Spectral Efficiency Optimization of Spatially-Correlated Multi-Pair Full-Duplex Massive MIMO Relaying

We consider a multi-pair two-way full-duplex (FD) amplify-and-forward relaying, where multiple FD multi-input multi-output (MIMO) users exchange information via a shared FD massive MIMO relay. We derive a closed-form spectral efficiency (SE) lower-bound for maximal-ratio combining/maximal-ratio transmission relay processing considering spatially correlated relay and user antennas, which most of the existing works have ignored. The derived SE lower-bound is applicable for arbitrary number of relay antennas, and simplifies to the following results available in the literature i) the asymptotic SE for number of relay antennas tending to infinity; and ii) the SE lower-bound with independent relay antennas and single-antenna users. We use this SE lower-bound to maximize the non-convex SE, which is of matrix fractional form. We optimize SE by approximating it as concave-convex function, and then by applying matrix quadratic transformation. We numerically validate the SE lower-bound for various system configurations and also characterize their performance for different spatial correlation and interference values. We investigate the gains achieved by the optimal SE over equal power allocation.