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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 letter proposes a modified non-orthogonal multiple-access (NOMA) scheme for systems with a multi-antenna base station (BS) and two single-antenna users, where NOMA transmissions are conducted only when the absolute correlation coefficient (CC) between the user channels exceeds a threshold and the BS uses matched-filter (MF) precoding along the user with the stronger average channel gain. We derive the average minimal transmit power to guarantee the signal-to-interference-plus-noise-ratio (SINR) levels of both users. Our results show that the average minimal power grows logarithmically in the reciprocal of the CC threshold and a non-zero threshold is necessary for the modified NOMA scheme to have finite average minimal transmit power. Further, for the massive MIMO scenario, we derive the scaling laws of the average transmit power and outage probability with respect to the antenna numbers, as well as their tradeoff law. Simulation results are shown to validate our theoretical results., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

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.

This letter is on the multi-user massive multi-input multi-output (MIMO) uplink with the mixed analog-to-digital converter (ADC) architecture and the zero-forcing (ZF) receiver at the base station (BS). Under imperfect channel state information (CSI), a closed-form approximation of the spectral efficiency (SE) is derived for a general resolution profile. Further, simplified SE results are provided for two common asymptotic massive MIMO scenarios. In the SE analysis, to overcome the difficulty induced by the mixed-ADC structure, new techniques are developed in calculating the average noise powers caused by the CSI error and the quantization.

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 linearlywith 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.

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 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 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.

In this paper, a decision-directed (DD)-channel estimation (CE) algorithm by employing deep learning (DL) is proposed for high mobility vehicular environments. The proposed algorithm relies on DL for channel prediction without prior knowledge about channel statistics, such as the channel covariance matrix and its time variation. Therefore, it does not require any prior Doppler rate estimation, which is highly complicated in high mobility environments. Based on the performed simulations, comparing to the Kalman filter-based DD-CE algorithm, our DL-based algorithm results in more reliable communications. It has been shown that comparing to the minimum mean square error (MMSE)-based DD-CE algorithm, our DL-based algorithm imposes much lower complexity to the system and the performance degradation is small compared to the MMSE-based DD-CE algorithm that requires the exact value of the Doppler rate.

To support reliable transmission of data at high rate in time-varying fading channels, adaptive transmission is required, where transmitter and receiver adjust their transmission and reception mode to the dynamics of the channel. The receiver, based on its channel estimation and prediction, decides the optimal link adaptation and feeds this back to the transmitter. In this paper, we develop a deep learning (DL)-based link adaptation algorithm for highly dynamic communication links, where adaptive transmission parameters are decided for $l\gt1$ forward time steps without a priori knowledge on channel statistics. Compared to conventional solutions, our approach reduces the feedback requirements from the receiver to the transmitter by a factor of l which significantly reduces the complexity. This achievement comes at no additional cost on the data rate and/or bit error rate.

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 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.

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 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.

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.

Beamforming is a powerful technique which has been widely used in signal processing, radar and sonar, biomedical, and particularly in communications, where the basic idea is to optimally process signals received over different antennas, or the signals which are to be transmitted over different paths by adjusting the signal amplitudes and phases to form a strong beam toward the direction of interest, and at the same time, to avoid receiving or creating interference. In the past decade, with booming research in cooperative relay communications, a new type of beamforming, namely network beamforming, has appeared and developed to fulfill the needs of the ever-evolving wireless systems. A network beamformer is implemented at neither the transmitter nor the receiver but at the intermediate relays to adaptively process signals and conduct the tasks of both the receive beamformer and the transmit beamformer. In this chapter, a systematic overview of various network beamforming approaches and solutions are presented for multi-relay cooperative networks with a wide variety of configurations, including one-way and two-way communications, single-user and multi-user cases, flat-fading and frequency-selective channel models, and networks with perfect and partial channel state information.

In this work, we study joint user-relay selection and association in multi-user multi-relay cooperative wireless relay uplinks with multi-antenna nodes. For non-regenerative and altruistic relays we propose a low-complexity joint scheme, which simultaneously selects multiple relays and users for cooperation as well as assigns the selected users to different selected relays for service. The proposed scheme is sub-optimal and utilizes only the channel gains between the nodes, which leads to reduced feedback and overhead in comparison to schemes that require full channel knowledge. Furthermore, the complexity of the scheme scales linearly as the product of the total number of relays, the total number of users and the number of selected users. Simulation results demonstrate the superiority of the proposed joint scheme compared to a scheme with neither user-relay selection nor user-relay association and another scheme with user-relay association, but no user-relay selection. The favorable performance and low-complexity of the proposed scheme make it very attractive for possible implementation in emerging broadband wireless relay networks (e.g., LTE-Advanced).

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 (MIMO) 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 work provides a comprehensive scaling law based performance analysis for single-cell multi-user massive multiple-input-multiple-output (MIMO) downlink systems with maximal-ratio transmission (MRT). Channel state information (CSI) error and channel spatial correlation are both considered. First, a sum-rate lower bound is derived by using Jensen's inequality and the asymptotically deterministic property of the received signal power. Via a general scaling model on the number of users, the CSI quality and the data transmission power, with respect to the number of base station (BS) antennas, the asymptotic performance scaling law is obtained, which reveals quantitatively the tradeoff of the above three parameters. In addition, the applicability of the derived asymptotic scaling law in practical systems with not-so-large antenna numbers is discussed. Finally, all analytical results are evaluated through simulations.

For massive MIMO public channel with any sector size in either microwave or millimeter wave (mmwave) band, this paper studies the beamforming design to minimize the transmit power while guaranteeing the quality of service (QoS) for randomly deployed users. First the ideal beampattern is derived via Parseval Identity, based on which a beamforming design problem is formulated to minimize the gap with the idea beampattern. The problem is transformable to a multiconvex one and an iterative optimization algorithm is used to obtain the full-digital beamformer. In addition, with the help of same beampattern theorem, the power amplifier (PA) efficiency of the beamformer is improved with unchanged beampattern. Finally, the practical hybrid implementation is obtained that achieves the full-digital beamformer solution. Simulations verify the advantages of the proposed scheme over existing ones., Accepted by IEEE Transactions on Vehicular Technology

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 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.

This work analyses the performance of multi-user massive MIMO relay networks, where the relay station is equipped with a large number of antennas. The combination of maximal-ratio-combining (MRC) and maximal-ratio-transmission (MRT) is utilized at the relay for low-complexity processing. Different from existing work, we consider the practical scenario with limited number of users, fixed source power, and fixed relay power. Our work shows that the interference is neither negligible nor asymptotically deterministic, and it dominates the statistical properties of the signal-to-interference-plus-noise ratio (SINR). Via deriving an approximation on the probability density function (PDF) of the interference power, analytical results on the sum-rate and outage probability performance of the multi-user relay network are obtained.

For single-cell multi-user massive multi-input-multi-output (MIMO) system downlink, we consider the per-antenna power constraint and propose a modified maximum-ratio-transmission (MRT) precoding scheme. The outage probability performance of the scheme are analyzed. To enable the analysis, we study the random behaviour of the signal-to-interference-plus-noise-ratio (SINR) and derive an approximation for the probability density function (pdf) of the interference power. Simulation results are shown to validate the theoretical derivations. Moreover, our work show that the massive MIMO system with per-antenna power constraint under the modified MRT precoding can achieve lower outage probability than that with a total power constraint under the standard MRT precoding, even though its power constraint is more strict.

This paper considers a multiuser single-relay wireless network, where the relay gets paid for helping users forward signals, and the users pay to receive the relay service. We study the relay power allocation and pricing problems and model the interaction between the users and the relay as a two-level Stackelberg game. In this game, the relay, which is modeled as the service provider and the leader of the game, sets the relay price to maximize its revenue, whereas the users are modeled as customers and followers who buy power from the relay for higher transmission rates. We use a bargaining game to model the negotiation among users to achieve a fair allocation of relay power. Based on the proposed fair relay power allocation rule, the optimal relay power price that maximizes the relay revenue is derived analytically. Simulation shows that the proposed power allocation scheme achieves higher network sum rate and relay revenue than the even power allocation. Furthermore, compared with the sum-rate-optimal solution, simulation shows that the proposed scheme achieves better fairness with comparable network sum rate for a wide range of network scenarios. The proposed pricing and power allocation solutions are also shown to be consistent with the laws of supply and demand.

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.

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, the power-normalized SNR (PN-SNR), in the design of multi-relay networks with an individual power constraint for each relay. We formulate the PN-SNR maximization problem with a received SNR constraint to maintain the quality of service (QoS) and propose a low complexity algorithm for a suboptimal solution. The average PN-SNR and average throughput of the proposed design are simulated and compared with existing designs. We also simulate the probability of no transmission with the proposed design for an arbitrary SNR level. We observe that the proposed design is more power efficient than existing ones with comparable performance in average throughput. When the transmitter power is moderate, with higher QoS constraint, the probability of no transmission gets higher; the average throughput decreases, but the PN-SNR of the network increases.

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.

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.

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.

In the previous chapter, distributed space-time coding (DSTC) is introduced for single-antenna multiple-relay network, where there are multiple relays in the network but every node (the transmitter, the receiver, or a relay) is equipped with a single antenna. In this chapter, DSTC is used for multiple-antenna multiple-relay network, where each node in the network can be equipped with multiple antennas. At first, the multiple-antenna multiple-relay network model is specified in Sect. 3.1. Then the DSTC scheme, its diversity order analysis, and code design are demonstrated in Sect. 3.2. After that, the combination of DSTC and maximum-ratio combining (MRC) is explained in Sect. 3.3. Finally, simulated error probabilities of some multiple-antenna multiple-relay networks are shown.

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.

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.

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.