On reduced-rank approaches to matrix Wiener filters in MIMO systems

Reduced-rank processing is a well-known strategy in the reduction of computational complexity and performance enhancement in the case of low sample support. In this paper, we use the eigenspace based principal component (PC) and cross-spectral (CS) method for rank-reduction of a matrix Wiener filter (WF) which estimates a signal vector instead of a scalar by minimizing the mean square error. Finally, we apply the resulting filters to a frequency-flat multi-input multi-output (MIMO) transmission channel. Although the matrix PC algorithm is computationally cheaper than the matrix CS algorithm, we have shown through analysis that the two methods are equal if we assume i.i.d. transmit symbols and uncorrelated white Gaussian noise. Simulation results have shown that the matrix multi-stage WF (MSWF), which approximates the WF in a Krylov subspace, is partially outperformed in the considered MIMO case.