Achievable rate analysis for multi-pair two-way amplify-and-forward MIMO system in Ricean fading

In this paper, the multi-pair two-way relaying multi-input multiple-output system is considered, in which K-pair users exchange information within communication pair, by a shared amplify-and-forward relay station equipped with N antennas, N ≫ 2K. Considering two kinds of receiver, i.e., maximum-ratio combining receiver and zero-forcing receiver, we investigate the achievable rate performance in Ricean fading under four typical power scaling schemes. The closed-form expression of the achievable rate for two kinds of receiver under four power scaling schemes are obtained, as N → ∞. Our analytical results reveal that when N → ∞, the effect of the small-scale fading can be averaged out, and the achievable rate can be maintained when the users' transmit power is scaled down by 1/N or the relay power is scaled down by 2K/N. In addition, it is shown that the achievable rate converges to a fixed value for MRC and ZF receivers, as N → ∞.