Finite-SNR Diversity-Multiplexing Tradeoff for Three-Phase ANC with Channel Estimation Errors

In this letter, we analyze the diversity-multiplexing tradeoff (DMT) performance of a two-way relay system that employs three-phase (3P) analog network coding (ANC) in the presence of channel estimation errors under Nakagami-m fading. By deriving an overall system outage probability expression, we compute the DMT for the considered scheme at finite signal-to-noise ratios (SNRs). We further derive an asymptotic and limiting behavior of the DMT, from which the effect of imperfect estimation on the system achievable performance is highlighted. Numerical and simulation results corroborate our theoretical findings and provide a comparison of the tradeoffs for the 3P ANC over its two-phase (2P) counterpart.