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Non-coherent two-way relaying with amplify-and-forward

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 transmit or receive knowledge of the channel 
realizations. We present a lower bound on the achievable sum-rate 
with amplify-and-forward (AF) 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. 
Additionally, we present a comparison a with 
time-division-multiple-access (TDMA) scheme, both in the coherent 
and non-coherent setup. The analysis is supported by a geometric 
interpretation, based on the paradigm of subspace-based 
communication.