Impact of Spatial Fading Correlation and Keyholes on the Capacity of MIMO Systems with Transmitter and Receiver CSI

This paper investigates the impact of fading correlation and channel degeneracy alias keyhole condition on the capacity of multiple-input multiple-output (MIMO) spatial multiplexing systems when instantaneous channel state information is available at the transmitter and receiver sides. Two special scenarios of a double scattering channel model are analyzed: (i) an extremely rich scattering environment corresponding to a conventional semi-correlated Rayleigh fading channel whereby correlation is accounted for either among the transmitting or the receiving antennas and (ii) a rank-deficient keyhole channel with a single degree of freedom and zero correlation at both sides of the wireless link. For both fading scenarios, closed-form capacity expressions are derived in terms of a cut-off signal- to-noise ratio which must be solved for numerically. In the case of semi-correlated Rayleigh fading, the capacity expressions are obtained for two kinds of correlation structures, namely, a constant correlation model and an arbitrary correlation model, the latter being induced by a full-rank covariance matrix with non-repeating distinct eigenvalues. Monte Carlo simulations are also carried out thereby upholding our theoretical analysis.