Exact and Asymptotic SER of Distributed TAS/MRC in MIMO Relay Networks

We propose distributed transmit antenna selection with receiver maximal-ratio combining (TAS/MRC) for use in a two-hop multiple-input multiple-output (MIMO) relay network. The network under consideration is equipped with N_S, N_R, and N_D antennas at the source, relay, and destination, respectively. First, we derive a new closed-form expression for the exact cumulative distribution function (cdf) of the end-to-end SNR. Based on this, we present a new closed-form expression for the exact symbol error rate (SER). Our analytical results are further evaluated in the high SNR regime, leading to practical design insights. Our asymptotic expressions are concise and have the added advantage of explicitly characterizing the diversity order and the array gain of the network. Our exact and asymptotic results are valid for general operating scenarios with distinct average received SNRs in each hop.