Relay Selection Strategies for MIMO Two-Way Relay Networks With Spatial Multiplexing

Relay selection strategies help to improve spectral and energy efficiencies, to enhance transmission robustness, or to reduce latency in multi-relay cooperative networks. Two novel relay selection strategies are proposed and analyzed here for multiple-input multiple-output (MIMO) amplify-and-forward (AF) two-way relay networks (TWRNs) with spatial multiplexing. Specifically, they are designed to maximize the effective end-to-end signal-to-noise ratio (SNR), and thereby minimize the overall outage probability or maximize the achievable sum rate. Interestingly, the first strategy amounts to maximizing the minimum of the eigenvalues of the Wishart matrices from the selected relay to the two user nodes. Counter-intuitively, the latter strategy amounts to maximizing the minimum of the determinant of the same Wishart matrices. The performance of these two strategies is investigated by deriving lower/upper bounds of the overall outage probability and the average sum rate approximations in closed form. Further, the asymptotic high-SNR approximations of the outage probability are derived, and thereby, the achievable diversity-multiplexing tradeoff is quantified. This tradeoff reveals that whenever the sum of relay antennas is fixed, the achievable diversity order is always a constant, and hence, the multiplexing gain can indeed be improved by equally distributing antennas among the available set of relays. Our results reveal that relay selection indeed significantly alleviates the inherent diversity-gain loss associated with the use of available degrees of freedom for spatial multiplexing.