Grassmannian Signalling Achieves the Ergodic High SNR Capacity of the Non-Coherent MIMO Relay Channel Within an SNR-Independent Gap

This paper considers the ergodic non-coherent capacity of a multiple-input multiple-output frequency-flat block Rayleigh fading relay channel. It is shown that for this channel restricting the input distribution to be isotropic on a compact Grassmann manifold maximizes an upper bound on the cutset bound at high Signal-to-Noise Ratios (SNRs). Furthermore, Grassmannian signalling at the source achieves this bound within an SNR-independent gap. For moderate-to-high SNRs, a Grassmannian Decode-and-Forward (DF) relaying scheme is devised, and the optimal signalling dimensionality that minimizes the gap to the upper bound is obtained.