On Outage Probability and Diversity-Multiplexing Tradeoff in MIMO Relay Channels

Fading MIMO relay channels are studied analytically, when the source and destination are equipped with multiple antennas and the relays have a single one. Compact closed-form expressions are obtained for the outage probability under i.i.d. and correlated Rayleigh-fading links. Low-outage approximations are derived, which reveal a number of insights, including the impact of correlation, of the number of antennas, of relay noise and of relaying protocol. The effect of correlation is shown to be negligible, unless the channel becomes almost fully correlated. The SNR loss of relay fading channels compared to the AWGN channel is quantified. The SNR-asymptotic diversity-multiplexing tradeoff (DMT) is obtained for a broad class of fading distributions, including, as special cases, Rayleigh, Rice, Nakagami, Weibull, which may be non-identical, spatially correlated and/or non-zero mean. The DMT is shown to depend not on a particular fading distribution, but rather on its polynomial behavior near zero, and is the same for the simple "amplify-and-forward" protocol and more complicated "decode-and-forward" one with capacity achieving codes, i.e. the full processing capability at the relay does not help to improve the DMT. There is however a significant difference between the SNR-asymptotic DMT and the finite-SNR outage performance: while the former is not improved by using an extra antenna on either side, the latter can be significantly improved and, in particular, an extra antenna can be traded-off for a full processing capability at the relay. The results are extended to the multi-relay channels with selection relaying and typical outage events are identified.Comment: accepted by IEEE Trans. on Comm., 201

Adaptive Randomized Distributed Space-Time Coding in Cooperative MIMO Relay Systems

An adaptive randomized distributed space-time coding (DSTC) scheme and algorithms are proposed for two-hop cooperative MIMO networks. Linear minimum mean square error (MMSE) receivers and an amplify-and-forward (AF) cooperation strategy are considered. In the proposed DSTC scheme, a randomized matrix obtained by a feedback channel is employed to transform the space-time coded matrix at the relay node. Linear MMSE expressions are devised to compute the parameters of the adaptive randomized matrix and the linear receive filter. A stochastic gradient algorithm is also developed to compute the parameters of the adaptive randomized matrix with reduced computational complexity. We also derive the upper bound of the error probability of a cooperative MIMO system employing the randomized space-time coding scheme first. The simulation results show that the proposed algorithms obtain significant performance gains as compared to existing DSTC schemes.Comment: 4 figure

Recovering Multiplexing Loss Through Successive Relaying Using Repetition Coding

In this paper, a transmission protocol is studied for a two relay wireless network in which simple repetition coding is applied at the relays. Information-theoretic achievable rates for this transmission scheme are given, and a space-time V-BLAST signalling and detection method that can approach them is developed. It is shown through the diversity multiplexing tradeoff analysis that this transmission scheme can recover the multiplexing loss of the half-duplex relay network, while retaining some diversity gain. This scheme is also compared with conventional transmission protocols that exploit only the diversity of the network at the cost of a multiplexing loss. It is shown that the new transmission protocol offers significant performance advantages over conventional protocols, especially when the interference between the two relays is sufficiently strong.Comment: To appear in the IEEE Transactions on Wireless Communication

A Simple Cooperative Diversity Method Based on Network Path Selection

Cooperative diversity has been recently proposed as a way to form virtual antenna arrays that provide dramatic gains in slow fading wireless environments. However most of the proposed solutions require distributed space-time coding algorithms, the careful design of which is left for future investigation if there is more than one cooperative relay. We propose a novel scheme, that alleviates these problems and provides diversity gains on the order of the number of relays in the network. Our scheme first selects the best relay from a set of M available relays and then uses this best relay for cooperation between the source and the destination. We develop and analyze a distributed method to select the best relay that requires no topology information and is based on local measurements of the instantaneous channel conditions. This method also requires no explicit communication among the relays. The success (or failure) to select the best available path depends on the statistics of the wireless channel, and a methodology to evaluate performance for any kind of wireless channel statistics, is provided. Information theoretic analysis of outage probability shows that our scheme achieves the same diversity-multiplexing tradeoff as achieved by more complex protocols, where coordination and distributed space-time coding for M nodes is required, such as those proposed in [7]. The simplicity of the technique, allows for immediate implementation in existing radio hardware and its adoption could provide for improved flexibility, reliability and efficiency in future 4G wireless systems.Comment: To appear, IEEE JSAC, special issue on 4

Performance Analysis of Optimal Single Stream Beamforming in MIMO Dual-Hop AF Systems

This paper investigates the performance of optimal single stream beamforming schemes in multiple-input multiple-output (MIMO) dual-hop amplify-and-forward (AF) systems. Assuming channel state information is not available at the source and relay, the optimal transmit and receive beamforming vectors are computed at the destination, and the transmit beamforming vector is sent to the transmitter via a dedicated feedback link. Then, a set of new closed-form expressions for the statistical properties of the maximum eigenvalue of the resultant channel is derived, i.e., the cumulative density function (cdf), probability density function (pdf) and general moments, as well as the first order asymptotic expansion and asymptotic large dimension approximations. These analytical expressions are then applied to study three important performance metrics of the system, i.e., outage probability, average symbol error rate and ergodic capacity. In addition, more detailed treatments are provided for some important special cases, e.g., when the number of antennas at one of the nodes is one or large, simple and insightful expressions for the key parameters such as diversity order and array gain of the system are derived. With the analytical results, the joint impact of source, relay and destination antenna numbers on the system performance is addressed, and the performance of optimal beamforming schemes and orthogonal space-time block-coding (OSTBC) schemes are compared. Results reveal that the number of antennas at the relay has a great impact on how the numbers of antennas at the source and destination contribute to the system performance, and optimal beamforming not only achieves the same maximum diversity order as OSTBC, but also provides significant power gains over OSTBC.Comment: to appear in IEEE Journal on Selected Areas in Communications special issue on Theories and Methods for Advanced Wireless Relay

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.Comment: 32 pages, 10 figure