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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 the 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 1 presents 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 1 fundamentally 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 applying Theorem 1 to 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 in Theorem 1 and 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, we analyze the average transmit power of non-orthogonal multiple access (NOMA) systems with requirements on the user signal-to-interference-plus-noise-ratios (SINRs), and propose new transmission schemes and user clustering algorithms to reduce the average transmit power. First, for systems with a multi-antenna base station (BS) and a single cluster of two single-antenna users, the average transmit power with SINR constraints is analyzed for channel-alignment-based NOMA and multi-user beamforming with matched filter (MF) beamformers. Properties of the average transmit power are obtained with respect to the alignment threshold and the BS antenna number. It is shown that using either scheme alone without the alignment consideration leads to unbounded average transmit power. With the observation that the two schemes have distinct preferred regions of channel alignment, hybrid transmissions of NOMA and multi-user beamforming are proposed for power saving and outage avoidance. Further, for systems with more than two users, clustering algorithms are developed to group users into multiple two-user clusters with respect to the minimization of the total transmit power for NOMA and hybrid schemes. Simulation results are provided to validate our theoretical results. In addition, the proposed transmission schemes and clustering algorithms are shown to achieve significant saving in the average transmit power.

This paper analyzes the performance of multi-user full-duplex (FD) massive multiple-input multiple-output (MIMO) systems with low resolution analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) under Rician fading channels. The maximum ratio combining and maximum ratio transmission are used at the base station (BS) for the uplink and downlink, respectively. By leveraging on the additive quantization noise model, tight closed-form approximations of the uplink and downlink achievable rates are obtained for both perfect and imperfect channel state information cases. The results show the impact of the Rician $K$ -factor, ADC/DAC resolution, loop interference, and inter-user interference of the systems. In addition, we adopt the power scaling law to show that to achieve a fixed level of the signal-to-interference-plus-noise ratio, the transmit power of each user and the BS can be scaled down proportionally to the inverse of the BS antenna number. Moreover, we compare the performance of the FD mode and the half-duplex mode, and study the trade-off between the achievable rate and BS energy efficiency. Numerical results show that the use of low-resolution ADCs/DACs can significantly improve the BS energy efficiency with only small reduction in the achievable rate of the FD system.

Extreme learning machine (ELM) is commonly adopted and best known for its extremely fast learning capability and notable performance. In this paper, a multiple split-complex ELM (Multi-SCELM) regressor based equalization and detection method is proposed for OFDM systems. This method combines ELM regressors for equalization and minimum-distance based symbol slicers for symbol detection. Furthermore, the proposed Multi-SCELM is extended to fully complex ELM (CELM) for channel equalization and detection. Simulations demonstrate that compared to existing ELM based methods, the proposed one owns the advantages of lower computational complexity, higher detection accuracy, stronger activation function adaptability, shorter training length and better subchannel number adaptability especially in strong frequency selective channels. Compared to the benchmark MMSE method, the proposed method has minor performance degradation but significant reduction in computational complexity.

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.

We address the problem of secure wireless communications over an untrusted full-duplex (FD) relay based on the source jamming scheme. The optimal power allocation between the confidential signal and the jamming signal is derived to maximize the secrecy rate. Then, the corresponding secrecy outage probability (SOP) and the average secrecy rate (ASR) are analyzed. A tight approximation and an asymptotic result are further obtained for the single-antenna destination case both in simple forms. The large-antenna destination case is also analyzed rigorously. Further discussion reveals that transmit-power dependent self-interference has significant negative impact on the secrecy performance.

This paper is on abnormality detection, where the observed data under the normal condition is assumed to be independent and identically distributed (i.i.d.) and follow the generalized Gaussian distribution (GGD) with shape parameter greater than 1. The Kullback–Leibler divergence (KLD) between the estimated GGD of the observed data and the normal one is used as the test statistic. An analytical expression of the KLD is derived under the normal condition when the number of samples is large; then, two algorithms with constant and adaptive thresholds are proposed. Extensive simulated and industrial case studies are conducted to verify the analytical results and to show the effectiveness of the proposed algorithms.

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.

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.

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 one selected user's interference to others into the precondition matrix, we propose the identity-plus-column NS (ICNS) method. By further exploiting the multi-user diversity gain via choosing the user with the largest interference to 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., Comment: 30 Pages, 9 figures, submitted to IEEE Transactions on Communications

In this paper, we study the beam-based training design jointly with the transmission design for hybrid massive antenna single-user (SU) and multiple-user (MU) systems where outage probability is adopted as the performance measure. For SU systems, we propose an interleaved training design to concatenate the feedback and training procedures, thus making the training length adaptive to the channel realization. Exact analytical expressions are derived for the average training length and the outage probability of the proposed interleaved training. For MU systems, we propose a joint design for the beam-based interleaved training, beam assignment, and MU data transmissions. Two solutions for the beam assignment are provided with different complexity-performance tradeoff. Analytical results and simulations show that for both SU and MU systems, the proposed joint training and transmission designs achieve the same outage performance as the traditional full-training scheme but with significant saving in the training overhead., 16 Pages (double column), 11 figures. This work has been accepted by the IEEE Journal of Selected Topics in Signal Processing (JSTSP), Special Issue on Hybrid Analog - Digital Signal Processing for Hardware-Efficient Large Scale Antenna Arrays. This version is different from the former one due to the revisions made for the comments of 1st and 2nd round review

This paper conducts sensitivity analysis and sensitivity-based design for linear filter alarm monitoring systems. Based on a derivative-based local sensitivity measure, models are proposed to assess the sensitivity of the system detection errors to changes in the trip point and to uncertainties in the collected data. Then, analytical expressions are derived to quantitatively evaluate the sensitivity of a general linear alarm filter with unknown data distributions. Subsequently, a new sensitivity-based linear filter design method is formulated to minimize a weighted sum of the detection errors subject to upper bounds on the system sensitivities. Extensive simulations with both Gaussian and industrial data are conducted to verify the analytical results and to show trade-offs between the detection errors and sensitivities of linear filter alarm system.

This paper provides a comprehensive scaling law-based performance analysis for multicell multiuser massive multiple-input-multiple-output (MIMO) downlink systems. Imperfect channel state information (CSI), pilot contamination, and channel spatial correlation are all considered. First, a sum-rate lower bound is derived by exploiting the asymptotically deterministic property of the received signal power, while keeping the random nature of other components in the signal-to-interference-plus-noise-ratio (SINR) intact. Via a general scaling model on important network parameters, including the number of users, the channel training energy and the data transmission power, with respect to the number of base station antennas, the asymptotic scaling law of the effective SINR is obtained, which reveals quantitatively the tradeoff of the network parameters. More importantly, pilot contamination and pilot contamination elimination (PCE) are considered in the analytical framework. In addition, the applicability of the derived asymptotic scaling law in practical systems with large but finite antenna numbers are discussed. Finally, sufficient conditions on the parameter scalings for the SINR to be asymptotically deterministic in the sense of mean square convergence are provided, which covers existing results on such analysis as special cases and shows the effect of PCE explicitly.

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.

Mean-squared-error (MSE) is one of the most widely used performance metrics for the designs and analysis of multi-input-multiple-output (MIMO) communications. Weighted MSE minimization, a more general formulation of MSE minimization, plays an important role in MIMO transceiver optimization. While this topic has a long history and has been extensively studied, existing treatments on the methods in solving the weighted MSE optimization are more or less sporadic and non-systematic. In this paper, we firstly review the two major methodologies, Lagrange multiplier method and majorization theory based method, and their common procedures in solving the weighted MSE minimization. Then some problems and limitations of the methods that were usually neglected or glossed over in existing literature are provided. These problems are fundamental and of critical importance for the corresponding MIMO transceiver optimizations. In addition, a new extended matrix-field weighted MSE model is proposed. Its solutions and applications are discussed in details. Compared with existing models, this new model has wider applications, e.g., nonlinear MIMO transceiver designs and capacity-maximization transceiver designs for general MIMO networks., 34 Pages, 4 figures

Early and accurate detection of incipient cable faults is of a great interest to the utility industry. Such faults can be classified into subcycle and multicycle types. Although a lot of research has been conducted on subcycle types of faults, little work has been done for multicycle types of faults. This paper proposes a novel method for detecting and locating a multicycle incipient fault in a cable. The incipient fault is modeled as a self-clearing arcing fault. The distortion degree of calculated voltage is used to detect the occurrence of an incipient fault. The degree of match between the measured and calculated waveforms is used to guide the search for the fault distance. The accuracy is further improved by taking into account the incipient fault angle as seen in the voltage waveform and the power loss characteristics. The proposed method has been verified by PSCAD/EMTDC simulations. Lab experiments are also conducted to further validate the proposed detection method.

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.

In recent years, power quality (PQ) disturbance data are increasingly applied to extract useful information about the condition of power systems, such as monitoring incipient equipment failures. A prerequisite for such applications is the ability for a PQ monitor to detect abnormal waveforms. In response to this need, a generic method for waveform abnormality detection is proposed in this paper. The proposed method has two unique features. First, abnormalities are detected by comparing the statistical distributions of waveform variations with and without disturbances. Kullback-Leibler divergence (KLD) is used to assess the difference of the distributions. An abnormality exists if the KLD is larger than a threshold. Second, current waveforms are used for detection since they are more sensitive to equipment conditions. The difficulty to set a proper threshold due to large variations of current values is overcome through the adoption of KLD as the distance measure and a systematic threshold selection scheme. The scheme maximizes the detection probability for a given false alarm probability. Field-measured data and simulated data are applied to verify the effectiveness of the method.

This work analyses the average signal-to-noise ratio (SNR) and ergodic capacity of large-scale relay networks with best relay selection (BRS). First, extreme value theory (EVT) is used to obtain an implicit expression for the asymptotic cumulative distribution function (cdf) of the received SNR when the number of relays is high. Then, via high power approximations, closed-form expressions for the cdf and probability density function (pdf) of the received SNR are achieved, from which closed-form expressions of the average received SNR and ergodic capacity are derived. Insights on the array gain and ergodic capacity behavior of BRS can be observed from the derived results. Simulations show that the derived approximations are tight, even for not-so-large relay networks.

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.

In this paper, we study the power allocation problem in a multiuser cooperative network, where users help each other's transmissions to an access point. We use iterative double auction (IDA) game to model the interaction among the users and the access point. In each iteration of this game, the users first submit bids for buying other users' power and asks for selling its own power, and then, the access point determines the power allocation based on users' bids and asks. We propose a distributed algorithm for the implementation of the IDA-based power allocation. We also show that the proposed algorithm achieves a weighted sum signal-to-noise ratio (sum-SNR)-optimal solution. Simulation results are conducted to verify the performance of the proposed algorithm.

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.

This paper investigates the relay selection (RS) problem in networks with multiple users and multiple common amplify-and-forward (AF) relays. Considering the overall quality-of-service of the network, we first specify our definition of optimal RS for multiple-user relay networks. Then an optimal RS (ORS) algorithm is provided, which is a straightforward 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. Then a suboptimal RS (SRS) scheme is 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 theoretically derived and compared with those of a naive RS scheme and the single-user RS network. It is shown that the ORS achieves full diversity; while the diversity order of the SRS decreases with the the number of users. For two-user networks, the outage probabilities and array gains corresponding to the minimum SNR of the RS schemes are derived in closed forms. 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.

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

This paper deals with optimal joint user power control and relay distributed beamforming for two-way relay networks, where two end-users exchange information through multiple relays, each of which is assumed to have its own power constraint. The problem includes the design of the distributed beamformer at the relays and the power control scheme for the two end-users to optimize the network performance. Considering the overall two-way network performance, we maximize the lower signal-to-noise ratio (SNR) of the two communication links. For single-relay networks, this maximization problem is solved analytically. For multi-relay networks, we propose an iterative numerical algorithm to find the optimal solution. While the complexity of the optimal algorithm is too high for large networks, two sub-optimal algorithms with low complexity are also proposed, which are numerically shown to perform close to the optimal technique. It is also shown via simulation that for two-way networks with both single relay and multiple relays, proper user power control and relay distributed beamforming can significantly improve the network performance, especially when the power constraints of the two end-users in the networks are unbalanced. Our approach also improves the power efficiency of the network largely.

In this paper, we propose a threshold-system-based detector (TD) for detecting a known deterministic signal in independent non-Gaussian noise whose probability density function (pdf) is unknown but is symmetric and unimodal. The optimality of the proposed TD is proved under the assumptions of white noise, small signal, and a large number of samples. While previous TD designs need accurate information of the noise pdf, the proposed TD is independent of the noise pdf, and thus is robust to the noise pdf. The detection probability and the receiver operating characteristic (ROC) of the proposed TD are analyzed both theoretically and numerically. It is shown that even without knowing the noise pdf, the proposed TD has close performance to the optimal detector designed with the noise pdf information. It also performs significantly better than the matched filter (MF) when the noise pdf has heavy tails. The practical implementation, robustness to both the noise pdf and the signal, and region of validity of the proposed TD are also investigated.

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.

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 transmission schemes in multi-access relay networks (MARNs) where $J$ single-antenna sources send independent information to one $N$-antenna destination through one $M$-antenna relay. For complexity considerations, we propose a linear framework, where the relay linearly transforms its received signals to generate the forwarded signals without decoding and the destination uses its multi-antennas to fully decouple signals from different sources before decoding, by which the decoding complexity is linear in the number of sources. To achieve a high symbol rate, we first propose a scheme called DSTC-ICRec in which all sources' information streams are concurrently transmitted in both the source-relay link and the relay-destination link. In this scheme, distributed space-time coding (DSTC) is applied at the relay, which satisfies the linear constraint. DSTC also allows the destination to conduct the zero-forcing interference cancellation (IC) scheme originally proposed for multi-antenna systems to fully decouple signals from different sources. Our analysis shows that the symbol rate of DSTC-ICRec is $1/2$ symbols/source/channel use and the diversity gain of the scheme is upperbounded by $M-J+1$. To achieve a higher diversity gain, we propose another scheme called TDMA-ICRec in which the sources time-share the source-relay link. The relay coherently combines the signals on its antennas to maximize the signal-to-noise ratio (SNR) of each source, then concurrently forwards all sources' information. The destination performs zero-forcing IC. It is shown through both analysis and simulation that when $N \ge 2J-1$, TDMA-ICRec achieves the same maximum diversity gain as the full TDMA scheme in which the information stream from each source is assigned to an orthogonal channel in both links, but with a higher symbol rate., Comment: submitted to IEEE Transaction on Signal Processing

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.

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.

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 is on beamforming in wireless relay networks with perfect channel information at relays, the receiver, and the 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 a network with any number of relays and no direct link, the optimal power control is solved analytically. The complexity of finding the exact solution is linear in the number of relays. Our results show that the transmitter should always use its maximal power and the optimal power used at a relay is not a binary function. It can take any value between zero and its maximum transmit power. Also, this value depends on the quality of all other channels in addition to the relay's own channels. Despite this coupling fact, distributive strategies are proposed in which, with the aid of a low-rate broadcast from the receiver, a relay needs only its own channel information to implement the optimal power control. Simulated performance shows that network beamforming achieves the maximal diversity and outperforms other existing schemes. Then, beamforming in networks with a direct link are considered. We show that 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, recursive numerical algorithms are proposed to solve the power control problem. Simulation shows that by adjusting the transmitter and relays' powers adaptively, network performance is significantly improved., 33 pages, 12 figures. This paper was submitted to IEEE Trans. on Information Theory. In this version, some modification is made on the presentation. Parts of this work were presented at ICASSP07 and ITA08

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 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 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 ldquoscale-freerdquo 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.

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 (log P/P)min{T,R}, 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.

Fully diverse constellations, i.e., a set of unitary matrices whose pairwise differences are nonsingular, are useful in multiantenna communications especially in multiantenna 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 give systematic design methods of space-time codes which are appropriate for three-transmit-antenna differential modulation. The structures of the codes are motivated by the special unitary Lie group SU(3). One of the codes, which is called the AB code, has a fast maximum-likelihood (ML) decoding algorithm using complex sphere decoding. Diversity products of the codes can be easily calculated, and simulated performance shows that they are better than group-based codes, especially at high rates and as good as the elaborately designed nongroup code.

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.