A pre-log region for the non-coherent MIMO two-way relaying channel

We study the two-user MIMO block fading two-way relay channel in the non-coherent setting, where neither the terminals nor the relay have knowledge of the channel realizations. We analyze the achievable sum-rate when the users employ independent, isotropically distributed, unitary input signals, with amplify-and-forward (AF) strategy at the relay node. As a byproduct, we present an achievable pre-log region of the AF scheme, defined as the limiting ratio of the rate region to the logarithm of the signal-to-noise ratio (SNR) as the SNR tends to infinity. We compare the performance with time-division-multiple-access (TDMA) schemes, both coherent and non-coherent. The analysis is supported by a geometric interpretation, based on the paradigm of subspace-based communication.