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Source and relay matrices optimization for multiuser multi-hop MIMO relay systems

In this paper, we consider multiaccess communication through multi-hop linear non-regenerative relays, where all users, all relay nodes, and the destination node may have multiple antennas. We design the user, relay, and destination matrices that jointly minimize the mean-squared error (MSE) of the signal waveform estimation. It is shown that the optimal amplifying matrix at each relay node can be viewed as a linear minimal MSE filter concatenated with another linear filter. As a consequence, the MSE matrix of the signal waveform estimation at the destination node is decomposed into the sum of the MSE matrices at all relay nodes. We show that at a high signal-to-noise ratio (SNR) environment, this MSE matrix decomposition significantly simplifies the solution to the problem of optimizing the user and relay matrices. Simulation results show that even at the low to medium SNR range, the simplified optimization algorithms have only a marginal performance degradation but a greatly reduced computational complexity and signalling overhead compared with the existing optimal iterative algorithm, and thus are of great interest for practical relay systems.