Simplified relay algorithm for two-way MIMO relay communications

In this paper, we investigate the challenging problem of joint source and relay optimization for two-way linear non-regenerative multiple-input multiple-output (MIMO) relay communication systems. First, a novel relay amplifying matrix is proposed which significantly reduces the computational complexity of the optimal relay design with only a marginal performance degradation. Interestingly, we show that the proposed relay matrix is indeed optimal for some special cases. Second, a semi-definite programming (SDP)-based source matrices optimization algorithm is developed. Then the source and relay optimization algorithms are carried out iteratively to minimized the sum mean-squared error of the signal waveform estimation in a two-way MIMO relay system. The performance of the proposed algorithm is demonstrated by numerical simulations.