Multiple-input Multiple-output Relay Research Articles

Tomlinson-Harashima Precoding Based Transceiver Design for MIMO Relay Systems With Channel Covariance Information

In this paper, we investigate the performance of the Tomlinson-Harashima (TH) precoder based nonlinear transceiver design for a nonregenerative multiple-input multiple-output (MIMO) relay system assuming that the full channel state information (CSI) of the source-relay link is known, while only the channel covariance information (CCI) of the relay-destination link is available at the relay node. We first derive the structure of the optimal TH precoding matrix and the source precoding matrix that minimize the mean-squared error (MSE) of the signal waveform estimation at the destination. Then we develop an iterative algorithm to optimize the relay precoding matrix. To reduce the computational complexity of the iterative algorithm, we propose a simplified precoding matrices design scheme. Numerical results show that the proposed precoding matrices design schemes have a better bit-error-rate performance than existing algorithms.

Joint optimization of source and relay precoding for AF MIMO relay systems

In this paper, we investigate a joint source and relay precoding design scheme for an amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay system with absence of the direct link. The joint optimization problem, which is to minimize an objective function based on the mean square error (MSE), is formulated as a nonconvex optimization problem in the AF MIMO relay system. Instead of the conventional iterative method, we use an inequality to derive a lower bound of the MSE under the power constraint for obtaining a suboptimal solution of the objective function, which makes the optimization problem convex and also approaches the existing upper bound of the MSE, especially at the high signal-to-noise ratio (SNR). Numerical results show that this scheme outperforms the previous schemes in terms of either MSE or bit error rate (BER).

Robust Precoder Design for MIMO Relay Networks Over Double Correlated Rician Channels

In this paper, a statistically robust precoder design for space-time coded amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay networks over double-correlated Rician fading channels is presented. In this network, the source, destination, and relay nodes are equipped with multiple-antenna. The precoder design is based on channel means and covariance matrices for the sake of reducing channel feedback. Since the average received signal-to-noise ratio (SNR) is closely related to the bit error rate (BER), it is adopted as an objective function. Unfortunately, this objective function is difficult to obtain a simple expression. An accurate approximation of a lower bound of the average received SNR is derived and used as the design criterion. With maximum ratio combining, an iterative algorithm for obtaining suboptimal precoding matrices at the source and relay nodes is derived. Simulation shows that the algorithm takes very few iterations to give converged precoders for the source and relay nodes. The design algorithm can be applied to relay nodes with single-antenna for the benefit of less computational complexity and feedback overhead. Numerical results demonstrate that the proposed scheme provides a substantial performance gain over the existing strategies. A diversity order analysis is developed. Experimental results show that the theoretical analysis is quite close to simulation. The relay system using multiple-antenna at the relay nodes can considerably improve coding gain and/or diversity gain.

Centralized Two-Way AF MIMO Multiple Dispersed Relay Network

This paper considers a two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay network consisting of two sources (each with multiple antennas) and multiple physically dispersed single-antenna relays. A central station finds the optimum relay amplifying matrices and transmit/receive beamforming vectors explicitly and iteratively under the transmit power constraints at the sources and the relays. The minimum-mean-square-error criterion is used. Numerical results show that the proposed scheme outperforms the existing two-way AF MIMO network schemes proposed by Arti et al. and Wang et al.

Space‐interweaving‐time‐convolutional space–time codes for full‐duplex MIMO relay networks

AbstractIn this paper, a space‐interweaving‐time‐convolutional space–time coding (SITC‐STC) scheme is proposed to collect cooperative diversity gain for full‐duplex multiple‐input multiple‐output (MIMO) relay systems. It is shown that because of the loop channel interference and crosstalk interference caused by different transmit and receive antenna pairs of the MIMO relay, the full‐duplex mechanism cannot be achieved effectively in MIMO relay networks by directly adopting relaying methods for half‐duplex systems. The traditional method to deal with this issue is removing the interference as much as possible. While, the proposed SITC‐STC scheme only needs to cancel partial interference signals and then amplify together with interweaving in space by a power control matrix. That is, the loop signals are not directly cancelled but used for coding in the SITC‐STC scheme. Simulation results verify the proposed SITC‐STC scheme by comparing it with existing STC schemes and show that it can collect most of the diversity gain in MIMO relay networks. Copyright © 2015 John Wiley & Sons, Ltd.

Ergodic Capacity Analysis of MIMO Relay Network Over Rayleigh-Rician Channels

We present an analytical characterization of the ergodic capacity for an amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay network over asymmetric channels. In the two-hop system that we consider, the source-relay and relay-destination channels undergo Rayleigh and Rician fading, respectively. Considering arbitrary-rank means for the relay-destination channel, we first investigate the marginal distribution of an unordered eigenvalue of the cascaded AF channel, and we provide an analytical expression for the ergodic capacity of the system. The closed-form expressions that we derive are computationally efficient and validated by numerical simulation. Our results also show the impact of the signal-to-noise ratio and of the Rician factor on this asymmetric relay network.

Channel Knowledge Acquisition in Relay and Multipoint-to-Multipoint Transmission Systems

Most of the relaying strategies exploit channel state information (CSI), but there exist only a few limited works on acquisition of the required CSI. In this paper, we present general protocols and pilot designs for CSI acquisition in different types of relay systems using multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) transmission. We propose new pilot forwarding mechanisms and a related estimator for obtaining CSI of individual MIMO channels of cascaded links at the end node(s). We develop new pilot designs with low overhead for channels with different lengths. We present several CSI acquisition protocols for relay MIMO systems with time-division duplexing and frequency-division duplexing. We introduce node multiplexing, which reduces overhead and delay for pilot or CSI feedback transmissions from multiple nodes. In addition, we present similar CSI acquisition protocols for multipoint-to-multipoint systems while keeping the overhead low. Simulation results are included to demonstrate the estimation performance of our proposed designs. Discussions on several protocol options are also provided.

MMSE-based joint source and relay optimization for interference MIMO relay systems

In this paper, we investigate the transceiver design for amplify-and-forward (AF) interference multiple-input multiple-output (MIMO) relay communication systems when the direct links between the source and destination nodes are taken into consideration. The minimum mean-squared error (MMSE) of the signal waveform estimation at the destination nodes is chosen as the design criterion to optimize the source, relay, and receiver matrices for interference suppression. As the joint source, relay, and receiver optimization problem is nonconvex with matrix variables, a globally optimal solution is computationally intractable to obtain. We propose two iterative algorithms to provide computationally efficient solutions to the original problem through solving convex subproblems. These two algorithms provide efficient performance-complexity trade-off. Simulation results demonstrate that the proposed algorithms converge quickly after a few iterations and significantly outperform existing scheme in terms of the system bit error rate.

Performance analysis of MIMO DF relay network with the Nth-best user selection scheme in the presence of co-channel interference

In this paper, we study the performance of multi-user multiple-input multiple-output (MIMO) relay network in the presence of co-channel interference (CCI) as well as additive white Gaussian noise (AWGN). Specifically, the Nth-best user selection scheme is applied to attain multi-user diversity. Both exact and asymptotic closed-form expressions for the outage probability and average symbol error rate (SER) of the considered system are derived, and corroborated by the Monte Carlo simulations. Based on the asymptotic SER expression, the diversity order and array gain are characterized, and the optimum power allocation between the source and the relay is also designed. The results reveal that the diversity order is NR×min{NS, ND(K−N+1)}, where NS, NR and ND represent the number of antennas at the source, the relay, and each destination, respectively, K is the number of the destinations, and N (1≤N≤K) represents the rank of the user chosen. The findings of this paper show that the CCI deteriorates the system performance by reducing the array gain, and optimal power allocation achieves better performance than that of uniform power allocation by offering extra array gain. These findings provide a valuable insight into the practical system design.

Robust Design for Amplify-and-Forward MIMO Relay Systems With Direct Link and Imperfect Channel Information

In this paper, we propose statistically robust design for multiple-input multiple-output (MIMO) relay systems with the direct source-destination link and imperfect channel state information (CSI). The minimum mean-squared error (MMSE) of the signal waveform estimation at the destination node is adopted as the design criterion. We develop two iterative methods to solve the nonconvex joint source, relay, and receiver optimization problem. In particular, we derive the structure of the optimal relay precoding matrix and show the effect of CSI mismatch on the structure of the optimal robust source and relay matrices. The proposed algorithms generalize the transceiver design of MIMO relay systems with the direct link to the practical scenario of imperfect CSI knowledge. Simulation results demonstrate an improved performance of the proposed algorithms with respect to the conventional methods at various levels of CSI mismatch.

Channel Estimation for Two-Way MIMO Relay Systems in Frequency-Selective Fading Environments

In this paper, we investigate the channel estimation problem for two-way multiple-input multiple-output (MIMO) relay communication systems in frequency-selective fading environments. We apply the method of superimposed channel training to estimate the individual channel state information (CSI) of the first-hop and second-hop links for two-way MIMO relay systems with frequency-selective fading channels. In this algorithm, a relay training sequence is superimposed on the received signals at the relay node to assist the estimation of the second-hop channel matrices. The optimal structure of the source and relay training sequences is derived to minimize the mean-squared error (MSE) of channel estimation. Moreover, the optimal power allocation between the source and relay training sequences is derived to improve the performance of channel estimation. Numerical examples are shown to demonstrate the performance of the proposed superimposed channel training algorithm for two-way MIMO relay systems in frequency-selective fading environments.

Joint Transceiver Optimization for Two-Way MIMO Relay Systems With MSE Constraints

Transceiver design for two-way multiple-input multiple-output (MIMO) relay systems has attracted much research interest recently. However, there is little research on the impact of quality-of-service (QoS) constraints on two-way MIMO relay systems, which greatly affects the user experience. In this letter, we propose a transceiver design for two-way MIMO relay systems which minimizes the total network transmission power subjecting to QoS constraints expressed as upper-bounds on the mean-squared error (MSE) of the signal waveform estimation at both destinations. An iterative algorithm is developed to optimize the source, relay, and receive matrices. Simulation results demonstrate the fast convergence of the proposed algorithm.

Outage Probability for MIMO Relay Channel

The channel capacity for the multiple-input multiple-output (MIMO) relay channel is still an open problem. In view of this gap, upper and lower bounds were found by Wang et al., 2005. This paper presents an extensive study of mutual information and outage probability of Rayleigh fading MIMO relay channels based on the eigenvalues distribution for the sum of complex Wishart matrices. Interestingly, for certain scenarios, upper and lower bounds are coincident providing the real channel capacity. To compute outage probability, a Gaussian approximation for mutual information has been used. Furthermore, it was proposed an equivalent distribution for the sum of Wishart matrices, which proves to be excellent in all scenarios. Closed-form expressions for probability density function and outage probability have been found for the general case of any number of antennas and any SNR values. Analytical expressions have been validated by means of Monte Carlo simulations.

Water-filling for full-duplex multiple-hop MIMO relay system

A water-filling (WF) method is one of the techniques to improve a performance of multiple-input multiple-output (MIMO) systems. However, the application of the WF method to multiple-hop MIMO relay systems (MMRSs) has not been discussed, especially in amplify-and-forward (AF) schemes. In this paper, the WF method for MMRSs with AF scheme is proposed and evaluated in both perfect and imperfect channel state information (CSI). The effect of imperfect CSI on optimization of transmit power at all transmitters and on co-channel interference is taken into account. Compared to the average transmit power, the end-to-end channel capacity of the WF method is higher in the perfect CSI; however, it is subject to the effect of imperfect CSI. Additionally, half-duplex and full-duplex transmission methods are also discussed in this paper. The end-to-end channel capacity of full duplex is higher and more robust than that of the half duplex due to a double of allocation time and a half of delay time.

Performance Analysis of TAS/MRC in MIMO Relay Systems With Outdated CSI and Co-Channel Interference

In this paper, we investigate the impact of outdated channel state information (CSI) and multiple co-channel interferers (CCI) on the performance of transmit antenna selection/receiver maximal-ratio combining (TAS/MRC) in a dual-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay network. The tight lower bound and asymptotic expressions for the outage probability are derived. The diversity order of the system with/without outdated CSI in the presence of multiple CCI is further discussed. Numerical and simulation results are presented to validate our analysis and to demonstrate the effect of outdated CSI and multiple CCI on the system performance.

Joint maximum likelihood detection and link selection for cooperative MIMO relay systems

In this study, the authors propose a cross layer design strategy that consists of a cooperative maximum likelihood detector operating in conjunction with link selection for cooperative multiple-input multiple-output relay networks. The system considered is a two phase relaying model, with amplify-and forward relays. The model considers the effect of relay placement and of large scale shadowing. The authors develop a cooperative maximum likelihood detector for an arbitrary number of relays, and link selection schemes are devised for two scenarios relating to the available knowledge at the destination node, which considers relay combination, with complexity analysis. The authors also propose a cooperative list sphere decoder that processes soft information and implements an iterative detection and decoding scheme. The results of simulations of the systems are presented, with comparisons to system models used in previous literature, and show how the cooperative detector and the proposed link selection schemes affect the bit error rate performance at the destination node, for both the hard decision non-iterative case, and the soft information iterative processing case.

Low complexity PARAFAC‐based channel estimation for non‐regenerative MIMO relay systems

In this study, the authors present a novel channel estimation scheme for a two-hop non-regenerative multiple-input multiple-output relay system. The proposed scheme has two stages. In the first stage, the source node transmits channel training sequence to the relay node. The relay node amplifies the received signal and forwards it to the destination node. During the second stage, the relay node amplifies the pre-received signal with another amplification matrix, and forwards it to the destination node. Based on the proposed scheme, by using parallel factor (PARAFAC) analysis, they further propose a low complexity channel estimation algorithm, where full knowledge of all channel matrices involved in the communication can be estimated at the destination node. Compared with existing algorithms, the proposed algorithm yields smaller channel estimation error with lower complexity. Numerical examples are shown to demonstrate the effectiveness of the low complexity PARAFAC-based channel estimation algorithm.

On Optimal Gaussian Signaling in MIMO Relay Channels With Partial Decode-and-Forward

For Gaussian multiple-input multiple-output (MIMO) relay channels with partial decode-and-forward, the optimal type of input distribution is still an open question in general. Recent research has revealed that in some other scenarios with unknown optimal input distributions (e.g., interference channels), improper (i.e., noncircular) Gaussian distributions can outperform proper (circular) Gaussian distributions. In this paper, we show that this is not the case for partial decode-and-forward in the Gaussian MIMO relay channel with Gaussian transmit signals, i.e., we show that a proper Gaussian input distribution is the optimal one among all Gaussian distributions. In order to prove this property, an innovation covariance matrix is introduced, and a decomposition is performed by considering the optimization over this matrix as an outer problem. A key point for showing optimality of proper signals then is a reformulation that reveals that one of the subproblems is equivalent to a sum rate maximization in a two-user MIMO broadcast channel under a sum covariance constraint, for which the optimality of proper signals can be shown.

A Low Complexity Antenna Switching for Joint Wireless Information and Energy Transfer in MIMO Relay Channels

In this paper, we investigate a low-complexity technique for simultaneous wireless information and energy transfer in multiple-input multiple-output relay channels. The proposed technique exploits the array configuration at the relay node and uses the antenna elements either for conventional decoding or for rectifying (rectennas). In order to keep the complexity low, a dynamic antenna switching between decoding/rectifying is proposed based on the principles of the generalized selection combiner (GSC); the L strongest paths are allocated for decoding while the remaining channel paths for rectifying (and vice versa). The optimal L as well as the allocation strategy that minimizes the outage probability are investigated via theoretical and numerical results. In addition, two performance bounds that provide the optimal performance without the limitation of GSC are proposed by solving a linear programming and a binary knapsack problem, respectively. The proposed technique is extended to scenarios with multi-user interference, where a zero-forcing receiver is used at the relay node; closed-forms expressions for the outage probability are also derived.

Performance Analysis of Optimal Beamforming in Fixed-Gain AF MIMO Relaying over Asymmetric Fading Channels

This paper analyzes the performance of an optimal single stream beamforming scheme for a multiple-input multiple-output (MIMO) relay network with dual-hop fixed-gain amplify-and-forward (AF) relaying. The source-relay and relay-destination channels undergo Rayleigh and Rician fading respectively. Different Rician fading scenarios are considered for relay-destination channel, depending on the rank of the Rician channel matrix. The channel state information is only available at the destination, and the destination computes the optimal transmit and receive beamforming vectors to maximize the instantaneous signal-to-noise ratio (SNR). The optimal transmit beamforming vector is sent back to the transmitter via a dedicated feedback link. We derive new analytical expressions for the cumulative distribution function, probability density function, and moments to statistically characterize the properties of the instantaneous SNR. These statistical properties are used to analyze the system performance in terms of the outage probability, average bit error rate, and the ergodic capacity. The performance analysis investigates the effects of the Rician factor, rank of the line-of-sight component, and number of antennas at the nodes on the system performance. The results reveal that the optimal single stream beamforming system provides better performance than an orthogonal space-time block coded based AF MIMO system.