Multiple-input Multiple-output Relay Research Articles

Channel Estimation of Dual-Hop MIMO Relay System via Parallel Factor Analysis

The optimal source precoding matrix and relay amplifying matrix have been developed in recent works on multiple-input multiple-output (MIMO) relay communication systems assuming that the instantaneous channel state information (CSI) is available. However, in practical relay communication systems, the instantaneous CSI is unknown, and therefore, has to be estimated at the destination node. In this paper, we develop a novel channel estimation algorithm for two-hop MIMO relay systems using the parallel factor (PARAFAC) analysis. The proposed algorithm provides the destination node with full knowledge of all channel matrices involved in the communication. Compared with existing approaches, the proposed algorithm requires less number of training data blocks, yields smaller channel estimation error, and is applicable for both one-way and two-way MIMO relay systems with single or multiple relay nodes. Numerical examples demonstrate the effectiveness of the PARAFAC-based channel estimation algorithm.

MMSE-DFE Based MIMO Relay System with Correlated Fading Channel

We consider a practical dual-hop nonregenerative multiple-input multiple-output (MIMO) relay system, where the relay node only knows the correlation matrix of the relay-destination channel. A nonlinear minimal mean-squared error (MMSE)-based decision feedback equalizer (DFE) is used at the destination node to retrieve the source signals. We derive the structure of statistically optimal source and relay precoding matrices to minimize a class of objective functions which are multiplicatively Schur-convex with respect to the diagonal elements of the MSE matrix. Simulation results demonstrate that the proposed algorithm has a very close performance compared to MIMO relay system with full channel knowledge at the relay node, and thus is very useful for practical relay systems.

Local CSI Based Selection Beamforming for Amplify-and-Forward MIMO Relay Networks

We investigate selection beamforming for a cooperative network that consists of a source, a destination, and two amplify-and-forward (AF) relays, which are all equipped with multiple antennas. The transmit and receive beamforming techniques are respectively applied at the source and destination, and the linear processing operator of the selected AF multiple-input multiple-output (MIMO) relay is optimized. We consider that the source has the instantaneous channel state information (CSI) of the channels from the source to relays but no information regarding the CSI of the channels from the relays to the destination. Partial relay selection (PRS) is employed, i.e., the source routes its information signal to the relay which offers better first-hop signal-to-noise ratio (SNR). Considering a Rayleigh fading environment, we derive an exact closed-form expression for the outage probability at the destination. The validity of the outage probability expression has been confirmed with numerical simulations. We also present the asymptotic analysis of the PRS scheme for the considered multiantenna system and derive the expressions of diversity gain. It is shown that, the overall diversity gain is <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\min(\min(n_{{\rm r},1}n_{\rm d},n_{{\rm r},2}n_{\rm d}),n_{{\rm r},1}n_{\rm s}+n_{{\rm r},2}n_{\rm s})$</tex></formula> where <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n_{\rm s}$</tex></formula> , <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n_{\rm d}$</tex></formula> , and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n_{{\rm r},q}$</tex></formula> are, respectively, the numbers of antennas at the source, destination and the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$q$</tex></formula> th relay. For the condition <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$C:\min(n_{{\rm r},1}n_{\rm d},n_{{\rm r},2}n_{\rm d})\geq n_{{\rm r},1}n_{\rm s}+n_{{\rm r},2}n_{\rm s}$</tex></formula> that can be easily met with practically realizable antenna configurations, it is shown that PRS provides the same diversity order as opportunistic relaying (OR).

Relay Precoding for Non-Regenerative MIMO Relay Systems with Partial CSI in the Presence of Interferers

In this paper, a relay precoding problem is considered in a non-regenerative multiple-input multiple output (MIMO) relay system, when multiple interferers exist near the destination. The relay has the perfect channel state information (CSI) of the source-relay link and only the covariance information of the relay-destination link. Also, we assume that the training signals of the interferers are known at the destination, and thus, the covariance information of the channels from the interferers to the destination can be estimated at the destination and the information is fed back to the relay. For this scenario, the structure of the optimal relay precoder is derived to maximize the average capacity seen by the relay under a relay transmit power constraint. For the derivation of the optimal relay precoder, a new partial ordering result for the outage probability and the ergodic capacity of spatially correlated MIMO channels is derived. Numerical results demonstrate that the proposed scheme considerably improves the performance. Overall, the contributions of this paper are twofold: i) a new partial ordering result for MIMO channels is derived and ii) the structure of the optimal relay precoder is derived using the partial ordering result.

Sum-Rate Maximization in Two-Way AF MIMO Relaying: Polynomial Time Solutions to a Class of DC Programming Problems

Sum-rate maximization in two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying belongs to the class of difference-of-convex functions (DC) programming problems. DC programming problems occur also in other signal processing applications and are typically solved using different modifications of the branch-and-bound method which, however, does not have any polynomial time complexity guarantees. In this paper, we develop two efficient polynomial time algorithms for the sum-rate maximization in two-way AF MIMO relaying. The first algorithm guarantees to find at least a Karush-Kuhn-Tucker (KKT) solution. There is a strong evidence, however, that such a solution is actually globally optimal. The second algorithm that is based on the generalized eigenvectors shows the same performance as the first one with reduced computational complexity. The objective function of the problem is represented as a product of quadratic fractional ratios and parameterized so that its convex part (versus the concave part) contains only one (or two) optimization variables. One of the algorithms is called POlynomial Time DC (POTDC) and is based on semi-definite programming (SDP) relaxation, linearization, and an iterative Newton-type search over a single parameter. The other algorithm is called RAte-maximization via Generalized EigenvectorS (RAGES) and is based on the generalized eigenvectors method and an iterative search over two (or one, in its approximate version) optimization variables. We derive an upper-bound for the optimal value of the corresponding optimization problem and show by simulations that this upper-bound is achieved by both algorithms. It provides an evidence that the algorithms find a global optimum. The proposed methods are also superior to other state-of-the-art algorithms.

Robust Transmitter Design for Amplify-and-Forward MIMO Relay Systems Exploiting Only Channel Statistics

In this paper, we address statistically robust transmit design problems that maximize the average mutual information of amplify-and-forward (AF) multiple-input multiple-output (MIMO) two-hop relay channels having perfect channel state information at the receiver (CSIR) and statistical channel state information at the transmitter (CSIT). In the selected scenario, the source, relay, and destination terminals are equipped with correlated antennas where a direct link between the source and the destination terminals can be found. Moreover, the statistical CSIT consists of the channel means and covariance matrices of various links. The design problem is taken into account for regimes in large systems because there are no closed-form expressions of the average mutual information in the MIMO relay channel. The contribution of this study includes the derivation of asymptotic mutual information expressions for the MIMO relay channel in the large system limit. Additionally, an efficient optimization algorithm based on the asymptotic mutual information is proposed in order to find the asymptotically optimal source covariance matrix and the relay amplifying matrix. Numerical simulation results show that the new approach achieves indistinguishable performance compared to those of the maximization approaches in finite-dimensional systems, even for a small number of antennas at each link. The impact of the CSI of various links on the throughput of the MIMO relay channel is studied using the new approach.

Effectiveness of Relay MIMO Transmission by Measured Outdoor Channel State Information

This paper investigates the effectiveness of the multiple input multiple output (MIMO) transmission with the aid of relay nodes by using measured outdoor channel state information (CSI) for the source, relay, and destination which are used in cooperative transmission. Single/multi-user MIMO (SU/MU-MIMO) systems have attracted much attention as the technology enhances the channel capacity with a limited frequency band. In this paper, cooperative transmission using the relay station is applied to SU/MU-MIMO systems: Relay MIMO transmission. Although the performance of relay MIMO transmission is affected by the actual propagation environment, the performance has not yet been investigated using measured propagation channel data in outdoor scenarios. In this paper, we demonstrate that the channel capacity with the relay MIMO transmission can be improved compared to the conventional MIMO transmission without the relay nodes, especially in multi-user scenarios. Moreover, orthogonal polarization is introduced and its effectiveness is shown in further improving the channel capacity of relay MIMO transmission.

Joint Relay and Antenna Selection for Dual-Hop Amplify-and-Forward MIMO Relay Networks

Four joint relay and antenna selection strategies for dual-hop amplify-and-forward (AF) multiple-input multiple-output relay networks are studied. Two of them require full channel state information (CSI) whereas the other two require only partial CSI. The relays are either channel-assisted AF or fixed-gain AF type. The first joint selection strategy involves choosing the best relay and the best single transmit antennas at the source and the relay. The second strategy jointly involves choosing the best relay and the best single transmit/receive antenna pairs at the source-to-relay and relay-to-destination channels. Moreover, two partial selection strategies, which can be used when the global CSI is not available, are also proposed and analyzed. In order to quantify the system performance analytically, the exact outage probability of all selection strategies is derived in closed-form. Direct insights into the system-design are obtained by deriving the asymptotic outage probability, asymptotic average symbol error rate, diversity order and array gain.

Performance Analysis of MIMO Relay Network via Propagation Measurement in L-Shaped Corridor Environment

Setting relays can address the shadowing problem between a transmitter (Tx) and a receiver (Rx). Moreover, the Multiple-Input Multiple-Output (MIMO) technique has been introduced to improve wireless link capacity. The MIMO technique can be applied in relay network to enhance system performance. However, the efficiency of relaying schemes and relay placement have not been well investigated with experiment-based study. This paper provides a propagation measurement campaign of a MIMO two-hop relay network in 5GHz band in an L-shaped corridor environment with various relay locations. Furthermore, this paper proposes a Relay Placement Estimation (RPE) scheme to identify the optimum relay location, i.e. the point at which the network performance is highest. Analysis results of channel capacity show that relaying technique is beneficial over direct transmission in strong shadowing environment while it is ineffective in non-shadowing environment. In addition, the optimum relay location estimated with the RPE scheme also agrees with the location where the network achieves the highest performance as identified by network capacity. Finally, the capacity analysis shows that two-way MIMO relay employing network coding has the best performance while cooperative relaying scheme is not effective due to shadowing effect weakening the signal strength of the direct link.

Cooperative Relaying for the Rank-Deficient MIMO Relay Interference Channel

Rank-deficient multiple-input multiple-output (MIMO) relay interference channel (IC) is investigated in which K source-destination pairs communicate with the help of N relays. For the K-user rank-deficient MIMO IC with no relays, an achievable sum degrees of freedom (DoF) is upper bounded by Krds, where rds denotes the rank of each point-to-point channel matrix. However, if relays assist the communication, we show that there can be significant improvement on the DoF compared to the case where there is no relay. The proposed cooperative relaying uses relays not only for increasing ranks of desired channel matrices but also nullifying inter-user interference.

Joint Secure Beamforming Design at the Source and the Relay for an Amplify-and-Forward MIMO Untrusted Relay System

An amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay network composed of a source, a relay, and a destination is considered, where transmit beamforming is employed both at the source and at the relay. The relay is a user who is willing to help the communication from the source to the destination. In our paper, however, the relay is untrusted in the sense that it may make a passive security attack; that is, it may decode messages of the source. We consider two ways to transmit confidential information of the source to the destination: noncooperative secure beamforming and cooperative secure beamforming. In the noncooperative scheme, the relay is simply treated as an eavesdropper, and does not participate in communication. In the cooperative scheme, the relay is asked to relay signals from the source to the destination. In this paper, the source and relay beamforming is jointly designed to maximize the secrecy rate in the cooperative scheme. The conditions under which the cooperative scheme achieves a higher secrecy rate than the noncooperative scheme are derived in the low and high signal-to-noise ratio (SNR) regimes of the source-relay and relay-destination links. The performance of the secure beamforming schemes is compared through extensive numerical simulations.

Capacity analysis for multiple-input multiple-output relay system in a low-rank line-of-sight environment

This article focuses on channel model and capacity of multiple-input multiple-output (MIMO) relay system in a low-rank line-of-sight environment. According to the channel characteristics of MIMO and the correlations among antenna arrays, the expression for system capacity is deduced. Various factors influencing MIMO relay system are analysed based on this expression, and the numerical simulation is performed for verification. The simulation results show that system capacity is greatly increased by adding relay nodes. However, the antenna array spacing and angle at the transmitting and receiving ends, relay node position, Rice K -factor and other factors can all produce certain effects on the capacity of MIMO relay system.

Superimposed Training-Based Channel Estimation for MIMO Relay Networks

We introduce the superimposed training strategy into the multiple-input multiple-output (MIMO) amplify-and-forward (AF) one-way relay network (OWRN) to perform the individual channel estimation at the destination. Through the superposition of a group of additional training vectors at the relay subject to power allocation, the separated estimates of the source-relay and relay-destination channels can be obtained directly at the destination, and the accordance with the two-hop AF strategy can be guaranteed at the same time. The closed-form Bayesian Cramér-Rao lower bound (CRLB) is derived for the estimation of two sets of flat-fading MIMO channel under random channel parameters and further exploited to design the optimal training vectors. A specific suboptimal channel estimation algorithm is applied in the MIMO AF OWRN using the optimal training sequences, and the normalized mean square error performance for the estimation is provided to verify the Bayesian CRLB results.

Joint source-and-relay beamforming for multiple-input multiple-output systems with single-antenna distributed relays

A joint source-and-relay beamforming scheme is proposed for multiple-input multiple-output (MIMO) systems with distributed single-antenna relays. First, a lower-bound of the signal-to-noise ratio at the destination is derived as an objective function to formulate a constrained beamforming optimisation problem. The joint beamforming problem is then divided into two sub-optimisation problems corresponding to the source and the relay beamforming, respectively. The first sub-problem is shown to be a quadratic concave minimisation, and is tackled by developing an iterative algorithm with each iteration solving a linear problem. The second one corresponds to a Rayleigh–Ritz ratio problem which is then solved by the generalised singular-value decomposition in a closed form. Based on the solutions to the subproblems, a global iterative algorithm is designed to implement the joint source-and-relay beamforming. Simulation results show that the proposed method outperforms some existing relaying schemes in terms of the capacity and outage probability of the whole MIMO relay system.

Joint Design of Uplink-Downlink MIMO Relay Networks Using Duality

This letter introduces a joint design method for uplink-downlink multiple-input multiple-output (MIMO) relay communication systems in which the source nodes transmit information to the destination nodes with the help of a relay. We propose a signal forwarding schceme based on the minimum mean-square error (MMSE) approach in uplink relay systems. Exploiting the duality of relay systems, we also propose a relaying scheme for downlink relay systems. Simulation results confirm that the proposed joint design method improves the performance of the relay systems compared with that of conventional relaying schemes in uplink and downlink MIMO relay systems.

Joint Source and Relay Precoding Designs for MIMO Two-Way Relaying Based on MSE Criterion

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 propose an iterative precoding design algorithm based on alternating optimization. The solution to each sub-problem is optimal and unique, thus the convergence of the iterative algorithm is guaranteed. Secondly, we propose a structured precoding design to lower the computational complexity. The proposed precoding structure is able to parallelize the channels in the multiple access (MAC) phase and broadcast (BC) phase. It thus reduces the precoding design to a simple power allocation problem. Lastly, for the special case where only a single data stream is transmitted from each source node, we present a source-antenna-selection (SAS) based precoding design algorithm. This algorithm selects only one antenna for transmission from each source and thus requires lower signalling overhead. Comprehensive simulation is conducted to evaluate the effectiveness of all the proposed precoding designs.

Mitigation of Loopback Self-Interference in Full-Duplex MIMO Relays

Full-duplex relaying is more spectrally efficient than half-duplex relaying as only one channel use is needed per two hops. However, it is crucial to minimize relay self-interference to render full duplex feasible. For this purpose, we analyze a broad range of multiple-input multiple-output (MIMO) mitigation schemes: natural isolation, time-domain cancellation, and spatial suppression. Cancellation subtracts replicated interference signal from the relay input while suppression reserves spatial dimensions for receive and transmit filtering. Spatial suppression can be achieved by antenna subset selection, null-space projection, i.e., receiving and transmitting in orthogonal subspaces, or joint transmit and receive beam selection to support more spatial streams by choosing the minimum eigenmodes for overlapping subspaces. In addition, minimum mean square error (MMSE) filtering can be employed to maintain the desired signal quality, which is inherent for cancellation, and the combination of time- and spatial-domain processing may be better than either alone. Targeting at minimal interference power, we solve optimal filters for each scheme in the cases of joint, separate and independent design. The performance of mitigation schemes is evaluated and compared by simulations. The results confirm that self-interference can be mitigated effectively also in the presence of imperfect side information.

Asymptotic Capacity of the Separated MIMO Two-Way Relay Channel

A multiple-input multiple-output two-way relay channel consisting of two communication nodes and a full-duplex relay node in which no direct link exists between the two communication nodes is considered. We propose an achievable scheme that employs horizontally encoded lattice codes combined with generalized singular value decomposition-based precoding for the first phase. The second phase of the proposed scheme follows the fundamentals of the previous scheme, which uses vertically encoded structural bining, with the only difference that the added codeword of the two codewords from the communication nodes, instead of those two individual codewords, is decoded and retransmitted in the proposed scheme. We show that the proposed scheme achieves the cut-set bound asymptotically as the signal-to-noise ratios of the channels tend to infinity.

Relay Precoder Optimization in MIMO-Relay Networks With Imperfect CSI

In this paper, we consider robust joint designs of relay precoder and destination receive filters in a nonregenerative multiple-input multiple-output (MIMO) relay network. The network consists of multiple source-destination node pairs assisted by a MIMO-relay node. The channel state information (CSI) available at the relay node is assumed to be imperfect. We consider robust designs for two models of CSI error. The first model is a stochastic error (SE) model, where the probability distribution of the CSI error is Gaussian. This model is applicable when the imperfect CSI is mainly due to errors in channel estimation. For this model, we propose robust minimum sum mean square error (SMSE), MSE-balancing, and relay transmit power minimizing precoder designs. The next model for the CSI error is a norm-bounded error (NBE) model, where the CSI error can be specified by an uncertainty set. This model is applicable when the CSI error is dominated by quantization errors. In this case, we adopt a worst-case design approach. For this model, we propose a robust precoder design that minimizes total relay transmit power under constraints on MSEs at the destination nodes. We show that the proposed robust design problems can be reformulated as convex optimization problems that can be solved efficiently using interior-point methods. We demonstrate the robust performance of the proposed design through simulations.

MIMO two-way relay channel with superposition coding and imperfect channel estimation

This paper deals with the superposition coding (SPC) scheme in multiple-input multiple-output two-way relay channels subject to imperfect channel estimation. In this scenario, two multiple antenna terminals, which are unable to communicate directly, exchange information with each other via a multiple antenna relay. We determine the impact of the channel estimation error degradation on the achievable rate region for two main SPC techniques: (a) SPC without channel state information (CSI) at the users, (b) SPC with an imperfect CSI at the users where a waterfilling power allocation is employed. We demonstrate that imperfect CSI significantly improves the achievable rate at low signal-to-noise ratios (SNRs) while it becomes less critical at high SNRs. In addition, a SPC power allocation technique that incorporates the average channel statistics and does not require any instantaneous CSI is also investigated. We show how the available power is split between the two bi-directional (superimposed) data flows in order to maximize the system performance and to support fairness as well as to maximize the achievable sum-rate.