MIMO Two-way Relay Systems Research Articles

Spectral- and Energy-Efficiency of Multi-Pair Two-Way Massive MIMO Relay Systems Experiencing Channel Aging

In this paper, we demonstrate the impact of channel aging on the spectral- and energy-efficiency performance of the multi-pair two-way massive MIMO relay (MTW-MMR) systems, where massive antennas are deployed at the relay and the amplify-and-forward (AF) protocol is operated. By assuming the maximum-ratio combining/maximum-ratio transmission (MRC/MRT) or zero-forcing reception/ zero-forcing transmission (ZFR/ZFT) relaying processing, we analyze the spectral efficiency (SE) and energy efficiency (EE) of the MTW-MMR systems experiencing both imperfect channel estimation and channel aging based on the four proposed power-scaling schemes. Furthermore, we compare the performance of the full-duplex (FD)-assisted MTW-MMR systems with that of the half-duplex (HD)-assisted MTW-MMR systems, showing that the FD mode outperforms the HD mode with the interference level not exceeding −15 dB. Our studies show that channel aging may significantly degrade the achievable performance in terms of SE and EE. However, the inter-pair interference caused by the other user pairs and the self-interference can be effectively mitigated by the MRC/MRT processing or ZFR/ZFT processing at the relay.

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.

PSK-Based Space Time Modulation for Two-User Two-Way Massive MIMO Relay Systems

In this letter, we consider a two-way relay system in which there are two source nodes with each having a single antenna and one relay node equipped with a large number of antennas. It is assumed that each node has no channel information. For such a relay system, we systematically design a pair of absolutely additively uniquely decomposable phase-shift keying (PSK) constellations such that when any linear combination of two PSK signals with positive weight coefficients is received, each individual PSK signal can be uniquely decoded. With this, a novel distributed space-time modulation scheme is proposed for the system. We prove that when the number of antennas at the relay node grows to infinite, two user PSK symbols and large scale coefficients can be uniquely determined in a noise-free case. In a noisy case, a minimum Riemannian distance detector is developed for efficiently and effectively estimating both the channel coefficients and the transmitted signals.

Joint Source and Relay Precoding Design for MIMO Two-Way Relay Systems With Transceiver Impairments

Physical transceiver impairments can degrade the performance of wireless communication systems significantly. Although partial impairments can be mitigated by some compensation algorithms, residual impairments still have substantial effects. In this letter, we investigate the joint source/relay precoding design for the multiple-input multiple-output two-way amplify and forward relay systems by considering hardware impairments. Unlike the ideal case, considering the effect of hardware impairments makes the precoding design more challenging. To tackle the problem, we use certain rules of trace operator to convert the original design problem and develop an iterative algorithm to find a local optimal solution. Simulation results show that the system is more sensitive to hardware impairments in the high signal noise ratio regimes and neglect of the residual hardware impairments will deteriorate the system performance significantly.

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.

User-Centric Precoding Designs for the Non-Regenerative MIMO Two-Way Relay Systems

In this letter, we jointly design the source and relay precoders for non-regenerative multi-input multi-output two-way relay systems from the user-centric perspective. The two sources are assumed to be both energy efficiency (EE) desirable and spectral efficiency (SE) desirable. We aim at studying the EE–SE tradeoff between the two sources. The resulting problem is a non-convex multi-objective problem. To address this issue, an iterative algorithm is proposed to design the relay precoding matrix and source beamforming vectors alternatively. We also show that the proposed iterative algorithm is guaranteed to converge.

Simplified MMSE Precoding Design in Interference Two-Way MIMO Relay Systems

We investigate the transceiver design for interference two-way amplify-and-forward multiple-input multiple-output relay communication systems. A novel algorithm with a closed-form solution is developed to optimize the relay precoding matrix based on its optimal structure and a modified transmission power constraint at the relay node. An iterative algorithm is proposed to minimize the sum mean-squared error of the signal waveform estimation. Simulation results demonstrate that the proposed algorithm achieves a better performance-complexity tradeoff compared with existing techniques.

Optimal Power Allocation between Training and Data for MIMO Two-Way Relay Channels

Power allocation between training and data in MIMO two-way relay systems is proposed, which takes into consideration both the symmetric and asymmetric cases of the two sources. For the former, we present a closed form for the optimal ratio of data energy to total energy, which is suitable for the single antenna case as well, and can be simplified when the number of antennas is large. We also show that the achievable rate is a monotonically increasing function of the data time. Concerning the asymmetric case, we prove that the difference of the two SNRs is either a concave or convex function of the energy ratio, depending on the imbalance between the two sources. Using this, the minimum SNR between the two sources is maximized.

Channel Capacity Delay Tradeoff for Two-Way Multiple-Hop MIMO Relay Systems with MAC–PHY Cross Layer

In multiple-hop MIMO relay systems, an end-to-end channel capacity is restricted by the bottleneck relay. Therefore, in order to obtain the high end-to-end channel capacity, we propose a simple mathematical method to optimize both distances and transmit powers simultaneously. Additionally, the end-to-end channel capacity of optimization based on an one-way and a two-ways transmissions is analyzed. The specific TDMA is proposed to control the transmission of all transmitters on MAC layer and then the distance and the transmit power are optimized based on MAC---PHY cross layer by the proposal particle filter method to obtain the higher end-to-end channel capacity. The calculation result indicates that there is the optimal number of relays that has the maximal end-to-end channel capacity and the trade-off between the end-to-end channel capacity and the delay time.

Linear Precoding for Multi-Pair Two-Way MIMO Relay Systems With Max-Min Fairness

Two-way relaying has demonstrated significant gain in spectral efficiency by applying network coding when a pair of source nodes exchange information via a relay node. This paper is concerned with the scenario where multiple pairs of users exchange information through a common relay node equipped with multiple antennas. We aim to design linear precoding at the relay based on amplify-and-forward strategy. The goal is to maximize the minimum achievable rate among all the users subject to a peak relay power constraint so as to achieve the max-min fairness. We first convert this nonconvex problem into a series of semidefinite programming problems using bisection search and certain transformation techniques. A quasi-optimal solution is then obtained by using semidefinite relaxation (SDR). To reduce the design complexity, we further introduce a pair-wise zero-forcing (ZF) structure that eliminates the interference among different user pairs. By applying this structure, the precoding design problem is simplified to a power allocation problem which can be optimally solved. A simplified power allocation algorithm is also proposed. Simulation results show that the proposed SDR-based precoding not only achieves high minimum user rate but also maintains good sum-rate performance when compared with existing schemes. It is also shown that the proposed pair-wise ZF precoding with simplified power allocation strikes a good balance between performance and complexity.

Joint Source and Relay Optimization for Non-Regenerative MIMO Two-Way Relay Systems with Imperfect CSI

In this paper, we consider a non-regenerative MIMO two-way relay system with imperfect channel state information (CSI). We employ a stochastic approach to model the channel uncertainties and address the robust joint source and relay optimization problem based on the minimum mean squared error (MMSE) criterion. With imperfect CSI, the self-interference (SI) cannot be completely canceled at destination nodes. Hence, both channel uncertainties and residual self-interference should be considered. We develop an optimization framework that unifies both frequency-division duplex (FDD) and time-division duplex (TDD) systems despite their different channel statistical properties. Two robust algorithms are proposed to minimize the sum mean squared error (MSE) averaged over channel uncertainties. The first algorithm adopts alternating optimization to update the source precoders, relay precoder and destination receivers iteratively with guaranteed convergence. In the second algorithm, only the relay precoder with certain structure is considered. Then the relay precoder design is reduced to the simple power allocation problem. Simulation results show that the proposed algorithms provide robustness against channel uncertainties, especially when the signal-to-noise ratio is high.

Transmission scheme and performance analysis for decode-and-forward MIMO two-way relay systems

In decode-and-forward (DF) MIMO two-way relay systems, the transmission schemes are designed and the closed-form expressions for the outage probability and average symbol error rate (ASER) of the twoway relay system are derived based on two different scenarios of channel state information (CSI). For perfect CSI, the maximum-ratio-transmission and combining (MRT-MRC) technique is applied to design the beamforming and combining vectors. Without perfect CSI, the transmission scheme with limited feedback is designed, and the analytical results are verified through two kinds of codebooks, i.e., random vector quantization and Grassmann. The simulation results show that, the proposed transmission schemes for the two-way relay system can outperform other transmission schemes in the performance of outage probability and ASER, and the accuracy of the derived closed-form expressions is also verified by the numerical simulations.