The ergodic capacity of spatially-correlated non-coherent multiple-input multiple-output channels is not known. In this paper upper and lower bounds are derived for this capacity at asymptotically high signal-to-noise ratios (SNRs). The bounds are accurate within an approximation error that decays as 1/SNR, and the gap between these bounds depends solely on the signalling dimensions and the condition number of the transmitter correlation matrix. The upper bound on the high SNR ergodic capacity is shown to decrease monotonically with the logarithm of the condition number of the transmitter correlation matrix. Furthermore, the lower bound on this capacity is achieved by input signals in the form of the product of an isotropically distributed random Grassmannian component and a deterministic component comprising the eigenvectors and the inverse of the eigenvalues of the transmitter correlation matrix.

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Conference IEEE Information Theory Workshop, ITW 2015
Gohary, R, & Yanikomeroglu, H. (2015). The ergodic high SNR capacity of the spatially-correlated non-coherent MIMO channel within an SNR-independent gap. In ITW 2015 - 2015 IEEE Information Theory Workshop (pp. 234–238). doi:10.1109/ITWF.2015.7360770