This paper considers the ergodic noncoherent capacity of a multiple-input multiple-output frequency-flat block Rayleigh fading full duplex relay channel at high signal-to-noise ratios (SNRs). It is shown that, for these SNRs, restricting the input distribution to be isotropic on a compact Grassmann manifold maximizes an upper bound on the cut-set bound. Furthermore, it is shown that, from a degrees of freedom point of view, no relaying is necessary and Grassmannian signalling at the source achieves the upper bound within an SNR-independent gap. When the source-relay channel is sufficiently stronger than the source-destination and relay-destination channels, it is shown that, with the number of relay transmit antennas appropriately chosen, a Grassmannian decode-And-forward scheme, which is devised herein, achieves the ergodic noncoherent capacity of the relay channel within an approximation gap that goes to zero as the SNR goes to infinity. Closed-form expressions for the optimal number of relay transmit antennas indicate that this number decreases monotonically with the source transmit power.

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Keywords decode-Andforward relaying, ergodic capacity., Grassmannian signaling, Noncoherent communication
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Journal IEEE Transactions on Information Theory
Gohary, R, & Yanikömeroǧlu, H. (2014). Grassmannian signalling achieves tight bounds on the ergodic high-SNR capacity of the noncoherent MIMO full-duplex relay channel. IEEE Transactions on Information Theory, 60(5), 2480–2494. doi:10.1109/TIT.2014.2310467