Sum Rate Analysis of Two-Way MIMO AF Relay Networks with Zero-Forcing

The sum rate of multiple-input multiple-output (MIMO) amplify-and-forward (AF) two-way relay networks (TWRNs) with zero-forcing (ZF) transmission is analyzed. Namely, (1) ZF at the two sources for transmission and reception and (2) ZF at the relay for transmission and reception, are treated. Specifically, the exact sum rate expressions and corresponding high signal-to-noise ratio (SNR) approximations are derived for uncorrelated and min-semi-correlated (i.e., correlation exists only at the minimum antenna terminal) Rayleigh fading cases in closed-form. Moreover, the closed-form upper and lower bounds of the sum rate are derived for max-semi-correlated (i.e., correlation exists only at the maximum antenna terminal) and doubly-correlated Rayleigh fading cases. Notably, these sum rate bounds and high SNR approximations provide valuable insights into practical MIMO AF TWRN system-design and the maximum achievable spatial multiplexing gain. All the analyses are verified by using Monte-Carlo simulations.