This paper introduces an unmanned aerial vehicle (UAV)-enabled network slicing problem to provide content delivery, sensing data gathering, and mobile edge computing (MEC) services. Three tenants provide services to their clients by sharing a common infrastructure of a set of UAVs. The content delivery tenant needs to guarantee that each of its clients (users) receives the required content, the sensing tenant aims to gather an adequate amount of uncorrelated data, and the MEC tenant provides computing service to its clients. An energy consumption minimization framework is considered to meet the tenants’ requirements by optimizing the number of deployed UAVs, the deployment location of each UAV, the transmit power of each deployed UAV, the user-UAV association, and the transmission power as well as the computing resources of each UAV. Taking into account the spatial correlation among the sensing users, a subset of these users is activated to gather the required sensing information. A solution approach technique inherited from graph theory is presented, in which the Lagrange approach derives the transmission power and computing resource allocation expressions. Simulation results illustrate that the proposed framework significantly reduces the total energy consumption.

This work is on the beamforming designs for the interference cancellation and mitigation in a system where multiple ground base stations equipped with uniform linear antenna arrays communicate with their associated unmanned aerial vehicle (UAV) users with the same time-frequency resource. Under the line-of-sight (LOS) channel condition, the interference between non-associated pairs of ground base stations and UAVs is a prominent issue that degrades the communication performance. For both the uplink and downlink communications, through identifying the beamforming vectors with polynomials, we derive beamforming solutions in closed-forms that can fully cancel the interference and have the highest SINR under the interference-free condition. The SINR expressions of the proposed interference-free designs are also obtained in closed-form, revealing the effect of the systems parameters and the UAV locations. For the uplink transmissions, the SINR-maximum receive beamforming design is also investigated, where the beamforming solution and the SINR result are obtained in closed-forms. Simulation results are provided for the sum-rate performance of the beamforming designs and for the validation of the theoretical analysis.

In this paper, we investigate the problem of jamming detection and channel estimation during multi-user uplink beam training under random pilot jamming attacks in beamspace massive multi-input-multi-output (MIMO) systems. For jamming detection, we distinguish the signals from the jammer and the user by projecting the observation signals onto the pilot space. By using the multiple projected observation vectors corresponding to the unused pilots, we propose a jamming detection scheme based on the locally most powerful test (LMPT) for systems with general channel conditions. Analytical expressions for the probability of detection and false alarms are derived using the second-order statistics and likelihood functions of the projected observation vectors. For the detected jammer along with users, we propose a two-step minimum mean square error (MMSE) channel estimation using the projected observation vectors. As a part of the channel estimation, we develop schemes to estimate the norm and the phase of the inner-product of the legitimate pilot vector and the random jamming pilot vector, which can be obtained using linear MMSE estimation and a bilinear form of the multiple projected observation vectors. From simulations under different system parameters, we observe that the proposed scheme improves the detection probability by more than 25% compared to the baseline at medium-to-high channel correlation level. In addition, the proposed scheme effectively supports zero-forcing precoding, thus enabling reliable data transmission in jamming scenarios, specifically, achieving a symbol error rate (SER) of less than 10−3at a jamming-to-signal ratio of 10 dB and a signal-to-noise ratio of 5 dB.

Integrated sensing and communication (ISAC) is an emerging technique to enable radar and communication systems deployment on a shared hardware, channel characteristics, signal processing methods, etc. This integration improves the deployment efficiency and requires more sophisticated resource allocation and optimization techniques. The ISAC signal is designed to sense targets and to carry private information which could be at risk of being eavesdropped. This paper considers an ISAC framework in which a set of aerial eavesdroppers poses the threat of intercepting the downlink communication from a base station to a set of users. The eavesdroppers are moving, and their unknown locations are estimated based on the echo signal. A maximum likelihood-based scheme is developed to estimate the eavesdroppers’ channels, including coarse estimation with refines to estimate each eavesdropper’s complex channel gain, elevation and azimuth angles. The corresponding Cramér-Rao lower bounds of the estimated parameters are also provided. Given that the eavesdroppers are moving, a long short-term memory (LSTM) deep network is employed to predict their channels and also to enable a less frequent estimation process. Meta-learner LSTM is also presented to provide few-shot learning and provide generalization capability to any trajectory with a few fine-tuning steps. Based on the predicted eavesdroppers’ channels, two secure precoding algorithms are developed based on successive convex approximation and zero forcing techniques to improve the sum secrecy rate for the users. Simulation results illustrate that the developed framework provides substantial improvement in communication secrecy when compared with other benchmark approaches.

This paper considers an integrated sensing and communication (ISAC) system framework, in which an aerial eavesdropper poses the threat to intercept the downlink communication from a base station to a set of users. The eavesdropper is moving and its unknown location is estimated based on the echo signal. A maximum likelihood-based scheme is developed to estimate the eavesdropper channel, which performs a coarse estimation and further refines the estimated parameters. A long short-term memory deep network is employed to predict the eavesdropper channel and also to enable a less frequent estimation process. Based on the predicted eavesdropper’s channel, a precoding optimization algorithm is developed to improve the sum secrecy rate for the users. Simulation results illustrate that the developed framework provides substantial improvement in the communication secrecy when compared with other benchmark approaches.

In frequency division duplexing (FDD) cell-free massive MIMO, the acquisition of the channel state information (CSI) is very challenging because of the large overhead required for the training and feedback of the downlink channels of multiple cooperating base stations (BSs). In this paper, for systems with partial uplink-downlink channel reciprocity, and a general spatial domain channel model with variations in the average port power and correlation among port coefficients, we propose a joint-port-selection-based CSI acquisition and feedback scheme for the downlink transmission with zero-forcing precoding. The scheme uses an eigenvalue-decomposition-based transformation to reduce the feedback overhead by exploring the port correlation. We derive the sum-rate of the system for any port selection. Based on the sum-rate result, we propose a low-complexity greedy-search-based joint port selection (GS-JPS) algorithm. Moreover, to adapt to fast time-varying scenarios, a supervised deep learning-enhanced joint port selection (DL-JPS) algorithm is proposed. Simulations verify the effectiveness of our proposed schemes and their advantage over existing port-selection channel acquisition schemes.

In this paper we derive the Fisher information matrix (FIM) and Cramér-Rao lower bound (CRLB) for positioning a terminal with a planar large intelligent surface (LIS), under Rician channel. For a disk-shaped continuous LIS and a terminal located on the central perpendicular line (CPL) of the LIS, we obtain expressions for the CRLBs in the form of a single integration. For the situation that the terminal is far from the LIS compared to the LIS radius and the situation with an asymptotically large LIS, closed-form approximations of the CRLBs are derived, based on which scalings and properties of the positioning precision with respect to different system parameters are obtained. For positioning a terminal with arbitrary location, we derive closed-form expressions of the CRLBs when the terminal is far from the LIS and the wavelength is small. When the surface area is small and the path-loss exponent is not larger than 5, the CRLBs of a CPL-terminal are smaller than those of a non-CPL terminal for all three dimensions, while the reverse may occur when the surface area grows large enough. We also carry out a comparative study of the continuous and discrete models of the LIS. Numerical results are presented to validate the precision of our theoretical analysis and approximated performance.

The downlink non-orthogonal multiple access (NOMA) transmissions from a holographic multi-input multi-output surface (HMIMOS) transmitter to multiple single-antenna users are investigated in this work. And we focus on the power saving design when the HMIMOS has a massive number of elements. For single-cluster NOMA transmissions implemented by a single-RF-chain HMIMOS-based transmitter, the required transmit power to maintain the quality of service (QoS) of all users are derived and two holographic beamforming schemes aiming at minimizing the required transmit power are developed. For multi-cluster NOMA transmissions implemented by a multi-RF-chain HMIMOS-based transmitter, a two-layer partitioning problem is formulated and solved to minimize the power consumption. Numerical results are provided to validate our theoretical analysis. It is shown that the NOMA scheme has lower power consumption than orthogonal multiple access (OMA) based multi-user transmission schemes when the number of RF chains is limited, and our proposed holographic beamforming schemes achieve lower power consumption than other holographic beamforming schemes.

Interleaved training has been studied for single-user and multi-user massive MIMO downlink with either fully-digital or hybrid beamforming. However, the impact of channel correlation on its average training overhead is rarely addressed. In this paper, we explore the channel correlation to improve the interleaved training for single-user massive MIMO downlink. For the beam-domain interleaved training, we propose a modified scheme by optimizing the beam training codebook. The basic antenna-domain interleaved training is also improved by dynamically adjusting the training order of the base station (BS) antennas during the training process based on the values of the already trained channels. Exact and simplified approximate expressions of the average training length are derived in closed-form for the basic and modified beam-domain schemes and the basic antenna-domain scheme in correlated channels. For the modified antenna-domain scheme, a deep neural network (DNN)-based approximation is provided for fast performance evaluation. Analytical results and simulations verify the accuracy of our derived training length expressions and explicitly reveal the impact of system parameters on the average training length. In addition, the modified beam/antenna-domain schemes are shown to have a shorter average training length compared to the basic schemes.

We propose an interleaved training design for multi-user massive MIMO downlink and study the performance thereof with the maximum-ratio transmission (MRT) precoding. In our proposed design, the channels are trained one BS antenna at a time and each training step is interleaved with the channel state information (CSI) feedback. The decision to continue training depends on whether or not the signal-to-interference-plus-noise (SINR) requirements of all users are satisfied with currently available instantaneous CSI. For the MRT precoding, we analyze the system performance in terms of the training length and the transmission success rate. Our simulation results show that the proposed training scheme has a significant performance advantage over existing full training scheme and fixed-length partial training scheme.

The channel state information (CSI) is crucial in communication systems assisted by intelligent reflecting surfaces (IRSs). This paper is on the phase estimation of individual channels in IRS-assisted communication systems with single-antenna transceivers under the correlated Rayleigh fading. We consider both the fully-active-IRS where all IRS elements are active and the hybrid-IRS where partially IRS elements are active, where an active IRS element is equipped with a sensing device for pilot signal reception. We derive the maximum likelihood (ML) estimator for channel phases of all IRS elements based on the observations on active IRS elements. This estimator is also proved to be the minimum mean square error (MMSE), maximum a posterior (MAP) and minimum mean absolute error (MMAE) estimators. Then we conduct performance analysis in terms of the gain and the capacity of the cascaded transmitter-IRS-receiver channel with perfectly known and estimated individual channel phases. Numerical results are provided to show that the performance of IRS-assisted communication systems with our proposed phase estimator is close to that with perfect CSI and validate our theoretical analysis.

An interleaved training scheme is proposed for multi-user massive multi-input-multi-output (MIMO) downlink with maximum-ratio-transmission (MRT). The base station (BS) sends pilots to train the channels antenna-by-antenna and the training steps are interleaved with the feedback of the channel state information (CSI) from the users. For each training step of the interleaved scheme, the BS decides whether to continue or to stop the training process based on the quality-of-service (QoS) provided by the available CSI. The training time and the transmission success rate of the proposed scheme are analyzed with closed-form approximations derived. Simulations show that the proposed scheme can largely save the average training time without sacrificing the QoS of users. The analytical results are also verified via simulation.

This paper proposes a new scheme for distributed spectrum sensing in the blind scenario, wherein the channel gains, the signal power, and the noise power are unknown. By utilizing energy detection and homogeneity test concepts, the cognitive radios (CRs) make binary local decisions based on whether a CR has the maximum sample energy within a sampling window among all CRs. With independent channels, the use of this maximum energy indicator generates a desirable discrepancy among the CR decisions when the frequency band is in use. Closed-form results on the distribution of the CR decisions are obtained for Gaussian noises and signal. Asymptotic analytical expressions are derived on the detection performance of the proposed scheme. Simulation results show the advantage of the proposed scheme and validate the analysis.

This paper proposes a new scheme for blind distributed spectrum sensing (DSS), where multiple distributed cognitive radios (CRs) and a fusion center (FC) collaboratively detect the availability of a frequency band of interest under communications constraints without knowledge on the channels, signal power, or noise power. By following the energy detection and homogeneity test concepts, in the proposed scheme, the CRs make local binary decisions based on relative comparison of the total energy in a sampling window, particularly, whether a CR has the maximum total energy. With independent channels, the use of the maximum function generates desirable discrepancy among the CR decisions when the frequency band is in use. The introduction of the window size enables the balancing between communications costs and the performance. Closed-form results on the distribution of the CR decisions are obtained for Gaussian noises and signals. Further, asymptotic analytical expressions are derived on the detection performance of the proposed scheme for both the generalized likelihood ratio test (GLRT) and$\chi ^{2}$-test at the FC. Simulation results are shown which validate the theoretical results and show the advantage of the proposed scheme to others.

In this paper we study an intelligent reflecting surface (IRS) assisted non-orthogonal multiple access (NOMA) network where the direct link between the base station (BS) and one of the users is blocked and the IRS is deployed to serve the blocked user. The IRS designs under both the ideal IRS with continuous phase shifting and the non-ideal IRS with discrete phase shifting are considered. For both cases, by leveraging the isotropic random vector and the Laguerre series, we derive insightful results and closed-form expressions on performance measures including the average required transmit power, the outage probability, and the diversity order. Our analytical results show that the transmit power scales down linearly with the BS antenna number and quadratically with the IRS element number. The diversity order equals the smaller of the BS antenna number and the IRS element number with a scaling coefficient. Our results also reveal the effect of the phase quantization resolution to the system performance when non-ideal IRS is used. Numerical results are provided to validate the accuracy of our analysis and the non-ideal IRS with four or more bits for quantization is shown to achieve nearly the same performance as the ideal IRS.

A popular technique of designing multiple-input multiple-output (MIMO) communication systems relies on optimizing the positive semidefinite covariance matrix at the source. In this paper, a unified MIMO optimization framework based on the Karush-Kuhn-Tucker (KKT) conditions is proposed. In this framework, with the aid of matrix optimization theory,Theorem 1presents a generic optimal transmit covariance matrix for MIMO systems with diverse objective functions subject to various power constraints and different levels of channel state information (CSI). Specifically,Theorem 1fundamentally reveals that for a diverse family of MIMO systems, the optimal transmit covariance matrices associated with different objective functions under various power constraints can be derived in a unified generic water-filling-like form. When applyingTheorem 1to the case of multiple general power constraints, we firstly equivalently transform multiple power constraints into a single counterpart by introducing multiple weighting factors based on Pareto optimization theory. The optimal weighting factors can be found by the proposed modified subgradient method. On the other hand, for the imperfect MIMO system with statistical CSI errors, we firstly address the non-convexity of the robust optimization problem by following the idea of alternating optimization. Finally, our numerical results verify the optimal solution structure inTheorem 1and the global optimality of the proposed modified subgradient method, as well as demonstrate the performance advantages of the proposed alternating optimization algorithm.

In this paper, a statistical-based sphere decoding with increasing radius search (S-SD-IRS) algorithm is proposed, where the radiuses of the decoding hyperspheres are determined based on the statistical properties of the communication channel and additive noise. We show that the probability density functions (PDFs) of the q lowest squared distances in the closest lattice point problem can be approximated by Gumbel distributions with different parameters. Based on the obtained PDFs and by considering the characteristics of the fading channels and additive noise, we choose the radiuses for sphere decoding more efficiently than the conventional methods that ignore the characteristics of system. The performance achieved by the proposed algorithm is very close to the optimal maximum likelihood decoding (MLD) over a wide range of signal-to-noise ratios (SNRs), while the computational complexity, compared to existing sphere decoding variants, is significantly reduced. It is shown that the average number of lattice points inside the decoding hyperspheres drastically reduces in the proposed S-SD-IRS algorithm.

Massive multiple-input-multiple-output (MIMO) system inevitably faces the hardware cost and energy efficiency problem due to its large number of antennas at the base station (BS). The use of low-resolution analog-to-digital converters (ADCs), e.g., typical 1-bit ADCs, can effectively reduce the system cost. In this paper, we consider a massive MIMO uplink with ternary/three level ADCs. The design of typical linear combiner based detectors is given along with their analytical symbol-error-rate (SER) performance results. Analytical and simulation results show that 1) ternary ADCs can effectively compensate the SER performance gap between 1-bit and full-resolution ADCs; 2) optimal design of ternary ADCs for SER minimization can be referred to the existing design for quantization error minimization; 3) ternary ADCs perform better than 2-bit ADCs in energy efficiency. Thus, for some low-cost scenarios where implementing 2-bit ADCs for each antenna in massive MIMO may be even unaffordable, ternary ADC can be a good choice.

In this letter, for outage performance orientated large intelligent surfaces (LISs)-assisted point to point wireless systems with severely blocked direct link and Rayleigh fading channels,we first propose a jointly interleaved training and transmission design. Then a semi-closed form expression is derived for the average training overhead. And it is shown to be upper bounded by the minimum between the LIS size and a value explicitly dependent on the target receiver signal-to-noise-ratio (SNR). The upper bound gives the condition on the target SNR for achieving overhead saving compared to the full CSI scheme. And the overhead saving increases linearly with the LIS size for constant target SNR. Non-negligible overhead saving is still available even though one increases the target SNR with larger LIS, e.g., as the square of the LIS size for fully exploiting the beamforming gain. Finally, we indicate the impact of practical phase quantization on the training and feedback overhead. Simulations verify these results and show that the proposed scheme can significantly reduce the training overhead without performance loss compared to the full CSI scheme.

High power consumption and hardware cost have motivated using low-resolution analog-to-digital converters (ADCs) for practical massive multiple-input multiple-output (mMIMO) systems. In this paper, we consider a general mMIMO multi-way relaying system with a multi-level mixed-ADC architecture in which each antenna is connected to an ADC pair with an arbitrary resolution. By leveraging on Bussgang's decomposition theorem and Lloyd-Max algorithm for quantization, tight closed-form approximations are derived for the average achievable rates of zero-forcing (ZF) relaying considering both perfect and imperfect channel state information (CSI). To handle such a challenging setup, we develop a novel method for the achievable rate analysis using distributions of the singular values of Gaussian matrices and properties of Haar matrices. We demonstrate that the average achievable rate has an almost linear relation with the square of the average of quantization coefficients pertaining to the ADC resolution profile. In addition, in the medium to high SNR region, the ADC resolutions have a more significant effect on the rate compared to the number of antennas. Our work also reveals that the performance gap between the perfect and imperfect CSI cases is smaller for lower ADC resolutions, hence imperfect CSI is better tolerated at lower resolutions.

This paper considers a multiple-input multiple-output (MIMO) multi-way relay network (MWRN) where users exchange their information via a multi-way relay equipped with a large-scale antenna array, i.e., massive MIMO multi-way relay. Further, each antenna at the relay station is assumed to have a pair of low-resolution analog-to-digital converters (ADCs) to reduce the energy consumption and hardware cost at the relay. Lloyd-max algorithm is used to find the mean-squared error (MSE) optimum quantization labels and thresholds for the ADCs. With perfect channel state information (CSI) and zero-forcing (ZF) beam-forming for both reception and transmission at the relay, a closed-form approximation for the average achievable rate of each pair of users is derived with the help of Bussgang's decomposition. The results enable us to understand the achievable rate behavior with respect to system parameters, and especially to quantify the performance degradation caused by low-resolution ADCs. Numerical results verify the validity of Bussgang's theorem in our case, and that the derived result is an accurate performance predictor of the network. Further, both analytical and theoretical results reveal that the effect of ADC resolutions on the rate performance is as significant as the relay and users' transmit powers.

We consider the use of deep neural network (DNN) to develop a decision-directed (DD)-channel estimation (CE) algorithm for multiple-input multiple-output (MIMO)-space-time block coded systems in highly dynamic vehicular environments. We propose the use of DNN for k -step channel prediction for space-time block code (STBC), and show that deep learning (DL)-based DD-CE can remove the need for Doppler rate estimation in fast time-varying quasi stationary channels, where the Doppler rate varies from one packet to another. Doppler rate estimation in this kind of vehicular channels is remarkably challenging and requires a large number of pilots and preambles, leading to lower power and spectral efficiency. We train two DNNs which learn the real and imaginary parts of the MIMO fading channels over a wide range of Doppler rates. We demonstrate that by these DNNs, DD-CE can be realized with only priori knowledge about Doppler rate range and not the exact value. For the proposed DD-CE algorithm, we also analytically derive the maximum likelihood (ML) decoding algorithm for STBC transmission. The proposed DL-based DD-CE is a promising solution for reliable communication over vehicular MIMO fading channels without accurate mathematical models. This is because DNNs can intelligently learn the statistics of the fading channels. Our simulation results show that the proposed DL-based DD-CE algorithm exhibits lower error propagation compared to existing DD-CE algorithms which require perfect knowledge of the Doppler rate.

This paper investigates the relay selection (RS) problem for multi-hop full-duplex relay networks where multiple source-destination (SD) pairs compete for the same pool of relays, under the attack of multiple eavesdroppers. To enhance the physical-layer security, within a given coherence time, our objective is to jointly assign the available relays at each hop to different SD pairs to maximize the minimum secrecy rate among all pairs. Two RS schemes, optimal RS and suboptimal RS (SRS), are proposed for two-hop networks based on global channel state information (CSI) and only SD pairs CSI, respectively. Since all users can communicate within the same coherence time, our joint RS schemes are important for the user-fairness and ultra-reliable low-latency communications. To evaluate the performance, the exact secrecy outage probability of the SRS scheme is derived under two residual self-interference models. The asymptotic analysis shows that the SRS scheme achieves full diversity. A relay-based jamming scheme is also proposed by using unassigned relays for user communications. Finally, the two-hop RS schemes and the analysis are extended to the general multi-hop network with multiple eavesdroppers. The numerical results reveal interesting fundamental trends where the proposed schemes can significantly enhance the secrecy performance.

In this paper, a deep learning (DL)-based sphere decoding algorithm is proposed, where the radius of the decoding hypersphere is learned by a deep neural network (DNN). The performance achieved by the proposed algorithm is very close to the optimal maximum likelihood decoding (MLD) over a wide range of signal-to-noise ratios (SNRs), while the computational complexity, compared to existing sphere decoding variants, is significantly reduced. This improvement is attributed to the DNN's ability of intelligently learning the radius of the hypersphere used in decoding. The expected complexity of the proposed DL-based algorithm is analytically derived and compared with existing ones. It is shown that the number of lattice points inside the decoding hypersphere drastically reduces in the DL-based algorithm in both the average and worst-case senses. The effectiveness of the proposed algorithm is shown through the simulation for high-dimensional multiple-input multiple-output (MIMO) systems, using high-order modulations.

In this paper, we study the beam-based training design for the single-user (SU) hybrid massive antenna system based on outage probability performance. First, an interleaved training design is proposed where the feedback is concatenated with the training procedure to monitor the training status and to have the training length adaptive to the channel realization. Then, the average training length and outage probability are derived for the proposed interleaved training and SU transmission. Analytical results and simulations show that the proposed interleaved scheme achieves the same outage performance as the traditional full-training scheme but with significant saving in the training overhead.

This paper studies the relay selection (RS) problem for full-duplex (FD) relay networks with multiple source-destination (SD) pairs under the attack of colluding eavesdroppers. Based on available channel state information (CSI), both optimal relay selection (ORS) and suboptimal relay selection (SRS) schemes are considered to maximize the minimum secrecy rate among all pairs in order to enhance the physical-layer security. The secrecy performance of the more practical SRS scheme is then evaluated in terms of intercept probability and diversity order. The SRS achieves full diversity when the gains of the main-to- eavesdropper and the main-to-interference channels increase asymptotically.

Zero-forcing (ZF) precoding plays an important role for massive MIMO downlink due to its near optimal performance in high signal-to- noise (SNR) region. However, the high computation cost of the involved matrix inversion hinders its application in practical large-scale systems. In this paper, we adopt the first order Neumann series (NS) expansion for a low-complexity approximation of matrix inversion. Compared to existing NS based schemes, we introduce a relaxation parameter jointly with one user's channel interference to others into the precondition matrix and propose the identity-plus- column NS (ICNS) method. By further exploiting the multi-user diversity gain via choosing the user with largest interference to others, the ordered ICNS method is also proposed. Moreover, the closed-form sum-rate approximation of the ICNS method is derived. Simulations verify our analytical results and the advantage of the proposed schemes over other existing low-complexity ZF precodings for massive MIMO systems with correlated channels and not-so-small loading factor.

Zero-forcing (ZF) precoding plays an important role for massive MIMO downlink due to its near optimal performance. However, the high computation cost of the involved matrix inversion hinders its application. In this paper, we adopt the first order Neumann series (NS) for a low-complexity approximation. By introducing a relaxation parameter jointly with the channel non-orthogonality between one selected user and others into the precondition matrix, we propose the identity-plus-column NS (ICNS) method. By further choosing the user with the least channel orthogonality with others, the ordered ICNS method is also proposed. Moreover, the sum-rate approximations of the proposed ICNS method and the competitive existing identity matrix based NS (INS) method are derived in closed-form, based on which the performance loss of ICNS due to inversion approximation compared with ideal ZF and its performance gain over INS are explicitly analyzed for three typical massive MIMO scenarios. Finally, simulations verify our analytical results and also show that the proposed two designs achieve better performance-complexity tradeoff than ideal ZF and existing low-complexity ZF precodings for practical large antenna number, correlated channels, and not-so-small loading factor.

The ever increasing demands for mobile network access have resulted in a significant increase in bandwidth usage. By improving the system spectral efficiency, multi-way relay networks (MWRNs) provide promising approaches to address this challenge. In this paper, we propose a novel linear beamforming design, namely partial zero-forcing (PZF), for MWRNs with a multiple-input-multiple-output relay. Compared to zero-forcing (ZF), PZF relaxes the constraints on the relay beamforming matrix such that only partial user-interference, instead of all, is canceled at the relay. The users eliminate the remaining interferences through self-interference and successive interference cancellation. A sum-rate maximization problem is formulated and solved to exploit the extra degrees-of-freedom resulted from PZF. Simulation results show that the proposed PZF relay beamforming design achieves significantly higher network sum-rates than the existing linear beamforming designs.

This paper analyzes the outage probability for the uplink of multi-user massive multi-input-multi-output systems with a mixed analog-to-digital converter (ADC) architecture, in which the base station (BS) is equipped with ADCs of different resolution levels. Maximum-ratio combining (MRC) is used at the BS. By deriving the distribution of the user-interference power and statistical properties of other components in the signal-to-interference-plus-noise-ratio (SINR), a tight closed-form approximation for the outage probability is obtained for a general mixed ADC structure with any resolution profile. Then, two methods for the ADC resolution profile optimization are proposed considering both the outage probability and the BS energy consumption. The first method uses low-complexity incremental search to minimize the BS energy consumption for given outage probability constraint. The other method is based on multi-objective optimization and adopts a discrete-variation of the classic non-dominated sorting genetic algorithm II (NSGA-II). Numerical results are presented to validate the outage probability results. Furthermore, it is shown that the two proposed mixed-resolution ADC designs largely outperform a two-level ADC structure and provide more choices than the uniform ADC structure for resolving the tradeoff between outage probability and BS energy consumption.

This paper provides a comprehensive scaling law and performance analysis for multi-user massive multiple-input-multiple-output (MIMO) relay networks, where the relay is equipped with a massive antenna array and uses maximal-ratio combining/maximal-ratio transmission (MRC/MRT) for low-complexity processing. Imperfect channel state information (CSI) is considered for both source-relay and relay-destination channels. First, a sum-rate lower bound is derived, which manifests the effect of system parameters, including the numbers of relay antennas and users, the CSI quality, and the transmit powers of the sources and the relay. Via a general scaling model on the parameters with respect to the relay antenna number, the asymptotic scaling law of the signal-to-interference-plus-noise-ratio (SINR) is obtained, which shows quantitatively the tradeoff of the network parameters. In addition, a sufficient condition on the parameter scalings for the SINR to be asymptotically deterministic is given, which covers existing results on such analysis as special cases. Then, the scenario where the SINR increases linearly with the relay antenna number is studied. The sufficient and necessary condition on the parameter scaling for this scenario is proved. It is shown that in this case, the interference power is not asymptotically deterministic, and then, the average bit error rate is analyzed.

Statistical beamforming is an important technique for multi-user massive MIMO downlink, since it depends on the downlink channel covariance only. In this paper, we first derive an explicit analytical sum-rate expression for generic channel covariance-based beamforming scheme. Then, a low-complexity joint statistical beamforming and user scheduling algorithm via greedy search is proposed, where the beamforming is based on the signal-to-leakage-and-noise-ratio (SLNR) for closed-form design and tractable analysis, while the user scheduling is based on the derived sum-rate expression. Further, with the help of large-scale asymptotic simplifications and the introduction of the interference user number parameter, a simple analytical sum-rate expression of the joint algorithm is derived for channels with flat power beam spectrum. The expression explicitly exhibits the sum-rate behavior with respect to different network parameters and captures the effect of sum-rate-based user scheduling. Finally, simulation results are provided to verify our analytical results and to show the advantage of the proposed joint design compared with existing schemes.

This letter analyzes the user-interference and outage probability for single-cell multi-user massive multi-input-multi-output (MIMO) systems with matched-filter (MF) precoding. Existing performance studies on massive MIMO systems have focused on the sum-rate by deriving the asymptotic deterministic equivalence. In this work, we treat the user-interference as random, and derive a tight closed-form approximation for the distribution of the interference power. This enables the analysis of the outage probability. The derived results are shown to have accurate match with the simulation.

We analyze the achievable rate of the uplink of a single-cell multi-user distributed massive multiple-input-multiple-output (MIMO) system. Each user is equipped with single antenna and the base station (BS) is equipped with a large number of distributed antennas. We derive an analytical expression for the asymptotic ergodic achievable rate of the system under zero-forcing (ZF) detector. In particular, we consider circular antenna array, where the distributed BS antennas are located evenly on a circle, and derive an analytical expression and closed-form bounds for the achievable rate of an arbitrarily located user. Subsequently, closed-form bounds on the average achievable rate per user are obtained under the assumption that the users are uniformly located. Based on the bounds, we can understand the behavior of the system rate with respect to different parameters and find the optimal location of the circular BS antenna array that maximizes the average rate. Numerical results are provided to assess our analytical results and examine the impact of the number and the location of the BS antennas, the transmit power, and the path-loss exponent on system performance. Simulations on multi-cell networks are also demonstrated. Our work shows that circularly distributed massive MIMO system largely outperforms centralized massive MIMO system.

Channel estimation schemes based on SVD (singular value decomposition) are proposed for reduced-rank multi-input-multi-output (MIMO) systems, where instead of estimating each entry of the channel matrix, the singular spaces and singular values are estimated. When the channel rank is fixed and known, the maximum-likelihood (ML) estimator is derived. When the channel rank is random and unknown, a threshold-based rank detection algorithm using the singular values is adopted. In finding the threshold, a lower bound on the correct detection probability is derived and the threshold is chosen to maximize the lower bound. Simulations show that the SVD-based estimation achieves lower MSE and higher capacity than the entry-based estimation for both cases.

For a multi-relay amplify-and-forward (AF) network, we investigate the power allocation problem during the channel training process for the destination to estimate the global channel state information (CSI) of the whole network. We consider two objective functions: the total mean-square-error (MSE) of all channel estimates and the end-to-end outage probability (OP) of the network under channel estimation error. Closed-form solutions for the joint power allocation among different relay paths and between the source and the relay at different training stages for each relay path are derived. Our simulation results demonstrate that the proposed MSE-based and OP-based power allocation schemes are superior to even power allocation.

In this paper, we adopt a novel efficiency measure, namely the received signal-to-noise-ratio (SNR) per unit power, in amplify-and-forward (AF) relay networks. The measure is addressed as the power-normalized SNR (PN-SNR). For several relay network scenarios, we solve the PN-SNR maximization problems and analyze the network performance. First, for single-relay networks, we find the optimal relay power control scheme that maximizes the PN-SNR for a given transmitter power. Then, for multi-relay networks with a sum relay power constraint, we prove that the PN-SNR optimization problem has a unique maximum, thus the globally optimal solution can be found using a gradient-ascent algorithm. Finally, for multi-relay networks with an individual power constraint on each relay, we propose an algorithm to obtain the globally optimal solution and also a low complexity algorithm for a suboptimal solution. Our results show that with the same average relay transmit power, the PN-SNR maximizing scheme is superior to the fixed relay power scheme not only in PN-SNR but also in the outage probability for both single and multi-relay networks. Compared with SNR-maximizing scheme, it is significantly superior in PN-SNR with moderate degradation in outage probability. Our results show the potential of using PN-SNR as efficiency measure in network design.

In this paper we study a cellular network, in which multiple-antenna users communicate with multiple-antenna base stations (BSs) through fixed infrastructure-based multiple antenna relay stations (RSs). With cooperation among the BSs and linear processing at the RSs, we aim to find the optimal precoding matrices at the users and the beamforming matrices at the RSs that jointly maximize the system sum rate. Unlike for the conventional uplink (without relays), the sum-rate optimization is non-convex. More so, there is cross-coupling of the RSs' channels due to the forwarded interferences by the RSs. Firstly, we incorporate interference pre-cancelation into the RSs' beamforming designs. Secondly, we match each RS's beamforming matrix to the corresponding backward and forward channels such that the end-to-end channel is diagonalizable. Furthermore, we propose an iterative alternating minimization based algorithm to maximize the system sum rate. Finally, we consider two user-RS scheduling/mapping schemes namely the “random” and “channel-aware” schemes. Simulation results show that the channel-aware scheme outperform the random scheme with the performance gap unchanged with increasing number of antennas at the nodes.

In this paper, we adopt a novel efficiency measure, namely, the received signal to noise ratio (SNR) per unit power, in relay network design. First, limitations of conventional efficiency measures, spectral efficiency and energy efficiency, are discussed to motivate the SNR-per-unit-power (SNR-PUP) measure. Then for a single-relay network which uses amplify-and-forward (AF) protocol, we find the optimal relay power that maximizes the SNR-PUP for a given transmitter power. The average relay power, the SNR-PUP, and the outage probability of the proposed design are investigated analytically and numerically, and are compared with the conventional design where the relay power is fixed. We also consider a general multi-relay network and use gradient-ascent method for the SNR-PUP maximization. Our results show that with the same average relay transmit power, the proposed design is superior not only in the SNR-PUP but also in the outage probability for both single and multi-relay networks.

For a multi-user multi-relay network with a total relay power constraint, we investigate the relay power allocation (PA) that maximizes the network sum-rate. Different users use orthogonal channels to avoid interference. With the optimal relay beamforming for each user, the problem reduces to finding the optimal power the relays use in total to help each user. We first prove that the problem is convex. Then a suboptimal solution is proposed in closed form. Further, the SNR and sum-rate are analyzed for networks with a large number of relay antennas. The asymptotic behaviour of the SNR is derived rigorously for the high transmit power regime. Simulation results are provided to show the significance of proper PA and to justify the analytical SNR and sum-rate results.

For a three-node amplify-and-forward (AF) relay network, we investigate the power allocation problem during the channel training process for the destination to estimate the global channel state information (CSI) of the whole network. Linear minimum-mean-square-error (LMMSE) estimation is adopted. The mean-square-error (MSE) of the channel estimation is analyzed, which shows that the quality of the source-to-relay channel estimation depends on the quality of the relay-to-destination channel and its estimation. The outage probability (OP) of the network with channel estimation error is also calculated. Then power allocations between the source and the relay for different training steps are derived based on the total MSE and the OP. The performance of the proposed power allocations is simulated and shown to be superior to even power allocation.

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

This letter considers the binary threshold system (TS) based detector for a general binary testing problem. First, the optimal binary TS that maximizes the area under the ROC curve (AUC), where ROC stands for the receiver operating characteristic, is derived. Then the noise-enhanced effect is investigated. The optimal noise that can achieve the maximum AUC is derived and shown to be deterministic. An example is shown to help justify the derived results.

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

In this paper, we consider a multi-user single-relay wireless network, where the relay facilitates transmissions of the users' signals to the destination. We study the relay power allocation among the users, and use bargaining theory to model the negotiation among the users on relay power allocation. By assigning a bargaining power to each user to indicate its transmission priority, we propose an asymmetric Nash bargaining solution (NBS)-based relay power allocation scheme. We also propose a distributed implementation for this solution, where each user only requires its local channel state information (CSI). We analytically investigate the impact of the bargaining powers on the relay power allocation and show that via proper selection of the bargaining powers, the proposed power allocation can achieve a balance between the network sum-rate and the user fairness. Then we generalize the NBS-based power allocation and its distributed implementation to multi-user multi-relay networks. Simulation results are shown to compare the proposed power allocation with sum-rate-optimal power allocation and even power allocation. The impact of the bargaining powers on the power allocation is also demonstrated via simulations.

This paper considers a multi-user single-relay wireless network, where the relay gets paid for helping the users forward signals, and the users pay to receive the relay service. We study the relay power allocation and pricing problem, and model the interaction between the users and the relay as a two-level Stackelberg game. In this game, the relay, modeled as the service provider and the leader of the game, sets the relay price to maximize its revenue; while the users are modeled as customers and the follower who buy power from the relay. For the relay power allocation among users, we use a bargaining game model to achieve a fair allocation. Based on the proposed fair relay power allocation rule, we then analyze the optimal relay power price that maximizes the relay's revenue, and derive the analytical solution. Simulation shows that the proposed power allocation scheme achieves a higher network sum-rate than the even power allocation, and is fairer than the sum-rate-optimal allocation. We also show that the proposed pricing and power allocation solution is consistent with the laws of supply and demand.

In this paper, we consider a multi-source single-relay wireless network, where the relay facilitates transmissions of the sources' signals to the destination. We study the relay power allocation among the sources, and use the bargaining theory to model the negotiation among the sources on fair allocation of the relay power. By assigning a bargaining power to each source to indicate its transmission priority, we propose an asymmetric Nash bargaining solution (NBS)-based relay power allocation scheme. The impact of the bargaining powers on the relay power allocation and network performance is analyzed. We show that the proposed scheme addresses the tradeoff between the sum-rate of the network and the fairness among the sources, and can be adapted to meet different requirements in different applications by proper selection of the bargaining powers.

For a general multi-input-multi-output (MIMO) relay network, an estimation method for the receiver to obtain the end-to-end channels is proposed. Instead of straightforwardly estimating entries of the end-to-end channel matrix, the proposed scheme takes into consideration the special structure of the end-to-end channel matrix. By parameterizing the channel matrix with its singular values and singular vectors using singular value decomposition (SVD), the proposed scheme estimates the singular values and left and right singular vectors, which are then combined to form an estimation of the overall channel matrix. The proposed estimation follows the maximum-likelihood (ML) estimation method. Simulations on the mean square error (MSE) of the channel estimation are presented, which show the advantage of the proposed scheme over straightforward estimation of the channel entries for networks whose transmitter and receiver are equipped with multiple antennas.

This paper investigates the channel estimations in a relay network with multiple transmit and receive antennas, including the estimation of the end-to-end channel matrix and the individual estimation of the transmitter-relay channels and the relay-receiver channels. For the end-to-end channel estimation, instead of directly estimating entries of the channel matrix, we use singular value decomposition (SVD) and estimate its largest singular value and singular vectors, which are then combined to form an estimation of the channel matrix. An approximate maximum-likelihood (ML) estimation is proposed, which is shown to become the exact ML estimation when the time duration of each training step equals the number of antennas at the transmitter. Simulation on the mean square error (MSE) shows that the SVD-based approximate ML estimation performs about the same as the exact ML estimation and is superior to entry-based estimations. For the individual channel estimation, we decompose each channel vector into the product of its length and direction, and find the ML estimation of each. By using an approximation on the probability density function (PDF) of the observations during training, an analytical ML estimation is derived. The ML estimation with the exact PDF is also investigated and a solution is obtained numerically. Simulation on the MSE shows that the two have similar performance. Compared with cascade channel estimations, its performance is superior for the relay-receiver channel estimation and comparable for the transmitter-relay channel estimation. Extension to the general multiple-antenna multiple-relay network is also provided.

In this paper, channel training and coherent decodings under channel estimation error are investigated for relay networks with one single-antenna transmitter, R single-antenna relays, and one R-antenna receiver. A two-stage training scheme is proposed to estimate both the relay-receiver and the transmitter-relay channels at the receiver, which are commonly required in amplify-and-forward (AF) relay networks. We use distributed space-time coding (DSTC) for data transmission and investigate the effect of channel estimation errors on network performance. Two coherent decodings are considered: mismatched decoding in which channel estimations are treated as if perfect, and matched decoding in which estimation error is taken into consideration. We show that for full diversity, with mismatched decoding, at least 3R symbol intervals are required for training; while with matched decoding, R+2 symbol intervals for training are enough. The complexities of the decoding schemes are investigated. To achieve a balance between performance and complexity, an adaptive decoding scheme is proposed. Simulated error rates are shown to justify the analytical results.

In this paper, channel training and coherent decodings with channel estimation errors are investigated in a relay network with one single-antenna transmitter, two single-antenna relays, and one double-antenna receiver. A two-stage training scheme is proposed to estimate both the relay-receiver and transmitter-relay channels at the receiver. We use distributed space-time coding (DSTC) for data transmission and investigate the effect of channel estimation errors on the diversity. Two coherent decodings are considered: mismatched decoding in which the channel estimations are treated as if perfect, and matched decoding which takes into account the estimation errors. We show that for full diversity, mismatched decoding requires at least 6 symbol intervals for training, while 4 symbol intervals for training are enough for matched decoding. On the other hand, the complexity of matched decoding is much higher. To achieve a balance between performance and complexity, an adaptive decoding scheme is proposed. Simulated network error rates are shown to justify the analytical results.

In this letter, we present an optimal joint relay selection (RS) and power allocation scheme for two-way relay networks which aim to establish a communication link between two transceivers with the help of one relay. Our approach is based on the maximization of the smaller of the received signal-to-noise-ratios (SNRs) of the two transceivers under a total transmit power budget. We show that this problem has a closed-form solution and requires only a single integer parameter (i.e, the index of the optimally selected relay) to be broadcasted to all relays. We also show that for large values of the total transmit power, the selection criterion can be approximated as the harmonic mean of the amplitudes of the relays' local channel coefficients. We evaluate the performance of our scheme numerically.

This letter considers two-relay networks with Rician fading channels. It is assumed that the receiver has full channel information while the relays know the channel means and covariances only. To optimize network performance, we combine distributed space-time coding (DSTC) with relay power allocation. For the high signal-to-noise ratio (SNR) regime, we analytically find the relay power allocation that minimizes an upper bound on the pairwise error probability (PEP). Simulation shows that the proposed scheme largely improves network reliability. In some cases, lack of power allocation causes diversity loss.

We study multi-user transmission and detection schemes for a multi-access relay network (MARN) with linear constraints at all nodes. In a (J, Ja, Ra, M) MARN, J sources, each equipped with Jaantennas, communicate to one M-antenna destination through one Ra-antenna relay. A new protocol called IC-Relay-TDMA is proposed which takes two phases. During the first phase, symbols of different sources are transmitted concurrently to the relay. At the relay, interference cancellation (IC) techniques, previously proposed for systems with direct transmission, are applied to decouple the information of different sources without decoding. During the second phase, symbols of different sources are forwarded to the destination in a time division multi-access (TDMA) fashion. At the destination, the maximum-likelihood (ML) decoding is performed source-by-source. The protocol of IC-Relay-TDMA requires the number of relay antennas no less than the number of sources, i.e., Ra≥ J. Through outage analysis, the achievable diversity gain of the proposed scheme is shown to be min {Ja(Ra- J + 1), RaM}. When M ≤ Ja(1- J-1/Ra), the proposed scheme achieves the maximum interference-free (int-free) diversity gain RaM. Since concurrent transmission is allowed during the first phase, compared to full TDMA transmission, the proposed scheme achieves the same diversity, but with a higher symbol rate.

This paper is on the channel training design for distributed space-time coding (DSTC) in multi-antenna relay networks. DSTC is shown to achieve full diversity in relay networks. To use DSTC, the receiver has to know both the channels between the relays and the receiver (Relay-Rx channels), and the channels between the transmitter and the relays (Tx-Relay channels). For the Relay-Rx channels, by sending pilot signals from the relays, the training problem can be solved using multi-input-multi-output (MIMO) training schemes. Given the knowledge of the Relay-Rx channels, to obtain estimations of the Tx-Relay channels at the receiver, DSTC is used. The linear minimum-mean-square-error (LMMSE) estimation at the receiver and the optimal pilot design that minimizes the estimation error are derived. We also investigate the requirement on the training time that can lead to full diversity in data transmission. An upper bound and a lower bound on the training time are provided. A novel training design whose training time length is adaptive to the quality of the Relay-Rx channels is also proposed. Simulations are exhibited to justify our analytical results and to show advantages of the proposed scheme over others.

This paper considers multi-access relay networks (MARNs) where two single-antenna users communicate to one N-antenna receiver via two hops of transmissions through one R-antenna relay. Nodes in the network are under two linear constraints. The relay linearly maps its received signal to generate its forwarding signal without decoding; the receiver has linear decoding complexity in the number of users. Since the relay-receiver link has more transmission paths than the link from each user to the relay, a two-step protocol, called TDMA-ICRec, is proposed. In the first step, both users timeshare the user-relay link. Linear combining is then performed at the relay to maximize the signal-to-noise-ratio (SNR) for each user. In the second step, the relay forwards both users' symbols concurrently to the receiver to enhance the transmission rate. At the receiver, an interference cancellation (IC) technique is used to decouple the users and ML decoding is conducted to recover each user's symbols. Two network scenarios are studied when the relay has two antennas and four antennas. Through analysis and simulation, when the receiver has more than two antennas, TDMA-ICRec achieves the same diversity as the full-TDMA-DSTC interference-free (int-free) scheme, yet with higher symbol rate.

This paper is on interference cancellation (IC) schemes for a two-user relay network where users are allowed to communicate simultaneously. The considered networks have one double-antenna half-duplex relay, single-antenna receiver but three scenarios on both users: single-antenna, double-antenna, and four-antenna. We apply the IC scheme, which was originally proposed for multi-antenna multi-user direct communication systems, to multi-user relay networks and propose a protocol called IC-Relay-TDMA, in which the relay cancels user interference and then amplifies and forwards the interference-free (int-free) user information to the receiver in TDMA. The maximum likelihood (ML) decoding at the receiver can be conducted symbol by symbol for both networks with single-antenna users and double-antenna users. Compared to the full TDMA scheme in which each user is allocated different time slots from end to end to avoid interference, IC-Relay-TDMA achieves the same diversity with a higher symbol rate when both users have two or four antennas.

This paper investigates the channel training and estimation problems for distributed space-time coding (DSTC). To use DSTC in multi-antenna relay networks, the receiver needs to know the channels between the relays and the receiver (Relay-R channels) and also the equivalent channels between the transmitter and the receiver (Equ-T-R channels). By sending pilot signals from the relays, the training of the Relay-R channels is equivalent to that of a multi-input-multi-output (MIMO) system. The training of the Equ-T-R channels can be conducted directly using DSTC; but it requires a long training period. Thus, a separate-training method is proposed, in which an estimation on the Equ-T-R channels is obtained from estimations on the channels from the transmitter to the relays (T-Relay channels) and the Relay-R channels. The pilot code designs that minimize the trace of the error covariance matrix are investigated. The requirements on the training period are also derived, from which an adaptive training-period design is proposed. Simulation shows that in some networks, even with shorter training period, the separate-training scheme can achieve better performance than the direct-training scheme.

Distributed space-time coding (DSTC) is a cooperative scheme for wireless relay networks that achieves full diversity without channel information at the relays. In this paper, the use of maximum-ratio combining (MRC) at multiple-antenna relays in combination with DSTC is proposed. Simulation and theoretical analysis show that the new scheme outperforms the original DSTC. In some network scenarios, it can even improve the scaling of the error rate with the transmit power. Furthermore, the proposed scheme requires a shorter training interval than DSTC.

This paper considers the interference cancellation (IC) problem in multi-user wireless relay networks. First, it is shown that using distributed space-time coding (DSTC), the multiple antenna IC scheme previously proposed for systems with direct transmissions can be applied to relay networks. The ML decoding after full IC can be performed symbol by symbol. Then, by allowing IC at relays, a new degree of freedom in relay network design is discovered. With this new idea, the required number of antennas at the receiver for full IC can be reduced and a balance between diversity and delay can be obtained.

This paper deals with beamforming in wireless relay networks with perfect channel information at the relays, receiver, and transmitter if there is a direct link between the transmitter and receiver. It is assumed that every node in the network has its own power constraint. A two-step amplify-and-forward protocol is used, in which the transmitter and relays not only use match filters to form a beam at the receiver but also adaptively adjust their transmit powers according to the channel strength information. For networks with no direct link, an algorithm is proposed to analytically find the exact solution with linear (in network size) complexity. It is shown that the transmitter should always use its maximal power while the optimal power of a relay ca.n take any value between zero and its maxima. Also, this value depends on the quality of all other channels in addition to the relay's own. Despite this coupling fact, distributive strategies are proposed in which, with the aid of a low-rate receiver broadcast, a relay needs only its own channel information to implement the optimal power control. Then, beamforming in networks with a direct link is considered. When the direct link exists during the first step only, the optimal power control is the same as that of networks with no direct link. For networks with a direct link during the second step only and both steps, recursive numerical algorithms are proposed. Simulation shows that network beamforming achieves the maximal diversity order and outperforms other existing schemes.

This paper is on relay selection schemes for wireless relay networks. First, we derive the diversity of many single-relay selection schemes in the literature. Then, we generalize the idea of relay selection by allowing more than one relay to cooperate. The SNR-optimal multiple relay selection scheme can be achieved by exhaustive search, whose complexity increases exponentially in the network size. To reduce the complexity, several SNR-suboptimal multiple relay selection schemes are proposed, whose complexity is linear in the number of relays. They are proved to achieve full diversity. Simulation shows that they perform much better than the corresponding single relay selection methods and very close to the SNR-optimal multiple relay selection scheme. In addition, for large networks, these multiple relay selection schemes require the same amount of feedback bits from the receiver as single relay selection schemes.

This paper is on beamforming in networks whose relays know the channel means and covariances. The question we answer is: To optimize the network performance, how much power should each relay use? Instead of the widely used aggregate relay power constraint, we use the more practical assumption that each relay has a separate power constraint. We generalize the distributed space-time coding scheme so that each relay can adapt its transmit power according to the channel information. For two-relay networks, we analytically solve the relay power control problem at high transmit powers using the pairwise error probability (PEP) minimization. Simulation shows that appropriate relay power control can largely improve the reliability, especially when the qualities of relay paths are far apart.

This paper is on quantized beamforming in wireless amplify-and-forward (AF) relay networks. We use the generalized Lloyd algorithm (GLA) to design the quantizer of the feedback information and specifically to optimize the bit error rate (BER) performance of the system. Achievable bounds for different performance measures are derived. First, we analytically show that a simple feedback scheme based on relay selection can achieve full diversity. Unlike the previous diversity analysis on the relay selection scheme, our analysis is not aided by any approximations or modified forwarding schemes. Then, for highrate feedback, we find an upper bound on the average signalto- noise ratio (SNR) loss. Using this result, we demonstrate that both the average SNR loss and the capacity loss decay at least exponentially with the number of feedback bits. In addition, we provide approximate upper and lower bounds on the BER, which can be calculated numerically.We observe that our designs can achieve both full diversity as well as high array gain with only a moderate number of feedback bits. Simulations also show that our approximate BER is a reliable estimation on the actual BER. We also generalize our analytical results to asynchronous networks, where perfect carrier level synchronization is not available among the relays.

Distributed space-time coding is a cooperative transmission scheme for wireless relay networks. With this scheme, antennas of the distributive relays work as transmit antennas of the sender and generate a space-time code at the receiver. It achieves the maximum diversity. Although the scheme needs no channel information at relays, it does require full channel information, both the channels from the transmitter to relays and the channels from relays to the receiver, at the receiver. In this paper, we propose a differential transmission scheme, which requires channel information at neither relays nor the receiver, for wireless relay networks. As distributed space-time coding can be seen as the counterpart of space-time coding in the network setting, this scheme is the counterpart of differential space-time coding. Compared to coherent distributed space-time coding, the differential scheme is 3dB worse. In addition, we show that Alamouti, square real orthogonal, and Sp(2) codes can be used differentially in networks with corresponding numbers of relays. We also propose distributed differential space-time codes that work for networks with any number of relays using circulant matrices.

This paper is on beamforming in wireless relay networks with perfect channel information at the receiver and relays. It is assumed that every node in the network has its own power constraint. An amplify-and-forward protocol is used. Relays use not only the channel direction information to form a beam at the receiver but also the channel strength information to adaptively adjust their transmit powers. Our results show that the optimal power used at a relay is not a binary function. It can take any value between zero and its maximal transmit power. Also, surprisingly, this value depends on the quality of all other channels in addition to the relay's own channels.

Distributed space–time coding was proposed to achieve cooperative diversity in wireless relay networks without channel information at the relays. Using this scheme, antennas of the distributive relays work as transmit antennas of the sender and generate a space–time code at the receiver. It achieves the maximal diversity when the transmit power is infinitely large. This paper is on the design of practical distributed space–time codes (DSTCs). We use orthogonal and quasi-orthogonal designs which are originally used in the design of space–time codes for multiple-antenna systems. It is well known that orthogonal space–time codes have full diversity and linear decoding complexity. They are particularly suitable for transmissions in the network setting using distributed space–time coding since their "scale-free" property leads to good performance. Our simulations show that they achieve lower error rates than the random code. We also compare distributed space–time coding to selection decode-and-forward using the same orthogonal designs. Simulations show that distributed space–time coding achieves higher diversity than selection decode-and-forward (DF) when there is more than one relay. We also generalize the distributed space–time coding scheme to wireless relay networks with channel information at the relays. Although our analysis and simulations show that there is no improvement in the diversity, in some networks, having channel information at the relays saves both the transmission power and the transmission time.

Distributed space-time coding was proposed to achieve cooperative diversity in wireless relay networks, in which antennas of relays work as transmit antennas of the sender and generate a space-time code at the receiver in a distributive way. It was proved that this scheme achieves the maximum diversity R when the total transmit power is infinitely large, where R is the number of relays in the network. This paper is on the design of practical distributed space-time codes for wireless relay networks. We use orthogonal and quasi-orthogonal designs which are originally used in the design of space-time codes for multiple-antenna systems. It is well known that orthogonal space- time codes have full diversity and linear decoding complexity. They are particularly suitable for transmissions in the network setting using distributed space-time coding since their 'scale-free' property leads to good performance. Our simulations show that they achieve lower error rates than the random code. We also compare the performance of distributed space-time coding to that of selection decode-and-forward using the same orthogonal designs. Simulations show that distributed space-time coding achieves higher diversity than selection decode-and-forward when there are more than one relay node.

We apply the idea of space-time coding devised for multiple-antenna systems to the problem of communications over a wireless relay network with Rayleigh fading channels. We use a two-stage protocol, where in one stage the transmitter sends information and in the other, the relays encode their received signals into a "distributed" linear dispersion (LD) code, and then transmit the coded signals to the receive node. We show that for high SNR, the pairwise error probability (PEP) behaves as (logP/P)min{TH}, with T the coherence interval, that is, the number of symbol periods during which the channels keep constant, R the number of relay nodes, and P the total transmit power. Thus, apart from the log P factor, the system has the same diversity as a multiple-antenna system with R transmit antennas, which is the same as assuming that the R relays can fully cooperate and have full knowledge of the transmitted signal. We further show that for a network with a large number of relays and a fixed total transmit power across the entire network, the optimal power allocation is for the transmitter to expend half the power and for the relays to collectively expend the other half. We also show that at low and high SNR, the coding gain is the same as that of a multiple-antenna system with R antennas. However, at intermediate SNR, it can be quite different, which has implications for the design of distributed space-time codes

In [1], the idea of distributed space-time coding was proposed to achieve a degree of cooperative diversity in a wireless relay network. In particular, for a relay network with a single-antenna transmitter and receiver and R single-antenna relays, it was shown that the pairwise error probability (PEP) decays as (log P/P)Rwhere P is the total transmit power. In this paper, we extend the results to wireless relay networks where the transmitter, receiver, and/or relays may have multiple antennas. Assuming that the transmitter has M antennas, the receiver has N antennas, the sum of all the antennas at the relay nodes is R, and the coherence interval is long enough, we show that the PEP behaves as (1/P)min{M,N}R, if M ne N, and (log1M/P/P)MR, if M = N. Therefore, for the case of M ne N, distributed space-time coding has the same PEP performance as a multiple-antenna system with min{M, N}R transmit and a single receive antenna. For the case of M = N, the penalty on the PEP compared to a multiple-antenna system is a log1M/ P factor, which is negligible at high SNR. We also show that for a fixed total transmit power across the entire network, the optimal power allocation is for the transmitter to expend half the power and for the relays to share the other half with the power used by each relay being proportional to the number of antennas it has

Fully diverse constellations, i.e., a set of unitary matrices whose pairwise differences are nonsingular, are useful in multi-antenna communications especially in multi-antenna differential modulation, since they have good pairwise error properties. Recently, group theoretic ideals, especially fixed-point-free (fpf) groups, have been used to design fully diverse constellations of unitary matrices. Here we give a systematic method to design space-time codes which are appropriate for three-transmit-antenna differential modulation. The structure of the code is motivated by the Lie group SU(3). The code has a fast decoding algorithm using sphere decode. The diversity product of the code can be easily calculated and simulated performance shows that the code is better than the group-based codes especially at high rates and is as good as the elaborately-designed nongroup code.

We apply the idea of space-time coding devised for multiple-antenna systems to the problem of communications over wireless relay networks. A two-stage protocol is used, where in one stage the transmitter sends information and in the other, the relay nodes encode their received signals into a "distributed" linear dispersion code, and then transmit the coded signals to the receiver. We show that for high SNR the proposed system has a diversity of order /spl alpha//sub 0/ min{T, R}, with T the coherence interval, R the number of relay nodes, and /spl alpha//sub 0/ the solution to the equation /spl alpha/ + log/spl alpha//logP = 1 - loglogP/logP, where P is the total transmit power in the network. In particular, we show that the pairwise error probability (PEP) decays no slower than (logP/P)/sup min{T,R}/. Thus, apart from the log P factor and assuming T /spl ges/ R, the system has the same diversity as a multiple-antenna system with R transmit antennas and one receive antenna, which is the same as assuming that the R relay nodes can fully cooperate and have full knowledge of the transmit signal. We further show that for a fixed total transmit power across the entire network, the optimal power allocation is for the transmitter to expend half the power and for the relays to collectively expend the other half. We also show that at low and high SNR, the coding gain is the same as that of multiple-antenna systems. However, at intermediate SNR, it can be quite different. We discuss some of the ramifications of using different space-time codes and finally verify our analysis through the simulation or randomly generated distributed space-time codes.

Fully diverse constellations, i.e., sets of unitary matrices whose pairwise differences are nonsingular, are useful in multiple-antenna communications, especially in multiple-antenna differential modulation, since they have good pairwise error properties. Recently, group theoretic ideas, especially fixed-point-free (fpf) groups, have been used to design fully diverse constellations of unitary matrices. Here we construct four-transmit-antenna constellations appropriate for differential modulation based on the symplectic group Sp(2). They can be regarded as extensions of Alamouti's celebrated two-transmit-antenna orthogonal design which can be constructed from the group Sp(1). We further show that the structure of Sp(2) codes lends itself to efficient maximum-likelihood (ML) decoding via the sphere decoding algorithm. Finally, the performance of Sp(2) codes is compared with that of other existing codes including Alamouti's orthogonal design, a 4/spl times/4 complex orthogonal design, Cayley differential unitary space-time codes and group-based codes.

Fully-diverse constellations, i.e., a set of unitary matrices whose pairwise differences are nonsingular, are useful in multi-antenna communications, especially in multi-antenna differential modulation, since they have good pairwise error properties. Recently, group theoretic ideas, especially fixed-point-free (FPF) groups, have been used to design fully-diverse constellations of unitary matrices. Here we construct four-transmit-antenna constellations appropriate for differential modulation based on the symplectic group Sp(2) These can be regarded as extensions of S.M. Alamouti's celebrated two-transmit-antenna orthogonal design which can be constructed from the group Sp(1) (see IEEE J. Sel. Area Commun., p.1451-8, 1998). We further show that the structure of the code lends itself to efficient maximum likelihood (ML) decoding via the sphere decoding algorithm. Finally, the performance of the code is compared with existing methods including Alamouti's scheme, Cayley differential unitary space-time codes and group based codes.

A recently proposed method for communicating with multiple antennas over block fading channels is unitary space-time modulation (USTM), so-called because the transmitted signals form a matrix with orthonormal columns. Since channel knowledge is not required at the receiver, USTM schemes are suitable for use on wireless links where channel tracking is undesirable or infeasible. Recent results have shown that, if suitably designed, USTM schemes can achieve full channel capacity at high SNR. While all this is well recognized, what is not clear is how to generate good performing constellations of (non-square) unitary matrices, that lend themselves to efficient encoding/decoding. The schemes proposed so far either exhibit poor performance, especially at high rates, or have no efficient decoding algorithms. In this paper, we propose to use the Cayley transform to design USTM constellations. This work is a generalization, to the non-square case, of the Cayley codes that have been proposed for differential USTM. The codes are designed based on an information-theoretic criterion, and lend themselves to polynomial-time (often cubic) near-maximum-likelihood decoding using a sphere decoding algorithm.