Two-way Multiple-input Multiple-output Relay Systems Research Articles

Training Based Two-Step Channel Estimation in Two-Way MIMO Relay Systems

In this paper, we study the performance of the training based two-step channel estimation in two-way multiple-input multiple-output relay systems over Rayleigh channels. We first estimate the forward channel during the first phase. During the second phase for the composite channel estimation, singular value decomposition based maximum likelihood method is applied in two way relay systems, which is extended from one way relay systems. Hence, the backward channel is estimated with the given forward channel and composite channel. In general, the proposed estimation scheme can also be extended from the system with a single relay antenna to multiple relay antennas. Moreover, we derive the proposed training sequences and relay gain that aim to minimizes the trace of the approximate Bayesian Cramér-Rao lower bound with respect to the individual channels. The numerical results are shown that although the training sequence is designed to improve individual channel mean square error performance, it can also improve composite channel estimator performance.

Linear Precoding Scheme Design for MIMO Two-Way Relay Systems with Imperfect Channel State Information

The aim of this paper is to investigate a linear precoding scheme design for a multiple-input multiple-output two-way relay system with imperfect channel state information. The scheme design is simplified as an optimal problem with precoding matrix variables, which is deduced with the maximum power constraint at the relay station based on the minimum mean square error criterion. With channel feedback delay at both ends of the channel and the channel estimation errors being taken into account, we propose a matrix decomposition scheme and a joint iterative scheme to minimize the average sum mean square error. The matrix decomposition method is used to derive the closed form of the relay matrix, and the joint iterative algorithm is used to optimize the precoding matrix and the processing matrix. According to numerical simulation results, the matrix decomposition scheme reduces the system bit error rate (BER) effectively and the joint iterative scheme achieves the best performance of BER against existing methods.

Sum Rate Maximization of an MIMO Two-Way Relay System Using MSE Duality

In this letter, we propose a novel joint beamforming scheme using mean-square error (MSE) duality to maximize the sum rate of a multiple-input multiple-output (MIMO) two-way relay system. It is difficult to solve the sum rate maximization problem directly due to its non-convexity. To manage this difficulty, the optimization problem is reformulated as a problem that minimizes the product of the minimum mean-square errors. Then, we show that the per stream MSE duality holds in a two-way relay system under cross power constraints. Based on the per stream MSE duality, an alternate algorithm is proposed to jointly optimize the linear transceivers. The simulation results demonstrate that the proposed scheme outperforms the existing linear schemes in view of the sum rate maximization.

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.

Channel Training Algorithms for Two-Way MIMO Relay Systems

Two-way relay systems are known to be capable of providing higher spectral efficiency compared with conventional one-way relay systems. However, the channel estimation problem for two-way relay systems is more complicated than that of one-way relay systems. In this paper, we propose and compare two channel estimation algorithms, namely the superimposed channel training scheme and the two-stage channel estimation algorithm, for two-way multiple-input multiple-output (MIMO) relay communication systems, where the individual channel state information (CSI) for the first-hop and second-hop links is estimated. For both algorithms, we derive the optimal structure of the source and relay training sequences which minimize the mean-squared error (MSE) of channel estimation. In the superimposed channel training scheme, the power allocation between the source and relay training sequences is optimized. For the two-stage channel estimation algorithm, we optimize the power allocation at the relay node between two stages to improve the performance of the algorithm. Numerical examples are shown to demonstrate and compare the performance of the proposed channel training algorithms.

Beamforming and Combining in Two-Way AF MIMO Relay Networks

In this letter, we propose a beamforming and combining scheme for a two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay network. An approximate expression for the symbol error rate of the scheme in Rayleigh fading for M-ary phase-shift keying is obtained based on the moment generating function of the instantaneous received signal-to-noise ratio. The diversity order is also analytically derived. It is shown by simulations that the proposed scheme outperforms existing schemes for beamforming and combining in two-way AF MIMO relay systems. We also discuss beamforming and combining in a two-way AF MIMO relay system with estimated channel gains.

Joint Tomlinson-Harashima source and linear relay precoder design in amplify-and-forward multiple-input multiple-output two-way relay systems

Existing minimum-mean-squared-error (MMSE) transceiver designs in amplified-and-forward (AF) multiple-input multiple-output (MIMO) two-way relay systems all assume a linear precoder at the sources. Nonlinear source precoders in such a system have not been considered yet. In this paper, we study the joint design of source Tomlinson-Harashima precoders (THPs), relay linear precoder and MMSE receivers in two-way relay systems. This joint design problem is a highly nonconvex optimization problem. By dividing the original problem into three sub-problems, we propose an iterative algorithm to optimize precoders and receivers. The convergence of the algorithm is ensured since the updated solution is optimal to each sub-problem. Numerical simulation results show that the proposed iterative algorithm outperforms other algorithms in the high signal-to-noise ratio (SNR) region.

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.

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.