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

This paper investigates the impact of spatial fading correlation and keyhole (pinhole) condition on the capacity of multiple-input multiple-output (MIMO) channels when instantaneous channel state information (CSI) is available at the transmitter and receiver sides. A separable correlation model is considered, whereby spatial fading correlation is accounted for at either or at both sides of the collocated MIMO wireless channel. Two extreme scenarios of a double scattering environment are analyzed: (i) an extremely rich scattering environment corresponding to a conventional semi-correlated Rayleigh fading channel and (ii) a double-correlated rank-deficient keyhole channel with a single degree of freedom. In the case of semi-correlated Rayleigh fading, the capacity expressions are derived for two types of correlation structures among the transmitting or the receiving antennas, namely, a constant correlation model and an arbitrary correlation model, the latter being induced by a full-rank Hermitian covariance matrix with non-repeating distinct eigenvalues. On the other hand, the capacity expressions pertaining to the double-correlated keyhole channel are derived given arbitrary Hermitian covariance matrices at the transmitter and the receiver. For all channel types and correlation structures, closed-form expressions for the capacity of the eigen-mode optimal power and rate adaptation policy as well as for the sub-optimal eigen-mode channel inversion and its truncated variant are derived. Monte Carlo simulations are also carried out thereby upholding our theoretical analysis.