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 cut-set 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.

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Conference 2012 IEEE Information Theory Workshop, ITW 2012
Gohary, R, & Yanikömeroǧlu, H. (2012). Grassmannian signalling achieves the ergodic high SNR capacity of the non-coherent MIMO relay channel within an SNR-independent gap. In 2012 IEEE Information Theory Workshop, ITW 2012 (pp. 442–446). doi:10.1109/ITW.2012.6404711