used. This letter derives bounds for the cdf of a sum of 2 or 3 arbitrarily correlated lognormal RVs and of a sum of any number of equally-correlated lognormal RVs. The bounds are single-fold integrals of readily computable functions and extend previously known bounds for independent lognormal summands. An improved set of bounds are also derived which are expressed as 2-fold integrals. For correlated lognormal fading channels, new expressions are derived for the moments of the output SNR and amount of fading for maximal ratio combining (MRC), selection combining (SC) and equal gain combining (EGC) and outage probability expressions for SC.

We present a unified detection framework for spatial multiplexing multiple-input multiple-output (MIMO) systems by generalizing Heller's classical feedback decoding algorithm for convolutional codes. The resulting generalized feedback detector (GFD) is characterized by three parameters: window size, step size and branch factor. Many existing MIMO detectors are turned out to be special cases of the GFD. Moreover, different parameter choices can provide various performance-complexity tradeoffs. The connection between MIMO detectors and tree search algorithms is also established. To reduce redundant computations in the GFD, a shared computation technique is proposed by using a tree data structure. Using a union bound based analysis of the symbol error rates, the diversity order and signal-to-noise ratio (SNR) gain are derived analytically as functions of the three parameters; for example, the diversity order of the GFD varies between 1 and N. The complexity of the GFD varies between those of the maximum-likelihood (ML) detector and the zero-forcing decision feedback detector (ZF-DFD). Extensive computer simulation results are also provided.

This letter considers multiple symbol differential detection for multiple-antenna systems over flat Ricean-fading channels when partial channel state information (CSI) is available at the transmitter. Using the maximum likelihood (ML) principle, and assuming perfect knowledge of the channel mean, we derive the optimal multiple symbol detection (MSD) rule for diagonal differential unitary space-time modulation (DUSTM). This rule is used to develop a sphere decoding bound intersection detector (SD-BID) with low complexity. A suboptimal MSD based decision feedback DD (DF-DD) algorithm is also derived. The simulation results show that our proposed MSD algorithms reduce the error floor of conventional differential detection and that the computational complexity of these new algorithms is reasonably low.

Space-time block codes (STBC) using coordinate interleaved orthogonal designs (CIOD) proposed recently by Khan and Rajan allow single-complex symbol decoding and offer higher data rates than orthogonal STBC. In this paper, we present the channel decoupling property of CIOD codes. A new general maximum likelihood method is derived, enabling the calculation of the symbol pair-wise error probability and union bound (UB) on symbol error rate (SER). Extensive simulation results show that the UB is within 0.1 dB from the simulated SER when SER-2. The UB thus can be used to accurately predict and optimize the performance of CIOD codes. Furthermore, a new signal design combining signal rotation and power allocation is presented for constellations with uneven powers of real and imaginary parts such as rectangular quadrature amplitude modulation.

Frequency offsets negatively impact the performance of closed-loop multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems. Particularly, when multiple users are active, the impact can be high. Linear precoding and non-linear Tomlinson-Harashima precoding (THP) are thus developed for spatially-multiplexed multiuser OFDM and orthogonal space-time block-coded (OSTBC) OFDM. The proposed precoders employ a limited feedback structure, which is implemented with a shared codebook of precoding matrices, and only the index of the selected optimal matrix is fed back to the transmitter. The conventional limited feedback design criterion for flat-fading MIMO channels is only applicable to single-user OFDM without frequency offsets. We show that the ICI matrix due to frequency offset does not impact users precoding individually, and precoding on a per-subcarrier basis is possible. Exploiting this property, the conventional design is generalized to multiuser OFDM with frequency offsets. Nonlinear precoding uses a modulo arithmetic precoding matrix (which reduces the power efficiency loss inherent in linear precoding and leads to a lower error rate) and outperforms linear precoding. Our precoders not only offer significant bit error rate (BER) improvement for spatially-multiplexed multiuser MIMO OFDM with frequency offsets, but are equally effective for both OSTBC MIMO OFDM and spatially correlated channels.

Multiple-input multiple-output (MIMO) systems achieve significant diversity and array gains by using transmit beamforming. When complete channel state information (CSI) is not available at the transmitter, a common set of beamformers (codebook) is used by both the transmitter and the receiver. For each channel realization, the best beamformer is selected at the receiver and its index is sent back to the transmitter via a limited feedback channel. In this paper, a codebook design method using the genetic algorithm is proposed, which reduces the design complexity and achieves large minimum-distance codebooks. Exploiting the specific structure of these beamformers, an order and bound algorithm is proposed to reduce the beamformer selection complexity at the receiver side. The exact bit error rate (BER) of the optimal beamforming in finite-series expression is used to facilitate the BER analysis of limited feedback beamforming. By employing a geometrical approach, an approximate BER of limited feedback beamforming is derived when the codebook size is relatively large (high resolution analysis). The simulation results show that the approximate BER is comparatively tight even for small size codebooks.

It is a challenging task for multi-hop wireless networks to support multimedia applications with quality-ofservice (QoS) requirements. This letter presents a joint crosslayer optimization approach, i.e., joint medium access control, routing, and energy distribution. User satisfaction represented by user utility is maximized within the required network lifetime, given the constraints on the total available energy in the network and the minimum user rates. Although the resulting optimization problem is nonlinear and nonconvex, we prove that it is approximately equivalent to a two-step convex problem. Furthermore, we prove that the problem of maximizing network utility within achievable network lifetime is quasiconvex

Optimal pilot design and placement for channel estimation in multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems with frequency offsets are considered. Both the single-frequency- offset case and the multiple-frequency-offset case are treated. We show that the constant-envelope (CE) condition is sufficient but not necessary for pilot design, and that pilots with multiple envelopes can also achieve the optimal performance in terms of the mean square error (MSE) minimization, provided that an additional constraint on the pilot placement is satisfied simultaneously. New pilot designs, which take into account the multiple-frequency-offset case, are proposed to eliminate inter- pilot-interference (IPI) and to optimize the MSE performance. The least-squares (LS) and linear minimum mean square error (LMMSE) channel estimators for the multiple-frequency- offset case are designed for uncorrelated and correlated MIMO-OFDM channels, respectively. The LMMSE estimator requires the channel covariance matrix. Both optimal adaptive pilot power allocation and suboptimal uniform pilot power allocation are developed for the proposed LMMSE estimator. The adaptive allocation performs 4 dB better than the uniform allocation in the high noise region, but they both perform identically in the low noise region. Performance comparisons are made against several previous pilot designs due to [1], [2]. The proposed LMMSE estimator significantly outperforms the LS estimator.

In this paper, we answer the question that "Can conventional differential unitary space time modulation (DUSTM) be applied when there is an unknown carrier frequency offset (CFO)?" and present a maximum likelihood (ML) detection rule for this scenario. We analyze the asymptotical performance of our ML detection and provide the code design criterion by using the modified diversity product. The analysis also brings the insight that our proposed decision rule is a new differential modulation scheme in both temporal and spatial domains. Various simulations are conducted, and the proposed algorithm is shown to be more robust to the CFO drifting than the existing double temporal differential modulation.

There has been considerable research on the design of space-time block codes (STBCs) that guarantee full diversity without sacrificing the data rate. The main challenge is to maximize the coding gain by maximizing the determinant criterion. It is shown that the most of previous STBCs with full rate and full diversity order (FRFD) (e.g. threaded algebraic space-time (TAST) codes) are constructed via a unitary generator matrix. However, the unitary matrix has been represented using only a small number parameters to enable algebraic code design. In this paper, for a 2 times 2 STBC, we use a more general unitary matrix with a large number of parameters for STBC design. We obtain an upper bound on the coding gain and show that the maximum coding gain is attainable only with PAM signaling. Since optimum parameters for the case of QAM signaling is analytically intractable, we search using the genetic algorithm (GA) method. We also use the union bound criterion for code parameter search by GA. Our simulation results show that with both criteria, the optimum code for QAM signaling is the Golden code. The proposed code significantly outperforms other existing STBCs with the gains about 2 dB at a symbol error rate of 10 for BPSK and 4-PAM. The proposed code performs identically to the Golden code for QAM.

This paper analyzes the performance of multiple- input multiple-output (MIMO) systems with transmit and receive antenna selection (T-RAS). The average bit error rate (BER), average symbol error rata (SER), outage probability and ergodic capacity are derived by utilizing the characteristic function (CF) of the joint output signal-to-noise ratios (SNR). Our approach can be used over not only independent but also arbitrary correlated Rayleigh,Nakagami-m and Rician fading channels. Simulation results are provided to validate our numerical calculations. We also illustrate the effect of antenna array configuration and the operating environment (fading, angular spread, mean angle-of- arrival(AOA), mean angle-of-departure (AOD)) on the average BER performance.

Optimal pilot design and placement for channel estimation in multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems in the presence of frequency offset are discussed. Both the single-frequency-offset case and the multiple-frequency-offset case are treated. Constant-envelope (CE) is shown to be a sufficient but not necessary condition for optimizing the mean square error (MSE). When the CE condition is relaxed, i.e., pilots with multiple envelope values, the power allocation and placement rules for the optimal MSE performance are derived. The least-squares (LS) and linear minimum mean square error (LMMSE) estimators are designed for uncorrelated and correlated MIMO-OFDM channels, respectively. Both optimal adaptive pilot power allocation and suboptimal uniform pilot power allocation strategies are developed for the proposed LMMSE estimator. The adaptive allocation performs 4 dB better than the uniform allocation in the high noise region, but they both perform identically in the low noise region. Performance comparisons are made against several previous pilot designs due to [1]. The proposed LMMSE estimator significantly outperforms the LS estimator.

Frequency synchronization is one of the most important components in orthogonal frequency-division multiplexing (OFDM) systems. Recently, the discrete cosine transform (DCT) based OFDM system has received wide attentions due to several advantages. Hence, the study of frequency synchronization issue for this newly raised system is well on its time. To provide a thorough study, we consider the non-circular transmissions, and the results can be easily generated to circular transmissions if the elliptic variance is set to zero. We present three joint maximum likelihood (ML) carrier frequency offset (CFO) and phase offset (PO) estimators. From both the theoretical analysis and the numerical comparisons, we found new advantages of the DCT-OFDM over the traditional discrete Fourier transform (DFT) based OFDM. These advantages, as well as those already studied in the early works on DCT-OFDM, support the belief that the DCT-OFDM is a new promising multi-carrier modulation (MCM) scheme.

We show a statistical pruning approach for maximum likelihood (ML) detection of multiple-input multiple-output (MIMO) systems. We present a general pruning strategy for sphere decoder (SD), which can also be applied to any tree search algorithms. Our pruning rules are effective especially for the case when SD has high complexity. Three specific pruning rules are given and discussed. From analyzing the union bound on the symbol error probability, we show that the diversity order of the deterministic pruning is only one by fixing the pruning probability. By choosing different pruning probability distribution functions, the statistical pruning can achieve arbitrary diversity orders and SNR gains. Our statistical pruning strategy thus achieves a flexible trade-off between complexity and performance.

In this paper, we derive new infinite series representations for the quadrivariate Nakagami-m distribution and cumulative distribution functions (cdf). we make use of the Miller's approach and the Dougall's identity to derive the joint density function. The classical joint density function of exponentially correlated Nakagami-m variables can be identified as a special case of our joint density function. Our results are based on the most general arbitrary correlation matrix possible. Moreover, the trivariate density function and cdf for an arbitrary correlation matrix is also derived from our main result. Bounds on the error resulting from truncation of the infinite series are also presented. Finally, numerical results are presented to verify the accuracy of our formulation.

This work presents precoding design for error-rate improvement in closed-loop multiuser orthogonal space-time block-coded (OSTBC) multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) downlink, where both mean feedback and covariance feedback are available. We derive adaptive linear precoding and nonlinear Tomlinson-Harashima precoding (THP) over a transmit-antenna-correlated, frequency-selective fading MIMO channel with estimation errors and feedback delay. In our precoder, mean-feedback precoding or covariance-feedback precoding, is adaptively chosen at the user terminal. The maximum achievable signal-to-noise power ratio (SNR) is used as the precoding-mode selection criterion. Each user calculates the selection metric and decides whether mean feedback is necessary. We confirm the intuition that mean-feedback precoding offers BER gains over covariance-feedback precoding when mean feedback becomes sufficiently accurate. Our adaptive precoding outperforms either mean-feedback precoding or covariance-feedback precoding in multiuser OSTBC OFDM, and considerably reduces the bit error rate (BER). Non-linear adaptive precoding is shown to outperform linear adaptive precoding.

Despite primary space-time coding where the channel state information (CSI) is available at the receiver only, the capacity and performance of multiple-input multiple-output (MIMO) systems can be increased significantly when a complete or partial CSI is available at the transmitter. Recently, limited feedback methods including antenna subset selection and unitary preceding have been proposed for orthogonal space-time codes where a partial knowledge of the channel is available at the transmitter via an error-free, zero-delay feedback channel. In this paper, we propose a general structure matrix rather than a unitary one for precoding. By maximizing the signal-to-noise ratio (SNR) per received symbol, we find the optimal precoder for general space-time codes with rate⩽1 symbol per channel use. The performance of the optimal scheme is analytically evaluated. Next, we extend the result for limited feedback systems. Simulation results show that the proposed precoder outperforms the previous work.

Since carrier frequency offset destroys user's signal orthogonality in orthogonal frequency-division multiplexing access (OFDMA) uplink transmission, resulting in an interference-limited system, its estimation/correction is very important. The residual carrier frequency offset of each user contributes inter-carrier-interference (ICI) and multiple-user-interference (MUI) to other users. In this paper, the effect of the carrier frequency offset on OFDMA uplink is analyzed. We first analyze the average uplink capacity losses as well as the signal-to-interference-and-noise ratio (SINR) reduction due to the carrier frequency offsets, and then discuss the capacity increases by using adaptive power allocation. The averaged bit error rate (BER) performance with the carrier frequency offsets on OFDMA uplink is also analyzed.

Performance analysis of multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems with carrier frequency offset and channel estimation errors is considered in this paper. Based on the analysis of the inter-carrier-interference (ICI) and inter-antenna-interference (IAI) due to the residual frequency offsets, the average signal-to-interference-and-noise ratio (SINR) is derived. The bit error rate of equal gain combining (EGC) and maximal ratio combining (MRC) with MIMO-OFDM is analyzed, and an infinite-series approximation for the bit error rate is derived. Simulation results illustrate the accuracy of the theoretical analysis.

In this paper, we derive a new infinite series representation for the trivariate non-central chi-squared distribution when the underlying correlated Gaussian variables have tridiagonal form of inverse covariance matrix. We make use of the Miller's approach and the Dougall's identity to derive the joint density function. Moreover, the trivariate cumulative distribution function (cdf) and characteristic function (chf) are also derived. Finally, bivariate noncentral chi-squared distribution and some known forms are shown to be special cases of the more general distribution. However, non-central chi-squared distribution for an arbitrary covariance matrix seems intractable with the Miller's approach.

In this paper, the authors derive the signal-to-interference-plus-noise ratio (SINR) for multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems in the presence of frequency offset and channel estimation errors. The channel is assumed to be frequency-selective Rayleigh fading. The analysis of the demodulated signal shows that the interference can be decomposed into two independent components: inter-carrier interference and interference contributed by other transmit antennas. The SINR for MIMO-OFDM systems with equal gain combining (EGC) and maximal ratio combining (MRC) are also derived.

The rate-one semi-orthogonal algebraic space-time (SAST) codes is recently introduced. In this paper, the authors propose a new signal design method for SAST codes so that the transmitted symbols can be divided into four groups for maximum likelihood (ML) detection; the authors call this new design of SAST codes four-group decodable SAST (4Gp-SAST) codes. The decoding complexity of 4Gp-SAST codes is greatly reduced compared with that of the original SAST codes, where the ML decoding of the transmitted symbols is made into two groups. The exact pair-wise error probability of 4Gp-SAST codes is derived and it is used to optimize the signal designs. Simulation results show that 4Gp-SAST codes perform better than several low complexity space-time block codes such as orthogonal and quasi-orthogonal codes.

The amount of fading (AF) is a simple measure for the performance of a diversity system. This paper provides approximations and bounds for AF as well as the methods to derive the exact AF calculations for transmit antenna selection (TAS) on Rayleigh fading channels. We also derive a simple approximate formula for the relationship between the AF and the coding gain in a TAS system. Simulation results are provided to verify the results.

This paper considers precoding for closed-loop multiuser orthogonal space-time block-coded (OSTBC) orthogonal frequency-division multiplexing (OFDM) downlink over multiple-input multiple-output (MIMO) channels. The authors present a general transmit-antenna-correlated, frequency-selective fading MIMO channel model with imperfect channel estimates and feedback delay, and derive the conditional means of the channel response. Exploiting the channel statistics, the authors develop new linear precoding and non-linear Tomlinson-Harashima precoding (THP) to maximize the signal-to-noise power ratio (SNR). By considering the conditional mean as the equivalent channel matrix, our precoding takes into account the estimation errors and channel time variations over feedback delay. The authors confirm the intuition that when channel state information at the transmitter (CSIT) becomes accurate, the full-CSIT precoder outperforms the covariance-feedback precoder. The proposed precoder has a bit error rate (BER) gain over unprecoded systems. As well, non-linear THP is shown to outperform linear precoding.

Despite their high spectral efficiencies, multiple-input multiple-output (MIMO) systems suffer from high cost and complexity due to multiple radio frequency chains at both link ends. A possible solution is to select a subset of the available antennas at transmitter and/or receiver based on maximal capacity or minimal error rates. This paper proposed a receive antenna selection algorithm to minimize the union bound on the vector error rate. By relaxing the antenna selection variables from discrete to continuous, the authors formulate the problem as a convex optimization problem. An efficient iterative method can be used to obtain the solution.

Despite their high spectral efficiencies, multiple-input multiple-output (MIMO) systems suffer from high cost and complexity due to multiple radio frequency chains at both link ends. A possible solution is to select a subset of the available antennas at transmitter and/or receiver based on maximal capacity or minimal error rates. In this letter, we propose a receive antenna selection algorithm based on the minimization of the union bound on the vector error rate. By relaxing the antenna selection variables from discrete to continuous, we arrive at a convex optimization problem. Efficient numerical methods such as interior-point algorithms can be applied to solve this optimization problem with polynomial complexity.

We develop blind data detectors for orthogonal frequency-division multiplexing (OFDM) systems over doubly selective channels by exploiting both frequency-domain and time-domain correlations of the received signal. We thus derive two blind data detectors: a time-domain data detector and a frequency-domain data detector. We also contribute a reduced complexity, suboptimal version of a time-domain data detector that performs robustly when the normalized Doppler rate is less than 3%. Our frequency-domain data detector and suboptimal time-domain data detector both result in integer least-squares (LS) problems. We propose the use of the V-BLAST detector and the sphere decoder. The time-domain data detector is not limited to the Doppler rates less than 3%, but cannot be posed as an integer LS problem. Our solution is to develop an iterative algorithm that starts from the suboptimal time-domain data detector output. We also propose channel estimation and prediction algorithms using a polynomial expansion model, and these estimators work with data detectors (decision-directed mode) to reduce the complexity. The estimators for the channel statistics and the noise variance are derived using the likelihood function for the data. Our blind data detectors are fairly robust against the parameter mismatch

This paper considers semiblind channel estimation and data detection for orthogonal frequency-division multiplexing (OFDM) over frequency-selective fading channels. We show that the samples of an OFDM symbol are jointly complex Gaussian distributed, where the mean and covariance are determined by the locations and values of fixed pilot symbols. We exploit this distribution to derive a novel maximum-likelihood (ML) semiblind gradient-descent channel estimator. By exploiting the channel impulse response (CIR) statistics, we also derive a semiblind data detector for both Rayleigh and Ricean fading channels. Furthermore, we develop an enhanced data detector, which uses the estimator error statistics to mitigate the effect of channel estimation errors. Efficient implementation of both the semiblind and the improved data detectors is provided via sphere decoding and nulling-canceling detection. We also derive the Crameacuter-Rao bound (CRB) and design optimal pilots by minimizing the CRB. Our proposed channel estimator and data detector exhibit high bandwidth efficiency (requiring only a few pilot symbols), achieve the CRB, and also nearly reach the performance of an ideal reference receiver

We consider joint estimation of carrier frequency offset and channel impulse response (CIR) for orthogonal frequency division multiplexing (OFDM) systems with pilot symbols and virtual subcarriers (VCs). We derive the receive-signal correlation structure due to the pilots and VCs, give the evidence of joint multivariate Gaussian distribution of the received samples, and derive an approximate maximum likelihood (ML) frequency offset estimator. We also derive the asymptotic mean-square error (MSE) and an approximate Cramer-Rao bound (CRB) and establish the asymptotic unbiasedness. Without pilots, in high signal-to-noise ratio, our estimator is equivalent to Liu and Tureli's estimator with Nvvirtual carriers. When the pilot number (Np) is greater than the channel length L, our estimator acts as a subspace-based estimator with Nv+ Np- L virtual carriers. A decision-directed joint ML estimator is derived to iteratively update the estimates of frequency offset, data symbols and CIR. The optimal pilot and virtual carrier placement strategies are also discussed. The resulting decision-directed joint estimator performs within 0.8 dB of the ideal case even when the frequency offset is as large as 20%

We consider stochastic blind maximum-likelihood detection of orthogonal space-time block codes (OSTBCs) over a quasi-static flat multiple-input multiple-output (MIMO) Rayleigh fading channel. A general decision rule for stochastic blind maximum-likelihood OSTBC detection is derived. This rule is simplified using OSTBC linear dispersion matrices to realize a blind detector, which is implemented by semi-definite relaxation or sphere decoding. For the latter, the modifications necessary for both unitary and non-unitary constellations are developed. Two totally blind detectors using dual constellations or a superimposed training scheme are proposed. As a side product, two conditions for a rotatable OSTBC are also derived. A decision-directed, minimum mean-square-error (MMSE) channel estimator is developed. We also derive the Cramer-Rao bound (CRB) for channel estimation and discuss the optimal power allocation. Extensive simulation results are used to compare the different detectors in terms of complexity and performance

In this paper, using Miller's approach and Dougall's identity, we derive new infinite series representations for the quadrivariate Nakagami-m joint density function, cumulative distribution function (cdf) and characteristic functions (chf). The classical joint density function of exponentially correlated Nakagami-m variables can be identified as a special case of the joint density function obtained here. Our results are based on the most general arbitrary correlation matrix possible. Moreover, the trivariate density function, cdf and chf for an arbitrary correlation matrix are also derived from our main result. Bounds on the series truncation error are also presented. Finally, we develop several representative applications: the outage probability of triple branch selection combining (SC), the moments of the equal gain combining (EGC) output signal to noise ratio (SNR) and the moment generation function of the generalized SC(2,3) output SNR in an arbitrarily correlated Nakagami-m environment. Simulation results are also presented to verify the accuracy of our theoretical results.

We propose a two-stage precoder/equalizer to suppress intercarrier interference (ICI) and multiuser interference (MUI) in downlink multiuser OFDM with multiple transmit antennas. The first stage, non-linear Tomlinson-Harashima preceding (THP) at the base station (BS) transmitter, mitigates the effect of the spatial inter-stream interference caused by transmission from multiple transmit antennas to decentralized users. In the second stage, each user's receiver employs low- complexity iterative linear minimum mean-square error (MMSE) equalization to suppress the ICI due to frequency offset. Our proposed technique virtually eliminates the bit error rate (BER) degradation due to normalized frequency offsets as high as 10%.

ABBA codes are an important class of quasi- orthogonal space-time block codes proposed by Tirkkonen et al.. Recently, they have become more attractive for practical applications because Yuen et al. have shown that ABBA codes allow pair-wise real-symbol decoding (or equivalently, single-complex symbol decoding) complexity; it is the minimum decoding complexity (MDC) achievable by any non-OSTBC. Additionally, MDC-ABBA codes can achieve full diversity while their code rate is higher than that of OSTBC. In this paper, we present anew,general,simple,andclosed-formmethod to decode MDC-ABBA codes. We explicitly derive the equivalent channel of MDC-ABBA codes and the maximum mutual information of MDC-ABBA. Furthermore, we prove that MDC-ABBA codes can achieve full diversity with transmit and/or receive antenna selection and full or limited feedback.

ABBA codes, a class of quasi-orthogonal space-time block codes (STBC) proposed by Tirkkonen et al., have been studied extensively for various applications. Yuen et al. have recently shown that a refined version of ABBA codes admit pair-wise real-symbol decoding, i.e. with minimum decoding complexity (MDC) achievable by non-orthogonal STBC. In this paper, we derive the exact symbol pair-wise error probability and the union bound on the symbol error rate (SER). The union bound is only 0.1 dB from the simulated SER at medium or high SNR-2. Thus, by minimizing the SER union bound, we can find the optimal signal designs for any constellation with an arbitrary geometrical shape. Furthermore, we propose a new method combining signal rotation and power allocation for inphase-quadrature power-unbalanced constellations such as rectangular QAM. Our new optimal signal designs perform better than the existing ones and offer lower encoding/decoding complexities.

This paper presents non-linear precoding design in closed-loop multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) over spatially- correlated, frequency-selective fading channels. Our analysis takes into consideration receiver channel mismatch due to imperfect channel estimates, and transmitter channel mismatch due to estimation errors, channel variations over feedback delay and feedback noise. We present a general spatially-correlated, frequency-selective fading MIMO channel model and derive the conditional means of the channel response. Exploiting the channel statistics, which are only available at the receiver, we design new non-linear zero-forcing (ZF) Tomlinson-Harashima precoding (THP) for uncoded MIMO OFDM. The channel statistics do not need to be sent back to the transmitter, which avoids the possible maximum-Doppler-shift transmitter mismatch. Our proposed precoders are robust against time variations, channel estimation errors and antenna correlations, and offer a significant system performance gain over conventional THP.

The path and antenna correlations significantly degrade the system capacity in spatially-multiplexed multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems and increase bit error rate (BER) in orthogonal space-time block coded (OSTBC) OFDM. We develop adaptive dual-mode precoding to improve system performance with transmit antenna and path correlations. Both linear and non-linear Tomlinson-Harashima (TH) precoders are considered. In our proposed approach, precoding for maximizing capacity in spatially-multiplexed OFDM or precoding for minimizing error rate in OSTBC OFDM, is adaptively chosen at the receiver, and only one-bit decision information per subcarrier needs to be sent back to the transmitter. The precoding mode selection depends on the channel conditions. To determine the precoding matrix only the statistical knowledge of the channel is needed at the transmitter, which significantly reduces the feedback requirements. In spatially correlated channels, proposed adaptive dual-mode precoding individually outperforms either capacity- maximization precoding in spatially-multiplexed OFDM or error-rate-minimization precoding in OSTBC OFDM.

Existing tone-reservation algorithms (such as the controlled clipper algorithm) for OFDM require a number of iterations to ensure the reduction of Peak-to-Average Power Ratio (PAR). Consequently, such algorithms entail high levels of computational complexity. In this paper, we propose a new adaptive-scaling tone reservation algorithm. It utilizes the filtered clipping noise as the PAR reduction signal, and adaptively scales it to reduce the PAR. Simulation results show that our proposed algorithm achieves a better PAR reduction and lower complexity than the controlled clipper algorithm.

A novel joint frame synchronization and carrier frequency offset estimation scheme for burst transmission mode multi-carrier systems is proposed, which uses a Central- Symmetric and Comb-Like training sequence (CSCL). This time-domain Comb-Like shape eases its power detection at the receiver without increasing the total training sequence power. Fine frame synchronization as well as carrier frequency offset acquisition with a maximum acquisition range of plusmnN/4timesSF times the subcarrier spacing can also be performed based on the proposed training sequence, where N denotes the Discrete Fourier Transform (DFT) length and SF stands for an integer-valued spreading factor that is used to generate the proposed training sequence. The remaining carrier frequency offset after acquisition can be further estimated and corrected by using a Fine Adjustment algorithm. In order to reduce the performance loss introduces by a higher Peak-to-Average Power Ratio (PAPR) in the CSCL, a time-domain Constant-Envelop training sequence (CE) is also proposed in this paper, which outperforms CSCL- based algorithm. The comparison of the proposed algorithms with the SS (Shi&Serpedin) algorithm by computer simulation illustrates the superior performance of the proposed algorithm with regard to estimation accuracy.

A heuristic tree search algorithm is developed for the maximum likelihood detection and decoding problem in a general communication system. We propose several "cheap" heuristic functions using constrained linear detectors and the minimum mean square errors (MMSE) detector. Even though the MMSE heuristic function does not guarantee the optimal solution, it has a negligible performance loss and provides a good complexity-performance tradeoff. For linear block coded systems, heuristic tree search is modified for soft decision decoding. High rate codes are decoded via the minimum state trellis, and low rate codes via the minimum complexity tree. Preprocessing is also discussed to further speed up the algorithms.

We develop a polynomial-time detector for maximum likelihood (ML) detection over multiple-input multiple-output (MIMO) channels. Our proposed polynomial moment relaxation (PMR) detection gives a unified framework for MIMO detection with relaxation including semi-definite relaxation as a special case. We give three approaches to replace a finite alphabet constraint with a polynomial constraint. Since both the objective function and the constraints are polynomials, we use a moment relaxation approach by applying the dual theories of moments and positive polynomials solvable by semi-definite programming. With different relaxation orders, our PMR achieve a flexible trade-off between complexity and performance.

This paper considers multiple symbol differential detection (DD) for both single-antenna and multiple-antenna systems over flat Ricean-fading channels. We derive the optimal multiple symbol detection (MSD) decision rules for both Mary differential phase-shift keying (MDPSK) and differential unitary space-time modulation (DUSTM). The sphere decoder (SD) is adopted to solve the MSD for MDPSK. As well, an improved SD is proposed by using the Schnorr-Euchner strategy. A suboptimal MSD based decision feedback DD algorithm is proposed for the MSD of DUSTM. We also develop a sphere decoding bound intersection detector (SD-BID) to optimally solve the MSD problem for DUSTM, which still maintains low complexity. Simulation results show that our proposed MSD algorithms for both single-antenna and multiple-antenna systems reduce the error floor of conventional DD but with reasonably low computational complexity.

We develop an efficient linear programming detector (LPD) for multiple-input multiple-output (MIMO) systems. Instead of using the usual l2norm, our proposed LPD uses the l1norm as the detection metric, resulting in a mixed-integer linear program (MILP). Two branch-and-bound algorithms are proposed to solve the MILP. The solution of the MILP achieves the same full diversity order as the maximum likelihood detector. The MILP is further relaxed to a linear program (LP), which can be readily solved using the standard simplex method. We show that in some cases the solution of the LP is guaranteed to be that of the MILP. The LPD is also extended to the joint detection and decoding of linear block coded MIMO systems. Our LPD can be immediately implemented using mature circuits design for the simplex algorithm

We present a unified algebraic structure of space-time block codes (STBC) with orthogonality called orthogonality-embedded space-time (OEST) codes. Previously known codes, including orthogonal, quasi-orthogonal, semi-orthogonal, and non-orthogonal rate-one circulant space-time codes, are special cases of OEST codes. To construct OEST codes, the generalized complex or real orthogonal designs are employed with two main differences: (1) each data symbol is replaced by a circulant matrix; (2) the scalar product is replaced by the Kronecker product. We show that each group of transmitted symbols embedded in the circulant matrices can be separately detected without any interference from other groups. Signal rotations are used to obtain full diversity and optimal coding gain

In recent investigations, several methods for limited feedback multiple-input multiple-output (MIMO) systems have been proposed. Antenna selection at the transmitter and(or) receiver side is one of the approaches to minimize the average probability of error by using a limited bits of feedback information. In this paper, by using a novel approach, we calculate the optimal signal-to-noise ratio (SNR) for each received symbol for a general space-time block code. We propose an antenna selection method at the transmitter to maximize the average SNR for each symbol. Since we propose the optimal selection, our antenna selection method outperforms antenna selection methods available in the literature for space-time codes with rate⪕ 1 symbol per channel use, derived either based on SNR or capacity maximization. The proposed selection performs better than unitary precoding schemes (even optimal precoding) for systems with small number of transmitter and receiver antennas (particularly for mobile systems), although precoding techniques exploit more bits of feedback information and computational complexity than the proposed method.

Because of their orthogonality properties, unitary matrices are an important class of matrices that are used in mathematics, physics, control, communications and others. In multiple-input multiple-output (MIMO) communication systems, there are two main applications that use unitary matrices: differential space-time modulation (DUSTM) and precoding. DUSTM is used when the channel state information (CSI) is not available for both transmitter and receiver, while unitary precoding is used when complete or partial CSI is available for both sides. For DUSTM and limited feedback MIMO systems, a codebook of unitary matrices should be designed. Conventionally, design parameters are optimized based on a cost function depending on the application. This optimization is time consuming when the system dimension and/or codebook size are increased. In this paper, we propose to relax the design parameters to be real rather than integer and use a genetic algorithm to find the optimal solution based on the related cost function. This approach provides better codes than the codes extracted from exhaustive search over integer parameters. The code extraction is rapid even when the system dimensions are large

Orthogonal space-time block-coded (OSTBC) orthogonal frequency-division multiplexing (OFDM) links for frequency-selective multiple-input multiple-output (MIMO) channels with correlated paths and transmit antennas are considered. In such systems, optimal precoding with only covariance feedback is derived using the minimum pair-wise error probability (PEP) criterion; linear and non-linear precoders are designed. The proposed precoding only needs the statistical knowledge of the channel at the transmitter, which significantly reduces the feedback requirements. Both linear and non-linear precoders substantially improve the system bit error rate (BER) for OSTBC OFDM in transmit-antenna and path-correlated channels. The proposed non-linear precoder outperforms the linear precoder.

Preceding is a well-known method to reach the promised performance and capacity of multiple-input multiple-output (MIMO) systems. Recent investigations, when the transmitter has the channel-state information (CSI), have revealed several preceding techniques. Minimum distance based precoders outperform precoders based on other criteria such as maximizing signal-to-noise ratio (SNR), minimizing the mean square error and maximizing the minimum singular value of the equivalent channel. On the other hand, when the CSI is not available at the transmitter, one resorts to limited feedback precoding methods. Previously, unitary matrices for precoding have been derived from subspace packing in the Grassmann manifold. In this paper, we use the same set of unitary matrices and enhance them by defining the precoder matrix to have a general form not unitary only. We extract the precoding parameters by applying the minimum-distance approach. Although in this case the number of feedback parameters is increased, the performance results are accordingly impressive. The optimality of quantization of feedback parameters is also presented.

In this paper, we propose an extended class of unitary signal constellations for differential unitary space-time modulation (DUSTM). We also derive an approximation of the upper bound on the symbol error probability (SEP) as a general criterion to find the optimum codes. This criterion is valid for both group or non-group constellations. For asymptotically high or low signal-to-noise ratio (SNR), signal-constellation parameters are usually determined based on the rank-and-determinant (diversity product) or the Euclidean distance (diversity sum) criterion. Since both these criterion are SNR-independent, the search results are not necessarily optimum parameters in medium to low SNRs. Thus instead of using diversity sum or product, we search for the constellation parameters to minimize the union-bound based criterion, taking into account the number of receive antenna and the operation SNR. Simulation results show that the constellations optimized for the union-bound based criterion outperform the previous codes resulting from rank-and- determinant (diversity product) or Euclidean distance (diversity sum).

In this paper, we multiple-input multiple-output (MIMO) systems employing transmit antenna selection and orthogonal space-time block codes (OSTBCs) are not available. We thus derive exact closed-form expressions for the BER of Gray-coded M-ary one and two-dimensional amplitude modulations when an OSTBC is employed and N transmit antennas out of total Lt antennas are selected for transmission. We also derive tight closed-form approximate BER for M-PSK constellations. Our BER expressions are valid for a frequency-flat Rayleigh fading MIMO channel and can be evaluated without numerical integration methods.

The active constellation extension (ACE) technique is a lossless (in terms of throughput) peak-to-average power ratio (PAR) reduction technique that adaptively extends the signal constellation while ensuring that the minimum distance between any two constellation points does not decrease. However, this technique increases the average transmit power. In this paper, we propose an adaptive-scaling algorithm for the implementation of ACE. This algorithm, based on the clipping and filtering technique, uses only the peak samples of clipping noise to reduce PAR. Simulation results show that the proposed algorithm has better PAR reduction, lower complexity and smaller BER than the previously proposed Smart Gradient-Project ACE algorithm.

The combination of space-time block codes (STBC) and spatial multiplexing (SM) schemes has the advantages of diversity gain and high data rate. For such STBC/SM hybrid systems, we propose a new detector based on the block structure of STBC and the sphere decoder (SD). By employing the SD, optimal detection is performed with computational complexity much less than the brute-force maximum likelihood (ML) search. Simulation results show that the new decoder significantly outperforms the previously developed zero-forcing (ZF) group/STBC detector, the minimum mean square error (MMSE) group/STBC detector, and the MMSE and ML detectors for equivalent SM systems.

In this paper, we consider efficient blind decoder design for orthogonal space-time block codes (OSTBCs). A general decision rule for blind OSTBC decoding is derived assuming a quasi-static flat multiple-input multiple-output (MIMO) Rayleigh fading channel. We use the linear dispersion representation of OSTBCs to derive a blind decoder that results in a quadratic minimization problem, which can be solved efficiently by semi-definite relaxation, sphere decoding or successive interference cancellation. To resolve phase ambiguity problems inherent in blind detectors, rather than using pilot symbols that results in a bandwidth loss, we propose novel totally blind decoders using dual constellations or a superimposed training scheme. To alleviate the computational burden, a minimum mean-square-error (MMSE) channel estimator is also proposed to track the time-varying channel without using the blind decoder

In this paper, we consider the signal detection for \nspace-time block coding over time-selective fading channels. \nWe derive a general maximum likelihood (ML) decision rule \nfor space-time block coding (STBC). The resulting detector is \nvalid for any number of receive antennas and for all STBC \nsystems that have the linear dispersion property. The detector \nresults in a quadratic minimization problem, which can be solved \nefficiently by sphere decoding or nulling-and-cancelling detection. \nFor orthogonal STBC systems, we also propose a suboptimal \ndetector using the principle of parallel interference cancellation \n(PIC) that is valid for systems with an arbitrary number of \nreceive antennas.

In this letter, we develop a family of approximate maximum-likelihood (ML) detectors for multiple-input multiple-output systems by relaxing the ML detection problem using constellation-specific polynomial constraints. The resulting constrained optimization problem is solved using a penalty function approach. Moreover, to escape from the local minima, which improves the detection performance, a differential equation algorithm using classical mechanics is proposed. Simulation results show that the polynomial constrained detector performs better than least-squares (LS) detector.

We develop new blind and semi-blind data detectors and channel estimators for orthogonal frequency-division multiplexing (OFDM) systems. Our data detectors require minimizing a complex, integer quadratic form in the data vector. The semi-blind detector uses both channel correlation and noise variance. The quadratic for the blind detector suffers from rank deficiency; for this, we give a low-complexity solution. Avoiding a computationally prohibitive exhaustive search, we solve our data detectors using sphere decoding (SD) and V-BLAST and provide simple adaptations of the SD algorithm. We consider how the blind detector performs under mismatch, generalize the basic data detectors to nonunitary constellations, and extend them to systems with pilots and virtual carriers. Simulations show that our data detectors perform well.

We consider superimposing pilot symbols on to data symbols for channel estimation for orthogonal frequency division multiplexing (OFDM) systems. We first derive maximum-likelihood (ML) and minimum-mean square error (MMSE) iterative channel estimators. Modeling the time domain signal as Gaussian, we derive an ML channel estimator by averaging the likelihood function for both data and channel impulse response (CIR) over the resulting Gaussian vector. Two data detectors are also proposed by eliminating the CIR from the likelihood function. The resulting integer least squares problem can be efficiently solved using a sphere decoder (SD). Furthermore, the Cramer-Rao bound (CRB) for the superimposed channel and data estimation is derived. The equispaced pilot placement is optimal in superimposed training. The ideal performance benchmarks are reached by our proposed estimators. Their performance is comparable to that of a separated training scheme, but they offer a higher data rate.

In this paper, we present a unified detection framework for spatial multiplexing multiple-input multiple-output (MIMO) systems. We propose a generalized feedback detector (GFD) by modifying the classical feedback decoding algorithm for convolutional codes. When the three controlling parameters of the GFD vary, the diversity order of the GFD varies between 1 and N and the SNR gain also varies. Many previous MIMO detectors are special cases of our GFD. The connection between MIMO detectors and tree search algorithms is also established. To reduce redundant computations in the GFD, a shared computation technique is proposed using a tree data structure. The complexity of the GFD varies between those of maximum-likelihood (ML) detection and zero-forcing decision feedback detector (ZF-DFD). Our proposed GFD provides a flexible performance-complexity tradeoff.

We develop a family of constrained detectors for multiple-input multiple-output (MIMO) channels by relaxing the maximum likelihood (ML) detection problem. Real constrained linear detectors and decision feedback detectors are proposed for real constellations by forcing the relaxed solution to be real. Generalized minimum mean-square error and constrained least squares detectors are generalized as MIMO detectors for both constant and non-constant modulus constellations. Using our constrained linear detectors, we propose a new ordering scheme to achieve a tradeoff between interference suppression and noise enhancement. Moreover, we introduce a combined constrained linear and decision feedback detector to mitigate the error propagation in decision feedback. Simulation results show that the combined detectors achieve significant performance gain over V-BLAST detection.

Quasi-orthogonal space-time block codes (QSTBC) achieve full diversity by constellation rotations. Several authors have introduced optimal rotation angles, found either by computer search or by analytical derivation. However, existing analytical methods do not seem general enough to analyze optimal rotations for arbitrary constellations, and some previous results seem to conflict. We present a novel method to exactly derive the coding gain of QSTBC as a function of the rotation angle and the minimum Euclidean distance of two-dimensional constellations such as the ones carved from lattices of squares and triangles, and phase-shift keying (PSK) constellations. The upper bound of coding gain for amplitude PSK (APSK) is also obtained. We find the whole range of optimal rotations for maximizing the coding gain of QSTBC. Simulation results confirm the theoretical analysis.

A new class of full-diversity space-time block codes (STBC) called semi-orthogonal algebraic space-time block codes (SAST codes) with rate one symbol per channel use is proposed. The SAST codeword matrix has a generalized Alamouti code structure where the transmitted symbols are replaced by circulant matrices. Properties of rate-one linear threaded algebraic space-time (LTAST) codes are exploited to construct SAST codes with maximal coding gain. SAST codes attain nearly 100% of the Shannon capacity of open-loop multiple-input single-output (MISO) channels. Our theoretical analysis and simulation results show that SAST codes gain several dB over LTAST codes and also outperform other STBC.

We consider preceding for intercarrier interference (ICI) reduction due to frequency offsets in closed-loop orthogonal frequency-division multiplexing (OFDM) systems. Since the complete channel state information (CSI) is difficult to obtain at the transmitter, we develop a novel non-linear limited-feedback Tomlinson-Harashima (LFB-TH) precoder to suppress ICI in closed-loop multiple-antenna OFDM. Our precoder applies a pre-designed codebook of matrices, which is available at both the transmitter and the receiver. The receiver selects the feedback matrix from the codebook according to a specific selection criterion and transfers the index of the chosen matrix to the transmitter. Hence the CSI is not required at the transmitter in the proposed precoder. The codebook design criterion and feedback matrix selection criteria are analyzed. Our LFB-TH precoder significantly reduces the bit error rate (BER) degradation due to frequency offset; the degradation is virtually eliminated for normalized frequency offsets as high as 10%.

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Based on experiments and numerical simulation, it has been widely believed that the time average mean square error in the first order sigma-delta modulator with input of bandlimited signals decays like O(/spl lambda//sup -3/) as the sampling ratio /spl lambda/ goes to infinity. This conjecture remains as an open problem for many years. Combining tools from number theory, harmonic analysis, real analysis and complex analysis, this paper shows that the conjecture holds in some reasonable sense.

This paper considers semi-blind channel estimation and data detection for OFDM systems over frequency-selective fading channels. Using the maximum likelihood (ML) principle, we derive a blind channel estimator by taking the time domain transmitted signal as Gaussian (due to the central limit theorem) and averaging the likelihood function over the resulting Gaussian distribution. This estimator is realized using the steepest descent algorithm. Similarly, our semi-blind data detector integrates the channel impulse response (CIR) out of the likelihood function, which is realized using sphere decoding and V-BLAST. Simulation results show that our proposed channel estimator and data detector perform a fraction of dB within an ideal reference receiver.

Multiple-shift complementary sequences (MCS), a generalized form of Golay complementary sequences, have recently been introduced to encode OFDM signals, allowing a better trade-off between the code rate and peak-to-mean envelope power ratio (PMEPR). However, a table of such sequences needs to be constructed by exhaustive search, a practically impossible task for a moderately large number of sub-carriers. As has been done for Golay complementary sequences and generalized Golay complementary sequences, this paper successfully identifies a class of MCS as the second order cosets of the first order Reed-Muller codes. We also present a new proof for the PMEPR of MCS.

Generalized Golay complementary sequences and multiple-shift complementary sequences have recently been introduced to encode orthogonal frequency division multiplexing (OFDM) signals, reducing the peak-to-mean envelope power ratio (PMEPR). Certain classes of these complementary sequences have been identified as a subset of second order cosets of the first order Reed-Muller codes. Since the code rates of these encoding schemes are prohibitively low for a large number of sub-carriers, it is necessary to find an efficient algebraic way to produce sufficient number of codewords such that the code rate of the encoding scheme is high enough. In this paper, we introduce generalized Rudin-Shapiro polynomials, a subset generalized Golay complementary sequences, to encode OFDM signals. In our encoding scheme, a matrix equation recursively produces a sufficient number of Rudin-Shapiro polynomials such that the code rate increases linearly with respect to the PMEPR. Therefore, it offers an excellent trade-off performance between the code rate and the PMEPR.

We derive a new decision rule for multiple-symbol detection (MSD) of differential unitary space-time modulation (DUSTM). It is valid for both diagonal and non-diagonal constellations, and for quasi-static fading channels. We then present a fast algorithm based on the extended Euclidean algorithm and bound principles for single symbol detection (SSD) with diagonal constellations. We call it bound-intersection detection (BID) and it is exact maximum likelihood (ML). In high SNR, the complexity of our algorithm is much less than that of the brute-force ML search. We also develop two BID variants for MSD. They are ML but with significantly reduced complexity using branch-and-bound (BnB).

We consider semi-blind data detectors for OFDM systems over fast fading channels. Three maximum-likelihood (ML) data detectors (MLD) are derived assuming exact channel correlation. The first two exploit the correlation among pre-DFT and post-DFT received signals and the third one average the ML metric over channel impulse response (CIR). We show that the first two MLDs for input data symbols are given by an integer least-squares (LS) minimization problem, which can be efficiently solved by V-BLAST detection (suboptimal) or by a sphere decoder (SD) (optimal). We contribute a low-complexity near-ML SD and an iterative detector for the third MLD. Despite its low complexity, MLDl performs robustly for normalized Doppler rates less than 3%, which meets the requirement of many practical systems. With iterative detection, both MLD1 and MLD3 can exploit time-diversity.

This paper considers carrier frequency offset (CFO) estimation for OFDM systems over frequency-selective fading channels. We derive three new maximum-likelihood (ML) CFO estimators. The first estimator takes the pre-DFT signal at the receiver as Gaussian and averages the likelihood function over the Gaussian variable. The other two estimators first remove the channel impulse response (CIR) and average the resulting likelihood function over time-domain transmitted symbols. We demonstrate that the presence of virtual carriers is critically important for estimation. All our proposed estimators can achieve the asymptotic Cramer Rao bound (ACRB) and can also be enhanced using embedded pilots.

In this paper, we investigate channel estimation (CE) and data detection for OFDM systems over doubly-selective channels. We derive an oversampling basis expansion model (BEM) for doubly-selective channels and its statistical properties. The time diversity in the Doppler-induced inter-carrier-interference (ICI) and its relationship to the carrier frequency offset (CFO) induced ICI are illustrated using the BEM. We derive two low complexity linear minimum mean-square-error (LMMSE) channel estimators using the BEM. The sphere decoder (SD) is modified to equalize the ICI channel. A low-complexity iterative equalizer without matrix inversion is also proposed. Our proposed channel estimators have low complexity and achieve good performance. Furthermore, the low-complexity iterative equalizer performs close to SD.

In this paper, we derive a general expression for the bit error rate (BER) performance of an arbitrary square/rectangular Gray-coded quadratic amplitude modulation (QAM) scheme. This general formula requires a number of conditional probabilities, which we derive in closed-form for independent and nonidentically distributed (i.n.d.) Rayleigh fading channels, when maximum ratio combining (MRC) with imperfect channel estimation (ICE) is employed. Our general formula determines the exact BER of any arbitrary square/rectangular QAM MRC receiver with ICE in i.n.d. Rayleigh fading channels, avoiding time consuming simulations. In addition, Monte Carlo simulations and analytical results are in excellent agreement.

Moments of the equal gain combiner (EGC) output signal-to-noise ratio (SNR) are only known for independent and exponentially correlated Nakagami-m fading channels. We derive the moments of the EGC output SNR in equally correlated Nakagami-m fading channels. Our moment expressions can be used to evaluate the outage and the average error rate of EGC as well as purely moments-based measures such as the average output SNR and the amount of fading as functions of the fading correlation. Numerical results that illustrate the effect of fading correlation on the distribution of the EGC output SNR are also provided. The average output SNR increases with the fading correlation.

We derive a new multistage sphere decoding (MSD) algorithm, which is a generalization of the conventional sphere decoder (SD). This new MSD exploits that many higher order signal constellations can naturally be decomposed into several lower order constellations. We develop a two-stage SD for a 16-ary quadrature amplitude modulation (16QAM) multi-input multi-output (MIMO) system by decomposing 16QAM into two 4QAM constellations. The first stage generates a list of 4QAM vectors. For each of these, the second stage computes an optimal 4QAM vector. In the low signal-to-noise ratio (SNR) region, our MSD performs close to the original (single-stage) SD, but it has a lower complexity. In the high SNR region, our MSD is not suitable for reaching near maximum likelihood (ML) performance.

The existing iterative clipping and filtering techniques require several iterations to mitigate the peak regrowth. In this letter, we analyze the conventional clipping and filtering using a parabolic approximation of the clipping pulse. We show that the clipping noise obtained after several clipping and filtering iterations is approximately proportional to that generated in the first iteration. Therefore, we scale the clipping noise generated in the first iteration to get a new clipping and filtering technique that, with three fast Fourier transform/inverse fast Fourier transform (FFT/IFFT) operations, obtains the same PAR reduction as that of the existing iterative techniques with 2K+1 FFT/IFFT operations, where K represents the number of iterations.

The study on generalized selection combining (GSC(N,L)) diversity systems that adaptively combines a subset of N paths with the highest instantaneous signal-to-noise ratios (SNRs) out of L available diversity paths has both theoretical and practical importance in the design of low-complexity receiver structures for cellular wideband CDMA, indoor millimeter-wave and ultra-wideband communications. This paper presents a novel mathematical framework to tackle the problem at hand by deriving a single integral expression for the moment generating function (mgf) of the GSC(N,L) output SNR when the L resolvable multipaths are independent with nonidentical fading statistics. The mgf is then used to unify the performance evaluation of a broad range of digital modulation/detection schemes in practical wireless channels.

Signal fading is a ubiquitous problem in mobile and wireless communications. In digital systems, fading results in bit errors, and evaluating the average error rate under fairly general fading models and multichannel reception is often required. Predominantly to date, most researchers perform the averaging using the probability density function method or the moment generating function (MGF) method. This paper presents a third method, called the characteristic function (CHF) method, for calculating the average error rates and outage performance of a broad class of coherent, differentially coherent, and noncoherent communication systems, with or without diversity reception, in a myriad of fading environments. Unlike the MGF technique, the proposed CHF method (based on Parseval's theorem) enables us to unify the average error-rate analysis of different modulation formats and all commonly used predetection diversity techniques (i.e., maximal-ratio combining, equal-gain combining, selection diversity, and switched diversity) within a single common framework. The CHF method also lends itself to the averaging of the conditional error probability involving the complementary incomplete Gamma function and the confluent hypergeometric function over fading amplitudes, which heretofore resisted to a simple form. As an aside, we show some previous results as special cases of our unified framework.

Few theoretical results are known about the joint distribution of three or more arbitrarily correlated Rayleigh random variables (RVs). Consequently, theoretical performance results are unknown for three- and four-branch equal gain combining (EGC), selection combining (SC), and generalized SC (GSC) in correlated Rayleigh fading. This paper redresses this gap by deriving new infinite series representations for the joint probability density function (pdf) and the joint cumulative distribution function (cdf) of three and four correlated Rayleigh RVs. Bounds on the error resulting from truncating the infinite series are derived. A classical approach, due to Miller, is used to derive our results. Unfortunately, Miller's approach cannot be extended to more than four variates and, in fact, the quadrivariate case considered in this paper appears to be the most general result possible. For brevity, we treat only a limited number of applications in this paper. The new pdf and cdf expressions are used to derive the outage probability of three-branch SC, the moments of the EGC output signal-to-noise ratio (SNR), and the moment generating function of the GSC(2,3) output SNR in arbitrarily correlated Rayleigh fading. A novel application of Bonferroni's inequalities allows new outage bounds for multibranch SC in arbitrarily correlated Rayleigh channels.

This paper considers multiple-symbol differential detection (MSD) of differential unitary space-time modulation (DUSTM) over multiple-antenna systems. We derive a novel exact maximum-likelihood (ML) detector, called the bound-intersection detector (BID), using the extended Euclidean algorithm for single-symbol detection of diagonal constellations. While the ML search complexity is exponential in the number of transmit antennas and the data rate, our algorithm, particularly in high signal-to-noise ratio, achieves significant computational savings over the naive ML algorithm and the previous detector based on lattice reduction. We also develop four BID variants for MSD. The first two are ML and use branch-and-bound, the third one is suboptimal, which first uses BID to generate a candidate subset and then exhaustively searches over the reduced space, and the last one generalizes decision-feedback differential detection. Simulation results show that the BID and its MSD variants perform nearly ML, but do so with significantly reduced complexity.

The recent literature has thoroughly treated two-branch selection combining (SC) over correlated Rayleigh fading and three-branch SC over exponentially correlated Rayleigh fading. However, a long-standing open problem involves the three-branch SC performance over arbitrarily correlated Rayleigh fading. We solve this problem completely by deriving new infinite series expressions for the cumulative distribution function, the probability density function, and the moment generating function (mgf) of the three-branch SC output signal-to-noise ratio (SNR). The output mgf can be used to derive the average symbol-error rate for any two-dimensional digital modulations. The outage probability and the higher moments of the SC output SNR are also derived. These analytical results are canonical, in that the three-branch SC performance is now completely solved for arbitrary correlation. Some previous results are shown to be special cases of our new results.

Selected mapping (SLM) and partial transmit sequence (PTS) are well-known techniques for peak-power reduction in orthogonal frequency-division multiplexing (OFDM). We derive a simplified maximum likelihood (ML) decoder for SLM and PTS that operates without side information. This decoder exploits the fact that the modulation symbols belong to a given constellation and that the multiple signals generated by the PTS or SLM processes are widely different in a Hamming distance sense. Pairwise error probability (PEP) analysis suggests how SLM and PTS vectors should be chosen. The decoder performs well over additive white Gaussian noise (AWGN) channels, fading channels, and amplifier nonlinearities.

Few theoretical results are known about the joint distribution of three or more correlated Rayleigh random variables (RVs). Consequently, theoretical results for the performance of 3-branch and 4-branch equal gain combining (EGC), selection combining (SC) and generalized SC (GSC) over arbitrarily correlated Rayleigh fading channels are not known. This paper derives new infinite series representations of the joint probability density function (pdf) and the joint cumulative distribution function (edf) of the tri-variate and a certain class of quadri-variate correlated Rayleigh distribution. The new pdf and cdf expressions are used to derive the outage probability of 3-branch SC and the moments of the 3-branch EGC output signal-to-noise ratio (SNR) over arbitrarily correlated Rayleigh fading. New bounds for the complementary cdf (ccdf) of the L-branch SC output SNR are also derived. These long-standing diversity theory problems, which have resisted a solution, can now be completely solved.

Despite the importance of the Rician fading model in describing microcellular, picocellular and mobile satellite channels, few theoretical results are known about the performance of selection combining (SC) and equal gain combining (EGC) in correlated Rician fading channels. In this paper, we develop a novel approach for performance analysis of L-branch diversity systems in equally correlated Rician fading channels. This approach involves transforming a set of equally correlated branch gains into a set of conditionally independent branch gains, analyzing the performance for the independent case and averaging the conditional results. Consequently, we derive novel expressions for the average error rates of various digital modulations and the output moments for both SC and EGC. We find that the performance of diversity systems in correlated Rician fading channels can be worse than that in correlated Rayleigh fading channels, which has never been observed for the independent fading case.

For optimizing pilot sequences for a general wideband direct-sequence (DS) code division multiple access (CDMA) system in a slow fading Rayleigh channel, we derive a design criterion by minimizing the mean square error (MSE) of the channel estimate. We analyze the effects of imperfect channel estimation (CE) on a CDMA system, based on the maximal ratio combining (MRC) RAKE receiver in both uniform power delay profile (UPDP) and non-uniform power delay profile (NPDP) channels. Published results on the effect of CE errors hold only for UPDP channels. We therefore use a characteristic function method to derive new closed-form expressions for the BER of RAKE receivers in NPDP channels. Constraining the energy per data frame to be constant, we optimize the length of the pilot symbols by minimizing the BER of the MRC receiver. We show an elegant result that the optimal number of pilot symbols is equal to the square root of the frame length for UPDP channels and for NPDP channels in the high SNR region.

We consider the joint estimation of channel impulse response (CIR) and frequency offset (FO) for a multiple-input multiple-output (MIMO) frequency selective fading channel. We average the joint likelihood function of the CIR and the FO over the distribution of CIR and maximize the resulting marginal likelihood function to estimate the FO. We also derive the design criteria for the training sequences (TS) which maximize the performance of our proposed estimator. Simulation results show that the optimal TS can improve the performance of the joint ML estimator.

We develop blind and semi-blind joint estimators of the channel impulse response (CIR) and data symbols for orthogonal frequency division multiplexing (OFDM) systems over a frequency selective fading channel. Using the maximum likelihood (ML) criterion, we derive two estimators for the transmit data symbols that require minimizing a complex, integer quadratic x/sup T/Gx* where x is a data vector and the matrix G characterizes each estimator. Avoiding computationally prohibitive exhaustive search, we use both sphere decoding (SD) and V-BLAST algorithms. We also modify the SD algorithm for our complex OFDM system, to handle any M-PSK, and incorporate a reduced complexity SD into the OFDM system. The quadratic for the blind estimator suffers from rank deficiency. We give an efficient solution to the rank deficiency problem. Simulation results confirm the good performance of our proposed estimators.

Emerging very high-data-rate wireless communications requires that traditional diversity systems be adapted so that some performance is sacrificed for complexity reduction. With this goal in mind, we investigate the recently-developed absolute threshold generalized selection combining (AT-GSC). We show that AT-GSC has poor bit-error rate (BER) performance when the average branch signal-to-noise ratio (SNR) is comparably lower than the preset threshold. This paper therefore develops a new diversity combining scheme, referred to as switching GSC (S- GSC). This scheme combines all branches whose SNR's exceed a preset threshold and if all the branches drop below the threshold, the output is the single branch with the maximum SNR. We prove that for any two-dimensional amplitude/phase linear modulation schemes, the symbol error rate (SER) of S-GSC lies between those of maximal ratio combining (MRC) and selection combing (SC). Importantly, the complexity of S-GSC is only slightly above that of AT-GSC. We derive the moment generating function (mgf) of the S-GSC output SNR over independent fading channels. For identically and independently distributed (i.i.d.) Rayleigh fading channels, we also derive the output probability density function (pdf) and cumulative distribution function (cdf) and analyze the error rate and the outage probability performance of S-GSC. Higher order moments of the S-GSC output SNR are also derived. These theoretical results are sufficient to completely characterize the performance of S-GSC and enable one to compare S-GSC with conventional diversity schemes.

We develop a novel approach to derive the cumulative distribution functions (cdfs) of the selection-combining (SC) output signal-to-noise ratio (SNR) in equally correlated Rayleigh, Ricean, and Nakagami-m fading channels. We show that a set of equally correlated channel gains can be transformed into a set of conditionally independent channel gains. Single-fold integral expressions are, therefore, derived for the cdfs of the SC output SNR. Infinite series representations of the output cdfs are also provided. New expressions are applied to analyze the average error rate, the outage probability, and the output statistics of SC. Numerical and simulation results that illustrate the effect of fading correlation on the performance of L-branch SC in equally correlated fading channels are provided.

A closed-form expression is derived for the moment-generating function of the Weibull distribution, valid when its fading parameter assumes integer values. Expressions for average signal-to-noise ratio, signal outage, and average symbol-error rate are derived for single-channel reception and independent multichannel diversity reception operating on flat Weibull slow-fading channels.

Orthogonal frequency division multiplexing suffers from large peak-to-average power ratios (PAR). Large PAR causes undesirable effects such as signal distortion and unwanted out of band radiation. Use of partial transmit sequences (PTS) is proposed to improve the PAR statistics of OFDM signals. Phase angles of the modulated symbols are changed in PTS to reduce the PAR. The information about these changes (side information) is critical for the successful operation of PTS. However, a proper way to send side information to the receiver without affecting the optimized PAR statistics has not been reported in the open literature so far. In this paper, we present a novel scheme to insert the side information into PTS-OFDM signals without affecting the improved PAR statistics. Simulation results show that the proposed scheme does not contribute to any peak-regrowth and the hit error rate performance of the system is improved.

The ability to capture significant amount of transmitted signal energy present in the resolvable multipaths using only a modest number of RAKE fingers (correlators) is an important receiver design consideration for ultra-wideband (UWB) and wideband CDMA communication systems. This, however, is achieved at the expense of RAKE receiver performance. Motivated by this need, several suboptimal hybrid receiver structures have been proposed in the literature. The study on generalized selection diversity combining with normalized threshold test per branch (T - GSC(/spl mu/,L)) is also important from a theoretical standpoint because this model encapsulates both the traditional selection diversity and maximal-ratio combining (coherent detection) or post-detection equal-gain combining (noncoherent detection) schemes as limiting cases. However, mathematical analysis for T - GSC(/spl mu/,L) has been limited to i.i.d. Rayleigh fading channels. This paper derives simple to evaluate formulas for the moment generating function (mgf) of T - GSC(/spl mu/,L) output SNR with L resolvable multipaths. In addition to providing new results for many cases that heretofore has resisted solution in a simple form, our approach also allows some of the previously obtained results to be simplified both analytically and computationally.

A generalized selection combiner (GSC) ranks the L available diversity paths and then combines a subset of M paths with the highest signal-to-noise ratios (SNRs). The cumulative distribution function (cdf) and moment generating function (mgf) of a linear sum of ordered random variables are therefore needed for computing the outage probability and error rates needed for computing the outage probability and error rates of a GSC receiver. Unfortunately, except for simple cases, these functions are either not known in closed form or exist only as multidimensional integrals. Consequently, an exact performance analysis is extremely difficult and time-consuming for many fading environments specifically when L is large. This paper therefore derives new upper and lower bounds for the cdf of GSC output SNR over generalized fading channels. These bounds are then used to derive new bounds for the average symbol error rates for a multitude of binary and M-ary digital modulation schemes in a variety of fading channel models that heretofore had resisted simple solutions.

Using a circular contour integral representation for the generalized Marcum-Q function, Q/sub m/(a,b), we derive a new closed-form formula for the moment generating function (MGF) of the output signal power of a dual-diversity selection combiner (SC) in bivariate (correlated) Nakagami-m fading with positive integer fading severity index. This result involves only elementary functions and holds for any value of the ratio a/b in Q/sub m/(a,b). As an aside, we show that previous integral representations for Q/sub m/(a,b) can be obtained from a contour integral and also derive a new, single finite-range integral representation for Q/sub m/(a,b). A new infinite series expression for the MGF with arbitrary m is also derived. These MGFs can be readily used to unify the evaluation of average error performance of the dual-branch SC for coherent, differentially coherent, and noncoherent communications systems.

Abstract The generalized selection combining (GSC) scheme that adaptively combines a subset of M strongest paths out of L available diversity paths finds applications in several wideband receivers and broadband wireless communications. In this paper, exact closed‐form expressions for the moment generating function (MGF), the probability density function (PDF) and the cumulative density function (CDF) of the GSC(M, L) output signal‐to‐noise ratio (SNR) in independent and identically distributed (i.i.d) Nakagami‐m fading channels are derived while the fading index is a positive integer. These expressions hold for any M and L and provide a comprehensive framework for performance analysis including the derivation of closed‐form formulas for the average symbol error probability (ASEP) of a broad class of binary and M‐ary modulations, mean combined SNR and the outage probability of GSC(M, L) receiver structures. When the Nakagami‐m fading index is not an integer, the MGF of GSC(M, L) output SNR is derived as an (M − 1)‐fold infinite series. With this MGF, analytical expressions for both the outage probability and error rates can be readily obtained. An easily programmable recursive solution of the MGF of GSC(M, L) output SNR is also outlined for both the positive integer and noninteger fading severity index cases. Copyright © 2002 John Wiley & Sons, Ltd.

Motivated by practical considerations in the design of low-complexity receiver structures for wideband cellular CDMA, millimeter-wave and ultra-wideband communications, the study on the generalized selection combining receiver that adaptively combines a subset of M "strongest" paths out of L available paths has intensified over the past few years. The study on GSC(M, L) receiver is also important from a theoretical standpoint because this model encapsulates both the classical selection diversity and maximal-ratio combining (coherent detection) or post-detection equal-gain combining (noncoherent detection) receiver structures as limiting cases. We first derive a concise analytical expression for the moment generating function (MGF) of the GSC(M, L) output signal-to-noise ratio with independent and identically distributed diversity paths over Rician fading channels (in terms of only a single finite range integral whose integrand is composed of tabulated functions). Previous studies have only treated either Rayleigh or Nakagami-m (1960) channel models using numerous ad-hoc approaches to simplify an M-dimensional nested integral that arise in the computation of the MGF. The novelty of our mathematical framework for computing the MGF relies on the fact that it allows us to treat all common multipath fading channel models (Rayleigh, Rician, Nakagami-m and Nakagami-q) in a unified sense, it leads to a much More elegant and computationally efficient expression than those available in the literature, and it holds for any combinations of M and L values. Using this newly derived MGFs, we provide a unified error probability analysis for many coherent and noncoherent digital modulation/detection schemes in a myriad of fading environments.

Performance evaluation of equal-gain combining (EGC) diversity receivers are known to be a much more difficult task in comparison with other diversity combining techniques such as the selection diversity or the maximal-ratio combining method. The difficulty of the above mathematical problem is compounded when the diversity branches are correlated. This paper presents a novel mathematical framework for analyzing a dual-branch EGC receiver performance over nonidentical Rayleigh and Nakagami-m fading channels when the diversity branches are correlated. It is also shown that the average bit error rate (ABER) formula for coherent BPSK and BFSK schemes reduces to the familiar expressions in the literature for the limiting case of independent diversity paths by setting the correlation coefficient to zero. Selected numerical plots that illustrate the effect of branch correction on the ABER performance are also provided.

The envelope power of MC-CDMA signals usually exhibits wide fluctuations, leading to a high value of the associated crest factor. However, when Shapiro-Rudin based sequences, namely a Shapiro-Rudin (1959) pair, a Shapiro-Rudin based sub-complementary pair and a Shapiro-Rudin based Sivaswamy's (1978) complementary set are used for two- and four-code BPSK modulated MC-CDMA spreading sequences, the crest factor is found to be bounded by 3dB. These sequences belong to the so-called orthogonal complementary set and Walsh-Hadamard sequences constitute a special case of these sets, when the sequence length is equal to the number of codes. When a typical nonlinear power amplifier is used, the low crest factor of the Shapiro-Rudin sequence based multi-code MC-CDMA scheme results in reduced amplifier-induced signal clipping. Hence a reduced power loss is imposed due to clipping in comparison to OFDM and to multicode MC-CDMA schemes based on other spreading sequences, such as Walsh codes, orthogonal Gold codes, Frank (1962) codes and Zadoff-Chu (1972) codes.

The paper examines the impact of Gaussian distributed weighting errors (in the channel gain estimates used for coherent combination) on both the output statistics of a hybrid selection/maximal-ratio (SC/MRC) receiver and the degradation of the average symbol-error rate (ASER) performance as compared with the ideal case. New expressions are derived for the probability density function, cumulative distribution function and moment generating function (MGF) of the coherent hybrid SC/MRC combiner output signal-to-noise ratio (SNR). The MGF is then used to derive exact, closed-form, ASER expressions for binary and M-ary modulations in conjunction a nonideal hybrid SC/MRC receiver in a Rayleigh fading environment. Results for both selection combining (SC) and maximal-ratio combining (MRC) are obtained as limiting cases. Additionally, the effect of the weighting errors on both the outage rate of error probability and the average combined SNR is investigated. These analytical results provide insights into the tradeoff between diversity gain and combination losses, in concert with increasing orders of diversity branches in an energy-sharing communication system.

Abstract A set of fixed permutations is used in this paper to reduce the peak‐to‐average power ratio (PAR) of an orthogonal frequency division multiplexing (OFDM) signal. For this technique, K − 1 interleavers are used to produce K − 1 permuted sequences from the same information sequence. The peak powers of the permuted sequences and the original information sequence are computed using K inverse discrete Fourier transforms; the sequence with the lowest PAR is chosen for transmission. Before the optimization process begins the identity of each interleaver is embedded into the data frame as side information (SI). SI which is critical to the receiver operation, is coded using a simple forward error correction code in order to increase its reliability. An adaptive approach is proposed for the reduction of this technique's complexity. Furthermore, theoretical expressions are derived for the complementary cumulative distribution function of the PAR and for the average number of permutations required by the adaptive approach. Computer simulations are performed for finding the PAR reduction capability of several types of interleavers. It is subsequently found that random interleavers and odd–even symmetric interleavers are performing equally well in reducing the PAR. Results are also presented for the out of band radiation and the bit error rate performance of interleaved OFDM (IOFDM) and conventional OFDM in an additive white Gaussian noise channel. IOFDM also has less adjacent channel interference than that of conventional OFDM. Copyright © 2002 John Wiley & Sons, Ltd.

Motivated by potential applications to wideband cellular DS-CDMA and millimeter-wave communications, the study of the generalized selection combining (GSC) receiver that adaptively combines a subset of M "strongest" paths out of L available paths has intensified over the past few years. The study of the GSC(M, L) receiver is also important from a theoretical standpoint because this model encapsulates both the classical selection combining receiver and the maximal-ratio combining receiver as limiting cases. Despite its importance, published results on GSC(M, L) receiver performance in a generalized fading channel are still very limited, mainly due to the mathematical difficulty encountered while computing the first-order statistics of a linear sum of ordered random variables. This paper provides a partial solution to the problem on hand by deriving relatively simple-to-evaluate expressions for the moment generating function (MGF) of GSC output SNR in a variety of fading environments given that the individual branch SNRs are independent and identically distributed. Moreover, our generic single integral expression for the MGF of GSC output SNR reduces to a closed-form formula if the branch amplitudes follow either Rayleigh or Nakagami-m (positive integer fading index) distribution. An easily programmable recursive solution of the MGF in Nakagami-m channels is also provided. Our expressions hold for any M and L values, and thus facilitate a comprehensive analysis of GSC systems including the average symbol error probability (ASEP) analysis of a broad class of binary and M-ary modulations, average combined SNR and the outage rate of error probability analysis.

Exact error probability expressions for noncoherent M-ary frequency-shift-keying (MFSK) systems that employ postdetection equal-gain diversity over Rayleigh, Rician and Nakagami-m channels are derived using a Laplace derivative formula. Both independent and generically correlated fading cases are considered. For independent fading, closed-form solutions are also derived for both Nakagami-q fading (either with identical or dissimilar fading statistics) and mixed fading cases. Previous results are shown to be specific instances of our general expressions. Additionally, a new concise, derivative formula is obtained for calculating the bit error rate of square-law detected multichannel binary differential phase-shift-keying (BDPSK) signals. All these expressions are applicable in many cases of practical interest and provide accurate predictions of the performance of both binary and M-ary orthogonal signalling over generalized fading channels (with arbitrary fading parameters). Several numerical examples are presented to illustrate the application of the theory, including the investigation into optimal diversity order in energy-sharing communications, characterization of block orthogonal codes with soft-decision decoding (i.e., MFSK may also be viewed as a form of repetition coding) and analysis of MFSK with space (antenna) diversity.

We investigate the spectrum, out-of-band radiation (OBR) and the use of extended guard interval (EGI) to reduce the out-of-band radiation of an OFDM signal when passing through different nonlinear devices. Spectra of the OFDM signal with different EGI lengths after passing through nonlinear devices are obtained through computer simulations. Mathematical expressions for the power spectral density of a conventional OFDM signal and an OFDM signal with different EGI lengths are also presented. Theoretical and simulated results are compared. Although the EGI reduces the OBR, this reduction is not significant in some cases. The effect of EGI on the OBR of an OFDM signal differs for different nonlinear devices. The EGI is also not capable of reducing the OBR caused by excessive clipping of the OFDM signal. Finally, it is also found that the length of the EGI does not have a considerable effect on the amount of OBR reduced when passing through a nonlinear device.

We investigate the peak-to-average power ratio (PAR) and its effects on the performance of Zipper-VDSL systems. The spectrum and the out of band power when passing through a nonlinear device is also investigated. We further evaluate the performance with a recently proposed PAR reduction technique for orthogonal frequency division multiplexing (OFDM). PAR reduction of Zipper-VDSL minimizes the distortion and out of band power of the signal, reducing the dynamic range of transceiver components and near-end crosstalk (NEXT).

Orthogonal frequency division multiplexing (OFDM) is sensitive to the carrier frequency offset (CFO). We introduce the peak interference-to-carrier ratio (PICR) to measure the resulting intercarrier interference (ICI). This paper shows that the PICR can be reduced by coding to select only those messages with low PICR as valid codewords. While explicit constructions of higher-rate, ICI-suppressing codes are rather difficult, we propose two new codes that map data onto three and four adjacent subcarriers. We also propose a new ICI reduction scheme, called tone reservation, that inserts optimized pilot tones in the data frame. Computing these pilot tones at the transmitter is a simple optimization technique.

Orthogonal frequency division multiplexing (OFDM) is sensitive to the carrier frequency offset (CFO) and phase noise, which destroys orthogonality and causes intercarrier interference (ICI). Previously, two methods were available for the analysis of the resultant degradation in performance. Firstly, the statistical average of the ICI could be used as a performance measure. Secondly, the bit error rate (BER) could be approximated by assuming the ICI to be Gaussian. However, a more precise analysis of the performance (i.e. BER or SER) degradation is desirable. We propose a precise numerical technique for calculating the effect of the CFO and phase noise on the BER or symbol error rate (SER) in an OFDM system. In particular, closed form expressions for SER are derived using a Beaulieu (1990) series.

The peak-to-average power ratio (PAR) of an orthogonal frequency division multiplexing (OFDM) signal can be substantially larger than that of a single carrier system. Partial transmit sequence (PTS) combining can improve the PAR statistics of an OFDM signal. For PTS, the search complexity increases exponentially with the number of subblocks. We present a new algorithm for computing the phase factors that achieves better performance than the exhaustive binary search approach. We also investigate the effects of non-linear amplifiers on the performance of the new algorithm, including the power spectral density and in-band distortion.

This paper derives new closed-form formulas for the error probabilities of single and multichannel communications in Rayleigh and Nakagami-m (1960) fading. Closed-form solutions to three generic trigonometric integrals are presented as part of the main result, providing a unified method for the derivation of exact closed-form average symbol-error probability expressions for binary and M-ary signals with L independent channel diversity reception. Both selection-diversity and maximal-ratio combining (MRC) techniques are considered. The results are generally applicable for arbitrary two-dimensional signal constellations that have polygonal decision regions operating in a slow Nakagami-m fading environments with positive integer fading severity index. MRC with generically correlated fading is also considered. The new expressions are applicable in many cases of practical interest. The closed-form expressions derived for a single channel reception case can be extended to provide an approximation for the error rates of binary and M-ary signals that employ an equal-gain combining diversity receiver.

Two unified expressions for computing the refined outage criterion (which considers the receiver noise) in cellular mobile radio systems are derived using the Laplace and Fourier inversion formulas. Since these expressions do not impose any restrictions on the signal statistics while being easy to program, they provide a powerful tool for outage analysis over generalized fading channels. We also assess compatibility and applicability of previously published approaches that treat noise as cochannel interference (noise-limited model) or consider a minimum detectable receiver signal threshold and receiver noise. The outage probability in an interference-limited case can be evaluated directly by setting the minimum power threshold to zero. The analysis of correlated interferers is presented. Results are also developed for a random number of interferers. Several new closed-form expressions for the outage probability are also derived. Some previous studies have suggested approximating Rician desired signal statistics by a Nakagami-m (1960) model (with positive integer fading severity index) to circumvent the difficulty in evaluating the outage in Rician fading. The suitability of this approximation is examined by comparing the outage performance under these two fading conditions. Surprisingly, some basic results for Nakagami-m channel have been overlooked, which has led to misleadingly optimistic results with the Nakagami-m approximation model. However, similar approximation for the interferer signals is valid.

Orthogonal frequency-division multiplexing (OFDM) is sensitive to the carrier frequency offset (CFO), which destroys orthogonality and causes intercarrier interference (ICI), Previously, two methods were available for the analysis of the resultant degradation in performance. Firstly, the statistical average of the ICI could be used as a performance measure. Secondly, the bit error rate (BER) caused by CFO could be approximated by assuming the ICI to be Gaussian. However, a more precise analysis of the performance (i.e., BER or SER) degradation is desirable. In this letter, we propose a precise numerical technique for calculating the effect of the CFO on the BER or symbol error in an OFDM system. The subcarriers can be modulated with binary phase shift keying (BPSK), quaternary phase shift keying (QPSK), or 16-ary quadrature amplitude modulation (16-QAM), used in many OFDM applications. The BPSK case is solved using a series due to Beaulieu (1990). For the QPSK and 16-QAM cases, we use an infinite series expression for the error function in order to express the average probability of error in terms of the two-dimensional characteristic function of the ICI.

The moment generating function (MGF) of the signal power at the output of dual-branch switch-and-stay selection diversity (SSD) combiners is derived. The first-order derivative of the MGF with respect to the switching threshold is also derived. These expressions are obtained for the general case of correlated fading and nonidentical diversity branches, and hold for any common fading distributions (e.g., Rayleigh, Nakagami-m, Rician, Nakagami-q). The MGF yields the performance (bit or symbol error probability) of a broad class of coherent, differentially coherent and noncoherent digital modulation formats with SSD reception. The optimum switching threshold (in a minimum error rate sense) is obtained by solving a nonlinear equation which is formed by using the first-order derivative of the MGF. This nonlinear equation can be simplified for several special cases. For independent and identically distributed diversity branches, the optimal switching threshold in closed form is derived for three generic forms of the conditional error probability. For correlated Rayleigh or Nakagami-m fading with identical branches, the optimal switching threshold in closed form is derived for the noncoherent binary modulation formats. We show previously published results as special cases of our unified expression. Selected numerical examples are presented and discussed.

Abstract The Cauchy–Schwarz bounding technique is used to derive useful bounds on the generalized Marcum Q‐function and its complement. Three new exponential‐type bounds on QM (α, β) are derived, and these are found to be tight and useful for a number of applications of interest. One such example is the derivation of an upper bound on the average symbol error rate probability for noncoherent and differentially coherent communication systems over generalized fading channels. It is shown that these exponential‐type bounds are considerably tighter than the Chernoff bound (Rappaport SS. IEEE Trans. on Information Theory 1971; 17: 497–498) counterpart. Numerical results also reveal that the tightness of one of the exponential‐type bounds is comparable to the bound obtained in Simon and Alouini (IEEE Trans. on Communications 2000: 359–366), while another is found to be superior than that obtained in Simon and Alouini over a wide range of arguments. Copyright © 2001 John Wiley & Sons, Ltd.

Polynomial cancellation coded orthogonal frequency division multiplexing (PCC-OFDM) with overlapping symbol periods is a modulation technique which overcomes many of the disadvantages of OFDM. PCC-OFDM is much less sensitive to frequency offset and Doppler spread than OFDM. Only the length of the equalizer used limits the delay spread that can be tolerated in a PCC-OFDM system. In this paper expressions are calculated for the intercarrier interference (ICI) and intersymbol interference (ISI) caused by timing errors in PCC-OFDM. Results are presented for simulations of PCC-OFDM in channels subject to frequency error and multipath. It is shown that good performance can be achieved using equalizers of only moderate complexity.

An interleaver based technique for improving the peak-to-average power ratio (PAP) of an orthogonal frequency division multiplexing (OFDM) signal is presented. For this technique, K-1 random interleavers are used to produce K-1 permuted sequences from the same information sequence. PAPs of the permuted sequences and the original information sequence are then computed using K oversampled FFTs (OFFTs). The sequence with the lowest PAP is chosen for transmission. The complementary cumulative density function (CCDF), of PAP of an interleaved OFDM signal is observed. Results show that for 256 subcarriers and QPSK data symbols, even with K=2, the 0.1% CCDF is reduced by 1.3 dB and with K=4, is reduced by 2 dB. The 0.1% CCDF can be reduced by 3 dB and 0.01% CCDF by 4 dB at a cost of 16 OFFTs and a data rate loss of less than 0.8% with K-16. Further statistical improvement for the PAP is obtained by combining this approach and the partial transmit sequence (PTS) approach. This paper also proposes an adaptive approach to reduce the complexity of the interleaving technique.

This paper presents a general method for calculating the average error rates and outage performance of a broad class of coherent, differentially coherent and noncoherent communication systems with/without diversity reception in a myriad of fading environments. Unlike the moment generating function (MGF) technique, the proposed characteristic function (CHF) method based on Parseval's theorem enables us to unify the average error rate analysis of different modulation formats and all commonly used predetection diversity techniques (i.e., maximal-ratio combining (MR), equal-gain combining (EG), selection diversity (SD), switched diversity (SW) and hybrid diversity systems) in a single common framework. The CHF method also lends itself to the averaging of the conditional error probability (CEP) involving the complementary incomplete Gamma function and the confluent hypergeometric function over fading amplitudes, which heretofore resisted to a simple form. As an aside, we show previous results as special instances of our unified framework.

The paper examines the impact of Gaussian distributed weighting errors (in the channel gain estimates used for coherent combination) on the statistics of the output of hybrid selection/maximal-ratio (SC/MRC) receiver as well as the degradation of the average symbol error rate (ASER) performance from the ideal case. New expressions for the probability density function (PDF), cumulative distribution function (CDF) and moment generating function (MGF) of the coherent hybrid SC/MRC combiner output signal-to-noise ratio (SNR) are derived. The MGF is then used to derive exact closed form ASER formulas for binary and M-ary modulations employing a nonideal hybrid SC/MRC receiver in Rayleigh fading. Results for both SC and MRC are obtained as limiting cases. The effect of the weighting errors on the outage rate of error probability and the average combined SNR are also investigated. These analytical results provide some insights into the trade-off between diversity gain and combination losses with the increasing order of diversity branches in an energy-sharing communication system.

The efficacy of an hybrid M/L-SC/MRC receiver structure (also known as generalized selection combining) in a variety of fading environments is analyzed by deriving considerably simpler expressions for the statistics (i.e., moment generating function (MGF) and cumulative distribution function (CDF)) of the combiner output signal-to-noise ratio (SNR) on Nakagami-m channels with arbitrary parameters. Different from previous studies, these results hold for arbitrary orders of M and L. As well as for any real values of fading severity index m/spl ges/0.5. A simple procedure for deriving an exact closed-form expression for the MGF of SNR when the fading index assumes a positive integer m value is also outlined. These MGFs are then used to derive the average symbol error probability (ASEP) for a broad class of binary and M-ary modulations employing coherent SC/MRC receiver. Analytical expressions for computing the outage rate of error probability and the average combined output SNR are also derived. Finally, computationally efficient but approximate solutions for the MGF of SNR are presented.

Performance analysis of equal-gain combining (EGC) diversity systems is notoriously difficult only more so given that the closed-form probability density function (PDF) of the EGC output is only available for dual-diversity combining in Rayleigh fading. A powerful frequency-domain approach is therefore developed in which the average error-rate integral is transformed into the frequency domain, using Parseval's theorem. Such a transformation eliminates the need for computing (or approximating) the EGC output PDF (which is unknown), but instead requires the knowledge of the corresponding characteristic function (which is readily available). The frequency-domain method also circumvents the need to perform multiple-fold convolution integral operations, usually encountered in the calculation of the PDF of the sum of the received signal amplitudes. We then derive integral expressions for the average symbol-error rate of an arbitrary two-dimensional signaling scheme, with EGC reception in Rayleigh, Rician, Nakagami-m (1960), and Nakagami-q fading channels. For practically important cases of second- and third-order diversity systems in Nakagami fading, both coherent and noncoherent detection methods for binary signaling are analyzed using the Appell hypergeometric function. A number of closed-form solutions are derived in which the results put forward by Zhang (see ibid., vol.45, p.270-73, 1997) are shown to be special cases.

A new, infinite series representation for the error function is developed. It is especially suitable for computing erfc(x) for large x. For instance, for any x/spl ges/4, the error function can be evaluated with a relative error less than 10/sup -10/ by using only eight terms. Similarly, the error function can be evaluated with a relative error less than 8/spl times/10/sup -7/ for any x/spl ges/2 using just six terms. An analytical bound is derived to show that the total error due to series truncation and undersampling rapidly decreases as x increases. Comparisons with two other series are provided.

A frequent problem in digital communications is the computation of the probability density function (PDF) and cumulative distribution function (CDF), given the characteristic function (CHF) of a random variable (RV). This problem arises in signal detection, equalizer performance, equal-gain diversity combining, intersymbol interference, and elsewhere. Often, it is impossible to analytically invert the CHF to get the PDF and CDF in closed form. Beaulieu (1990, 1991) has derived an infinite series for the CDF of a sum of RVs that has been widely used. We rederive his series using the Gil-Pelaez (1951) inversion formula and the Poisson sum formula. This derivation has several advantages including both the bridging of the well-known sampling theorem with Beaulieu's series and yielding a simple expression for calculating the truncation error term. It is also shown that the PDF and CDF can be computed directly using a discrete Fourier transform.

New, simple yet very accurate closed-form expressions for calculating the symbol error probability (SER) of multilevel quadrature amplitude modulation (MQAM) in conjunction with L-fold antenna diversity on a Nakagami (1960) fading channel are presented. Both maximal-ratio (MRC) and equal-gain (EGC) predetection diversity combining techniques have been considered. The exact closed-form formula for a MRC diversity system removes the limitations of previous studies in the literature which have been limited to Rayleigh fading. Moreover, an exact analysis of EGC for MQAM has not been reported previously despite its practical interest. The exact SER is expressed as a finite-range integral. Our unified expressions are sufficiently general to handle arbitrary fading parameters as well as dissimilar mean signal strengths across the diversity branches. The generality and computational efficiency of these new formulas render themselves as a powerful tool for SER analysis in different fading conditions.

A unified expression for computing the probability of outage in cellular mobile radio systems is derived. The method handles non-integer Nakagami fading indexes, unequal Rice factors, dissimilar shadowing spreads, unequal transmit powers as well as all the common fading distributions (Rayleigh, Rice, Nakagami-m, Nakagami-q, lognormal-Rice, Suzuki and lognormal-Nakagami-m). The exact outage probability is expressed in terms of a finite-range integral. The integral can also be approximated by a Gauss-Chebychev quadrature (GCQ) formula requiring the knowledge of the moment generating function (MGF) at only a small number of points. An estimate of the remainder term is also derived. This technique lends itself to a powerful tool for outage analysis since it does not impose any restrictions while being easy to program. Some previous studies have suggested approximating Rician desired signal statistics by a Nakagami-m model to circumvent the difficulty in evaluating the outage in Rician fading. We asses the suitability of this approximation by providing a comparison study of the outage performance in these two fading conditions. Surprisingly, some basic results for Nakagami-m channel have been overlooked, which has led to misleadingly optimistic results with the Nakagami-m approximation model.

An exact analytical expression in a simple form for computing the average symbol error rate (SER) of an arbitrary two-dimension signaling format with equal-gain diversity (EGC) receiver is not available in the literature despite its practical and theoretical importance. The principle difficulty is finding a closed-form expression for the probability density function (PDF) of a sum of L (i.e., diversity order) random fading amplitudes. We develop an alternative, direct technique to evaluate the exact performance of EGC diversity systems (expressed in terms of a single or double finite-range integrals) in Rayleigh, Rician and Nakagami fading channels. Our new approach relies on the use of Parseval's theorem to transform the error integral into the frequency domain. Since the Fourier transform of the PDF is the characteristic function (CHF), which is available in this case, our solution is general and exact. The CHF method also circumvents the need to perform an L-fold convolution integral which is usually encountered in the calculation of the PDF of the sum of the received signal amplitudes. Interestingly, we can also get some new closed-form solutions for binary CPSK and CFSK in the Nakagami fading channel for all L/spl les/3. Closed-form formulas for binary DPSK and NCFSK with EGC may also be obtained for L<3.

This paper outlines a unified approach to performance evaluation of a broad class of coherent, differentially coherent and noncoherent digital communication systems, with dual-branch switched diversity (SWC) reception over generalized fading channels. The moment generating function (MGF) of the signal power at the output of the SWC combiner and the first-order derivative of the MGF with respect to the switching threshold are derived. These expressions are obtained for the general case of correlated fading and nonidentical diversity branches, and hold for any common fading distributions (e.g., Rayleigh, Nakagami-m, Rician, Nakagami-q). The optimum switching threshold (in a minimum error rate sense) is obtained by solving a nonlinear equation which is formed by using the first-order derivative of the MGF. This nonlinear equation can be simplified for several special cases: (a) closed-form expressions for the optimal switching threshold are derived for three generic forms of the conditional error probability by assuming independent and identically distributed diversity branches; and (b) a closed-form formula for the optimal switching threshold is derived for the non-coherent binary modulation formats in correlated Rayleigh or Nakagami-m fading with identical fading statistics.

Exact integral expressions are derived for calculating the symbol-error rate (SER) of multilevel quadrature amplitude modulation (MQAM) in conjunction with L-fold antenna diversity on arbitrary Nakagami fading channel. Both maximal-ratio combining (MRC) (in independent and correlated fading) and equal-gain combining (EGC) predetection (in independent fading) diversity techniques have been considered. Exact closed-form SER expressions for two restricted Nakagami fading cases (MRC reception) are also derived. An exact analysis of EGC for MQAM has not been reported previously, despite its practical interest. Remarkably, the exact SER integrals can also be replaced by a finite-series approximation formula. A useful procedure for computing the confluent hypergeometric series is also presented.

This article provides a novel, efficient numerical solution to evaluate the moment generating function of a Suzuki probability density function using the sampling theorem. Applications include outage probability calculations for mobile radio networks in Rayleigh fading and shadowing.

Frequency-offset correction is considered for a HIPERLAN (HIgh-PErformance Radio LAN) system over the indoor radio channel. Since the multipath channel response is not known a priori, a viable frequency-offset estimator should not depend on such knowledge. Such an estimator, using a single sample per symbol, is derived for HIPERLAN. The estimator is shown to approach the Cramer-Rao bound for frequency-offset estimation over a multipath channel. A HIPERLAN system simulation example shows that the performance with an offset of 150 kHz is within 0.5 dB of that of a system with zero frequency offset.

This paper addresses the problem of selecting the optimum training sequence for channel estimation in communication systems over time-dispersive channels. By processing in the frequency domain, a new explicit form of search criterion is found, the gain loss factor (GLF), which minimizes the variance of the estimation error and is easy to compute. Theoretical upper and lower bounds on the GLF are derived. An efficient directed search strategy and optimal sequences up to length 42 are given. These sequences are optimal only for frequency domain estimation, not for time domain estimation.

This paper surveys some of the diversity techniques commonly used in cellular radio and satellite communication systems to mitigate the detrimental effects of signal fading. Subsequently, an analytical technique well suited to numerical analysis is presented for computing the average symbol error probability (SER) of a wide class of coherent, differentially coherent and noncoherent communication systems with microdiversity reception under a myriad of fading scenarios. We restrict our analysis to a predetection maximal-ratio combining (MRC) scheme, although this method applies to other diversity combining techniques as well. Our novel derivation relies upon the properties of the moment generating function (MGF) of the fading channels, the use of an alternative exponential form of the complementary error function, and the application of Gauss-Chebychev quadrature (GCQ) rules. The closed-form expressions obtained are sufficiently general to allow for arbitrary fading parameters as well as dissimilar mean signal strengths across the diversity branches. Moreover, this method is computationally stable and approximates the true value of average SER within any degree of accuracy.

An analytic technique is presented for computing the performance of trellis coded q-ary PSK in Rayleigh fading. A contour-integral expression for the pairwise error probability (PEP) is used to define a transfer function, enabling the union bound to be evaluated exactly for the ideal CSI (channel state information) case and imperfect-CSI case. The case of TCM in Nakagami fading and dual diversity reception is also analysed.

A fast computation method for the tap weights of a linear equaliser is developed. By approximating the channel autocorrelation matrix, which has a Toeplitz structure, by a circulant matrix, the tap weights can be solved via discrete fourier transform (DFT) techniques. For an equaliser with N taps, the approximate tap weights approach the exact tap weights as N/spl rarr//spl infin/. Excess mean-square error and bit error rate (BER) degradation caused by the approximate tap weights are computed for a representative channel.

To reduce the effects of intersymbol interference resulting from the dispersive nature of the indoor radio channel most HIPERLAN receivers will incorporate an adaptive equaliser. The computational complexity of several equaliser algorithms is estimated. The effect of frequency offset between the transmitter and receiver on the performance of such an equaliser is investigated. By employing a decision feedback equaliser incorporating a second order phase locked loop, the effect of both the intersymbol interference and frequency offset can be significantly reduced. Using such a technique, the packet error ratio (PER) of a HIPERLAN radio link in a multipath channel is found by simulation.

An analytical technique is presented for computing the exact union bound on the average bit error probability of trellis coded modulation schemes over Rayleigh, Rician, or shadowed Rician-fading channels. To this end, an integral expression is derived for the pairwise error event probability (PEP). Existing bounds can be obtained as special cases of this expression. It turns out that a Gauss-Chebyshev quadrature rule offers excellent accuracy for this integral. By extension, the exact union bound (i.e., the weighted sum of an exact PEPs of a code) can readily be evaluated. This method has the same complexity as the union-Chernoff bound, and a few examples are given to show its application.

Bit error probability evaluation of trellis-coded modulation (TCM) over fading channels is rather complicated, and the analytical results are limited to loose upper bounds leaving the system designer with the only option of simulation. Cavers and Ho (see IEEE Trans. Commun., vol.40, no.1, p.74-83, 1992) have derived an exact analytical expression for pairwise error-event probability. In this paper, using a different approach, the authors give an alternative method to compute the exact pairwise error event probability of TCM schemes in Rayleigh or Rician fading channels with perfect side information. For example, for a particular TCM scheme, they find the asymptotic difference between the exact and the upper bound of the pairwise error event probability to be 2.68 dB. As it turns out, for Rayleigh fading, the exact pairwise error probability can be calculated in closed-form. For the case of Rician fading, however, a closed-form expression is apparently impossible to obtain. It is observed that an accurate estimate of the bit error probability can be obtained by evaluating a sufficient number of pairwise error-event probabilities. Hence, this approach is a computationally feasible alternative to the simulation.>