Robust Joint Design of Linear Relay Precoder and Destination Equalizer for Dual-Hop Amplify-and-Forward MIMO Relay Systems

• Published in: IEEE transactions on signal processing Vol. 58; no. 4; pp. 2273 - 2283
• Main Authors: Xing, Chengwen, Ma, Shaodan, Wu, Yik-Chung
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Amplify-and-forward (AF); Applied sciences; Channel estimation; Channels; Closed-form solution; Covariance matrix; Design engineering; Detection, estimation, filtering, equalization, prediction; Economic models; Economic theory; equalizer; Equalizers; Exact sciences and technology; Exact solutions; Information, signal and communications theory; Iterative algorithms; Mathematical analysis; MIMO; minimum mean-square-error (MMSE); Miscellaneous; multiple-input multiple-output (MIMO); precoder; relay; Relay systems; Relays; Robustness; Signal and communications theory; Signal processing; Signal, noise; Studies; Telecommunications and information theory; Uncertainty; Performance evaluation; Parameter estimation; Relay; Amplify-and-forward (AF); Iterative method; Equalizer; Mean square error; Relaxation; Channel estimation; Convergence rate; MIMO system; Estimation error; minimum mean-square-error (MMSE); Gaussian channel; precoder; Output signal; Covariance matrix; multiple-input multiple-output (MIMO); Joint; Algorithm; Multihop network; Relay channel; Algorithm performance; Simulation; Optimal solution; Signal processing
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2009.2038961

This paper addresses the problem of robust linear relay precoder and destination equalizer design for a dual-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay system, with Gaussian random channel uncertainties in both hops. By taking the channel uncertainties into account, two robust design algorithms are proposed to minimize the mean-square error (MSE) of the output signal at the destination. One is an iterative algorithm with its convergence proved analytically. The other is an approximated closed-form solution with much lower complexity than the iterative algorithm. Although the closed-form solution involves a minor relaxation for the general case, when the column covariance matrix of the channel estimation error at the second hop is proportional to identity matrix, no relaxation is needed and the proposed closed-form solution is the optimal solution. Simulation results show that the proposed algorithms reduce the sensitivity of the AF MIMO relay systems to channel estimation errors, and perform better than the algorithm using estimated channels only. Furthermore, the closed-form solution provides a comparable performance to that of the iterative algorithm.