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
