This paper addresses the training signal design for the channel estimation in two-way multiple-input-and-multipleoutput (MIMO) relay systems, where the channels are correlated. We first derive the backward channel estimator with the optimal training signal sent by the relay node. Given the estimated backward channels and the probabilistic knowledge of the estimation error, we mainly focus on the forward channel estimation and the related training signal design. We further propose a novel training signal. The design criterion is to minimize the relaxation of the total mean square error (MSE) of the forward channel estimators, which is conditioned on the estimated backward channels. Finally, the numerical results show that the proposed training signal can improve the MSE performance.
In this paper, we consider the transceiver and relay design for multiple-input multiple-output (MIMO) cellular two-way relay channel (cTWRC), where a multi-antenna base station (BS) exchanges information with multiple multi-antenna mobile stations via a multi-antenna relay station (RS). We propose a novel two-way relaying scheme to approach the sum capacity of the MIMO cTWRC.
In this paper, the filter-and-forward (FF) relay design for multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems is considered. Due to the considered MIMO structure, the problem of joint design of the linear MIMO transceiver at the source and the destination and the FF relay at the relay is considered. As the design criterion, the minimization of weighted sum mean-square-error (MSE) is considered first, and the joint design in this case is approached based on alternating optimization that iterates between optimal design of the FF relay for a given set…
This paper considers the multi-input multi-output (MIMO) relay channel where multiple antennas are employed by each terminal. Compared to single-input single-output (SISO) relay channels, MIMO relay channels introduce additional degrees of freedom, making the design and analysis of optimal cooperative strategies more complex. In this paper, a partial cooperation strategy that combines transmit-side message splitting and block-Markov encoding is presented. Lower bounds on capacity that improve on a previously proposed non-cooperative lower bound are derived for Gaussian MIMO relay channels.
A multiple input multiple output (MIMO) two-way relay channel is considered, where two sources want to exchange messages with each other using multiple relay nodes, and both the sources and relay nodes are equipped with multiple antennas. Both the sources are assumed to have equal number of antennas and have perfect channel state information (CSI) for all the channels of the MIMO two-way relay channel, whereas, each relay node is either assumed to have CSI for its transmit and receive channel (the coherent case) or no CSI for any of the channels (the non-coherent case). The main results in thi…
We consider a multi-pair two-way amplify-and-forward massive multi-input multi-output (MIMO) hybrid relay with MIMO user-pairs. A hybrid relay has lesser number of radio frequency (RF) chains than the antennas, which significantly reduces the implementation cost. We employ block-diagonalization-based baseband processing at the hybrid relay to cancel the inter user-pair interference and equal-gain-combining-based RF processing to maximize the beamforming gain. We also use an algebraic norm maximizing relay transmit strategy to maximize the spectral efficiency (SE) of each user-pair. We numerica…
We derive optimal SNR-based transmit antenna selection rules at the source and relay for the nonregenerative half duplex MIMO relay channel. While antenna selection is a suboptimal form of beamforming, it has the advantage that the optimization is tractable and can be implemented with only a few bits of feedback from the destination to the source and relay. We compare the bit error rate of optimal antenna selection at both the source and relay to other proposed beamforming techniques and propose methods for performing the necessary limited feedback.
In this paper, we study the energy efficiency (EE) maximization problem in multiple-input multiple-output (MIMO) two-way relay networks with simultaneous wireless information and power transfer (SWIPT). The network consists of a multiple-antenna amplify-and-forward relay node which provides bidirectional communications between two multiple-antenna transceiver nodes
In this paper we study and analyze coverage region for half-duplex multiple-input multiple-output (MIMO) relay channel with amplify-and-forward (AF) strategy at the relay station. By assuming mixed Rayleigh and Rician fading channels with two different relay station situations, we consider the objective of maximizing coverage region for a given transmission rate and find the optimal relay location in the sense of maximizing coverage region. using Monte Carlo simulations, the coverage region and capacity bounds are shown for different fading cases and different relay station locations. Finally,…
We study and analyze coverage region in MIMO communication systems for a multiple-relay network with decode-and-forward (DF) strategy at the relays. Assuming that there is a line-of-sight (LOS) propagation environment for source-relay channels and channel state information is available at receivers (CSIR), we consider the objective of maximizing coverage region for a given transmission rate and show numerically the significant effect of propagation environment on capacity bounds, optimal relay location and coverage region. Also, we study the situation in which two adjacent relays cooperate in …
In this paper, we address the problem of optimal power allocation at the relay in two-hop secure communications under practical conditions. To guarantee secure communication during the long-distance transmission, the massive MIMO (M-MIMO) relaying techniques are explored to significantly enhance wireless security. The focus of this paper is on the analysis and design of optimal power assignment for a decode-and-forward (DF) M-MIMO relay, so as to maximize the secrecy outage capacity and minimize the interception probability, respectively. Our study reveals the condition for a nonnegative the s…
This letter considers simultaneous wireless information and power transfer (SWIPT) for a multiple-input multiple-output (MIMO) relay system. The relay is powered by harvesting energy from the source via time switching (TS) and utilizes the harvested energy to forward the information signal. Our aim is to maximize the rate of the system subject to the power constraints at both the source and relay nodes. In the first scenario in which the source covariance matrix is an identity matrix, we present the joint-optimal solution for relaying and the TS ratio in closed form. An iterative scheme is the…
This paper considers the partial decode-and-forward (PDF) strategy for the Gaussian multiple-input multiple-output (MIMO) relay channel. Unlike for the decode-and-forward (DF) strategy or point-to-point (P2P) transmission, for which Gaussian channel inputs are known to be optimal, the input distribution that maximizes the achievable PDF rate for the Gaussian MIMO relay channel has remained unknown so far. For some special cases, e.g., for relay channels where the optimal PDF strategy reduces to DF or P2P transmission, it could be deduced that Gaussian inputs maximize the PDF rate. For the gene…
The deterministic capacity of a relay network is the capacity of a network when relays are restricted to transmitting \emph{reliable} information, that is, (asymptotically) deterministic function of the source message. In this paper it is shown that the deterministic capacity of a number of MIMO relay networks can be found in the low power regime where $\SNR\to0$. This is accomplished through deriving single letter upper bounds and finding the limit of these as $\SNR\to0$. The advantage of this technique is that it overcomes the difficulty of finding optimum distributions for mutual informatio…
In this paper, we investigate joint source precoding matrices and relay processing matrix design for multi-user multiple-input multiple-output~(MU-MIMO) non-regenerative relay networks in the presence of the direct source-destination~(S-D) links. We consider both capacity and mean-squared error~(MSE) criterions subject to the distributed power constraints, which are nonconvex and apparently have no simple solutions. Therefore, we propose an optimal source precoding matrix structure based on the point-to-point MIMO channel technique, and a new relay processing matrix structure under the modifie…
We consider two-way amplify and forward relaying, where multiple full-duplex user pairs exchange information via a shared full-duplex massive multiple-input multiple-output (MIMO) relay. We derive closed-form lower bound for the spectral efficiency with zero-forcing processing at the relay, by using minimum mean squared error channel estimation. The zero-forcing lower bound for the system model considered herein, which is valid for arbitrary number of antennas, is not yet derived in the massive MIMO relaying literature. We numerically demonstrate the accuracy of the derived lower bound and the…
This paper studies the achievable degrees of freedom for multi-user MIMO two-way relay channels, where there are $K$ source nodes, each equipped with $M$ antennas, one relay node, equipped with $N$ antennas, and each source node exchanges independent messages with an arbitrary set of other source nodes via the relay. By allowing an arbitrary information exchange pattern, the considered channel model is a unified one. It includes several existing channel models as special cases: $K$-user MIMO Y channel, multi-pair MIMO two-way relay channel, generalized MIMO two-way X relay channel, and $L$-clu…
This paper considers the setup of a parallel MIMO relay network in which $K$ relays, each equipped with $N$ antennas, assist the transmitter and the receiver, each equipped with $M$ antennas, in the half-duplex mode, under the assumption that $N\geq{M}$. This setup has been studied in the literature like in \cite{nabar}, \cite{nabar2}, and \cite{qr}. In this paper, a simple scheme, the so-called Incremental Cooperative Beamforming, is introduced and shown to achieve the capacity of the network in the asymptotic case of $K\to{\infty}$ with a gap no more than $O(\frac{1}{\log(K)})$. This result …
We consider efficient communications over the multiple-input multiple-output (MIMO) multiway distributed relay channel (MDRC) with full data exchange, where each user, equipped with multiple antennas, broadcasts its message to all the other users via the help of a number of distributive relays. We propose a physical-layer network coding (PNC) based scheme involving linear precoding for channel alignment nested lattice coding for PNC, and lattice-based precoding for interference mitigation, We show that, with the proposed scheme, distributed relaying achieves the same sum-rate as cooperative re…
A multi-hop relay channel with multiple antenna terminals in a quasi-static slow fading environment is considered. For both full-duplex and half-duplex relays the fundamental diversity-multiplexing tradeoff (DMT) is analyzed. It is shown that, while decode-and-forward (DF) relaying achieves the optimal DMT in the full-duplex relay scenario, the dynamic decode-and-forward (DDF) protocol is needed to achieve the optimal DMT if the relay is constrained to half-duplex operation. For the latter case, static protocols are considered as well, and the corresponding achievable DMT performance is charac…
This paper investigates the degrees of freedom (DoF) of the L-cluster, K-user MIMO multi-way relay channel, where users in each cluster wish to exchange messages within the cluster, and they can only communicate through the relay. A novel DoF upper bound is derived by providing users with carefully designed genie information. Achievable DoF is identified using signal space alignment and multiple-access transmission. For the two-cluster MIMO multi-way relay channel with two users in each cluster, DoF is established for the general case when users and the relay have arbitrary number of antennas,…
We consider a multipair massive multiple-input multiple-output (MIMO) two-way relaying system, where multiple pairs of single-antenna devices exchange data with the help of a relay employing a large number of antennas $N$. The relay consists of low-cost components that suffer from hardware impairments. A large-scale approximation of the spectral efficiency (SE) with maximum ratio (MR) processing is derived in closed form, and the approximation is tight as $N \to \infty$. It is revealed that for a fixed hardware quality, the impact of the hardware impairments vanishes asymptotically when $N$ gr…
In this paper, we study the problem of physical layer security in a large-scale multiple-input multiple-output (LS-MIMO) relaying system. The advantage of LS-MIMO relaying systems is exploited to enhance both wireless security and spectral efficiency. In particular, the challenging issue incurred by short interception distance is well addressed. Under very practical assumptions, i.e., no eavesdropper's channel state information (CSI) and imperfect legitimate channel CSI, this paper gives a thorough investigation of the impact of imperfect CSI in two classic relaying systems, i.e., amplify-and-…
In this paper, we consider a large scale multiple input multiple output (LS-MIMO) relaying system, where an information source sends the message to its intended destination aided by an LS-MIMO relay, while a passive eavesdropper tries to intercept the information forwarded by the relay. The advantage of a large scale antenna array is exploited to improve spectral efficiency and enhance wireless security. In particular, the challenging issue incurred by short-distance interception is well addressed. Under very practical assumptions, i.e., no eavesdropper channel state information (CSI) and impe…
In this paper, we consider a dual-hop Multiple Input Multiple Output (MIMO) relay wireless network, in which a source-destination pair both equipped with multiple antennas communicates through a large number of half-duplex amplify-and-forward (AF) relay terminals. Two novel linear beamforming schemes based on the matched filter (MF) and regularized zero-forcing (RZF) precoding techniques are proposed for the MIMO relay system. We focus on the linear process at the relay nodes and design the new relay beamformers by utilizing the channel state information (CSI) of both backward channel and forw…
This paper considers a multiple-input multiple-output (MIMO) relay system with an energy harvesting relay node. All nodes are equipped with multiple antennas, and the relay node depends on the harvested energy from the received signal to support information forwarding. In particular, the relay node deploys power splitting based energy harvesting scheme. The capacity maximization problem subject to power constraints at both the source and relay nodes is considered for both fixed source covariance matrix and optimal source covariance matrix cases. Instead of using existing software solvers, iter…
This paper investigates the system achievable rate and optimization for the multiple-input multiple-output (MIMO)-orthogonal frequency division multiplexing (OFDM) system with an energy harvesting (EH) relay. Firstly we propose a time switchingbased relaying (TSR) protocol to enable the simultaneous information processing and energy harvesting at the relay. Then, we discuss its achievable rate performance theoretically and formulated an optimization problem to maximize the system achievable rate. As the problem is difficult to solve, we design an Augmented Lagrangian Penalty Function (ALPF) me…
The K-user MIMO Y-channel consisting of K users which want to exchange messages among each other via a common relay node is studied in this paper. A transmission strategy based on channel diagonalization using zero-forcing beam-forming is proposed. This strategy is then combined with signal-space alignment for network-coding, and the achievable degrees-of-freedom region is derived. A new degrees-of-freedom outer bound is also derived and it is shown that the proposed strategy achieves this outer bound if the users have more antennas than the relay.
We propose a greedy minimum mean squared error (MMSE)-based antenna selection algorithm for amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay systems. Assuming equal-power allocation across the multi-stream data, we derive a closed form expression for the mean squared error (MSE) resulted from adding each additional antenna pair. Based on this result, we iteratively select the antenna-pairs at the relay nodes to minimize the MSE. Simulation results show that our algorithm greatly outperforms the existing schemes.
We consider a multiple-input multiple-output (MIMO) relaying boardcast channel in downlink cellular networks, where the base station and the relay stations are both equipped with multiple antennas, and each user terminal has only a single antenna. In practical scenarios, channel estimation is imperfect at the receivers. Aiming at maximizing the SINR at each user, we develop two robust linear beamforming schemes respectively for the single relay case and the multi-relay case. The two proposed schemes are based on sigular value decomposition (SVD), minimum mean square error (MMSE) and regularize…
We propose a joint discrete stochastic optimization based transmit diversity selection (TDS) and relay selection (RS) algorithm for decode-and-forward (DF), cooperative MIMO systems with a non-negligible direct path. TDS and RS are performed jointly with continuous least squares channel estimation (CE), linear minimum mean square error (MMSE) receivers are used at all nodes and no inter-relay communication is required. The performance of the proposed scheme is evaluated via bit-error rate (BER) comparisons and diversity analysis, and is shown to converge to the optimum exhaustive solution.
In this paper, we investigate relay selection for cooperative multiple-antenna systems that are equipped with buffers, which increase the reliability of wireless links. In particular, we present a novel relay selection technique based on switching and the Max-Link protocol that is named Switched Max-Link. We also introduce a novel relay selection criterion based on the maximum likelihood (ML) principle denoted maximum minimum distance that is incorporated into. Simulations are then employed to evaluate the performance of the proposed and existing techniques.
The remarkable promise of multiple-input multiple-output (MIMO) wireless channels has motivated an intense research activity to characterize the theoretical and practical issues associated with the design of transmit (source) and receive (destination) processing matrices under different operating conditions. This activity was primarily focused on point-to-point (single-hop) communications but more recently there has been an extensive work on two-hop or multi-hop settings in which single or multiple relays are used to deliver the information from the source to the destination. The aim of this t…
For massive MIMO AF relays, symbol detection becomes a practical issue when the number of antennas is not large enough, since linear methods are non-optimal and optimal methods are exponentially complex. This paper proposes a new detection algorithm that offers Bayesian-optimal MSE at the cost of $O(n^3)$ complexity per iteration. The algorithm is in essence a hybrid of two methods recently developed for deep learning, with particular optimization for relay. As a hybrid, it inherits from the two a state evolution formulism, where the asymptotic MSE can be precisely predicted through a scalar e…
This paper studies the interference channel with two transmitters and two receivers in the presence of a MIMO relay in the low transmit power regime. A communication scheme combining block Markov encoding, beamforming, and Willems' backward decoding is used. With this scheme, we get an interference channel with channel gains dependent on the signal power. A power allocation for this scheme is proposed, and the achievable rate region with this power allocation is given. We show that, at low transmit powers, with equal power constraints at the relay and the transmitters, the interference channel…
In this paper, robust transceiver design based on minimum-mean-square-error (MMSE) criterion for dual-hop amplify-and-forward MIMO relay systems is investigated. The channel estimation errors are modeled as Gaussian random variables, and then the effect are incorporated into the robust transceiver based on the Bayesian framework. An iterative algorithm is proposed to jointly design the precoder at the source, the forward matrix at the relay and the equalizer at the destination, and the joint design problem can be efficiently solved by quadratic matrix programming (QMP).
This paper investigates a three-node amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay network, where an autonomous relay harvests power from the source information flow and is further helped by an energy flow in the form of a wireless power transfer (WPT) at the destination. An energy-flow-assisted two-phase relaying scheme is proposed, where a source and relay joint optimization is formulated to maximize the rate. By diagonalizing the channel, the problem is simplified to a power optimization, where a relay channel pairing problem is solved by an ordering operation. The pr…
A wireless relay with multiple antennas is called a multiple-input-multiple-output (MIMO) switch if it maps its input links to its output links using "precode-and-forward." Namely, the MIMO switch precodes the received signal vector in the uplink using some matrix for transmission in the downlink. This paper studies the scenario of $K$ stations and a MIMO switch, which has full channel state information. The precoder at the MIMO switch is either a zero-forcing matrix or a network-coded matrix. With the zero-forcing precoder, each destination station receives only its desired signal with enhanc…
In this paper, we study the degrees of freedom (DoF) of the MIMO relay networks. We start with a general Y channel, where each user has $M_i$ antennas and aims to exchange messages with the other two users via a relay equipped with $N$ antennas. Then, we extend our work to a general 4-user MIMO relay network. Unlike most previous work which focused on the total DoF of the network, our aim here is to characterize the achievable DoF region as well. We develop an outer bound on the DoF region based on the notion of one sided genie. Then, we define a new achievable region using the Signal Space Al…
This paper considers a decode-and-forward (DF) multi-way massive multiple-input multiple-output (MIMO) relay system where many users exchange their data with the aid of a relay station equipped with a massive antenna array. We propose a new transmission protocol which leverages successive cancelation decoding and zero-forcing (ZF) at the users. By using properties of massive MIMO, a tight analytical approximation of the spectral efficiency is derived. We show that our proposed scheme uses only half of the time-slots required in the conventional scheme (in which the number of time-slots is equa…
This paper studies MIMO relays with non-identical link coherence times, a frequently occurring condition when, e.g., the nodes in the relay channel do not all have the same mobility, or the scatterers around some nodes have different mobility compared with those around other nodes. Despite its practical relevance, this condition, known as coherence diversity, has not been studied in the relay channel. This paper studies the performance of MIMO relays and proposes efficient transmission strategies under coherence diversity. Since coherence times have a prominent impact on channel training, we d…
In this paper, we address the problem of secure wireless information and power transfer in a large-scale multiple-input multiple-output (LS-MIMO) amplify-and-forward (AF) relaying system. The advantage of LS-MIMO relay is exploited to enhance wireless security, transmission rate and energy efficiency. In particular, the challenging issues incurred by short interception distance and long transfer distance are well addressed simultaneously. Under very practical assumptions, i.e., no eavesdropper's channel state information (CSI) and imperfect legitimate channel CSI, this paper investigates the i…
In this paper we investigate the optimal relay location in the sense of maximizing suitably defined coverage region for MIMO relay channel. We consider the general Rayleigh fading case and assume that the channel state information is only available at the receivers (CSIR), which is an important practical case in applications such as cooperative vehicular communications. In order to overcome the mathematical difficulty regarding determination of the optimal relay location, we provide two analytical solutions, and show that it is possible to determine the optimal relay location (for a desired tr…
Hardware impairments, such as phase noise, quantization errors, non-linearities, and noise amplification, have baneful effects on wireless communications. In this paper, we investigate the effect of hardware impairments on multipair massive multiple-input multiple-output (MIMO) two-way full-duplex relay systems with amplify-and-forward scheme. More specifically, novel closed-form approximate expressions for the spectral efficiency are derived to obtain some important insights into the practical design of the considered system. When the number of relay antennas $N$ increases without bound, we p…
In this paper, we address the problem of optimal power allocation at the relay in two-hop secure communications. In order to solve the challenging issue of short-distance interception in secure communications, the benefit of large-scale MIMO (LS-MIMO) relaying techniques is exploited to improve the secrecy performance significantly, even in the case without eavesdropper channel state information (CSI). The focus of this paper is on the analysis and design of optimal power allocation for the relay, so as to maximize the secrecy outage capacity. We reveal the condition that the secrecy outage ca…
Robust transceiver design against unresolvable system uncertainties is of crucial importance for reliable communication. For instance, full-duplex communication suffers from such uncertainties when canceling the self-interference, since the residual self-interference (RSI) remains uncanceled due to imperfect channel knowledge. We consider a MIMO multi-hop system, where the source, the relay and the destination are equipped with multiple antennas. We allow multi-stream beamforming granted by MIMO technique, without restricting the transmissions to single streaming. The relay can operate in eith…
A multi-hop two-way relay channel is considered in which all the terminals are equipped with multiple antennas. Assuming independent quasi-static Rayleigh fading channels and channel state information available at the receivers, we characterize the optimal diversity-multiplexing gain tradeoff (DMT) curve for a full-duplex relay terminal. It is shown that the optimal DMT can be achieved by a compress-and-forward type relaying strategy in which the relay quantizes its received signal and transmits the corresponding channel codeword. It is noteworthy that, with this transmission protocol, the two…
Despite the deleterious effect of hardware impairments on communication systems, most prior works have not investigated their impact on widely used relay systems. Most importantly, the application of inexpensive transceivers, being prone to hardware impairments, is the most cost-efficient way for the implementation of massive multiple-input multiple-output (MIMO) systems. Consequently, the direction of this paper is towards the investigation of the impact of hardware impairments on MIMO relay networks with large number of antennas. Specifically, we obtain the general expression for the ergodic…
This paper considers multiple-input multiple-output (MIMO) relay communication in multi-cellular (interference) systems in which MIMO source-destination pairs communicate simultaneously. It is assumed that due to severe attenuation and/or shadowing effects, communication links can be established only with the aid of a relay node. The aim is to minimize the maximal mean-square-error (MSE) among all the receiving nodes under constrained source and relay transmit powers. Both one- and two-way amplify-and-forward (AF) relaying mechanisms are considered. Since the exactly optimal solution for this …
In this paper, we consider the arbitrary MIMO two-way relay channels, where there are $K$ source nodes, each equipped with $M_i$ antennas, for $i=1,2,\cdots,K$, and one relay node, equipped with $N$ antennas. Each source node can exchange independent messages with arbitrary other source nodes assisted by the relay. We extend our newly-proposed transmission scheme, generalized signal alignment (GSA) in [1], to arbitrary MIMO two-way relay channels when $N>M_i+M_j$, $\forall i \neq j$. The key idea of GSA is to cancel the interference for each data pair in its specific subspace by two steps. Thi…
In this paper, we investigate the robust transceiver design for dual-hop amplify-and-forward (AF) MIMO relay systems with Gaussian distributed channel estimation errors. Aiming at maximizing the mutual information under imperfect channel state information (CSI), source precoder at source and forwarding matrix at the relay are jointly optimized. Using some elegant attributes of matrix-monotone functions, the structures of the optimal solutions are derived first. Then based on the derived structure an iterative waterfilling solution is proposed. Several existing algorithms are shown to be specia…
In this paper, we consider linear MIMO transceiver design for a cellular two-way amplify-and-forward relaying system consisting of a single multi-antenna base station, a single multi-antenna relay station, and multiple multi-antenna mobile stations (MSs). Due to the two-way transmission, the MSs could suffer from tremendous multi-user interference. We apply an interference management model exploiting signal space alignment and propose a transceiver design algorithm, which allows for alleviating the loss in spectral efficiency due to half-duplex operation and providing flexible performance opti…
Unified performance analysis is carried out for amplify-and-forward (AF) multiple-input-multiple-output (MIMO) beamforming (BF) two-way relay networks in Rayleigh fading with five different relaying protocols including two novel protocols for better performance. As a result, a novel closed-form sum-bit error rate (BER) expression is presented in a unified expression for all protocols. A new closed-form high signal-to-noise-ratio (SNR) performance is also obtained in a single expression, and an analytical high-SNR gap expression between the five protocols is provided. We compare the performance…
In this paper, we investigate the optimization problem of joint source and relay beamforming matrices for a twoway amplify-and-forward (AF) multi-input multi-output (MIMO) relay system. The system consisting of two source nodes and two relay nodes is considered and the linear minimum meansquare- error (MMSE) is employed at both receivers. We assume individual relay power constraints and study an important design problem, a so-called determinant maximization (DM) problem. Since this DM problem is nonconvex, we consider an efficient iterative algorithm by using an MSE balancing result to obtain …
Properly designed precoders can significantly improve the spectral efficiency of multiple-input multiple-output (MIMO) relay systems. In this paper, we investigate joint source and relay precoding design based on the mean-square-error (MSE) criterion in MIMO two-way relay systems, where two multi-antenna source nodes exchange information via a multi-antenna amplify-and-forward relay node. This problem is non-convex and its optimal solution remains unsolved. Aiming to find an efficient way to solve the problem, we first decouple the primal problem into three tractable sub-problems, and then pro…
We consider a multi-way massive multiple-input multiple-output relay network with zero-forcing processing at the relay. By taking into account the time-division duplex protocol with channel estimation, we derive an analytical approximation of the spectral efficiency. This approximation is very tight and simple which enables us to analyze the system performance, as well as, to compare the spectral efficiency with zero-forcing and maximum-ratio processing. Our results show that by using a very large number of relay antennas and with the zero-forcing technique, we can simultaneously serve many ac…
Capacity bounds are studied for the multiple-antenna complex Gaussian relay channel with t1 transmitting antennas at the sender, r2 receiving and t2 transmitting antennas at the relay, and r3 receiving antennas at the receiver. It is shown that the partial decode-forward coding scheme achieves within min(t1,r2) bits from the cutset bound and at least one half of the cutset bound, establishing a good approximate expression of the capacity. A similar additive gap of min(t1 + t2, r3) + r2 bits is shown to be achieved by the compress-forward coding scheme.
We investigate achievable degrees of freedom (DoF) for a multiple-input multiple-output (MIMO) multiway relay channel (mRC) with $L$ clusters and $K$ users per cluster. Each user is equipped with $M$ antennas and the relay with $N$ antennas. We assume a new data exchange model, termed \emph{clustered full data exchange}, i.e., each user in a cluster wants to learn the messages of all the other users in the same cluster. Novel signal alignment techniques are developed to systematically construct the beamforming matrices at the users and the relay for efficient physical-layer network coding. Bas…
In this work, we investigate the diversity-multiplexing tradeoff (DMT) of the multiple-antenna (MIMO) static half-duplex relay channel. A general expression is derived for the DMT upper bound, which can be achieved by a compress-and-forward protocol at the relay, under certain assumptions. The DMT expression is given as the solution of a minimization problem in general, and an explicit expression is found when the relay channel is symmetric in terms of number of antennas, i.e. the source and the destination have n antennas each, and the relay has m antennas. It is observed that the static half…
