Large-System Analysis of AF Full-Duplex Massive MIMO Two-Way MRC/MRT Relaying

The massive multiple-input multiple-output (MIMO) full-duplex two-way relaying (FD-TWR) literature has extensively investigated power scaling for rate guarantees by considering a fixed number of users. We investigate the pairwise error probability (PEP) and the per-user rate of a FD-TWR with <inline-formula> <tex-math notation="LaTeX">$N_{r}$ </tex-math></inline-formula> relay antennas that employs maximal ratio combining/transmission to enable two-way communication between <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> FD users. We propose novel relay and user powers scalings, with both <inline-formula> <tex-math notation="LaTeX">$N_{r}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> tending to infinity, and show that the PEP of each user converges almost surely to its AWGN counterpart. These power scalings are different from the existing ones, which are derived by fixing <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> and by assuming that only <inline-formula> <tex-math notation="LaTeX">$N_{r}$ </tex-math></inline-formula> tends to large values. We show that the analysis developed herein applies to both Gaussian and non-Gaussian complex channels with finite number of moments. We numerically show that when both <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$N_{r}$ </tex-math></inline-formula> increase concurrently to large values, the proposed power scaling schemes not only have better per-user PEP and rate than the existing schemes, but they are also robust to the FD self loop-interference power.