Consider a single-input multiple-output (SIMO) 1 ×Nsystem in independent and identically distributed (i.i.d.) flat fading with fully noncoherent detection ofL-level one-sided amplitude-shift keying (ASK) symbols using an energy detection receiver. Let Фi(·) denote the conditional cumulative distribution function (c.d.f.) of the normalized received signal energy, conditioned on theith ASK symbol, that is, theith conditional c.d.f., fori= 1, . . . ,L. For this SIMO system, the symbol error probability (SEP) is analytically represented in terms of theLconditional c.d.f.s and theL− 1 detection thresholds. For the particular situation of i.i.d. Nakagami-mfading withm> 1, an analytical expression for theith conditional c.d.f. is obtained. In the cases of finitemandm→ ∞, high signal-to-noise ratio (SNR) approximations of the detection thresholds are derived. Under the high SNR condition with first level zero, the approximate optimal amplitude levels that minimize the SEP subject to a total energy constraint are shown to be in geometric progression for finitemand in arithmetic progression form→ ∞. Furthermore, for i.i.d. Nakagami-mfading withNmas a positive integer, a closed form expression for theith conditional c.d.f. is presented. Numerical results show the accuracy of the high SNR approximations.

This paper investigates the optimization of physical layer security (PLS) in intelligent reflecting surface (IRS)-assisted wireless networks under imperfect channel state information (CSI). Traditional PLS techniques often assume perfect CSI, which is difficult to obtain in IRS-assisted systems due to their passive nature and limited signal processing capabilities. To address this challenge, we derive, under the imperfect CSI condition, a novel expression for the secrecy outage probability (SOP) and propose an optimization framework to minimize the SOP by jointly designing the beamforming vector and the IRS phase-shift matrix. The proposed approach employs alternating optimization, utilizing the generalized Rayleigh quotient for beamforming and the generalized Dinkelbach algorithm for phase-shift adjustments. Furthermore, we derive a power scaling law that reveals significant energy efficiency gains with an increasing number of IRS elements. Simulation results validate the effectiveness of the proposed framework, demonstrating substantial improvements in secrecy performance over baseline schemes. This work underscores the potential of IRS-assisted systems in enhancing secure communications for future wireless networks.

Terrestrial free-space optical (FSO) communication systems, while designed to operate on large unlicensed optical bandwidths, are fundamentally power-constrained due to stringent eye-safety regulations. Moreover, channel fluctuations inherent to terrestrial FSO links further reduce the received optical power. Consequently, the achievable signal-to-noise ratio (SNR) per hertz could become limited, especially for future terrestrial FSO systems based on coherent communications. This necessitates the development of efficient and adaptive communication strategies at both the optical transmitter and receiver. However, a comprehensive assessment of adaptive coherent terrestrial FSO systems remains largely unexplored in the existing literature. This paper investigates terrestrial FSO communication links employing adaptive coherent transmission and synchronous heterodyne detection-based reception operating in the shot-noise-limited regime. Specifically, we propose a novel exact closed-form expression for the average spectral efficiency limit of coherent FSO communication systems with optimal adaptive signaling over gamma-gamma turbulence channels with pointing errors. More importantly, we provide a detailed assessment of the impact of turbulence and pointing error impairments on the coherent FSO system performance, revealing several novel and counterintuitive insights. Extensive numerical results help elucidate the intricacies of analyzing these terrestrial FSO systems and clarify a few misconceptions alluded to in recent related literature.

For a single-antenna fluid antenna system (FAS) with N fixed antenna locations or ports, analytical expressions for the error performance of four types of signaling schemes for digitally modulated data transmission and reception are found. The signaling schemes are: (1) M-ary phase-shift keying with coherent reception, (2) two-sided M-ary amplitude-shift keying (M-ASK) with coherent reception, (3) one-sided M-ASK with noncoherent reception, and (4) one-sided M-ASK with partially noncoherent reception. The N ports are evenly distributed on a line. The FAS error performance is analyzed when the ports are subject to identically distributed Rayleigh fading with uniform correlation between the channels at the ports. A series expression for the characteristic function (c.f.) of the random complex channel coefficient magnitude squared of the chosen FAS port, in terms of a series of elementary c.f.s, where each elementary c.f. is the c.f. of a sum of N independent gamma random variables, is obtained. Series expressions for the symbol error probabilities as weighted sums of functions in closed form are presented. Closed form asymptotic high signal-to-noise ratio results for error performance are also derived. Numerical are presented to show the variation of the error performance with respect to the spacing between the first and Nth ports and N.

Efficient bandwidth utilization is essential for nextgeneration cellular networks such as 5G -Advanced and 6G, to support diverse services with varying quality-of-service (QoS) requirements. Grant-free (GF) communication, introduced in 5G NR, enables unscheduled data transmission, significantly reducing latency. However, it often leads to inefficiencies, such as underutilized GF bandwidth in scenarios involving sporadic status messages. In contrast, grant-based (GB) communication, which relies on scheduled transmissions, offers greater reliability. This paper proposes a novel deep reinforcement learning (DRL)-based mechanism to strategically offload GB traffic to underutilized GF resources. Termed “soft access class barring” (SACB), the approach dynamically offloads traffic from GB to GF bandwidth to optimize spectrum utilization while maintaining QoS, without requiring complex bandwidth reconfigurations. Simulation results demonstrate the potential of SACB to address challenges in hybrid traffic management, paving the way for its adoption in future network standards.

This paper presents an in-depth evaluation of a dualhop hybrid radio frequency-terahertz wireless communication system that enables end-to-end connectivity from a stable source to a hovering drone. Specifically, we derive exact analytical expressions for the probability density function, cumulative distribution function, moment generating function, and n-th moment of the end-to-end signal-to-noise ratio of the considered system utilizing the decode-and-forward protocol. We also obtain closed-form expressions, along with asymptotic expressions, for crucial performance metrics, including outage probability and average bit error rate. We also determine the diversity order, present a precise upper bound on the channel capacity, and derive a closed-form expression for the ergodic mutual information of the M-QAM constellation. Furthermore, critical insights are drawn by analyzing the impact of different design parameters on the system performance.

The data-oriented communications approach was initially introduced to develop novel transmission strategies for individual data sessions by accounting for instantaneous channel conditions under latency constraints. However, existing studies are limited to scenarios where channel state information (CSI) is either fully or partially available at the receiver, which may be impractical for short-packet transmissions. In this context, the present work focuses on analyzing the delay-outage rate (DOR), a data-oriented performance metric, under the noncoherent communications paradigm, where accurate CSI is not required. To this end, we first derive and calculate the DOR metric, which is then used to define transmission as well as receiver design requirements based on data and bandwidth parameters. Beyond emphasizing the significance of the new data-oriented DOR metric, the results provide valuable insights for designing and facilitating delay-sensitive and highly reliable noncoherent data transmission in future networks.

This paper quantifies and evaluates the performance of a unique system model that offers end-to-end connectivity from a stable source to flying drones. Specifically, we examine a relay-assisted double-hop hybrid radio frequency (RF)-terahertz (THz) uplink wireless communication system. Exact analytical expressions of the cumulative distribution function, probability density function, characteristic function, and nth moment of the end-to-end signal-to-noise ratio of the system under consideration are obtained in the form of univariate Fox’s H-function (UFH). Rayleigh fading is employed to model the RF link, while the joint effect of the deterministic path loss, fluctuating two-ray fading, and recently introduced alignment error model is utilized to characterize the THz transmission link with fixed-gain amplify-and-forward relaying. Utilizing these statistical expressions, crucial performance indicators like outage probability (OP) and average bit error rate (ABER) are calculated in terms of the UFH. For a comprehensive insight into the system performances, we conduct the asymptotic analysis for both the OP and ABER and determine the diversity order of the system. Furthermore, a closely estimated upper bound on the average channel capacity (ACC) is provided. The impact of various design parameters is examined on the system performances in terms of the OP, ABER, and ACC.

Massive machine-type communication (mMTC) has been identified as a key service type in fifth-generation new radio (5G NR) communication systems. The third-generation partnership (3GPP) project, starting with 5G, has introduced grant-free (GF) or configured grant (CG) scheduling for uplink traffic with small data packets to reduce signaling and latency overheads as compared to prevalent grant-based (GB) schemes. However, when heterogeneous MTC devices compete for pre-configured, shared GF resources, the access results in collisions. No standardized methods exist for ensuring priority-based access in the shared GF scheduling scheme. In this work, we introduce novel methods which utilize both heuristic and multi-objective deep reinforcement learning (DRL) techniques for priority-enabled GF access. The proposed methods adaptively partition GF bandwidth resources per allocation interval for scheduling configured grants to heterogeneous MTC device groups in a way which improves their probability of successful transmission, thereby resulting in a lower average age of information and packet drop rate and simultaneously ensuring fairness. Through extensive simulations set in the context of cyber-physical systems (CPS) with diverse quality-of-service (QoS) requirements across various 5G NR numerology schemes, we exemplify that our proposed approach provides significantly better performance and resource utilization than conventional schemes.

A single-input multiple-output system in flat Rayleigh fading, with pilot-symbol-aided least squares channel norm estimate based energy detection of one-sided multi-level amplitude-shift keying (ASK) data symbols, is considered. A suboptimum minimum distance (SMD) receiver is presented; it minimizes, over all ASK data symbols, the square of the difference between the received signal vector norm to the power of a real-valued non-zero parameter$\alpha $and the ASK-data-symbol-scaled channel norm estimate to the power of$\alpha $. For the SMD receiver, a closed form expression for the exact SEP is derived using a characteristic function approach. Furthermore, analytical methods of optimizing the ASK levels by SEP minimization, with high signal-to-noise ratio, large number of receive diversity branches, and one pilot symbol, are obtained for$\alpha \lt 2$and$\alpha =2$. Numerical results illustrate the performance variation of this receiver with respect to system parameters.

In reconfigurable intelligent surface (RIS) aided communication implementing space-shift keying at the transmitter for index modulation, the RIS is proposed to perform the dual function of selecting the phases of the reflecting elements optimally according to the phases of the channel gains, and acting as a modulator by transmitting$M$-ary phase-shift keying (PSK) modulated symbols via reflection phase modulation. The target antenna at the receiver is chosen by utilizing the optimal maximum likelihood (ML) detection rule and a hardware- and energy-efficient greedy detector, which performs detection based on the maximum received energy. For these detection scenarios, closed-form expressions for the probability of erroneous detection (PED) of the target antenna are derived, considering Nakagami-$m$channel fading. Numerical results supporting the analytical framework show the role of the rotation of the$M$-PSKconstellation to improve the reliability of the system. In particular,$\pi/M{-}$rotated$M$-PSK constellation is optimal for the greedy detector, whereas the ML detector is not dependent on such rotation to yield minimum PED.

The transmission range and the quality of service of terahertz ($\mathbf{T H z}$) wireless communications are constrained by the significant effects of factors such as short-term fading, path loss, and alignment errors. Cooperative relaying is a viable technique that can be used to improve link reliability and transmission range. In this study, we analyze the bit error performance of a dual-hop mixed radio frequency (RF)-THz wireless system with the fixed-gain amplify-and-forward protocol. To model the RF link between the stable source and the fluctuating relay, we consider the effect of Rayleigh fading and path loss. Modeling of the THz link between the fluctuating relay and the destination (relay and destination are considered as unstable drones, equipped with uniform standard $N_{a} \times N_{a} \mathbf{T H z}$ high directional antenna arrays fluctuating uniformly in yaw and pitch directions) is done considering the combined effect of $\alpha-\mu$ fading, path loss, and alignment errors (the recently introduced alignment error model is employed). To have a better insight into the system performance, we provide an asymptotic analysis and calculate the diversity order of the system based on system and channel parameters. Furthermore, we examine the influence of various design parameters by analyzing the average bit error rate and diversity order. The analytical results are verified by computer simulations, averaged over $10^{7}$ channel realizations.

Energy detection for single-input multiple-output (SIMO) systems using perfect estimates of the channel norm has been shown to exhibit the same diversity order as that of a coherent system. In this work, we analyze the performance of energy detection for SIMO when only least squares estimates of the channel norm are available. The configuration of on-off keying in a flat Rayleigh fading environment is considered. A closed form expression for the approximate conditional symbol error probability (SEP), conditioned on the normalized channel norm and its estimate, is derived. A Gaussian approximation for the received signal energy is applied in the derivation. Furthermore, a closed form approximation of the SEP at high signal-to-noise ratio is obtained. Numerical results are presented to show SEP variation with system parameters and comparison of error performance with that of fully noncoherent energy detection.

In this paper, we design a double-hop relay-supported mixed RF-THz wireless link utilizing the fixed-gain amplify-and-forward protocol and the decode-and-forward protocol with static source and dynamic relay and destination (relay and destination are taken as unstable drones fluctuating uniformly in yaw and pitch directions). We consider the joint effect of Rayleigh fading and path-loss to model the RF link, and the combined effect of α−µ fading, path-loss, and alignment errors to model the THz transmission link. Precise closed-form analytical expressions for the cumulative distribution function, the probability density function, the characteristic function, and the n-th moment of the end-to-end signal-to-noise ratio of the considered system are obtained in terms of the univariate Fox’s H-function (UFH). Utilizing these expressions, closed-form analytical expressions for the outage probability (OP), average bit error rate (ABER), and average channel capacity (ACC) are obtained in terms of the UFH. To have a better insight into the system performances, we provide an asymptotic analysis for OP and calculate the diversity order of the system in terms of the system and channel parameters. Moreover, the impact of different system and channel parameters on the OP, ABER, and ACC is analyzed.

Semantic communication (SC) aims to convey the meaning of data instead of focusing on its bit-by-bit reconstruction. SC finds applications in beyond 5G and 6G networks for artificial intelligence-empowered multimedia content delivery. In this paper, we propose a novel semantic-aided autoencoder-based image transmission system that leverages semantic information in the form of the segmentation map of an image. We demonstrate up to 23% and 18% improvement (in terms of mean square error and peak signal-to-noise ratio, respectively) in the quality of the received image with only 2% extra bandwidth over a traditional autoencoder-based image transmission system. The study also explores channel coding strategies for our proposed system. We focus on the intrinsically robust nature of semantic data, as compared to traditional data, to design low-density parity check code, Hamming code, and polar code-based unequal error protection (UEP) schemes. Comparative evaluations between UEP and equal error protection schemes show that while both approaches yield similar performance, UEP schemes are more efficient.

For anNt-inputNr-output system, noncoherent reception of spatially multiplexed one-sidedL-level amplitude-shift keying symbols transmitted over a flat Rayleigh fading channel, with energy detection, is considered. The symbol vector is passed through anNt×Ntdeterministic precoder matrix. Two precoders are presented:diagonal, having positive diagonal elements in geometric progression (GP);rank-one, having positive row elements in GP. Each symbol vector is transformed into a precoded scalar. For a one-to-one correspondence between integers 0, 1,...,LNt- 1 and precoded scalars, a sufficient condition relating the precoder GP ratio ρ to the amplitude levels is derived for each precoder. To ease the difficulty of computing the exact symbol vector error probability (SVEP) for largeNr, a Gaussian approximation of the received signal energy is made and a closed form expression for a largeNrSVEP approximation is derived. With first level zero, the cases of: levels in arithmetic progression, non-zero levels in GP with amplitude ratio ϵ, are considered. Parameters ρ and ϵ are chosen to minimize the SVEP saturation value (approached at high signal-to-noise ratio). Furthermore, symbol-vector-dependent scale factors are introduced for error performance enhancement. Visible light communication and sensor network are two practical application scenarios for this work.

This paper investigates the information-theoretic security of multi-particle diffusive molecular timing (DMT) channels for noise-limited and interference-limited scenarios. By utilizing a channel capacity upper bound expression, we obtain the secrecy outage probability (SOP), average secrecy outage rate (ASOR), and average secrecy outage duration (ASOD) expressions when the number of molecules arriving at Eve from Alice and Interferer follows Gaussian distribution. Subsequently, the effect of various channel parameters, such as Lévy noise parameter, molecular degradation, and molecular correlation on various secrecy metrics, is studied for both scenarios. In the noise-limited system, increasing molecular degradation leads to secrecy compromisation, with an increase in SOP and ASOD and a simultaneous decrease in ASOR.We also observe a significant improvement in the system’s secrecy, especially in terms of ASOR, on increasing the Lévy noise parameter. Concurrently, we analyze the channel parameter’s effect on the secrecy of the interference-limited scenario. From the ASOR and ASOD perspectives, we find that with increasing molecular degradation and correlation, the information-theoretic security of the system increases. However, increasing the Lévy noise parameter negatively impacts the system’s secrecy. Finally, extending our analysis to a three-dimensional environment reveals that additional dimensions lead to secrecy deterioration for the noise-limited and interference-limited cases.

This paper studies intelligent reflecting surface (IRS)-assisted free space optical (FSO) quantum communication systems. An IRS can relax the requirement of a line-of-sight (LoS) link between Alice and Bob for FSO quantum key distribution (QKD) applications. The IRS focuses the laser beam toward Bob by introducing a phase shift to the incoming incident beam from Alice. Both discrete variable QKD (DV-QKD) and continuous variable QKD (CV-QKD) protocols for IRS-assisted QKD systems are studied. For DV-QKD, we characterize the average quantum bit error rate (QBER) and the achievable secret key rate (SKR) under a log-normal fading turbulence model. For CV-QKD, we present the ultimate quantum information-theoretic bounds for the SKR and entanglement distribution rates. We also characterize the achievable SKR of a practical CV-QKD protocol implemented using Gaussian coherent states. Our results reveal that Alice and Bob can generate a quantum secure key even if the LoS link between them is blocked by utilizing the IRS. Furthermore, with a quadratic phase shift profile, the IRS-assisted link achieves a higher SKR as compared to the direct LoS link and a relay-assisted link for large transmission distances.

A challenge of ambient backscatter communication (AmBC) systems is signal recovery because the transmitted information bits are embedded in the ambient RF signals and these are unknown and uncontrollable. To meet this challenge, averaging-based energy detectors are typically used but consequently the data rate is low and there is an error floor. Here we propose a new detection strategy based on the ratio between signals received from a multiple-antenna Reader. The advantage of using the ratio is that ambient RF signals are removed directly from the embedded signals without averaging and hence it can increase data rates and avoid the error floor. Different from the original ratio detector that uses the magnitude ratio of the signals between two Reader antennas, in our proposed approach, we utilize the complex ratio so that phase information is preserved and propose an accurate linear channel model approximation. This allows the application of existing linear detection techniques from which we can obtain a minimum distance detector and closed-form expressions for bit error rate (BER). Methods for the estimation of channel state information (CSI) are also provided. In addition, coding and interleaving are also included to further enhance the BER. The results are also general, allowing any number of Reader antennas to be utilized in the approach. Numerical results demonstrate the proposed approach performs better than approaches based on energy detection and the original ratio detectors.

Multi-level signaling for a single-input multiple-output system over a Rayleigh fading channel with noncoherent detection is considered. The decision rule for the optimum noncoherent receiver, that has features of both noncoherent amplitude-shift keying (ASK) and noncoherent frequency-shift keying (FSK) receivers, is derived. Using a characteristic function approach, a closed form expression for the union bound on the symbol error probability (SEP) is obtained; this serves as an approximation for the SEP under the condition of high signal-to-noise ratio (SNR). A new M-ary signaling scheme, termed amplitude-frequency keying (AFK), which uses$M_{\!a}$amplitude levels and$N_{\!f}$orthogonal tones such that$M=M_{\!a}^{N_{\!f}}$, is presented, and its diversity order as well as a closed form high SNR approximation for its SEP is obtained. The advantages of AFK over ASK and FSK schemes are shown through numerical results.

Ensuring security in terahertz (THz)-based communications is the prime objective in 6G-based systems. This paper investigates the information-theoretic security of a THz-based communication system over fluctuating two-ray (FTR) fading. We analyze the system from a partial secrecy regime and utilize fractional equivocation to obtain closed-form expressions for the generalized secrecy outage probability (GSOP), the average fractional equivocation (AFE), and the average information leakage rate (AILR) metrics. Further, the effect of fading parameters, such as the fading severity index, the average power ratio factor, and the dominant waves similarity index, on the secrecy metrics are also analyzed. Numerical results show that with increasing average power ratio factor, the system’s secrecy is compromised from the AFE and AILR perspectives, whereas from the GSOP perspective, increasing the average power ratio factor results in secrecy improvement. Concurrently, degradation in the system’s secrecy in terms of the GSOP is observed for increasing similarity index and fractional equivocation values. However, from AFE and AILR metrics perspective, increasing the similarity index results in secrecy improvement. Finally, the confidential information rate effect on the system’s secrecy is also analyzed. Increasing the confidential information rate leads to secrecy compromisation, as observed by increasing GSOP and AILR and decreasing AFE.

Abstract This paper focuses on symbol detection for a multi‐user single‐input multiple‐output (MU‐SIMO) uplink using supervised machine learning techniques. An extreme learning machine (ELM) is chosen as the equalizer at the receiver end due to its super‐fast learning ability and minimum training error. To tune the parameters, a pilot based online training for an ELM network is proposed, and those parameters are further used to detect the unknown transmitted symbols. Conventionally, the channel matrix is estimated using known pilot symbols explicitly and then the transmitted symbol is recovered using a linear equalizer. Here, instead of directly estimating the channel coefficients, the symbols are detected using an ELM based direct equalizer followed by a hard decision rule. To reduce the pilot requirement of the proposed model, a method is discussed where the channel is estimated using a small number of pilot symbols and the ELM network is trained using a separate training dataset along with the channel estimate. Furthermore, the performance comparison between the proposed ELM based equalizers, linear equalizers, and nonlinear detection techniques is shown.

This paper focuses on precoder optimization of a spatially multiplexed multiple-input multiple-output (MIMO) system with noncoherent reception in a correlated Rayleigh fading environment. We consider a Kronecker product model for the channel correlation with a transmit equicorrelation matrix and a receive correlation matrix which is diagonal. The transmit symbol vector, in which the symbols are taken from two binary constellations$\{0,1\}$and$\{1,-r\}$(with$0\leq r < 1$), is premultiplied by a diagonal precoder matrix with positive precoder parameters. As the average signal-to-noise ratio per diversity branch becomes large, the symbol vector error probability (SVEP) tends to reach saturation. We minimize this saturation value with respect to the precoder parameters and the constellation parameter$r$. It is found from computation that the optimal precoder parameters are approximately in geometric progression for both constellations. By observing the patterns in optimal values obtained from computation, we simplify the optimization problem. This simplification reduces the computational effort required to solve the complex minimization problem without affecting the SVEP significantly. Furthermore, in the case of the constellation$\{1,-r\}$, it is found from computation that as the number of transmit antennas increases, the optimal value of$r$decreases.

Optimum and suboptimum energy detection receivers with diversity reception in Rayleigh fading, that only require limited channel state information based on the channel norm, are introduced. The importance of these channel norm based energy detection (CNBED) receivers is that they achieve the same diversity order as that of a coherent receiver. Furthermore, their performance degradation when compared to a coherent receiver can be made sufficiently low by appropriate choice of parameters. Due to their performance and the low complexity of energy detection, the CNBED techniques have potential applications to internet of things. Analysis of the CNBED receivers is performed for multi-level amplitude-shift keying (ASK). For the optimum receiver, an analytical approximation of the symbol error probability (SEP) as a sum of univariate integrals involving averaging of Gaussian$Q$-functions is derived. For the suboptimum receiver, closed form expressions for the exact SEP and for the approximate SEP under the condition of high signal-to-noise ratio (SNR) are obtained; in addition, using asymptotic approximations, expressions for the optimal ASK transmit levels with high SNR and large number of receive diversity branches, that minimize the SEP subject to an energy constraint, are found. Numerical results are provided to demonstrate the performance of the receivers.

We study the secret key rate (SKR) of a multiple-input multiple-output (MIMO) continuous variable quantum key distribution (CVQKD) system operating at terahertz (THz) frequencies, accounting for the effects of channel estimation. We propose a practical channel estimation scheme for the THz MIMO CVQKD system which is necessary to realize transmit-receive beamforming between Alice and Bob. We characterize the input-output relation between Alice and Bob during the key generation phase, by incorporating the effects of additional noise terms arising due to the channel estimation error and detector noise. Furthermore, we analyze the SKR of the system and study the effect of channel estimation error and overhead. Our simulation results reveal that the SKR may degrade significantly as compared to the SKR upper bound that assumes perfect channel state information, particularly at large transmission distances.

This paper investigates the channel capacity of coherent reception with antenna diversity in Rayleigh fading using asymmetric constellations, such as nonbinary two-sided amplitude-shift keying (ASK) and quadrature amplitude modulation (QAM) with ≥ 8 levels. Due to the asymmetries, the capacity achieving input or a priori probability distributions deviate from uniformity. To perform the investigation, an analytical expression for the mutual information, in terms of an integral over a single variable, between the input (transmitted symbol) and the output (received signal vector comprising signals at receive antennas), is derived. For two-sided ASK, 8-QAM with cross constellation, and 16-QAM, analytical closed form expressions for the high and low signal-to-noise (SNR) approximations, respectively, of the capacity achieving input probability distribution, the capacity, and the relative gain in mutual information (between using the uniform and the capacity achieving input probability distributions) are obtained. Numerical results show that at low SNRs, the use of the capacity achieving nonuniform input probability distribution offers significant advantage over the use of the uniform input probability distribution, while at high SNRs, this advantage is significant only for configurations with one receive antenna. Furthermore, the high and low SNR approximations are shown to be reasonably accurate.

Hovering inaccuracy of unmanned aerial vehicle (UAV) degrades the performance of UAV-aided radio frequency energy transfer (RFET). Such inaccuracy arises due to positioning error and rotational motion of UAV, which lead to localization mismatch (LM) and orientation mismatch (OM). In this paper, antenna array beam steering based UAV hovering inaccuracy mitigation strategy is presented. The antenna beam does not accurately point towards the field sensor node due to rotational motion of the UAV along with pitch, roll, and yaw, which leads to deviation in the elevation angle. An analytical framework is developed to model this deviation, and its variation is estimated using the data collected through an experimental setup. Closed-form expressions of received power at the field node are obtained for the four cases arising from LM and OM. An optimization problem to estimate the optimal system parameters (transmit power, UAV hovering altitude, and antenna steering parameter) is formulated. The problem is proven to be nonconvex. Therefore, an algorithm is proposed to solve this problem. Simulation results demonstrate that the proposed framework significantly mitigates the hovering inaccuracy; compared to reported state-of-the-art the same performance can be achieved with substantially less transmit power.

NarrowBand-Internet of Things (NB-IoT) is a new 3GPP radio access technology designed to provide better coverage for a massive number of low-throughput low-cost devices in delay-tolerant applications with low power consumption. To provide reliable connections with extended coverage, a repetition transmission scheme is introduced to NB-IoT during both Random Access CHannel (RACH) procedure and data transmission procedure. To avoid the difficulty in replacing the battery for IoT devices, the energy harvesting is considered as a promising solution to support energy sustainability in the NB-IoT network. In this work, we analyze RACH success probability in a self-powered NB-IoT network taking into account the repeated preamble transmissions and collisions, where each IoT device with data is active when its battery energy is sufficient to support the transmission. We model the temporal dynamics of the energy level as a birth-death process, derive the energy availability of each IoT device, and examine its dependence on the energy storage capacity and the repetition value. We show that in certain scenarios, the energy availability remains unchanged despite randomness in the energy harvesting. We also derive the exact expression for the RACH success probability of a randomly chosen IoT device under the derived energy availability, which is validated under different repetition values via simulations. We show that the repetition scheme can efficiently improve the RACH success probability in a light traffic scenario, but only slightly improves that performance with very inefficient channel resource utilization in a heavy traffic scenario.

The channel capacity of noncoherent reception of multi-level one-sided amplitude-shift keying (ASK), which is an asymmetric constellation, in Rayleigh fading with receive diversity and energy detection is considered. The asymmetries result in capacity achieving input probability distributions, that is, a priori probability distributions, that deviate from uniformity. An analytical expression for the mutual information in terms of a single integral is derived, and from it the set of equations, which can be solved to obtain the optimum or capacity achieving input probabilities, is obtained. High and low signal-to-noise ratio (SNR) approximations of the optimum input probabilities and the capacity are derived next. Furthermore, a logarithmic upper bound on the mutual information is obtained. Numerical results confirm that the uniform distribution of input probabilities is not capacity achieving. For example, with average SNR per symbol per branch of 6 dB, the relative deviation of the mutual information (with uniform input distribution) from the capacity is nearly 20% for 4-level ASK with one transmit diversity branch and two receive diversity branches. Furthermore, the derived high and low SNR approximations to the capacity are shown to be reasonably accurate.

We consider a point-to-point mm-wave massive multiple-input multiple-output hybrid beamforming system where the transmitter is impaired with in-phase and quadrature-phase imbalance (IQI). We propose a novel channel estimation and IQI parameter estimation algorithm which first estimates the true sparse channel parameters using which it then estimates the IQI parameters. We show that the transmitter IQI limits the spectral efficiency of hybrid beamforming systems at high signal-to-noise ratio irrespective of the choice of hybrid precoder/combiner. We also propose a novel IQI symbol-level pre-compensation scheme at the transmitter which modifies the input symbol vector to the transmit radio frequency (RF) chains in such a way that the symbol vector received at the output of the RF chains is free from any IQI. Analysis and simulations confirm the effectiveness of the proposed IQI pre-compensation technique.

We consider the downlink communication of a point-to-point mm-wave massive multiple-input multiple-output hybrid beamforming (HB) system in which the transmitter is free from in-phase and quadrature-phase (IQ) imbalance whereas the receiver is IQ-impaired. We show that, irrespective of the design of the hybrid precoder/combiner, the receiver IQ imbalance (Rx-IQI) limits the spectral efficiency (SE) of HB systems at high signal-to-noise ratio. To solve this problem, we propose a novel Rx-IQI compensation scheme which completely mitigates the effects of Rx-IQI in HB systems. Analysis and simulations confirm the effectiveness of our Rx-IQI compensation scheme.

A new digital modulation scheme, termed frequency-phase keying (FPK), that combines frequency-shift keying (FSK) and phase-shift keying (PSK), is presented. Optimized signal designs for $M$ -ary FPK that jointly select the phase and frequency of the modulating signal in order to minimize the union bound on the symbol error probability with maximum likelihood reception are obtained. Solutions for baseband communication in additive white Gaussian noise channels and for passband communication in Rayleigh fading with receive diversity are derived. In contrast to conventional FSK and PSK, and to existing hybrid FSK/PSK schemes, the designed FPK signal constellations have the desirable property that the maximum correlation coefficient between any two signals is negative. We demonstrate that the proposed FPK solutions yield improved error performance for both baseband and passband communication.

Cooperative non-orthogonal multiple access (NOMA) scheme is emerging as an important part of the next generation wireless systems. Recently, device-to-device (D2D) networks with NOMA have received considerable attention by the researchers due to the advantages offered by them. D2D communication involves direct contact between the devices in proximity and the devices can also be used as relays for cooperative communication. In this paper, we present the performance analysis of a downlink cooperative D2D network with NOMA and amplify-and-forward (AF) relaying with fixed gain assuming that the D2D communication links experience independent Nakagami-m fading. We derive closed-form expressions for the outage probability of strong and weak D2D users with the assumption that there exists a direct communication link between the base station and the D2D users. Further, we also present the system throughput and the asymptotic outage analysis for both strong D2D user and weak D2D user. As a special case, we also provide the outage expressions for both strong D2D user and weak D2D user when the D2D communication links experience Rayleigh fading. Furthermore, numerical results are in agreement with the derived analytical expressions.

We analyze the outage performance of a buffer- aided dual-hop decode-and-forward cooperative relaying network with co-channel interference (CCI) and additive white Gaussian noise (AWGN) at the relay and the destination nodes. We propose a max-signal-to-interference plus noise ratio (max- SINR) relaying protocol in which the data transmission takes place in the link having the maximum SINR among the available source-relay and relay-destination links. It is assumed that the envelopes of the desired signal and the interfering signal follow asymmetric channel configuration with Rayleigh distributed fading. We consider a finite size data buffer equipped at the relay nodes. A discrete Markov chain approach is adopted to model the evolution of the relay buffers' status and to derive a closed-form expression for the outage probability. Numerical results demonstrate that in the cooperative networks with CCI and AWGN, employing a data buffer at the relays and adopting the max- SINR relaying protocol lead to an improvement in the performance of outage in comparison to the max-min relaying protocol without a buffer. The buffer-aided relaying protocol can improve the reliability of a cooperative network with CCI and AWGN as compared to the non buffer-aided relaying protocol.

In this study, the authors consider a two‐way relaying (TWR) system with source terminals and and a relay terminal . They analyse the performance of a fixed‐gain amplify‐and‐forward‐based TWR system over Rayleigh fading channels with co‐channel interference at all the terminals. Expressions are derived for the outage probability of the system at a medium‐to‐high signal‐to‐interference‐plus‐noise ratio (SINR) range. They also obtain the expression for the value of outage floor and use this to optimise relay location and power allocation. Simulation results demonstrate accuracy of the derived expressions in different SINR ranges.

In this study, the authors propose a novel virtual full‐duplex relaying scheme, which is referred to as centre‐partition max‐link relaying by using buffer‐aided half‐duplex relays for multi‐hop decode‐and‐forward cooperative networks. In the proposed scheme, they aim to select two independent available links for data packet transmission in the same time slot, which, in turn, improves the overall performance of the system. By modelling the evolution of buffer state transition as a Markov chain, the performance of the system is analysed in terms of outage probability and end‐to‐end average packet delay. The state transition matrix of the Markov chain is constructed and its steady‐state distribution is obtained to derive the outage probability. Numerical results demonstrate that the proposed scheme has a potential to provide significant outage performance with reduced average packet delay as compared to that of buffer‐aided multi‐hop decode‐and‐forward relaying networks using the conventional max‐link scheme.

In this study, the authors consider a diffusive molecular communication channel where the information to be transmitted is the time of release of the information molecules. Using the truncated Lévy distribution to model the first passage time of a molecule, the authors develop some general statistics for a random variable described by a truncated Lévy distribution. The authors then consider a multi‐particle molecular communication system, where the average arrival time of the information particles can be represented by a truncated Lévy flight, and the number of molecules required for the cross‐over from the Lévy regime to the Gaussian regime to occur is calculated. Furthermore, they use these results to analyse single as well as multi‐particle molecular communication channels in terms of capacity bounds and symbol error probability.

In this article, three low complexity multiple-input multiple-output (MIMO) receivers using energy detection and multilevel amplitude-shift keying (ASK) for Internet of Things (IoT) applications are described. To circumvent the inherent nonlinearity of the noncoherent MIMO system, an equivalent linear system model for the channel is introduced. This allows the proposed receivers to be configured analogously to coherent-based approaches. The tradeoff is that increased numbers of receive antennas need to be used but the overall complexity is decreased compared to existing noncoherent approaches. The receivers can also easily be integrated with energy harvesting systems. The three receiver structures considered are zero forcing (ZF), ZF with ordered successive interference cancellation (ZF-OSIC), and weighted envelope detection (WENVD), and their performance in flat Rayleigh fading channels with multilevel ASK is investigated. For the WENVD receiver, the error performance under the condition of high signal-to-noise ratio is also analyzed, and closed form approximations of the conditional (conditioned on the channel matrix) symbol vector error probability (SEP) and the average of the conditional SEP are derived. It is found that the ZF receiver has the lowest complexity and the WENVD receiver the highest; however, error performance comparison through numerical results reveals that the WENVD receiver has the best performance and the ZF-OSIC receiver has the next best. When combined with multiport energy harvesting technology the receivers have significant potential for use in IoT.

There is an increase in usage of smaller cells or femtocells to improve performance and coverage of next-generation heterogeneous wireless networks (HetNets). However, the interference caused by femtocells to neighboring cells is a limiting performance factor in dense HetNets. This interference is being managed via distributed resource allocation methods. However, as the density of the network increases so does the complexity of such resource allocation methods. Yet, unplanned deployment of femtocells requires an adaptable and self-organizing algorithm to make HetNets viable. As such, we propose to use a machine learning approach based on Q-learning to solve the resource allocation problem in such complex networks. By defining each base station as an agent, a cellular network is modeled as a multi-agent network. Subsequently, cooperative Q-learning can be applied as an efficient approach to manage the resources of a multi-agent network. Furthermore, the proposed approach considers the quality of service (QoS) for each user and fairness in the network. In comparison with prior work, the proposed approach can bring more than a four-fold increase in the number of supported femtocells while using cooperative Q-learning to reduce resource allocation overhead.

In this paper, we propose, for decode-and-forward cooperative networks, a relaying scheme which is based on giving a priority to the status of relay buffers along with the highest channel gain of wireless links. Specifically, we divide the set of relay buffer status into three priority classes: i) the first priority is given to relay buffers which are full, ii) the second priority to relay buffers which are empty, and iii) the third priority to relay buffers which are neither full nor empty. Within a priority class, a relay node is selected corresponding to the link having the highest channel gain. We adopt a Markov chain approach to analyze the state transition matrix that models the evolution of the relay buffer status. Analytical expressions for the outage probability and the diversity order are derived. The proposed scheme is illustrated with an example and analytical expressions for the steady-state probability vector are obtained. It is also shown that the states having the same probabilities can be grouped. Furthermore, we explain the construction of the reduced state transition matrix. Our analytical and simulation results demonstrate that the proposed scheme has the potential to provide better outage performance over the conventional maxlink scheme.

The authors consider a single‐channel power line communication (PLC) system in the presence of Middleton Class‐A impulsive noise employing multi‐level amplitude‐shift keying (ASK) modulation at the transmitter and non‐coherent detection at the receiver. An asymptotically optimal detector for the PLC system is obtained using a tight approximation of the noise statistics. The magnitude of the received symbol is obtained as the decision variable, whose statistics is utilised to derive a series expression for the symbol error rate (SER). An asymptotic expression for the SER at high signal‐to‐noise ratio (SNR) is also obtained which is further utilised to find the optimal ASK constellation minimising the SER. It is shown by numerical examples that the optimal solution is extremely close to the equally spaced ASK constellation set at high SNR. It is also observed that the SER variation of the system with the impulsive index of the noise validates the optimality of the proposed detector at high SNR.

In a communication system employing coherent reception, pilot symbols are used for estimating the channel state information (CSI) at the receiver. The amount of training, which is quantified by the fractional pilot duration for a fixed-length pilot-plus-data frame, should be kept as low as possible for saving bandwidth and increasing data rate. However, reducing training leads to degraded error performance due to poor CSI estimate although it increases data rate, while increasing training improves error performance but reduces data rate. Expressing the tradeoff between symbol error probability (SEP) and data rate by the normalized error-free data rate, we present an analytical framework for its maximization with respect to pilot symbol duration fraction in a pilot-aided single-input multiple-output wireless communication system with reception over independent and identically distributed flat Rayleigh fading diversity branches, employing M -ary phase-shift keying, and using maximal-ratio combining. Closed-form expressions for the approximate optimal pilot symbol duration fraction are derived for the high signal-to-noise ratio (SNR) case. Numerical results are presented to highlight the system behavior with changes in parameters like SNR, pilot symbol quality, and number of receive diversity branches. It is found that the optimization maximizes normalized error-free data rate with close to minimum SEP.

We consider two low-complexity receivers, namely, the energy detection (ED) receiver and the weighted envelope detection (WENVD) receiver, employing receive diversity, operating in flat Rayleigh fading with multi-level amplitude-shift keying, and having only channel magnitude information, that is, knowledge of the magnitudes of the fading gains of the receive diversity branches. A closed form expression for the approximate symbol error probability (SEP) of the WENVD receiver for high signal-to-noise ratio (SNR) is derived. Furthermore, analytical results on the optimization of the transmit symbol amplitude levels to minimize the SEP subject to a total energy constraint for high SNR and large number of receive diversity branches for both the ED and the WENVD receivers are presented. The performance improvement obtained by using these optimal levels over using symbol amplitude levels with equal spacing, that is, in arithmetic progression, for both the receivers is shown through numerical results.

In this paper, we propose a new relaying scheme, referred to as priority-based max-link relay selection, for buffer-aided decode-and-forward cooperative networks. We give the first priority to the relay buffers having status full, the second priority to the relay buffers having status empty, and the third priority to the relay buffers having status neither full nor empty. The best relay node is selected corresponding to the link having the highest channel gain among the links within a priority class. By adopting a Markov chain approach to analyze the state transition matrix that models the evolution of the buffers status, we derive analytical expressions for the outage probability and the average bit error rate. Analytical expressions for the steady-state probability vector are also obtained, and through these expressions, it is shown that states with the same probabilities can be grouped, thus reducing the size of the state transition matrix. We propose a general state-grouping-based method to obtain the reduced state transition matrix, which in turn reduces the computational complexity in obtaining the steady-state distribution. Our analytical and simulation results demonstrate that the proposed relaying scheme has better performance gain over the conventional max-link scheme.

We consider a complex-valued L × L exponential correlation matrix. Such a matrix has unit diagonal elements; each lower off-diagonal element is the correlation coefficient raised to the power of the modulus of the difference of the row and column indices, while each upper off-diagonal element is the complex conjugate of the correlation coefficient raised to the power of the modulus of the difference of the row and column indices. This makes it a Hermitian Toeplitz matrix. Analytical expressions for the eigenvectors of the exponential correlation matrix are presented, and closed form approximations of the eigenvalues for the low and high correlation cases and for the cases of linear interpolation and large matrix size are derived. Closed form expressions for the eigenvalues of exponential correlation matrices of sizes ranging from 3 to 8 in terms of the correlation coefficient, by a novel method of transformation of the characteristic polynomial and subsequent factorization of the transformed characteristic polynomial, are also derived. Furthermore, applications of the results obtained to the performance evaluation of wireless communication systems employing diversity are presented.

In this paper, we use the truncated Lévy distribution to model the first arrival time in a molecular communication channel where information on the release time of the molecules is modulated and the molecules have an exponentially distributed lifetime. The general statistics for a random variable described by a truncated Lévy distribution are developed. Considering systems where a large number of molecules is used so that the average arrival time can be represented by a truncated Lévy flight, we derive an expression for the number of molecules required for the cross-over from the Lévy regime to the Gaussian regime to occur. We also use these statistics to obtain bounds on the capacity of these channels in an information theoretic sense.

In this paper, an incremental selective decode-and-forward (ISDF) relay strategy is proposed for power line communication (PLC) systems to improve the spectral efficiency. Traditional decode-and-forward (DF) relaying employs two time slots by using half-duplex relays which significantly reduces the spectral efficiency. The ISDF strategy utilizes the relay only if the direct link quality fails to attain a certain information rate, thereby improving the spectral efficiency. The path gain is assumed to be log-normally distributed with very high distance dependent signal attenuation. Furthermore, the additive noise is modeled as a Bernoulli-Gaussian process to incorporate the effects of impulsive noise contents. Closed-form expressions for the outage probability and the fraction of times the relay is in use, and an approximate closed-form expression for the average bit error rate (BER) are derived for the binary phase-shift keying signaling scheme. We observe that the fraction of times the relay is in use can be significantly reduced compared to the raditional DF strategy. It is also observed that at high transmit power, the spectral efficiency increases while the average BER decreases with increase in the required rate.

Device‐to‐device (D2D) communication, unlike conventional cellular communication, is described as the direct communication between devices bypassing the network infrastructure. This mode of direct communication, due to its advantages, is being proposed as an integral part of the next generation cellular networks with the additional interference between the users being a challenge. In this study, the authors develop an analytical framework for a D2D‐enabled downlink cellular network with Nakagami‐ m fading between the D2D communication links. The authors derive tractable expressions for the coverage probability of D2D links and cellular users, considering different propagation conditions experienced by D2D and cellular links. Using stochastic geometry, the authors provide the coverage probability analysis for the dedicated network, having orthogonal frequency resource allocation, and for the shared network, where the frequency resources are reused. Furthermore, the authors extend the coverage probability analysis to include interference‐limited dedicated and shared networks. Numerical results corroborate their analysis. The authors also derive the expressions for ergodic spectral efficiency of D2D links for both dedicated and shared networks. The results obtained are helpful in understanding the system behaviour and show the dependence of network performance on the system parameters.

A novel low complexity energy detection receiver, which utilizes knowledge of the magnitudes of the fading gains of the receive diversity branches, is presented. Its error performance in flat Rayleigh fading with multi-level amplitude-shift keying is analyzed, resulting in a closed form expression for the symbol error probability (SEP) as well as analytical results for high signal-to-noise ratios. These show that the receiver has the same diversity order as that of coherent receivers but maintains the low complexity structure of energy detectors. Numerical results show that the SEP performance of the energy detection receiver is much closer to that of a coherent receiver than to that of a noncoherent one. Furthermore, we also consider transmit constellation optimization and conclude that an equally spaced amplitude level constellation performs close to the optimal solution in Rayleigh fading. A significant advantage of this receiver is that it performs much better than noncoherent detection but maintains the low complexity structure of noncoherent detectors. Training to obtain the channel magnitudes is, however, required but the low complexity receiver can be used to perform that with the only additional overhead being the training time.

This paper proposes to use N-branch diversity reception for a power line communication (PLC) system with binary phase-shift keying to improve the reliability of data transmission. The PLC channel is subject to Rayleigh fading and additive Nakagami-m background noise with m <; 1, which is caused by multiple noise sources. The optimal detector for this system is derived by approximating the noise distribution by Hoyt distribution. A closed form expression and a series expression for the symbol error probability for even and odd N, respectively, are obtained. The advantage of using multiple receive branches in terms of achieving better error performance and its power efficiency are shown through numerical results. The effect of the shape parameter m of the background noise on the performance of the optimal receiver is also demonstrated.

Multi-hop relaying is an important strategy for improved link performance and increasing the range of communication, while the buffers at the relays improve the diversity advantage of the system. In this paper, we investigate the performance of multiple clusters of relays with buffers using max-link relay selection scheme for decode-and-forward cooperative networks. A generalized Markov chain is proposed to model the evolution of buffer status for more than one cluster. Construction of the state diagram for two clusters of relays is discussed as an example. Analytical expressions for the outage probability and the average packet delay are derived. It is shown through numerical results that at moderate to high signal-to-noise ratios, the outage improves with increasing number of clusters. Furthermore, closed-form analytical expressions are obtained for the steady-state probability vector by considering different numbers of clusters and relays. Through examples, we observe that states with the same steady-state probabilities can be grouped. The size of the state transition matrix grows with increasing number of clusters and relays in each cluster. Thus, by exploiting the property of grouping the same state probabilities, we provide an approach to reduce the size of the state transition matrix.

In this paper, we consider the subject of diagonal precoder matrix design for a three-input multiple-output system using spatial multiplexing with binary symbols from the constellation {0,1} and noncoherent reception in flat Rayleigh fading having a uniform transmit covariance matrix. For this system, the symbol vector error probability (SEP) tends to saturate at high values of average signal-to-noise ratio per symbol vector per diversity branch. The saturation value of the SEP is minimized with respect to the precoder parameters to obtain the best error performance. It is found that when the number of receive antennas is large, the optimal values of the precoder parameters are almost independent of the number of receive antennas. Numerical results show the advantage of using noncoherent reception over coherent reception with imperfect channel state information.

The authors presents a study of the effect of correlation among the multi‐hop path gains on the average channel capacity and the outage performance of a power line communication system equipped with decode‐and‐forward relays. The path gain of each hop follows a log‐normal distribution and the joint density is modelled by a multivariate log‐normal distribution with exponential correlation. A distance dependent signal attenuation factor is added to the channel model to incorporate the effect of physical distance between the nodes. Furthermore, a Gaussian mixture (Bernoulli‐Gaussian) noise is included in the system model to analyse the effect of impulsive noise together with thermal noise. Approximate closed‐form expressions for the end‐to‐end average channel capacity and the outage probability are derived. Numerical results showing the impact of the amount of correlation, the number of hops, the impulsive noise power, and the spread of the average power of the path gains on the performance are presented. The results show that for a fixed transmit power and end‐to‐end distance between source and destination, the performance improves with increasing number of hops; however, the amount of improvement reduces with increasing channel correlation.

A noncoherent quadratic diversity reception system for multilevel amplitude-shift keying (ASK) signals in Rayleigh fading with different cases of the channel covariance matrix is considered. These include the important case of distributed antennas, which exhibit uncorrelated fading with distinct mean-squared channel gains (uncorrelated nonidentical fading) and weighted energy detectors, and the cases of exponentially correlated and uniformly correlated channels with equal mean-squared channel gains. For these cases, closed-form expressions for the symbol error probability (SEP) of the system are derived using the decision statistics obtained from the maximum likelihood receiver. The problem of determining the optimal amplitude levels that minimize the SEP under a total signal energy constraint is formulated and solved analytically for the high signal-to-noise ratio (SNR) configuration and numerically for the general configuration. For the high SNR configuration, it is shown that the optimal ASK levels should follow an approximately geometric progression. It is also observed that an equally spaced ASK constellation is not optimal in terms of achieving the minimum SEP. Numerical results are presented to highlight performance trends for channel gain imbalance and correlation.

This paper analyzes the performance of a buffer-aided multi-hop relaying system using the max-link relay selection scheme for decode-and-forward cooperative networks. A Markov chain approach is adopted to analyze the state transition matrix that models the evolution of the status of relay buffers. Analytical expressions for the steady-state probability vector are obtained for a three-hop buffer-aided system, and through these expressions, we observe that states with the same probabilities can be clustered, thus reducing the size of the state transition matrix. We propose a state-clustering-based method to obtain the reduced state transition matrix, which is further used to derive an analytical expression for the outage probability with reduced computational complexity. The method is general in the sense that it does not require any prior knowledge about the steady-state probability vector and the state transition matrix. Furthermore, we illustrate, in detail, the construction of the reduced state transition matrix and the related steady-state distribution by an example. An analytical expression for the average packet delay is also derived. Both analytical and simulation results are provided to investigate the performance of buffer-aided multi-hop relaying networks.

This paper develops a tractable framework for exploiting the potential benefits of physical layer security in three-tier wireless sensor networks (WSNs) using stochastic geometry. In such networks, the sensing data from the remote sensors are collected by sinks with the help of access points, and the external eavesdroppers intercept the data transmissions. We focus on the secure transmission in two scenarios: 1) the active sensors transmit their sensing data to the access points and 2) the active access points forward the data to the sinks. We derive new compact expressions for the average secrecy rate in these two scenarios. We also derive a new compact expression for the overall average secrecy rate. Numerical results corroborate our analysis and show that multiple antennas at the access points can enhance the security of three-tier WSNs. Our results show that increasing the number of access points decreases the average secrecy rate between the access point and its associated sink. However, we find that increasing the number of access points first increases the overall average secrecy rate, with a critical value beyond which the overall average secrecy rate then decreases. When increasing the number of active sensors, both the average secrecy rate between the sensor and its associated access point, and the overall average secrecy rate decrease. In contrast, increasing the number of sinks improves both the average secrecy rate between the access point and its associated sink, and the overall average secrecy rate.

This paper develops a tractable framework for exploiting the potential benefits of physical layer security in three-tier wireless sensor networks. In such networks, the sensing data from the remote sensors are collected by sinks with the help of access points, and the external eavesdroppers intercept the data transmissions. We adopt the stochastic geometry approach to model the random locations and spatial densities of the sensors, access points, sinks, and eavesdroppers. We focus on the secure transmission in two scenarios: i) the active sensors transmit their sensing data to the access points, and ii) the active access points forward the data to the sinks. We derive new compact expressions for the overall average secrecy rate in such networks. Numerical results corroborate our analysis and show that multiple- antenna technique at the access points can enhance the security. Our results show that the overall average secrecy rate first increases with increasing the number of access points, and there exists a critical value beyond which the overall average secrecy rate decreases with increasing the number of access points. When adding the number of active sensors, the overall average secrecy rate decreases. In contrast, increasing the number of sinks improves the overall average secrecy rate.

The authors present a study on the end‐to‐end average bit error rate (BER), the average channel capacity and the outage performance of a multi‐hop power line communication (PLC) system equipped with decode‐and‐forward (DF) relays. To combat the issue of distance dependent signal attenuation, multi‐hop data transmission has recently been introduced for PLC systems. However, apart from the distance dependent signal attenuation, PLC systems also suffer from (i) the variation in signal amplitude (fading) because of reflections and (ii) impulsive noise. Thus, in this study, the channel for each hop of the multi‐hop PLC system is modelled by a log‐normal fading amplitude, which is clubbed to a distance dependent signal attenuation factor. To consider the effect of the impulsive noise along with the background noise, the additive noise at each node is modelled by a Bernoulli–Gaussian process. Analytical expressions for the end‐to‐end average BER for binary phase‐shift keying, the average channel capacity and the outage probability are obtained. The merit of the multi‐hop PLC system over a conventional direct transmission PLC system for fixed transmission power is shown through numerical results. The authors' results show that with increasing number of DF relays, the end‐to‐end average BER, the average channel capacity and the outage performance improve.

The authors present a novel frequency division multiplexing scheme which can generate a signal whose worst‐case peak‐to‐average power ratio (PAPR) is tunable by an input parameter; they call this scheme tunable PAPR frequency division multiplexing (TP‐FDM). Special cases of TP‐FDM are orthogonal FDM (OFDM) and single carrier (SC) modulation. Unlike several other proposed PAPR reduction schemes, TP‐FDM requires no per‐symbol side information to be sent from transmitter to receiver. TP‐FDM has overall computational requirements almost the same as OFDM. The author's study of the symbol error rate (SER) of TP‐FDM in a Rayleigh fading channel shows that higher PAPR signals give a better SER performance. Thus, instead of choosing either of the extremes, OFDM and SC modulation, as is currently done in some cellular systems, one can tune the PAPR with TP‐FDM to the maximum suitable for the transmitter and receiver device electronics, so as to minimise SER. They compare and contrast TP‐FDM with transform precoded OFDM methods in terms of SER and PAPR. They also extend TP‐FDM to a multi‐user scenario.

The use of repeaters (relays) has recently been introduced in power line communication (PLC) systems for long-distance data transfer and thus, it becomes important to analyze the performance of relay based PLC systems. A simplified system model with distance dependent signal attenuation and additive white Gaussian noise may not cover all the factors affecting the data transfer, such as variation in amplitude (fading) and occurrence of impulsive noise. Hence, a more realistic system model with log-normal fading, distance dependent signal attenuation, and a Bernoulli-Gaussian impulsive noise is considered in this paper to study the end-to-end average bit error rate (BER) and the end-to-end average channel capacity of a PLC system equipped with amplify-and-forward (AF) relays. Approximate closed-form expressions of the end-to-end average BER for binary phase-shift keying and the average channel capacity for high signal-to-noise ratio are obtained. The performance of the PLC system with AF relays is found to be superior compared to that of a direct transmission PLC system for fixed transmission power.

We consider signal design for multiple-input multiple-output (MIMO) systems with spatial multiplexing and noncoherent reception in a flat Rayleigh fading environment. We obtain the symbol vector error probability (SEP) of noncoherent detection as a function of the signal amplitude levels and the effective precoder matrix, which depends on the precoder structure and the channel transmit covariance matrix. It is found that at high values of average signal-to-noise ratio (SNR) per symbol vector per diversity branch, the SEP tends to reach saturation. To obtain the best error performance, we need to find the optimal precoder and constellation parameters that minimize the saturation value of the SEP. Optimization of the saturation value of the SEP is carried out using the binary signal constellations {0,1} and {1, -r}, r > 1, two transmit antennas, a real valued transmit covariance matrix with equal diagonal elements, and a diagonal precoder. Results show that the optimal values of the parameters are almost independent of the number of receive antennas when the number of receive antennas is large. We also observe that the error performance of MIMO noncoherent reception is better than that of MIMO coherent reception with imperfect channel state information for a certain range of average SNR.

In this paper, we investigate modulation techniques for end-to-end communication between two nanomachines placed in a fluid medium. The information is encoded as the number of molecules transmitted leading to such schemes being aptly named as amplitude modulation schemes. The propagation of molecules obeys the laws of Brownian motion with a positive drift from the transmitter to the receiver nanomachine. The channel is characterized by two parameters of the fluid medium: the drift velocity and the diffusion coefficient. Assuming the molecules degrade over time, the life expectancy of the molecules also plays a significant role in such communication scenarios. We consider anM-ary modulation scheme and also propose an extended scheme, which is a slight variation of a binary modulation scheme. The received symbol is corrupted by interference from the previous symbols as well as other noise sources present in the medium. Considering maximum likelihood detection at the receiver, we derive analytical expressions for the end-to-end symbol error probability and the capacity for these modulation schemes. Numerical results bring out the impact of various parameters on the performance of the system. Our results show that these schemes offer a promising approach to set up molecular communication over diffusion-based channels.

We propose transmit antenna selection with receive generalized selection combining (TAS/GSC) in dual-hop cognitive decode-and-forward (DF) relay networks for reliability enhancement and interference relaxation. In this paradigm, a single antenna which maximizes the receive signal-to-noise ratio (SNR) is selected at the secondary transmitter and a subset of receive antennas with the highest SNRs are combined at the secondary receiver. To demonstrate the impact of multiple primary users on the cognitive relay network, we derive new closed-form expressions for the exact and asymptotic outage probability with TAS/GSC in the secondary network. Several important design insights are reached. We corroborate that the full diversity gain is achieved, which is entirely determined by the total number of antennas in the secondary network. The negative impact of the primary network on the secondary network is reflected in the SNR gain.

This paper considers transmit antenna selection (TAS) and receive generalized selection combining (GSC) for secure communication in MIMO wiretap channel, where confidential messages transmitted from an NA-antenna transmitter to an NB-antenna legitimate receiver are overheard by an NE-antenna eavesdropper. We assume that the main channel and the eavesdropper's channel undergo Nakagami-m fading with fading parameters mBand mE, respectively. In an effort to assess the secrecy performance, we present a closed-form expression for the secrecy outage probability. We then derive closed-form expressions for the secrecy outage probability at high signal-to-noise ratio (SNR) for two realistic scenarios: 1) the legitimate receiver is located close to the transmitter, and 2) the legitimate receiver and the eavesdropper are located close to the transmitter. In the first scenario, we confirm that the secrecy diversity order is mBNBNA. In the second scenario, we confirm that the secrecy diversity order collapses to zero. While this may appear discouraging at a first glance, we show that low secrecy outage probability can still be achieved.

In this paper, we consider three different amplitude modulation schemes for molecular communication through a fluid medium with a positive drift velocity. The channel is divided into time slots of equal duration and transmission is done at the beginning of every slot. The molecules, transmitted by a nanomachine, propagate via Brownian motion and reach the receiver nanomachine. The amplitude levels are represented by the number of molecules transmitted. The communication is corrupted by randomness due to diffusion as well as interference from the previous slots. Considering maximum likelihood detection at the receiver, the probability of error is analyzed for all the three schemes, and its variation with the parameters involved is studied. The results are also compared with previously proposed time modulation schemes, where the information is encoded as the transmit time of molecules.

We develop an analytical framework for the end-to-end (e2e) asymptotic performance of pilot-symbol assisted Mary phase-shift keying (M-PSK) dual-hop relaying communication networks. The relays use the selective-decode-and-forward protocol and are equipped with multiple receive antennas. Channel estimation per antenna branch is done based on the least-squares estimation technique by means of pilot symbols. Also, maximal-ratio combining and coherent detection are performed at the receiving end. Simple approximate average symbol error probability (ASEP) expressions are obtained for high signal-to-noise ratio (SNR) when M ≥2. Our analysis is generic enough to account for any frequency-flat, time-selective, and/or arbitrarily correlated fading channel model per hop. As a case study, we provide e2e M-PSK ASEP expressions considering arbitrarily correlated Nakagami fading channels. Moreover, the optimal power allocation is studied, while the cooperation-gain and diversity-order are extracted. Numerical results are finally presented to verify the accuracy of our asymptotic expressions.

The authors analyse an L ‐channel selection combining (SC) scheme for a power line communication (PLC) system with binary phase‐shift keying. The focus is on improving the reliability in data transfer of the system instead of improving the data rate. To enhance the reliability in data transfer, multiple PLC channels are used to send the same information‐bearing signal to the receiver. The L PLC channels are subject to log‐normal fading, which is modelled by a multivariate log‐normal distribution with an exponential correlation. The channels are also corrupted by additive impulsive noise as well as thermal noise. To consider the effect of both types of noises, they adopt a Gaussian mixture noise model, in which the additive noise samples are taken from a Bernoulli–Gaussian process. The system performance is evaluated in terms of the average bit error rate and the average channel capacity, for which approximate closed form expressions are derived. Numerical results showing the impact of the number of PLC channels, the amount of correlation, the noise scenarios, and the fading environments on the performance are presented. The authors' results show that the performance improves with increasing number of PLC channels; however, the amount of improvement reduces with increasing channel correlation.

In this study, the authors consider molecular communication between two nanomachines placed in a fluid medium for three different amplitude modulation schemes. The number of molecules transmitted represents the amplitude levels for these schemes. Each molecule released by the transmitter travels with Brownian motion and a positive drift to reach the receiver nanomachine. They consider a time slotted channel, where the information in every slot is corrupted by stray molecules from the previous slots. The capacity of such a molecular communication channel is investigated for all the three modulation schemes. Analytical expressions for the end‐to‐end symbol error probability are derived, considering maximum likelihood detection at the receiver. Numerical results indicate that arbitrarily low probabilities of error can be achieved for high drift velocities. An increase in the slot length further improves the performance, albeit at the cost of data rate. The results also demonstrate the improvements offered by the amplitude modulation schemes over the previously proposed time modulation schemes.

We consider a communication system with receive diversity in flat Rayleigh fading employing multi-level amplitude-shift keying (ASK) and noncoherent reception. Using the statistics of the decision variable of the quadratic receiver, a closed form expression for the symbol error probability (SEP) is derived. A formulation to determine the optimal signal amplitude levels of ASK constellation that minimize the SEP subject to a total signal energy constraint is presented. By approximating the derivative of the objective function, an approximate semi-analytical solution is obtained. We also present an asymptotic SEP expression that shows the variation of the SEP at high signal-to-noise ratio (SNR) and the diversity order of the system. An important result is that the optimum signal amplitude levels at high SNRs follow an approximately geometric progression in contrast to the more typical case of signal amplitude levels in arithmetic progression. Numerical results show the superiority of error performance of ASK with optimal signal amplitude levels as compared to that of ASK with signal amplitude levels in arithmetic progression.

In this paper, we consider optimal power allocation for conventional and buffer-aided link adaptive energy harvesting (EH) relay systems, where an EH source communicates with the destination via an EH decode-and-forward relay {over fading channels}. In conventional relaying, source and relay transmit signals in consecutive time slots whereas in buffer-aided link adaptive relaying, the state of the source-relay and relay-destination channels {as well as the amounts of energy available at source and relay} determine whether the source or the relay is selected for transmission. Our objective is to maximize the system throughput over a finite number of transmission time slots for both relaying protocols. In case of conventional relaying, we propose an offline and several online joint source and relay transmit power allocation schemes. For offline power allocation, we formulate {a convex optimization problem} whereas for the online case, we propose a dynamic programming (DP) approach to compute the optimal online transmit power. To alleviate the complexity inherent to DP, we also propose several suboptimal online power allocation schemes. For buffer-aided link adaptive relaying, we show that the joint offline optimization of the source and relay transmit powers along with the link selection results in a mixed integer non-linear program which we solve optimally using the spatial branch-and-bound method. We also propose efficient online power allocation schemes for buffer-aided link adaptive relaying. Simulation results show that buffer-aided link adaptive relaying provides significant performance gains compared to conventional relaying but requires a higher complexity for computation of the power allocation solution. We also show that buffer-aided link adaptive relaying is more robust to changes in the EH rate than conventional relaying.

We propose transmit antenna selection with receive generalized selection combining in dual-hop cognitive decode-and-forward relay networks with spectrum sharing for reliability enhancement and interference relaxation. In this network, a single antenna, which maximizes the receive signal-to-noise ratio (SNR) is selected at the secondary transmitter, and a subset of receive antennas with the highest SNRs is combined at the secondary receiver. To demonstrate the advantages of our proposed framework, we derive new exact closed-form expressions for the outage probability and the symbol error rate of the secondary network in Rayleigh fading. We also derive easy-to-evaluate asymptotic expressions in the high-SNR regime to gain practical insights. Several important design insights are reached. Under the proportional interference power constraint, the full diversity gain is achieved and is entirely determined by the total number of antennas available in the secondary network. This result is independent of the number of receive antennas combined and the number of primary users. The positive impact of the number of receive antennas combined and the negative impact of the number of primary users on the secondary network are showcased in the SNR gain. Under the fixed interference power constraint, error floors are displayed, and the diversity gain is lost.

In this paper, we study the application of bit-interleaved coded modulation (BICM) and orthogonal frequency division multiplexing (OFDM) to reap the benefits of wireless multiuser network coding in practical frequency-selective fading channels. We propose a mapping based symbol level network coding (SLNC) scheme for a cooperative diversity system comprising multiple sources, multiple relays, and one common destination. A simple cooperative maximum-ratio combining scheme is used at the destination and is shown to successfully exploit both the full spatial and the full frequency diversity offered by the channel for arbitrary numbers of sources, arbitrary numbers of relays, and arbitrary linear modulation schemes. To gain analytical insight for system design, we derive a closed-form upper bound for the asymptotic worst-case pairwise error probability (PEP) and obtain the diversity gain of the considered SLNC scheme for BICM-OFDM systems. These analytical results reveal the influence of the various system parameters, such as the number of sources, the free distance of the code, and the frequency diversity of the involved links, on performance. Furthermore, we propose two different relay selection schemes for the considered system: a) bulk selection, i.e., a single best relay is selected to transmit on all sub-carriers, and b) per-subcarrier selection, where a best relay is selected on each sub-carrier. Last but not least, we exploit the derived PEP expression for selecting a subset of sources from the set of active sources when the number of active sources is larger than the number of available orthogonal relay channels. We study the achievable diversity gain for the proposed relay and source subset selection schemes. Numerical results corroborate the derived diversity gain expressions and confirm the performance gains.

This paper considers transmit antenna selection (TAS) and receive generalized selection combining (GSC) for secure communication in the multiple-input-multiple-output wiretap channel, where confidential messages transmitted from an NA-antenna transmitter to an NB-antenna legitimate receiver are overheard by an NE-antenna eavesdropper. We assume that the main channel and the eavesdropper's channel undergo Nakagami-m fading with fading parameters mB and mE, respectively. In order to assess the secrecy performance, we present a new unifying framework for the average secrecy rate and the secrecy outage probability. We first derive expressions for the probability density function and the cumulative distribution function of the signal-to-noise ratio with TAS/GSC, from which we derive exact expressions for the average secrecy rate and the secrecy outage probability. We then derive compact expressions for the asymptotic average secrecy rate and the asymptotic secrecy outage probability for two distinct scenarios: 1) the legitimate receiver is located close to the transmitter, and 2) the legitimate receiver and the eavesdropper are located close to the transmitter. For these scenarios, we present new closed-form expressions for several key performance indicators: 1) the capacity slope and the power offset of the asymptotic average secrecy rate, and 2) the secrecy diversity order and the secrecy array gain of the asymptotic secrecy outage probability. For the first scenario, we confirm that the capacity slope is one and the secrecy diversity order is mBNBNA. For the second scenario, we confirm that the capacity slope and the secrecy diversity order collapse to zero.

In the existing literature, a single sample based improved energy detector has been analyzed for multiple antennas based cooperative spectrum sensing. In this paper, we derive the expressions of the probability of false alarm and missed detection of multiple antenna based dual-hop cooperative spectrum sensing scheme which uses multiple samples of the primary user's signal in the improved energy detector. By minimizing the total error rate (weighted sum of the probability of missed detection and probability of false alarm), we derive a closed-form solution of optimal number of CRs required for dual-hop cooperation. It is shown by simulations that this generalized scheme significantly outperforms the conventional energy detector based spectrum sensing, while keeping quality-of-service in desired limits. A multi-hop cognitive radio network containing multiple antenna based CRs and using an improved energy detector with multiple samples is also analyzed in this paper. It is inferred by analysis and simulation that the error performance of the multi-hop cognitive relaying can be significantly improved by using multiple antennas and improved energy detector.

This paper investigates the problem of channel estimation and decoding of orthogonal space time block codes (OSTBCs) in a two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay network. We propose a joint decoder for a pilot symbol-aided twoway AF based MIMO cooperative system. The proposed decoder jointly processes the received OSTBC data and pilot matrix by using vector derivative over the two-way MIMO relay channel. We derive a closed-form expression in Rayleigh fading for the moment generating function of the received signal-to-noise ratio at both cooperating users for the proposed decoder; and then investigate the system performance based on analytical expressions for the symbol error rate, diversity order, and array gain.

In this study, schemes for optimisation of power allocation (OPA) for asymmetric relay placement are presented for multi‐hop communication in a Rayleigh‐fading environment. For a decode‐and‐forward (DF) multi‐hop communication system, expressions are derived for optimised power allocation based on symbol error probability (SEP) and global channel state information (GCSI). The analysis for OPA based on GCSI is extended to a hybrid combination of amplify‐and‐forward (AF) and DF relays. Analysis is done for two kinds of modulation schemes: M ‐ary phase‐shift keying with coherent detection and orthogonal M ‐ary frequency‐shift keying with non‐coherent detection. Simulation results show that for a multi‐hop system with asymmetric relay placement, power optimisation schemes perform better than the conventional equal power allocation scheme. In addition, power optimisation based on GCSI shows substantially improved performance compared with power allocation based on end‐to‐end SEP. Further, performance comparison is shown for increase in number of relay nodes in an AF and DF multi‐hop system with and without power allocation. The performance of a DF system improves with increase in number of relay nodes whereas performance of an AF system degrades. Hybrid relaying provides an option to exercise switching between DF and AF so as to extract the maximum advantage of the two relaying schemes.

Consider wireless local area network (WLAN) service providers (SPs) operating in an overlapping service area. The SPs compete with each other to attract users. The price charged is utilised by the SPs as a tool to maximise revenue, resulting in a price competition between the WLAN SPs. The users are assumed to be selfish, trying to maximise their individual utility. They have varied sensitivity towards quality of service experienced and the price charged. In such a scenario, the user demand distribution is the one that achieves Wardrop equilibrium. Approximate analytical expressions are obtained for the best response of SPs to each other's price. Existence of a Nash equilibrium (NE) between the competing SPs is proved and the price vector at which the NE occurs is obtained. It is found that, while in one extreme monopoly leads to very high revenue for WLAN SPs with minimal consumer surplus, in the other extreme unregulated duopoly/oligopoly leads to high consumer surplus at the cost of minimal revenue generation for the competing SPs. Thus, price regulation is proposed in the WLAN market for equitable distribution of the surplus among the SPs and the users.

We consider a wireless system with a multi-branch diversity receiver employing noncoherent reception. The receiver has information on the channel statistics instead of the instantaneous channel state information, and the average branch signal-to-noise ratios (SNRs) are all distinct. In such a scenario, a deterministically weighted square-law combining scheme can be used to improve the error performance over conventional square-law combining. We focus on such a scheme for a system with orthogonal signaling in uniformly correlated Rayleigh fading. We obtain suboptimal weights, by least squares fit of the matrix elements of the characteristic functions of the decision variables of the weighted square-law combining and the optimum quadratic combining receivers, in closed form that are computed easily using an iterative algorithm. For the case of a dual-diversity system, an implicit expression for the optimal weights, chosen to minimize the symbol error probability, is obtained; for binary signaling, we derive closed form expressions for the weights. It is found that weighted square-law combining offers significant performance improvement over conventional square-law combining at a cost of increased complexity, and the performance gap increases with increasing branch SNR imbalance and number of branches.

This paper proposes a selection combining (SC) scheme for a power line communication (PLC) system with binary phase-shift keying. The main purpose is to utilize multiple of independent and non-interfering channels to send an information-bearing signal and to use SC at the receiver end to improve the reliability of the PLC system. The fading coefficient of each PLC channel is modeled by a log-normal distribution, and to include the effects of both background noise and impulsive noise, the additive noise samples are taken from a Bernoulli-Gaussian process. We obtain a closed-form approximation of the bit error rate and an expression for the outage probability of the proposed scheme. The merit of the L-channel PLC system with SC when compared with a single channel PLC system over different fading and impulsive noise scenarios is demonstrated through numerical results.

In this paper, we investigate the sensing-throughput tradeoff in multi-antenna cognitive radio (CR) systems. Specifically, we optimize the sensing threshold, sensing time, and transmit power of a multi-input multi-output (MIMO) CR system for maximization of the opportunistic system throughput under transmit power and probability of false alarm and detection constraints. To this end, we propose a new transmission protocol which allows the CR user to simultaneously perform data transmission and spectrum sensing on different spatial subchannels. We formulate a non-convex optimization problem for the optimal choice of the sensing threshold, sensing times, and transmit powers in the different spatial subchannels of MIMO CR systems. Since finding the global optimal solution entails a very high complexity, we develop an efficient iterative algorithm that is based on the concept of alternating optimization and solves only convex subproblems in each iteration. Simulation results show that the developed algorithm closely approaches the global optimal performance and achieves significant performance gains compared to baseline schemes employing equal powers or equal sensing times in all subcannels.

This paper analyzes optimal power allocation schemes for a multi-hop decode-and-forward relay system in a Rayleigh fading environment at high signal-to-noise ratio. Analysis is done for two kinds of modulation schemes: M-ary phase-shift keying with coherent detection and orthogonal M-ary frequency-shift keying with noncoherent detection. An optimal power allocation scheme based on end-to-end symbol error probability is derived for asymmetric relay placement and it is found that for fixed asymmetric relay locations equal power allocation is not optimal. When we have global channel state information at each node, a scheme for optimal power allocation based on relay link quality is also derived. Simulation results for a multi-hop system with optimal power allocation show significant improvement in performance compared to those of a system with equal power allocation. The gap in performance increases further with increase in number of relay nodes.

Coded cooperation is an attractive user cooperation scheme for wireless systems, where different parts of a coded packet are transmitted over different channels. In this paper, we propose a new approach to improve the performance of coded cooperation. We present cooperative maximum-ratio combining (C-MRC) based coded cooperation to guarantee full diversity even if the inter-user link is not ideal. Moreover, we combine bit-interleaved coded modulation (BICM) with orthogonal frequency division multiplexing (OFDM) to overcome frequency-selective fading. Taking possible decision errors at the cooperating sources into account, we develop a closed-form upper bound on the asymptotic worst-case pairwise error probability (PEP) of the considered C-MRC based coded cooperation scheme and obtain the diversity gain as function of free distance of the code and frequency diversity of the links. Furthermore, we discuss the optimization of the puncturing pattern based on the frequency diversity of the involved links. Simulation results corroborate the derived analytical results.

Using energy harvesting nodes can be a viable solution for energy limited cooperative communication systems. In this paper, we consider the optimization of an energy harvesting (EH) relay system, where an EH source communicates with the destination via an EH decode-and-forward (DF) relay. Our objective is to maximize the system throughput over a finite number of transmission intervals. To this end, we propose an offline and several online joint source and relay transmit power allocation schemes. For offline power allocation, we formulate a convex optimization problem which can be solved either in closed form or using standard optimization tools. For the online case, we propose a dynamic programming (DP) approach to compute the optimal online transmit power. To alleviate the complexity inherent to DP, we propose several suboptimal online power allocation schemes. Our simulation results show that the developed suboptimal schemes provide a good complexity-performance tradeoff compared to optimal online power allocation.

In this paper, we provide a high signal-to-noise ratio (SNR) error rate analysis of amplify-and-forward (AF) best relay selection in networks impaired by Rayleigh fading and generic, possibly non-Gaussian noise. The derived closed - form asymptotic error rate expressions are applicable to any type of noise with finite moments. Exploiting these analytical results, we formulate a power allocation problem with energy consumption fairness constraints for the source and the relays, which is solved using monomial fitting and a series of geometric programs. The accuracy of the derived analytical results and the effectiveness of the proposed power allocation scheme are confirmed with computer simulations.

In the presence of several wireless local area network (WLAN) service providers, the users have to make a choice. The price charged and the congestion experienced by the users play an important role in making this choice. In this paper, we analyze the duopoly price competition between two WLAN service providers in the presence of four types of users. We prove that the distribution of heterogeneous user demand is governed by the Wardrop equilibrium. We also show the existence of the Nash equilibrium between competing WLAN service providers. It is further shown through analysis that the social welfare in Nash equilibrium is close to its maximal value. We find that compared to a strictly regulated monopoly, an unregulated WLAN duopoly market results in significant transfer of the surplus from service providers to users with negligible losses in efficiency.

In this letter, we investigate the performance of generalized selection combining in channels impaired by generalized fading and generic noise with finite moments. In particular, we derive accurate high signal-to-noise ratio approximations for the bit and symbol error rates of linear modulation schemes, which offer significant insight into the impact of the number of selected diversity branches, the type of fading, and the type of noise. Our analysis is applicable to all practically relevant types of fading including Rayleigh, Rician, Nakagami-q, and Nakagami-m fading, all types of noise with finite moments including Gaussian noise, Gaussian mixture noise, generalized Gaussian noise, and co-channel interference, and non-identically distributed fading and noise across the diversity branches. Our results reveal that while performance always improves with increasing number of selected branches for identically distributed noise, this is not necessarily true for non-identically distributed noise.

The performance of decode-and-forward multi-hop communication is analyzed in a Rayleigh fading environment. Analytical expressions for the end-to-end symbol error probability are derived in the cases of M-ary phase-shift keying with coherent detection and orthogonal M-ary frequency-shift keying with non-coherent detection using a difference equation approach. When the path loss exponent is greater than one, each node transmits with the same power as that of a direct transmission source, and the relays are equispaced along the line joining the source and the destination, the performance improves with increasing number of hops. Furthermore, for fixed average signal-to-noise ratio per hop, the incremental degradation in performance when adding more hops decreases with each extra hop.

Cooperative diversity achieves enhanced data rates and throughput using distributed spatial diversity techniques. We consider a cooperative diversity system comprising of a source, a relay, and a destination, with decode and forward (DF) protocol at the relay. The drawback of conventional instantaneous signal-to-noise ratio (SNR) based selection combining is that it fails to use the instantaneous SNR of the source-relay channel at the destination while selecting the best channel from source-destination and relay-destination channels. Full channel state information (CSI) selection combining, which effectively utilizes the instantaneous SNR of the source-relay channel at the destination, is used to overcome this drawback. The exact end-to-end symbol error probability (SEP) of full CSI selection combining for this DF system, with M-ary phase-shift keying in a flat Rayleigh fading environment, is derived. The analysis is validated through simulations. The diversity gain analysis is also studied for this scheme. Further, we compare the full CSI selection combining scheme with some other existing schemes. Numerical results show that full CSI selection combining has performance similar to that of instantaneous SEP based selection combining, but offers SNR gain over instantaneous SNR based selection combining, max-min selection, and selection cooperation.

Best relay selection (BRS) has received considerable attention in the literature as it makes efficient use of the system resources and achieves full diversity. Partial relay selection (PRS) is an alternative to BRS and performs relay selection based on local channel state information (CSI) only at the expense of a loss in diversity. Although, in practice, relays may be deployed in unfavorable environments exposing them to non-Gaussian impairments, existing analyses and design guidelines for BRS and PRS are limited to additive white Gaussian noise channels. In this paper, we analyze the error rate of BRS and PRS in the asymptotic regime of high signal-to-noise ratio (SNR) for amplify-and-forward (AF) relays and impairment by generic noise and interference. The derived analytical results are valid for Gaussian and non-Gaussian noises with finite moments, independent and non-identically distributed Rayleigh fading, and arbitrary linear modulation schemes. In order to reduce the signaling overhead required for CSI acquisition, we propose a relay subset selection scheme for BRS and PRS. Furthermore, to guarantee fairness in energy resource usage across the relays, we introduce a fair and flexible power allocation scheme with energy consumption constraints which does not affect the achievable diversity gain. The proposed relay subset selection and power allocation schemes only require knowledge of the average CSI of the links and certain moments of the noises impairing the relays and the destination.

In this paper, we study a cooperative diversity scheme for wireless systems employing network coding and the combination of bit-interleaved coded modulation (BICM) and orthogonal frequency division multiplexing (OFDM). The considered system comprises multiple sources, one relay, and one destination. The relay decodes the signal received from all sources and performs network coding before forwarding the signal to the destination. We propose a simple cooperative maximum-ratio combining scheme for the destination which can successfully exploit the full spatial and frequency diversity offered by the channel for arbitrary numbers of sources and arbitrary linear modulation schemes. Furthermore, we propose techniques to reduce the signaling overhead and the decoding complexity at the destination. To gain insight for system design, we derive a closed-form upper bound for the asymptotic worst-case pairwise error probability and the diversity gain of the considered network coded cooperative BICM-OFDM system. These analytical results reveal the influence of various system parameters, including the number of sources, the free distance of the code, and the frequency diversity of the involved links, on performance. Based on the derived analytical results, we develop schemes for optimal relay placement and power allocation. Simulation results corroborate the derived analytical results and confirm the effectiveness of the developed optimization framework.

In this paper, we investigate the sensing-throughput tradeoff in multi-antenna cognitive radio (CR) systems. Specifically, we optimize the sensing threshold, sensing time, and transmit power of a multi-input multi-output (MIMO) CR system for maximization of the opportunistic system throughput under transmit power, probability of false alarm, and probability of missed detection constraints. To this end, we propose a new transmission protocol which allows the CR user to simultaneously perform data transmission and spectrum sensing on different spatial subchannels. We formulate non-convex optimization problems for the optimal choice of the sensing threshold, sensing times, and transmit powers in each spatial subchannel for both single-band and multi-band MIMO CR systems. Since finding the global optimal solution of these problems entails a very high complexity, we develop two iterative algorithms that are based on the concept of alternating optimization and solve only convex subproblems in each iteration. Thus, the complexity of these algorithms is low, and we prove their convergence to a fixed point analytically. Simulation results show that the developed algorithms closely approach the global optimal performance and achieve significant performance gains compared to baseline schemes employing equal powers or equal sensing times in all subchannels.

The problem of distributed power allocation for an interference relay network is considered, where multiple source-relay-destination (S-R-D) links communicate concurrently in the same frequency and interfere over two hops, referred to as a two-hop interference channel. The direct source-destination connections are not considered in this work. Power allocation in this scenario is challenging as it necessitates not only performance tradeoff among multiple links but also power distribution for each link along spatial dimensions. We approach the problem from a game-theoretic perspective and propose a novel implicit-based approach to prove the uniqueness of the Nash equilibrium (NE). This technique complements the existing literature on equilibria analysis by revealing the benefits of expressing the best responses in implicit forms. To benchmark the performance of the NE, we have investigated the non-convex sum-utility maximization problem, and have (1) identified the optimal solution structures; (2) proved that linear pricing is locally optimal in maximizing the sum utilities. A simple and distributed pricing algorithm is then proposed. Simulation results show that for a two-user network, the proposed scheme closely approaches the optimal sum rate, while, for a ten-user network, the improvement is up to 340% compared to the non-cooperative game model without pricing.

In this paper, we study a cooperative diversity scheme for wireless systems employing network coding and the combination of bit-interleaved coded modulation (BICM) and orthogonal frequency division multiplexing (OFDM). The considered system comprises multiple sources, one relay, and one destination. The relay decodes the signal received from all sources and performs network coding before forwarding the signal to the destination. We propose a simple cooperative maximum-ratio combining scheme for decoding at the destination which can successfully exploit the full spatial and frequency diversity offered by the channel for arbitrary number of sources and arbitrary modulation schemes. We derive a closed-form upper bound for the asymptotic worst-case pairwise error probability and the diversity gain of the considered network coded cooperative BICM-OFDM scheme. Simulation results corroborate the derived diversity gain and show the effectiveness of a low complexity decoding scheme.

This paper considers the problem of resource allocation for a large-scale wireless network consisting of multiple amplify-and-forward cooperative systems. The traditional competitive design leads to a network collapse where every system obtains almost zero throughput. We resolve this issue by resorting to the novel economic model of coalition formation with externalities by first letting the systems (modeled as players) self-organize into mutually beneficial coalitions, followed by a sequential non-cooperative game with improved player profiles. The results on the two-player game has been generalized to the case of an arbitrary number of players, incorporating additional peak power constraints as well. The uniqueness of the Nash equilibrium is proved analytically. Simulation results show that the proposed method improves the sum rate over 200% relative to the non-cooperative case due to improved frequency reuse.

This paper analyzes the performance of a multi-hop wireless communication system, consisting of a source node, N intermediate nodes or relays, and a destination node in a Rayleigh fading environment with decode-and-forward relaying at each intermediate node. The data is therefore transmitted from source to destination through N+1 hops. Two types of modulation, namely, M-ary phase-shift keying (MPSK) and orthogonal M-ary frequency-shift keying (OMFSK), are considered for the transmitted data. In case of MPSK, each relay performs coherent detection, while in case of OMFSK, each relay performs non-coherent detection. Using a difference equation approach, analytical expressions for the end-to-end symbol error probability are derived in both cases. We find that (1) although the performance degrades with increasing number of hops for fixed average signal-to-noise ratio per hop, the incremental degradation in performance with the addition of each extra hop decreases, (2) when each node transmits with fixed power, multi-hop transmission offers significant performance improvement over direct transmission.

When a multi-branch diversity receiver has information on the channel statistics instead of the instantaneous channel state information and noncoherent reception is employed, a deterministically weighted square-law combining scheme can be used to improve the error performance over conventional square-law combining when the average branch signal-to-noise ratios are not equal. We consider such a scheme for a dual-diversity system with orthogonal signaling in correlated Rayleigh fading. The square-law output of each branch is multiplied by a deterministic weight and the weighted outputs are additively combined. The weights are chosen so as to minimize the symbol error probability (SEP). The SEP in terms of these weights is derived in closed form, and from it a method for computing the weights is obtained. The merit of this scheme when compared with conventional square-law combining is demonstrated through numerical examples.

Optimization of cooperative spectrum sensing with an improved energy detector in each cognitive radio (CR)over imperfect reporting channels is discussed in this paper. The improved energy detector compares an arbitrary positive power p of the amplitude of the received samples of the signals of a primary user (PU)with a threshold to make a decision. The binary decision of each CR is forwarded over an imperfect reporting channel to a fusion center which makes a final decision on the presence of the PU. We obtain an expression of the total error rate of detection of a spectrum hole for this cooperative set-up. The optimized values of the normalized threshold and p in each CR and optimal number of CRs required for the decision are obtained by minimizing the total error rate. It is shown by simulations that the proposed scheme significantly outperforms an existing scheme using the conventional energy detector.

In this paper, we study a decode-and-forward cooperative diversity scheme for wireless systems using the combination of bit-interleaved coded modulation (BICM) and orthogonal frequency division multiplexing (OFDM). We propose a simple cooperative maximum-ratio combining scheme for the destination which can successfully exploit the full spatial and frequency diversity offered by the channel. Taking possible decision errors at the relay into account, we develop a closed- form upper bound on the asymptotic worst-case pairwise error probability (PEP) of the considered cooperative diversity system which provides insight into the influence of various code and channel parameters on performance. The PEP expression is then exploited for optimal relay placement. Simulation results corroborate the derived analytical results regarding the diversity gain of the system and confirm the effectiveness of the proposed relay placement scheme.

In this paper we study the statistics of the sum of not necessarily identically distributed kappa, that is, K, random variables (RV)s. Assuming half-integer values for the shaping parameters, novel closed-form expressions for the probability density function (PDF) of the sum of independent K RVs are obtained, while for arbitrary values of the shaping parameters, a corresponding PDF expression is derived in terms of fast converging infinite series. Furthermore, an infinite series representation for the PDF of the sum of two arbitrarily correlated K RVs is derived. The proposed analysis is employed to the performance analysis of equal-gain combining (EGC) receivers operating over composite fading/shadowing channels modeled by the K distribution. More specifically, the outage and the average bit error probabilities, as well as the average channel capacity of EGC receivers operating over such composite environment are studied. Considering different channel fading/shadowing conditions and correlation effects, various numerical performance evaluation results are presented. These results are complemented by equivalent computer simulated ones that validate the accuracy of the proposed analysis.

We investigate the capacity and beamforming optimality of multi-antenna relaying systems, given access to statistical channel information at the relay and source. Multi-antenna relay configurations are considered, for which the source as well as either the relay or destination have multiple antennas, and the relay operates with amplify-and-forward. We first compute the optimal transmission strategies at both the source and relay, and derive necessary and sufficient conditions for which beamforming achieves capacity. To gain more insight, we then employ tools from stochastic majorization theory to characterize the impact of the destination correlation and the relay gain on the capacity and beamforming optimality range. These results demonstrate some intriguing behavior, which arises due to the joint interplay between the transmit power, relay gain, and level of correlation at the destination. It is shown, among other things, that for certain transmit powers and relay gains, the beamforming optimality region becomes independent of the destination correlation. By relaxing the beamforming optimality condition, we also derive a simple explicit upper bound which gives further insights into the joint effect of the SNR and the transmit correlation on the beamforming optimality range.

In this paper, we propose a novel cooperative diversity scheme for wireless systems employing the combination of bit-interleaved coded modulation (BICM) and orthogonal frequency division multiplexing (OFDM). The proposed scheme utilizes an amplify-and-forward protocol where relays are assigned to multiple groups. Relays in the same group transmit concurrently over disjoint sets of sub-carriers and relays in different groups transmit in different time slots. We derive closed-form expressions for the asymptotic worst-case pairwise error probability and the diversity gain of the proposed cooperative BICM-OFDM scheme. Based on the derived analytical results we develop design guidelines for sub-carrier allocation, relay grouping, and relay selection. Simulation results corroborate the derived analytical results and confirm the effectiveness of the developed optimization framework.

Let X and Y be two independent L x 1 complex Gaussian random vectors distributed as CN (m×, σ2× IL) and CN (mY, σY2IL), respectively, where I_L denotes the L x L identity matrix. The joint characteristic function (c.f.) of the real and imaginary parts of the inner product YHX is derived in closed form, with (·)Hdenoting the conjugate transpose. Based on this joint c.f., a unified analytical framework for the derivation of the average symbol error probability (ASEP) of a multibranch diversity reception system over flat correlated fading using M-ary phase-shift keying is developed. The receiver employs maximal-ratio combining with least squares channel estimation by means of pilot symbols. The optimal average pilot-to-noise power ratio is obtained in closed form, and the analytical framework is applied to Nakagami and Rice fading. For Nakagami fading, closed form ASEP expressions are obtained for the cases of high signal-to-noise (SNR) and binary phase-shift keying, while for Rice fading, high SNR approximate expressions are obtained in terms of a single integral under the constant correlation model and for independent and identically distributed channels. Both analytical and computer simulation results are presented and compared in order to verify the validity of the proposed analysis.

For a single-relay cooperative diversity system employing the decode-and-forward protocol in Rayleigh fading, a scaled signal-to-noise ratio-based selection combining scheme, which uses a deterministic scale factor for link selection to incorporate the effect of the source-to-relay link, is presented. Its error probability for binary phase-shift keying is derived in closed-form.

Cognitive radio (CR) networks require reliable spectrum sensing in order to avoid interference to the primary users of the spectrum. Most existing spectrum sensing techniques are based on simple energy detection. However, in practice, the signals transmitted by primary users often also contain known pilot symbols for synchronization and channel estimation purposes. Coherent correlation based spectrum sensing techniques can exploit these known symbols but fail to utilize the energy contained in the data symbols. In this paper, we propose a hybrid coherent/energy detection scheme for spectrum sensing which exploits both the pilot and the data symbols transmitted by the primary user. Since the complexity of the globally optimal hybrid detection metric is very high, we develop a simple locally optimal hybrid metric, which turns out to be a linear combination of an energy detection metric and a correlation metric. We derive the probabilities of false alarm and missed detection of the proposed hybrid detector, and investigate the asymptotic behavior of both quantities for low signal-to-noise ratio and large sample size assuming that the CR network is optimized using a Neyman-Pearson framework. Simulation and analytical results confirm that the hybrid metric outperforms both energy detection and coherent detection even if the positions of the pilot symbols are not known a priori.

In this paper, we propose a novel amplify-and- forward cooperative diversity scheme for wireless systems using the combination of bit-interleaved coded modulation (BICM) and orthogonal frequency division multiplexing (OFDM). In the proposed scheme, multiple relays transmit concurrently over disjoint sets of sub-carriers. A careful joint design of the sub- carrier allocation at the relays and the interleaver at the source ensures that the proposed scheme can exploit the maximum spatial and frequency diversity offered by the wireless channel. An upper bound on the asymptotic worst-case pairwise error probability of the proposed cooperative diversity scheme is developed which provides insight into to the influence of various code and channel parameters on performance. Simulation results corroborate the analytical results regarding the diversity gain of the system and confirm the effectiveness of a newly developed relay selection criterion.

Cognitive radio (CR) networks require reliable spectrum sensing techniques in order to avoid interference to the primary users of the spectrum. Most existing spectrum sensing techniques are based on simple energy detection. However, in practice, the signals transmitted by primary users usually also contain known symbol such as pilots and preambles for synchronization and channel estimation purposes. Coherent, correlation based spectrum sensing techniques can exploit these known symbols but waste the energy contained in the data symbols. In this paper, we propose a hybrid spectrum sensing scheme which exploits both the pilot and the data symbols transmitted by the primary user. For the practically relevant low signal-to-noise ratio regime, we derive a locally optimal hybrid detection metric, which turns out to be a linear combination of an energy detection metric and a correlation metric. Simulation and analytical results confirm that the hybrid metric outperforms both energy detection and coherent detection even if the pilot positions are not known a priori and have to be estimated by the CR receiver.

This paper considers resource allocation for two-hop interference channels where N independent source-destination pairs share the same spectrum band and interfere with each other. The absence of a central coordinating system motivates us to tackle the problem from a non-cooperative game-theoretic perspective. It is shown that when the number of transmission pairs is greater than two, analyzing the properties of the Nash Equilibrium (NE) becomes greatly challenging. With the help of a game scalarization technique, we derive sufficient conditions that guarantee the uniqueness of the NE, as well as the global convergence of the best response dynamics. Numerical results are presented to illustrate the significant rate enhancement over conventional schemes.

We analyze the optimality of beamforming in multiple-input single-output relay channels without a direct link between the source and the destination. Assuming that the source has access to the channel correlation information, and that the relay operates in amplify and forward mode with a long term power constraint, we first show that the optimal transmission strategy is to transmit along the eigen-vectors of the transmit correlation matrix. The optimality of beamforming is then studied via the power allocation problem at the source. In particular, we derive a necessary and sufficient condition under which beamforming achieves the capacity. Our results demonstrate that the finite relay gain decreases the range at which beamforming is optimal.

We consider the problem of power control for two independent relay-assisted wireless systems that operate in the same spectral band. A general scenario where both systems are allowed to select between amplify-and-forward relaying and decode-and-forward relaying is studied. We adopt a game-theoretic approach and show that once both systems act non-cooperatively to optimize their own rate, they can always reach a unique Nash equilibrium (NE) from an arbitrary starting point in a totally distributed and asynchronous manner. We also provide insights on the impacts of network topology and relaying protocols on the sum rate performance of the NE through extensive numerical results.

Full search L1-norm (FS-L1) and sphere decoding L∞-norm (SD-L∞) detectors have been previously proposed for multiple-input multiple-output (MIMO) systems as they entail a lower receiver complexity than the optimal L2-norm detector. However, the performance loss caused by application of these suboptimal detectors in additive white Gaussian noise (AWGN) has not been well investigated yet. In this paper, we analyze the asymptotic bit error rate of general FS-Lpand SD-Lp detectors in independent identically distributed Rayleigh fading channels. Our results are valid for all types of noise with finite moments including AWGN. We show that both FS-Lpand SD-Lp detectors achieve a diversity gain equal to the number of receive antennas independent of the metric parameter p and the type of noise. However, except for the conventional L2case, the performances of FS-Lpand SD-Lp detectors are not identical and the performance differences may be several dB for large numbers of receive antennas. Also, our results show that p=2 is not optimal in non-Gaussian noise and L1and L∞detectors may result in large performance gains or degradations compared to L2detectors depending on the type of noise.

This paper considers orthogonal space-time block coded transmission for a multiple-input multiple-output channel (MIMO) with non-coherent amplify-and-forward (AF) relaying in Rayleigh fading. We first characterize the statistical properties of the instantaneous signal-to-noise ratio (SNR) at the destination, by deriving new exact closed form expressions for the moment generating function, cumulants, and first and second moments. These results show a reciprocity relationship between the number of antennas at the relay and destination. The probability density function and cumulative distribution function of the SNR are also derived for certain system configurations, and for various asymptotic regimes. We then investigate the system performance by presenting new analytical expressions for the symbol error rate, outage probability, amount of fading, as well as the diversity order and array gain. Our results indicate that the proposed scheme can achieve the maximum diversity order of the non-coherent AF MIMO relay channel.

The Nakagami-m distribution approximates a Rician distribution for the fading parameter m in the range 1 <; m <; ∞, and approximates a Hoyt or Nakagami-q distribution for m in the range 1/2 ≤ m <; 1, while it becomes a Rayleigh distribution for m=1. A uniformly distributed phase for all m ≥ 1/2 does not satisfy all these requirements. By using the distributions of the real and imaginary parts of complex fading gains having Rician and Hoyt distributed envelopes, we propose in this paper a new statistical model of the complex Nakagam-m fading gain for which the envelope has a Nakagami-m distribution and the phase has a nonuniform distribution. Numerical results show that, for a signal having a Nakagami-m distributed fading envelope, the proposed model closely approximates the distributions of the real and imaginary parts of signals with Rician and Hoyt fading envelopes for 1 <; m <; ∞ and 1/2 ≤ m <; 1, respectively, as well as the distributions of the corresponding phases.

In this paper, linear combining receivers with deterministic weights are considered for a communication system employing receive diversity in flat Rician fading. We propose two receiver structures: (1) a modified maximum likelihood (ML) receiver in which detection is performed by maximizing the likelihood function of the combined received signal, (2) a deterministic maximal-ratio combining (MRC) receiver which uses the same structure as that of an MRC receiver but with deterministic weights. The deterministic weight vector is chosen such that it minimizes the union bound on the symbol error probability. Methods of computing this deterministic weight vector are presented. The error performance of the receivers is numerically compared with that of the square-law combining receiver and the equal-gain combining (EGC) receiver (which requires more complex phase estimation rather than using fixed, deterministic weights). Numerical results show that in the case of phase-shift keying, the EGC receiver performs better than the modified ML receiver (which has the same performance as that of the deterministic MRC receiver), but the performance gap decreases with increase of the Rician K-factor. It is also seen that in the case of orthogonal frequency-shift keying, the modified ML and deterministic MRC receivers outperform the square-law combining receiver.

In this paper, coherent detection for multilevel correlated signaling sets in additive white Gaussian noise is addressed. The contribution is twofold. Firstly, correlation structures that minimize the symbol error probability (SEP) of M-ary frequency-shift keying as well as of arbitrarily correlated signaling sets are investigated, while secondly, a general and analytical expression for the SEP is derived in the form of a single integral. The structure of the associated correlation matrix is generic and includes various known signaling sets as special cases. Specific correlation structures that minimize the SEP are also studied. Based on eigendecomposition or LU decomposition, generic methods for constructing a correlated signaling set for any correlation matrix under consideration are also provided.

This paper considers orthogonal space-time block coded (OSTBC) transmission for non-regenerative multiple- input multiple-output dual-hop channels. We focus on scenarios where the relay does not have access to instantaneous channel state information, and as such operates according to a noncoherent amplify-and-forward protocol based on a long-term power constraint. We investigate the performance of the proposed OSTBC approach by employing tools from finite-dimensional random matrix theory. In particular, we derive exact closed-form expressions for the moment generating function, high order cumulants, and first and second moments of the signal-to-noise ratio at the destination. Based on these results, we also derive analytical expressions for the symbol error rate with M-ary phase-shift keying, and the amount of fading.

For a communication system employing receive diversity in flat Rician fading, we consider linear combining receivers with deterministic weights. Two receiver structures are proposed: (1) a modified maximum likelihood receiver in which detection is performed by maximizing the likelihood function of the combined received signal, (2) a deterministic maximal-ratio combining (MRC) receiver which uses the same structure as that of an MRC receiver with deterministic weights. The deterministic weight vector is chosen such that it minimizes the union bound on the symbol error probability. The error performance of the receivers is compared with that of the square-law combining and the equal-gain combining receivers.

Atmospheric turbulence induced fading is one of the main impairments affecting free-space optics (FSO) communications. In recent years, Gamma-Gamma fading has become the dominant fading model for FSO links because of its excellent agreement with measurement data for a wide range of turbulence conditions. However, in contrast to RF communications, the analysis techniques for FSO are not well developed and prior work has mostly resorted to simulations and numerical integration for performance evaluation in Gamma-Gamma fading. In this paper, we express the pairwise error probabilities of single-input single- output (SISO) and multiple-input multiple-output (MIMO) FSO systems with intensity modulation and direct detection (IM/DD) as generalized infinite power series with respect to the signal- to-noise ratio. For numerical evaluation these power series are truncated to a finite number of terms and an upper bound for the associated approximation error is provided. The resulting finite power series enables fast and accurate numerical evaluation of the bit error rate of IM/DD FSO with on-off keying and pulse position modulation in SISO and MIMO Gamma-Gamma fading channels. Furthermore, we extend the well-known RF concepts of diversity and combining gain to FSO and Gamma-Gamma fading. In particular, we provide simple closed-form expressions for the diversity gain and the combining gain of MIMO FSO with repetition coding across lasers at the transmitter and equal gain combining or maximal ratio combining at the receiver.

We consider a space-time coded system in a correlated Rayleigh flat fading environment with imperfect channel estimation. Two receiver structures are considered: a suboptimum receiver and the optimum maximum likelihood receiver. The system performance of both receivers is analyzed in terms of the pairwise error probability.

In this paper, we present three new detection schemes for the nonorthogonal amplify and forward (NAF) protocol in a cooperative diversity system based on a multiuser detection approach, namely, a channel inversion type detector, a maximal-ratio combining (MRC) type detector, and a biased maximum likelihood (ML) detector. The decision variables in these schemes are linear functionals of the transmitted symbol vector and therefore they are termed as ldquolinearrdquo detectors. A cooperative relay network using the NAF protocol with N - 1 relays is considered where the source transmits symbols in N - 1 blocks of two time slots in a Rayleigh fading environment. For the case of a general linear space-time block coding scheme using K symbols, we present the performance of this protocol in terms of the code symbol error probability when the symbols come from an M-ary phase-shift keying constellation. The approach is further extended to the transmission in N - 1 blocks of L time slots. Numerical results show that the performance of the MRC type detector is superior to that of the channel inversion type detector, while the biased ML detector has the best performance. However, the MRC type detector has the lowest complexity while the biased ML detector the highest.

A space-time block coded system in a correlated Rayleigh flat fading environment with transmit and receive correlation is considered. The channel state information (CSI) is estimated from a sequence of pilot code vectors which are known to the receiver and transmitted prior to data code transmission. Two receiver structures, namely the optimum receiver in which the estimated CSI is used in the maximum likelihood sense and the joint processing receiver that jointly processes the received data code and the received pilot code vectors, are presented and their equivalence is shown.

We analyze the error performance of a cooperative diversity system having two cooperating mobile units or users (designated as source and relay) and a destination. The relay cooperates with the source through the decode and forward protocol to enable the transmission of a data symbol from the source to the destination in a flat Rayleigh fading environment. A selection combining scheme is used to obtain an easily implementable receiver structure at the destination. An analytical expression for the end-to-end symbol error probability (SEP) of the system for M-ary phase shift keying is derived using a new approach, which we call a paired error approach. As a special case, we obtain, in closed form, the end-to-end SEP for binary phase shift keying. We also present a modified selection combining scheme to incorporate the effect of the interuser link, that is, the source to relay link, in the evaluation of the error performance. Results show that cooperative diversity becomes effective for a larger range of average signal-to-noise ratio (SNR) of the user to destination link as the average SNR of the interuser link increases. We also find that the modified selection combining scheme offers a substantial SNR gain over selection combining based cooperation.

This paper considers the multiuser power control problem in Gaussian frequency-flat interference relay channels using a game-theoretic framework. While a lot of attention has been paid to Gaussian interference games, where sufficient conditions for the uniqueness of the Nash equilibrium (NE) have been established, these types of games have not been studied in the context of interference relay channels. We consider here Gaussian interference relay games (GIRGs), where instead of allocating the power budget across a set of sub-channels, each player aims to decide the optimal power control strategy across a set of hops. We show that the GIRG always possesses a unique NE for a two-player version of the game, irrespective of any channel realization or initial system parameters such as power budgets and noise power. Furthermore, we derive explicitly a sufficient condition under which the NE achieves Pareto-optimality. To facilitate decentralized implementation, we propose a distributed and asynchronous algorithm. We also prove that the proposed algorithm always converges to the unique NE from an arbitrary starting point. We then conclude that the distributed game-theoretic approach exhibits great potential in the context of interference relay channels and qualifies as a practically appealing candidate for power control.

We consider cooperative spectrum sensing in which multiple cognitive radios collaboratively detect the spectrum holes through energy detection and investigate the optimality of cooperative spectrum sensing with an aim to optimize the detection performance in an efficient and implementable way. We derive the optimal voting rule for any detector applied to cooperative spectrum sensing. We also optimize the detection threshold when energy detection is employed. Finally, we propose a fast spectrum sensing algorithm for a large network which requires fewer than the total number of cognitive radios in cooperative spectrum sensing while satisfying a given error bound.

Atmospheric turbulence induced fading is one of the main impairments affecting free-space optics (FSO). Gamma-gamma fading has become the dominant fading model for FSO links because of its excellent agreement with measurement data for a wide range of turbulence conditions. In this paper, we express the bit error rate of intensity modulated FSO with direct detection in single-input single-output and multiple-input multiple-output gamma-gamma fading channels as generalized infinite power series with respect to the signal-to- noise ratio. For fast numerical evaluation these power series are truncated to a finite number of terms and an upper bound for the associated approximation error is provided. Another contribution of this paper is the extension of the well-known RF concepts of diversity and combining gain to FSO and gamma-gamma fading.

In this paper, coherent detection for multilevel correlated signaling sets in additive white Gaussian noise is addressed. From the decision rule, a general analytical expression for the symbol error probability (SEP) is derived, which is in the form of a single integral. Our new result is not only in agreement with a known equivalent expression, but it also has a much simpler analytical form. The structure of the correlation matrix under consideration of the signaling set is quite generic, including various known signaling sets as special cases. Hence the derived SEP expression is useful for analyzing the performance of various coherent modulation schemes such as multilevel phase-shift and frequency-shift keying. Specific correlation structures which minimize the SEP are also studied. Based on eigendecomposition or LU decomposition, generic methods for constructing a correlated signaling set for any correlation matrix under consideration are also provided.

Consider two independent complex Gaussian vectors having arbitrary mean vectors and covariance matrices which are scaled versions of the identity matrix. The joint characteristic function (c.f.) of the real and imaginary parts of the inner product of these two vectors is derived in closed form. This joint c.f. is applied to the analysis of the symbol error probability (ESP) of a multibranch diversity reception system in flat Rayleigh fading using M-ary phase-shift keying (MPSK). The receiver employs maximal- ratio combining with least squares channel estimation by means of pilot symbols. Closed form expressions of the SEP are obtained for the cases of binary phase-shift keying, MPSK with high signal- to-noise ratio approximation, and MPSK with independent and identically distributed fading.

Cognitive radio is being recognized as an intelligent technology due to its ability to rapidly and autonomously adapt operating parameters to changing environments and conditions. In order to reliably and swiftly detect spectrum holes in cognitive radios, spectrum sensing must be used. In this paper, we consider cooperative spectrum sensing in order to optimize the sensing performance. We focus on energy detection for spectrum sensing and find that the optimal fusion rule is the half-voting rule. Next, the optimal detection threshold of energy detection is determined numerically. Finally, we propose a fast spectrum sensing algorithm for a large network which requires fewer than the total number of cognitive radios to perform cooperative spectrum sensing while satisfying a given error bound.

User cooperation is a method where single antenna users or mobile phones share their antennas with other users or mobile phones so that they create space diversity and combat the effect of fading. In this paper, we derive, in closed form, the end to end symbol error probability when two users cooperate through the decode and forward protocol with binary phase-shift keying in a flat Rayleigh fading environment. Results show that cooperative diversity becomes effective for a larger range of average signal-to-noise ratio (SNR) of the user to destination link as the average SNR of the interuser link increases.

The average of the product of two Gaussian Q- functions having arguments as different scaled versions of the same Nakagami distributed fading gain magnitude is derived in closed-form. Both the cases when (1) the fading parameter is an integer, and (2) the fading parameter is an odd multiple of one-half, are considered. The results are applied to evaluating in closed-form (a) the symbol error probability (SEP) of rectangular quadrature amplitude modulation with maximal-ratio combining in independent Nakagami fading, and (b) the outage probability of a two-user synchronous code-division multiple-access system having signal-to-noise ratio (SNR) imbalance among users in Nakagami fading. It is found in application (a) that with increase in the degree of fading, the robustness to decision distance imbalance between in-phase and quadrature signals increases. In addition, there exists an optimum decision distance ratio at which the SEP has a minimum. In application (b), we find that the outage probability increases sharply with SNR imbalance factor at low SNR imbalance and tends to reach saturation as the imbalance increases.

A transmit-receive diversity system in correlated Rayleigh fading in which the receiver estimates the channel through pilot symbols, and feeds this information back to the transmitter through a feedback path, is considered. The imperfect channel state information (CSI) is used by the transmitter to obtain the transmit weight vector for data transmission. The optimum receiver in the maximum-likelihood (ML) sense obtained from the conditional distribution of the received signal vector, conditioned on the imperfect CSI and the transmit weight vector, is derived for the system. For the case ofM-ary phase-shift keying (MPSK), an analytical expression for the conditional symbol error probability (SEP), conditioned on the channel estimate and the transmit weight vector, is obtained, with the transmit weight vector chosen to minimize this conditional SEP. For the receive-only and transmit-only correlation scenarios with ill-conditioned eigenvalues of the receive and transmit covariance matrices (that is, some of the eigenvalues are very small), we derive expressions for the diversity gain. Numerical results are presented to compare the performance of our receiver with that of a conventional receiver in case of exponentially correlated fading. These results show that the optimum receiver typically has about a 0.5-dB gain over a conventional receiver when the correlation coefficient exceeds 0.5 and the number of receive antennas is much larger than the number of transmit antennas.

We analyze the performance of the decorrelating multiuser detector for a code-division multiple-access system in a correlated Rayleigh fading environment in terms of the bit error probability (BEP) of an user. The fading gains are independent among the users but correlated among the receive diversity branches. The branches are combined using maximal ratio combining, which requires channel estimation. The channel is estimated by means of pilot symbols, and both maximum likelihood criterion and maximum aposteriori probability criterion are considered. A closed-form expression for the BEP is obtained using a characteristic function approach. Numerical results for the case of exponentially correlated branches and equicorrelated signature waveforms show that (1) the signature cross-correlation has a stronger effect on the performance than the branch correlation, (2) the BEP steadily decreases with increase in the number of branches, and increases with increase in the number of users, rapidly tending to reach saturation as the number of users becomes large.

Motivated by the transmit antenna selection (TAS) concept, used in Multiple-Input-Multiple-Output systems, we argue fordistributedtransmitantennaselection(DTAS), which corresponds to a method of selecting a subset of available relays in cooperative diversity systems. Assuming amplify and forward relays, the proposed selection method represents a low-complexity tool for determining the optimum relaying set. Two optimization problems are studied: the error probability minimization subject to total energy consumption constraints, and the dual one, the total energy consumption minimization under error performance constraints. Numerical examples verify the advantage of the proposed method in adapting the number of relaying terminals to the desired performance-consumption tradeoff.

We consider a transmit-receive diversity system in correlated Rayleigh fading in which the receiver estimates the channel through pilot symbols, and feeds this information back to the transmitter through a feedback path. The imperfect channel state information is used by the transmitter to obtain the transmit weight vector for data transmission. The optimum receiver in the maximum likelihood sense obtained from the conditional distribution of the received signal vector, conditioned on the imperfect channel estimate and the transmit weight vector, is derived for the system. For the case of M-ary phase-shift keying, an analytical expression for the conditional symbol error probability (SEP), conditioned on the channel estimate and the transmit weight vector, is obtained. The transmit weight vector is chosen to minimize this conditional SEP. Numerical results are presented to compare the performance of our receiver with that of a conventional receiver.

The average of the product of two Gaussian Q-functions having arguments as different scaled versions of the same Nakagami distributed fading gain magnitude is derived in closed-form. Both the cases when (1) the fading parameter is an integer, and (2) the fading parameter is an odd multiple of one-half, are considered. The results are applied to evaluating in closed-form the symbol error probability (SEP) of rectangular quadrature amplitude modulation with maximal-ratio combining (MRC) in independent Nakagami fading. It is found that with increase in the degree of fading, the robustness to decision distance imbalance between in-phase and quadrature signals increases. In addition, there exists an optimum decision distance ratio at which the SEP has a minimum.

We consider a space-time coded system in a correlated Rayleigh flat fading environment. The channel state information (CSI) is obtained from the known pilot code matrix prior to data reception. We consider three receiver structures: (1) a suboptimum one in which the imperfect CSI is used in place of perfect CSI in a perfect CSI optimum receiver, (2) the optimum receiver I in which the imperfect CSI is used in the maximum likelihood sense (3) the optimum receiver II that jointly processes the received data codes and the pilot codes. The system performance in the cases of all three receivers is analyzed in terms of the pairwise error probability.

We consider a complex-valued L times L square matrix whose diagonal elements are unity, and lower and upper diagonal elements are the same, each lower diagonal element being equal to a (a ne 1) and each upper diagonal element being equal to b (b ne 1). We call this matrix the generalized semiuniform matrix, and denote it as M(a, b, L). For this matrix, we derive closed-form expressions for the characteristic polynomial, eigenvalues, and eigenvectors. Treating the non-real-valued uniform correlation matrix M(a, a*,L), where (middot)*denotes the complex conjugate and a ne a*, as a Hermitian generalized semi-uniform matrix, we obtain the eigenvalues and eigenvectors of M(a, a*, L) in closed form. The results are applied to the analysis of communication systems using diversity.

The authors derive the structure of the optimal receiver for MPSK signaling over a correlated Rayleigh fading channel. The channel is estimated using the minimum mean square error criterion by means of pilot symbols. For the case of high signal-to-noise ratio, an approximate expression for the symbol error probability (SEP) of this scheme is obtained as an integral, and compared with the SEP of a suboptimal receiver which uses maximal-ratio combining. Numerical results show that the performance gap between the optimal and sub-optimal receivers increases with increase of the channel correlation and the number of diversity branches, whereas it decreases with increase of pilot-to-signal ratio.

We consider a complex-valued L times L square matrix whose diagonal elements are unity, and lower and upper diagonal elements are the same, each lower diagonal element being equal to a (a ne 1) and each upper diagonal element being equal to b (b ne 1). We call this matrix the generalized semiuniform matrix, and denote it as M(a, b,L). For this matrix, we derive closed-form expressions for the characteristic polynomial, eigenvalues, eigenvectors, and inverse. Treating the non-real-valued uniform correlation matrix M(a, a*, L), where (middot)* denotes the complex conjugate and a ne a*, as a Hermitian generalized semiuniform matrix, we obtain the eigenvalues, eigenvectors, and inverse of M(a, a*, L) in closed form. We present applications of these results to the analysis of communication systems using diversity under correlated fading conditions

To compute the optimal bias in equal-gain combining (EGC) receivers with unequal energy constellations such as M-ary pulse amplitude modulation (M-PAM) and M-ary square quadrature amplitude modulation (M-QAM), the estimation of the instantaneous fading gain magnitude in each diversity branch is needed, thus defeating the usefulness of EGC. In this paper, we present an exact analytical equation, which can be efficiently used to compute a suboptimal value for the bias, both for M-PAM and M-QAM constellations. The proposed suboptimal bias minimizes the symbol error probability, and depends on the statistics of the fading gain magnitudes and not on their instantaneous values. For the case of large number of branches, where the central limit theorem can be applied, the proposed equation for the computation of the suboptimal bias is derived hi closed-form. Moreover, an approximate simple closed-form expression for the suboptimal bias is obtained, suitable for the high signal-to-noise ratio region. Numerical results verify the correctness and the accuracy of the proposed analytical formulation

For a space-time coded system subject to flat Rayleigh fading, we formulate the pairwise error probability (PEP) in a unified expression, which accounts for the cases of perfect channel-state information, imperfect channel estimation, and unknown channel. The unified PEP expression is then bounded by an exponential-type inequality leading to a tight upper bound on the PEP. The bound indicates that to design a good code set, we not only need to maximize the geometric mean of the nonzero eigenvalues of the code difference matrix, but also minimize their harmonic mean.

Multi-user cooperative diversity is a recent technique promising great improvement of the performance of wireless communication systems operating in fading environments. Based on combinatorial optimization theory and specifically on the so-called knapsack problem, this paper presents a method of optimizing the selection among the potential cooperating users, when amplify-and-forward relays are used. In particular, two optimization problems are studied: the error probability minimization subject to total energy consumption constraints, and the dual one, the energy consumption minimization under error performance constraints. Depending on the frequency of repeating this selection, the above problems are categorized into short-term and long-term node selection. Numerical examples verify the expected knapsack scheme's advantage of adapting the number of cooperating users, depending on the desired performance-consumption tradeoff. Moreover, long-term node selection seems to lead to similar error or consumption performance compared to the short-term one, despite its simplicity.

This paper investigates detection mechanisms for time hopping pulse position modulated multiple access systems in both additive white Gaussian noise environment and fading environment. In such systems, the raw data is not linearly related to the received signal. One technique is to express the pulse position modulated signal as the sum of linearly modulated signals with the input being a nonlinear function of the raw data. This reduces the system to an equivalent pulse amplitude modulated system with significant increase in complexity. We present two new lower complexity detectors. The first detector uses the properties of the pulse correlation matrix to develop a lower complexity detector. The second detector relies on the knowledge of the time-hopping sequence to despread the received signal. The detection is then done on chip-by-chip basis. The performance of these detectors is compared in terms of the probability of at least one user being in error and the average number of correctly decoded users.

For a space-time coded system subject to flat Rayleigh fading, we formulate the pairwise error probability (PEP) in a unified expression, which accounts for the cases of perfect channel-state information, imperfect channel estimation, and unknown channel. The unified PEP expression is then bounded by an exponential-type inequality leading to a tight upper bound on the PEP. The bound indicates that to design a good code set, we not only need to maximize the geometric mean of the nonzero eigenvalues of the code difference matrix, but also minimize their harmonic mean.

Consider a wireless communication system in flat fading with N transmit and M receive antennas using space-time block coding, where N/spl times/1 code vectors are transmitted over L symbol intervals, resulting in an N/spl times/L code matrix. A least-squares estimate (LSE) as well as a minimum mean-square estimate (MMSE) of the M/spl times/N channel matrix is obtained from a sequence of pilot code vectors. For the case of linear square (i.e., with N=L) orthogonal codes over constant envelope constellations, we obtain an expression for the exact decoding error probability (DEP) for coherent maximum-likelihood decoding. We also find the coding gain for high average signal-to-noise ratio (SNR) per diversity branch in the case of Rayleigh fading. A comparison between both channel-estimation techniques is done in terms of the average pilot-power-to-signal-power ratio (APPSPR). It is found that MMSE requires lower pilot power than LSE for the same DEP and the same average SNR per diversity branch. In addition, the error performance with LSE approaches that with MMSE, with an increase of average SNR per branch or an increase of APPSPR.

In this letter, we analyze the performance of the minimum mean-square error (MMSE) detector for a code-division multiple-access system employing binary phase-shift keying. The performance is measured in terms of the probability distribution and the average number of correctly decoded users. We consider the case of equipower users having equicorrelated signature waveforms. The distribution of the number of correctly decoded users is expressed as an integral over sum of products of Gaussian Q-functions. From it, a closed-form expression for the average number of correctly decoded users is derived.

We present closed-form lower bounds for the performance of multihop transmissions with nonregenerative relays over not necessarily identically distributed Nakagami-m fading channels. The end-to-end signal-to-noise ratio is formulated and upper bounded by using an inequality between harmonic and geometric means of positive random variables (RVs). Novel closed-form expressions are derived for the moment generating function, the probability density function, and the cumulative distribution function of the product of rational powers of statistically independent Gamma RVs. These statistical results are then applied to studying the outage probability and the average bit-error probability for phase- and frequency-modulated signaling. Numerical examples compare analytical and simulation results, verifying the tightness of the proposed bounds.

In a communication system using receive diversity and linear combining in the presence of cochannel interference (CCI), optimum combining (OC) is known to give the best error performance since it maximizes the instantaneous signal-to-interference-plus-noise ratio of the combiner output, and consequently, in the presence of Gaussian interference plus noise, it minimizes the error rate. However, this is based on the assumption that a perfect estimate of the channel is available. Channel estimation methods in reality use some overhead. When the channel is time-invariant, the estimation error decreases with increase in the amount of overhead, like the number of pilot symbols. With the growing need for high data rate applications, the amount of overhead that can be allocated for the estimation of the channel needs to be reduced, and the channel estimation error cannot be ignored. In this situation, replacing the channel by its imperfect estimate in the OC weight vector no longer results in an optimum scheme. We have to find an optimum scheme based on the channel estimation method and the detection criterion, which results in what we call optimized diversity combining (ODC). Here we focus on ODC resulting from a pilot symbol based maximum likelihood (ML) channel estimation method applied to a correlated flat Rayleigh fading channel in the presence of CCI and additive noise. The channel is randomly time-invariant during the reception of pilot and data symbols. The decision rule, which is optimum in the ML sense, is derived using concepts of Gaussian and Wishart statistics. Numerical results show that ODC can perform significantly better than OC with imperfect channnel estimates by appropriate choice of system parameters.

Consider a wireless communication system in flat fading with N transmit and M receive antennas using space-time block coding, where N /spl times/ 1 code vectors are transmitted over L symbol intervals resulting in an N /spl times/ L code matrix. A least-squares estimate as well as a minimum mean-square estimate of the channel matrix is obtained from the sequence of L/sub p/ pilot code vectors. For the case of linear orthogonal codes with N = L over constant envelope constellations, we obtain an expression for the exact decoding error probability. We also find the coding gain for high average signal-to-noise ratio per diversity branch.

We present closed-form bounds for the performance of multihop transmissions with non-regenerative relays over Nakagami-m fading channels. The end-to-end signal-to-noise ratio (SNR) is formulated and upper bounded by using the inequality between harmonic and geometric mean of positive random variables (RVs). Novel closed-form expressions are derived for the moment generating function, the probability density function, and the cumulative distribution function of the product of arbitrary powers of statistically independent Gamma RVs in terms of the Meijer's G-function. Using these theoretical results, closed-form lower bounds are obtained for the outage and average bit error probability of phase or frequency modulated signallings, while simple asymptotic expressions are also given for the bounds at high SNRs. Numerical results are compared to computer simulations, to show the tightness of the proposed bounds.

We analyze the error performance of minimum selection generalized selection combining (MS-GSC), in which the minimum number of diversity branches are selected such that their combined signal-to-noise ratio (SNR) is above a given threshold. A flat Rayleigh fading channel with independent and distinctly distributed branch SNR is considered. By transforming the ordered instantaneous branch SNR to their differences, we derive the distribution of the number of selected branches in closed-form. We then modify the derivation of this distribution to get the characteristic function (c.f.) of the combiner output SNR. This c.f. is used to obtain the symbol error probability for different coherent digital modulation schemes.

We analyze the error performance of an improved hybrid selection/maximal-ratio combining (H-S/MRC) technique called minimum selection H-S/MRC in flat Rayleigh fading for coherent digital modulation schemes. Here the minimum number of diversity branches are selected such that their combined signal-to-noise ratio is above a given threshold. We derive a closed-form expression for the distribution of the number of selected branches. This distribution is used to obtain the symbol error probability.

We analyze the error performance of a space-time coding system using N transmit and M receive antennas with imperfect channel estimation in flat Rayleigh fading. A least-squares estimate of the channel matrix is obtained by using a sequence of pilot code vectors. The estimate is found to be perturbed by an M/spl times/N perturbation matrix with zero-mean circular Gaussian entries. Using the characteristic function of the decision variable, we derive a closed-form expression for the pairwise error probability (PEP). From the same expression, the PEP in case of perfect channel estimation is also obtained. Numerical results show the degradation in performance due to imperfect channel estimation that can be compensated by increasing the number of receive antennas.

We analyze the problem of optimum combining with a single spatially correlated interferer in white Gaussian noise and Rayleigh fading by focussing on the conditional characteristic function (c.f.) of the combiner output signal-to-interference-plus-noise ratio, given the interference propagation vector. Unconditioning of this c.f. using the interference statistics, along with a finite-range integration, results in the symbol error probability (SEP) integral, which is a common integral factor to most digital-modulation schemes. We obtain an exact expression, partly in closed form, for the SEP integral. For the case of large values of average signal-to-noise ratio and signal-to-interference ratio per antenna element, we obtain closed-form asymptotic formulas for the SEP integral. Using the SEP integral, we can easily evaluate the symbol error performance of various modulation schemes. The correctness of our analytical results are verified by some numerical examples.

We consider an antipodal signaling system using wavelet modulation with scale diversity over a frequency-selective fading channel. The channel introduces a random gain for each scale. These scale gains are estimated by sending a block of pilot symbols. Coherent demodulation is carried out along with maximal-ratio combining using the estimated scale gains. From the characteristic function of the decision variable, we analyze the error performance. For the case of large signal-to-noise ratio, we obtain a closed-form expression for the bit error probability. We also compare the error performance of wavelet modulation with that of frequency diversity.

This paper analyzes the error performance of an improved generalized selection combining (GSC) technique called minimum selection GSC (MS-GSC) in flat Rayleigh fading for coherent digital modulation schemes. Here the minimum number of diversity branches is selected such that their combined signal-to-noise ratio (SNR) is above a given threshold. The threshold chosen here is determined by the combiner output SNR rather than individual branch SNRs as done in absolute threshold GSC (AT-GSC) and normalized threshold GSC (NT-GSC). As a result, MS-GSC uses less resource than AT-GSC or NT-GSC to give the same performance. We obtain a closed-form expression for the distribution of the number of selected branches followed by a closed-form expression for the characteristic function (c.f.) of the combiner output SNR. This c.f. is used to obtain the symbol error probability for different digital modulation schemes. Numerical results for M-ary phase-shift keying are presented as an example.

Direct-sequence code-division multiple-access (DS-CDMA) is a popular multiple-access technology for wireless communications. However, its performance is limited by multiple-access interference and multipath distortion. Multiuser detection and space-time processing are two signal processing techniques employed to improve the performance of DS-CDMA. Two minimum probability of error-based space-time multiuser detection algorithms are proposed in this paper. The first algorithm, minimum joint probability of error (MJPOE), aims to minimize the joint probability of error for all users. The second algorithm, minimum conditional probability of error (MCPOE), minimizes the probability of error of each user conditioned on the transmitted bit vector, for each user individually. In both the algorithms, the optimal filter weights are computed adaptively using a gradient descent approach. The MJPOE algorithm is blind and offers a bit-error-rate (BER) performance better than the nonadaptive minimum mean squared error (MMSE) algorithm, at the cost of higher computational complexity. An approach for reducing the computational overheads of MJPOE using Gram-Schmidt orthogonalization is suggested. The BER performance of the MCPOE algorithm is slightly inferior to MMSE, however, it has a computational complexity linear in the number of users. Both blind and training-based implementations for MCPOE are proposed. Both MJPOE and MCPOE have a convergence rate much faster than earlier known adaptive implementations of the MMSE detector, viz. least mean square and recursive least squares. Simulation results are presented for synchronous single path channels as well as asynchronous multipath channels, with multiple antennas employed at the receiver.

We derive an exact bit-error probability (BEP) expression for coherent detection of binary signals with optimum combining in wireless systems in the presence of multiple cochannel interferers and thermal noise. A flat Rayleigh fading environment with space diversity, uncorrelated equal-power interferers, and additive white Gaussian noise is considered. The approach is to use the chain rule of conditional expectation together with the joint probability density function (pdf) of the eigenvalues of the interference correlation matrix. This joint pdf is related to the Vandermonde determinant. Let N/sub A/ denote the number of antennas and N/sub I/ the number of interferers. We consider both the cases of an overloaded system, in which N/sub I//spl ges/N/sub A/, and an underloaded system, in which N/sub I/

We derive closed-form expressions for the single-user capacity of maximal ratio combining diversity systems taking into account the effect of correlation between the different branches. We consider a Rayleigh fading channel with two kinds of correlation: 1) equal branch signal-to-noise ratios (SNRs) and the same correlation between any pair of branches and 2) unequal branch SNRs and arbitrary correlation between branches such that the eigenvalues of the branch covariance matrix are all distinct. Three adaptive transmission schemes are analyzed: 1) optimal simultaneous power and rate adaptation; 2) optimal rate adaptation with constant transmit power; and 3) channel inversion with fixed rate.

We analyze the performance of the decorrelating multiuser detector for a wireless communication system. Instead of looking at the error probability for each user, we focus on the probability distribution of the number of correctly decoded users at the receiver and the average number of correctly decoded users under the conditions of equicorrelated signatures and perfect power control. The approach is motivated by the fact that the error events for different users are not independent. Numerical results show that when the number of users is large, instead of using a set of long signatures with a very low negative cross-correlation, we can use a set of shorter signatures with a reasonably high positive correlation without sacrificing the performance. It is also found that the average number of correctly decoded users increases with increase in signal-to-noise ratio and decreases when the cross-correlation between users becomes more negative or more positive.

In Rake receiver for coherent binary antipodal signaling with weight estimation by matched filtering using the reference signal along with the decision of the previous M symbol intervals, and predetection maximal-ratio combining (MRC), the estimation errors are not independent of the additive noise, and do not fit into the Gaussian weighting error model for MRC. Here we analyze the error performance of the receiver by: (1) obtaining the conditional symbol error probability (SEP), conditioned on past decisions, from the characteristic function of the decision variable, (2) getting the unconditional SEP using a Markov model of the decision process.

We derive an upper bound and investigate some approximations on the symbol error probability (SEP) for coherent detection of M-ary phase-shift keying, using an array of antennas with optimum combining in wireless systems in the presence of multiple uncorrelated equal-power cochannel interferers and thermal noise in a Rayleigh fading environment. Our results are general and valid for an arbitrary number of antenna elements as well as an arbitrary number of interferers. In particular, the exact SEP is derived for an arbitrary number of antennas and interferers; the computational complexity of the exact solution depends on the minimum number of antennas and interferers. Moreover, closed-form approximations are provided for the cases of dual optimum combining with an arbitrary number of interferers, and of two interferers with an arbitrary number of antenna elements. We show that our bounds and approximations are close to Monte Carlo simulation results for all cases considered in this paper.

We analyze the error performance of a wireless communication system employing transmit-receive diversity in Rayleigh fading. By focusing on the complex Gaussian statistics of the independent and identically distributed entries of the channel matrix, we derive a formula for the characteristic function (c.f.) of the maximum output signal-to-noise ratio. We use this c.f. to obtain a closed-form expression of the symbol error probability (SEP) for coherent binary keying. The method is easily extended to obtain the SEP for the coherent reception of M-ary modulation schemes.

Consider a Rake receiver for coherent binary antipodal signaling with: 1) a delayed received signal configuration; 2) weight estimation by matched filtering using the reference signal along with the decisions of the previous M symbol intervals; and 3) predetection maximal-ratio combining (MRC). The weight estimation errors here are not independent of the additive noise, and do not fit into the Gaussian weighting error model for MRC. Here we analyze the error performance of the receiver by obtaining the conditional symbol error probability, conditioned on past decisions, from the characteristic function of the decision variable, and getting the unconditional error probability (UEP) for a block of M consecutive symbols using a Markov model of the decision process. The channel is Rayleigh fading with independent and identically distributed branch gains. Results show that the error performance of the Gaussian distributed weighting error model is a bound for that of multiple symbol weight estimation by matched filtering, and the steady state UEP decreases with increase of M, but the amount of decrease reduces as M increases.

In this paper, expressions for multivariate Rayleigh and exponential probability density functions (PDFs) generated from correlated Gaussian random variables are presented. We first obtain a general integral form of the PDFs, and then study the case when the complex Gaussian generating vector is circular. We consider two specific circular cases: the exchangeable case when the variates are evenly correlated, and the exponentially correlated case. Expressions for the multivariate PDF in these cases are obtained in integral form as well as in the form of a series of products of univariate PDFs. We also derive a general expression for the multivariate exponential characteristic function (CF) in terms of determinants. In the exchangeable and exponentially correlated cases, CF expressions are obtained in the form of a series of products of univariate gamma CFs. The CF of the sum of exponential variates in these cases is obtained in closed form. Finally, the bivariate case is presented mentioning its main features. While the integral forms of the multivariate PDFs provide a general analytical framework, the series and determinant expressions for the exponential CFs and the series expressions for the PDFs can serve as a useful tool in the performance analysis of digital modulation over correlated Rayleigh-fading channels using diversity combining.

The pseudo-Wishart distribution arises when a Hermitian matrix generated from a complex Gaussian ensemble is not full-rank. It plays an important role in the analysis of communication systems using diversity in Rayleigh fading. However, it has not been extensively studied like the Wishart distribution. Here, we derive some key aspects of the complex pseudo-Wishart distribution. Pseudo-Wishart and Wishart distributions are treated as special forms of a Wishart-type distribution of a random Hermitian matrix generated from independent zero-mean complex Gaussian vectors with arbitrary covariance matrices. Using a linear algebraic technique, we derive an expression for the probability density function (p.d.f.) of a complex pseudo-Wishart distributed matrix, both for the independent and identically distributed (i.i.d.) and non-i.i.d. Gaussian ensembles. We then analyze the pseudo-Wishart distribution of a rank-one Hermitian matrix. The distribution of eigenvalues of Wishart and pseudo-Wishart matrices is next considered. For a matrix generated from an i.i.d. Gaussian ensemble, we obtain an expression for the characteristic function (cf) of eigenvalues in terms of a sum of determinants. We present applications of these results to the analysis of multiple-input multiple-output (MIMO) systems. The purpose of this work is to make researchers aware of the pseudo-Wishart distribution and its implication in the case of MIMO systems in Rayleigh fading, where the transmitted signals are independent but the received signals are correlated. The results obtained provide a powerful analytical tool for the study of MIMO systems with correlated received signals, like systems using diversity and optimum combining, space-time systems, and multiple-antenna systems.

We use a virtual-branch technique to derive higher order statistics of the output signal-to-noise ratio (SNR) of antenna subset diversity in a multipath fading environment. In particular, closed-form expressions of the cumulants, central moments, skewness, and kurtosis for various antenna subset diversity schemes are derived. These measures characterize the statistical behavior of the output SNR distribution.

We present an analysis of a hybrid selection/maximal-ratio combining (H-S/MRC) diversity system over an evenly correlated slow frequency-nonselective Nakagami fading channel. In this system, the L branches with the largest instantaneous signal-to-noise ratio (SNR) out of N available branches are selected and combined using maximal-ratio combining. From the joint characteristic function (c.f.) of the instantaneous branch SNR, we obtain an expression for the c.f. of the combiner output SNR as a series of elementary c.f.'s. The expression can be conveniently used to obtain the symbol error probability of coherent detection of different M-ary modulation schemes.

We analyze the acquisition of direct-sequence-spread-spectrum signals by an antenna array of M elements in a flat Rayleigh fading environment subject to additive stationary temporally-uncorrelated zero-mean Gaussian interference. The observations are complex baseband sampled signal vectors received at the array elements at discrete time instants. The pseudorandom code is periodic with period K and orthogonal to all its shifted versions. The acquisition process requires estimation of the received code lag from K consecutive M /spl times/ 1 received signal vectors. We find the maximum likelihood estimate of the code lag when the data, which is binary, is constant during the acquisition process. Using the sufficient statistic of the estimate, we analyze the performance of the acquisition system. In the case of independent and identically distributed Rayleigh fading and spatially-white Gaussian interference, we derive a closed-form expression for the probability of correct decision. The bias of the code lag estimate and the mean-square estimation error are also presented.

We analyze the error performance of coherent binary keying with optimum combining in interference and noise using the joint probability density function of the eigenvalues of the interference correlation matrix. A flat Rayleigh fading environment with space diversity, equipower interferers, and additive white Gaussian noise is considered. Let L denote the diversity order and N the number of interferers. The interference correlation matrix follows a Wishart distribution when N/spl ges/L, and a pseudo-Wishart distribution when N<L. We treat both the cases of N/spl ges/L and N

We present an analysis of a hybrid selection/maximal-ratio combining diversity system over an evenly correlated slow frequency-nonselective Nakagami fading channel, where the correlation coefficient between any pair of the diversity branch gain amplitudes is the same, and all average branch signal-to-noise ratios (SNRs) are equal. In this system, the L branches with the largest instantaneous SNR out of N available branches are selected and combined using maximal-ratio combining. From the joint characteristic function (cf) of the instantaneous branch SNRs, we obtain an expression for the cf of the combiner output SNR as a series of elementary cfs. The expression can be conveniently used to obtain the symbol error probability of coherent detection of different M-ary modulation schemes. We illustrate our methodology using M-ary phase-shift keying as an example.

The bit error probability (BEP) for coherent detection of binary signals with dual-diversity predetection equal gain combining is derived using the Beaulieu (1991) series. In particular, we consider a correlated Rayleigh fading channel with unequal branch signal-to-noise ratios. The BEP expression is in terms of the power correlation coefficient of the branches, is easy to compute, and depicts clearly the effect of correlated fading on the error performance.

We analyze the performance for the noncoherent reception of M-ary orthogonal frequency shift keying with postdetection equal gain combining over a correlated fading channel. Two kinds of correlated fading statistics are considered: (1) Nakagami fading in which the diversity branches can have unequal signal-to-noise ratios (SNRs) as well as different m-parameters and (2) Rician fading in which the diversity branches can have unequal SNRs. Using the characteristic function of the combiner output SNR, closed-form expressions for the symbol error probability are obtained.

We analyze the error performance of a wireless communication system employing transmit-receive diversity in Rayleigh fading. By focussing on the complex Gaussian statistics of the independent and identically distributed entries of the channel matrix, we derive a formula for the characteristic function (cf) of the maximum output signal-to-noise ratio (SNR). We use this cf to obtain a closed-form expression of the symbol error probability (SEP) for coherent binary keying. An approximate expression for the SEP when the average SNR per branch is large is also obtained. The method can be easily extended to obtain the SEP of M-ary modulation schemes.

We consider a K-transmit dual-receive diversity communication system employing K antennas for transmission and two antennas for reception. The desired signal is corrupted by N interfering sources apart from additive white Gaussian noise. The channel is Rayleigh fading. As a result, the channel matrix for the desired signal and the propagation vectors of the interferers have zero-mean complex Gaussian entries; the entries are assumed to be independent and identically distributed. The complex receive weight vector used for combining the received signals is chosen so as to maximize the output signal-to-interference-plus-noise ratio (SINR). From the statistics of the channel matrix and the propagation vectors of the interferers, we derive a closed-form expression for the probability density function (p.d.f.) of the maximum output SINR. This p.d.f. can be used to obtain the symbol error probability for various digital modulation schemes.

We analyze the error performance for the noncoherent reception of M-ary orthogonal frequency shift keying with postdetection equal gain combining (EGC) over a correlated fading channel. Two kinds of correlated fading statistics are considered: (1) Nakagami fading in which the diversity branches can have different m-parameters, (2) Rician fading in which the in-phase component of the complex channel gain of any branch can be correlated with the quadrature components of the gains of all other branches. Using the characteristic function of the combiner output signal-to-noise-ratio, closed-form expressions for the symbol error probability are obtained.

Using a series approach, expressions for the average symbol error probability (SEP) of coherent binary signals over a correlated Rayleigh fading channel with dual predetection equal gain combining (EGC) and selection diversity (SD) are derived. For both EGC and SD cases, the SEP is in terms of the correlation coefficient of the branch amplitudes, which is easy to compute and depicts clearly the effect of correlated fading on the error performance.

We use a virtual branch technique to derive higher order statistics of the output signal-to-noise ratio (SNR) of hybrid selection/maximal-ratio combining (H-S/MRC) in a multipath fading environment. In particular, the cumulants, central moments, skewness and kurtosis are derived. We consider the case of independent Rayleigh fading with equal receive SNR averaged over the fading on each diversity branch.

The process of communication jamming can be modeled as a two-person zero-sum noncooperative dynamic game played between a communicator (a transmitter-receiver pair) and a jammer. We consider a one-way time-slotted packet radio communication link in the presence of a jammer, where the data rate is fixed and (1) in each slot, the communicator and jammer choose their respective power levels in a random fashion from a zero and a positive value; (2) both players are subject to temporal energy constraints which account for protection of the communicating and jamming transmitters from overheating. The payoff function is the time average of the mean payoff per slot. The game is solved for certain ranges of the players' transmitter parameters. Structures of steady-state solutions to the game are also investigated. The general behavior of the players' strategies and payoff increment is found to depend on a parameter related to the payoff matrix, which me call the payoff parameter, and the transmitters' parameters. When the payoff parameter is lower than a threshold, the optimal steady-state strategies are mixed and the payoff increment constant over time, whereas when it is greater than the threshold, the strategies are pure, and the payoff increment exhibits oscillatory behavior.

For binary noncoherent orthogonal frequency-shift keying and binary differential phase-shift keying over slow nonselective Rician fading channels having arbitrarily correlated branches and unequal branch powers, a closed-form expression for the symbol-error probability in the case of postdetection equal-gain combining is obtained directly from the characteristic function of the decision variable.

Hybrid selection/maximal-ratio combining (H-S/MRC) is a reduced-complexity diversity combining scheme, where L out of N diversity branches (with the largest signal-to-noise ratio (SNR) at each instant) are selected and combined using maximal-ratio combining (MRC). We derive closed-form expressions for the symbol error probability (SEP) of a H-S/MRC diversity system with arbitrary L and N. We consider coherent detection of M-ary phase-shift keying (MPSK) for the case of independent Rayleigh fading with equal SNR averaged over the fading.