Schur Complement Based Analysis of MIMO Zero-Forcing for Rician Fading

For multiple-input/multiple-output (MIMO) spatial multiplexing with zero-forcing detection (ZF), signal-to-noise ratio (SNR) analysis for Rician fading involves the cumbersome noncentral-Wishart distribution (NCWD) of the transmit sample-correlation (Gramian) matrix. An approximation with a virtual CWD previously yielded for the ZF SNR an approximate (virtual) Gamma distribution. However, analytical conditions qualifying the accuracy of the SNR-distribution approximation were unknown. Therefore, we have been attempting to exactly characterize ZF SNR for Rician fading. Our previous attempts succeeded only for the sole Rician-fading stream under Rician-Rayleigh fading, by writing the ZF SNR as scalar Schur complement (SC) in the Gramian. Herein, we pursue a more general matrix-SC-based analysis to characterize SNRs when several streams may undergo Rician fading. On one hand, for full-Rician fading, the SC distribution is found to be exactly a CWD if and only if a channel-mean-correlation condition holds. Interestingly, this CWD then coincides with the virtual CWD ensuing from the approximation. Thus, under the condition, the actual and virtual SNR-distributions coincide. On the other hand, for Rician-Rayleigh fading, the matrix-SC distribution is characterized in terms of the determinant of a matrix with elementary-function entries, which also yields a new characterization of the ZF SNR. Average error probability results validate our analysis vs. simulation.