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

In this 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.

This paper conducts the performance sensitivity analysis for linear alarm filters. With a derivative-based local sensitivity measure, models are proposed to assess the sensitivity of the system detection errors to changes in the trip point and uncertainties in the collected data. Then, sensitivity formulations for a general linear alarm filter framework with unknown data distributions are studied. Extensive simulations with Gaussian and Gamma data using two typical linear filters, the moving average (MA) filter and the linear weighted (LW) filter, are conducted to verify the analytical results and to show the trade-offs among different system parameters.

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.

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

This paper 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.

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

This paper 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.

In practical multi-input multi-output (MIMO) systems, the channel matrices often have reduced rank. Reliable detection of the channel rank is essential in achieving the significant gain provided by MIMO configuration. Existing work on MIMO channel rank detection assume a static channel model, so the proposed methods only consider the noise distributions while the distributions of the MIMO channels are not considered. In this paper, we employ a random channel model and propose three threshold-based rank detection methods which take into account the distributions of both the channels and the noises. In our first algorithm, following existing single-threshold rank detection scheme, we rigorously derive an analytical lower bound on the correct rank detection probability and propose a systematic threshold selection method by maximizing the lower bound. Then we propose two new rank detection methods which use multiple thresholds, where each threshold corresponds to one possible rank value. The thresholds are optimized based on the derived lower bounds on the rank detection probability for different channel rank values. The convergence and complexity of the proposed algorithms are analyzed. Simulation results on the correct rank detection probability of the proposed schemes are provided to show their advantage over existing schemes. The mean-squared-error (MSE) and outage probability are also simulated to show the importance of reliable rank detection in MIMO communications.

In practical multi-input-multi-output (MIMO) systems, the channel matrices often have reduced rank especially for propagation environments with limited scattering. For this scenario, reliable detection of the channel rank is essential in achieving the high performance provided by the MIMO configuration. In traditional rank detection schemes, a single threshold is used and the channel rank is detected as the number of singular values of the observation matrix that are larger than the threshold. In this work, we propose a multiple-threshold-based rank detection scheme, where each threshold corresponds to one possible rank value. The thresholds are optimized based on the derived lower bounds on the rank detection probability for different channel rank values. Simulation results show that the proposed detection scheme outperforms existing schemes in the probability of correct rank detection.

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.

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

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

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

In this paper, we analyze the achievable rate of the uplink of a single-cell multi-user distributed massive multiple-input-multiple-output (MIMO) system. The multiple users are equipped with single antenna and the base station (BS) is equipped with a large number of distributed antennas. We derive an analytical expression for the asymptotic ergodic achievable rate of the system under zero-forcing (ZF) detector. In particular, we consider circular antenna array, where the distributed BS antennas are located evenly on a circle, and derive an analytical expression and closed-form tight bounds for the achievable rate of an arbitrarily located user. Subsequently, closed-form bounds on the average achievable rate per user are obtained under the assumption that the users are uniformly located in the cell. Based on the bounds, we can understand the behavior of the system rate with respect to different parameters and find the optimal location of the circular BS antenna array that maximizes the average rate. Numerical results are provided to assess our analytical results and examine the impact of the number and the location of the BS antennas, the transmit power, and the path-loss exponent on system performance. It is shown that circularly distributed massive MIMO system largely outperforms centralized massive MIMO system., Single column, 30 pages, 8 figures. Submitted to IEEE Transactions on Wireless Communications

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.

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.

For a three-node amplify-and-forward (AF) two-way relay network (TWRN), we investigate the power allocation problem during the channel training process for both terminals to estimate the global channel state information (CSI) of the whole network. This includes the power allocations between different training steps and among different nodes. Two power allocation schemes are proposed: a mean-square-error (MSE) based scheme and an outage probability (OP) based scheme. Our simulation results demonstrate that the proposed power allocations are superior to even power allocation.

This chapter is on the differential use of distributed space-time coding (DSTC). First, the transmission protocol and decoding of differential DSTC are explained in Sect. 4.1. Then several code designs are introduced in Sect. 4.2. Finally, simulated error probability of differential DSTC is shown in Sect. 4.3.

The coherent distributed space-time coding (DSTC) schemes introduced in Chaps. 2 and 3 require full channel state information (CSI) at the receiver. In reality, training and channel estimations need to be conducted to obtain the required CSI at the receiver. The estimated CSI is then used in the data transmission. This chapter is on channel training and training-based DSTC. First, the training and estimation of the global and individual channels of the relay network are considered in Sect. 5.1. Then, training-based DSTC, i.e, DSTC with estimated CSI, is studied in Sect. 5.2. After that, the training and estimation of the end-to-end channels for single-antenna relay network and multiple-antenna relay network are explained in Sects. 5.3 and 5.4, respectively.

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.

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

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.