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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.

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.

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 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.

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.

High power consumption and hardware cost are two barriers for practical massive multiple-input multiple-output (mMIMO) systems. A promising solution is to employ low-resolution analog-to-digital converters (ADCs). In this paper, we consider a general mMIMO multi-way relaying system with a multi-level mixed-ADC architecture, in which each antenna is connected to an ADC pair of an arbitrary resolution. By leveraging on Bussgang's decomposition theorem and Lloyd-Max algorithm for quantization, tight closed-form approximations are derived for the average achievable rates of zero-forcing (ZF) relaying considering both perfect and imperfect channel state information (CSI). To conquer the challenges caused by multi-way relaying, the complicated ZF beam-forming matrix, and the general mixed-ADC structure, we develop a novel method for the achievable rate analysis using the singular-value decomposition (SVD) for Gaussian matrices, distributions of the singular values of Gaussian matrices, and properties of Haar matrices. The results explicitly show the achievable rate behavior in terms of the user and relay transmit powers and the numbers of relay antennas and users. Most importantly, it quantifies the performance degradation caused by low-resolution ADCs and channel estimation error. We demonstrate that the average achievable rate has an almost linear relation with the square of the average of quantization coefficients pertaining to the ADC resolution profile., Comment: Part of this work on the performance analysis of mMIMO multi-way relay networks with low-resolution uniform-ADC structures has been presented at the IEEE International Conference on Communications (ICC) 2019 [1]

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.

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.

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.

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.

For a multi-relay amplify-and-forward (AF) network, an improved training scheme is proposed and the corresponding training power allocation problem is investigated for the individual channel estimation at the destination. Compared with a previous scheme where the training of the source-relay channels is conducted sequentially, the proposed scheme exploits the broadcast nature of the source-relay links to save training time and power. By analyzing the total mean square error (MSE) of all channel estimates and with the help of approximations, we derive a training power allocation solution among the source and the relays. Simulation results demonstrate that our improved training scheme and power allocation solution obtain lower total MSE than the existing schemes.

The ever increasing demands for mobile Internet access have resulted a significant growth in bandwidth usage. Multi-way relay networks (MWRNs) can address this challenge by improving the system spectral efficiency. In this work, we further improve the spectral efficiency of MWRNs by proposing a novel linear beamforming design, namely partial zero-forcing (PZF), for MWRNs with a multiple-input-multiple-output relay. Compared to zero-forcing (ZF), in PZF, the constraints on the relay beamforming are relaxed such that only partial user-interference, instead of all, is canceled at the relay. After receiving the relay's signal, the users eliminate the remaining interferences through self-interference and successive interference cancellation. By taking such two-stage interference cancellation, PZF better exploits the degrees-of-freedom in MWRNs and achieves higher data rates than ZF.

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 bidirectional multi-relay networks, where each node is assumed to have its own power constraint, the optimal relay and user power control is considered via maximizing the smaller signal-to-noise ratio (SNR) of the two end users in the network. A numerical algorithm is proposed to find the optimal solution. Then, a suboptimal algorithm with low complexity is proposed. The performance of this algorithm is shown numerically to be close to the optimal. It is also shown via simulation that proper user and relay power control significantly improves the network performance, especially when the power constraints of the two end-users in the networks are unbalanced.

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.

This paper studies a multiple-input multiple-output (MIMO) broadcast relay channel (BRC) in which a multiple-antenna base station (BS) communicates with multiple-antenna users through a fixed infrastructure-based multiple-antenna relay station (RS). Applying dirty paper coding (DPC) at the BS and linear processing at the RS, our goal is to find the optimal input covariance matrices at the BS and the beamforming matrix at the RS that jointly maximize the system sum-rate. To solve the optimization problem, a more tractable dual multiple access relay channel (MARC) is investigated and an iterative algorithm is proposed to obtain the optimal matrices for the dual system. The mapping from the resulting covariance matrices for the MARC to the covariance matrices for the original BRC is derived. Unlike other existing MIMO BRC schemes, designed for networks with single-antenna users only, our solution is applicable to networks with multiple-antenna users. Compared with two such single-antenna-user schemes, simulations show that the proposed scheme outperforms the all-pass relay design and performs similar to the SVD-relay design. Also, the proposed design performs close to a sum-rate upper bound with the gap decreasing with increasing number of users' antennas.

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

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

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

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

Distributed space-time coding (DSTC) is a cooperative scheme proposed for wireless relay networks that achieves full diversity when the transmit power is infinitely high. In this paper, we propose to employ maximum-ratio combining (MRC) at the multiple-antenna relay to improve the performance of DSTC. Simulations and analysis show that the new scheme achieves a much better performance in relay networks than DSTC. In some network scenarios, it can even improve the scaling of the error rate with the transmit power. Furthermore, the new scheme requires a shorter training interval than DSTC.

A relay selection (RS) scheme for two-way networks with multiple amplify-and-forward relays is proposed. The scheme maximizes the worse receive signal-to-noise ratio (SNR) of the two end users. It is proved to coincide with the best-worse RS scheme originally proposed for one-way relay networks. Through rigorous error rate analysis, the scheme is shown to achieve full diversity. For networks with two relays and any power condition and constellation, an approximation on the block error rate (BLER) of the scheme is derived in closed-form. It is shown by simulation to be effective in estimating the network reliability in the high transmit power region.

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

This paper is on relay selection (RS) schemes for wireless relay networks. First, we derive the diversity of many single RS schemes in the literature. Then, we generalize the idea of RS by allowing more than one relay to cooperate. Several multiple RS schemes are proposed, which are proved to achieve full diversity. Simulation results show that they perform much better than the corresponding single RS methods and very close to the optimal multiple RS scheme. However, the computational complexity of the suboptimal schemes are linear in the number of relays, far superior to the optimal selection, which has exponential complexity. In addition, when the number of relays is large, the multiple RS schemes require the same amount of feedback bits from the receiver as single RS schemes.

This paper is on relay beamforming in wireless networks, in which the receiver has perfect information of all channels and each relay knows its own channels. Instead of the commonly used total power constraint on relays and the transmitter, we use a more practical assumption that every node in the network has its own power constraint. A two-step amplify-and-forward protocol with beamforming is used, in which the transmitter and relays are allowed to adaptively adjust their transmit power and directions according to available channel information. The optimal beamforming problem 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, interestingly, this value depends on the quality of all other channels in addition to the relaypsilas own ones. 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 full diversity and outperforms other existing schemes.