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

Reduced-rank processing is a well-known strategy in order to reduce computational complexity and enhance the performance in 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 computational cheaper than the matrix CS algorithm, we show analytically that the two methods are equal if we assume i.i.d. transmit symbols and uncorrelated white Gaussian noise. Simulation results show additionally that the matrix Multi-Stage WF (MSWF) which approximates the WT in a Krylov subspace is partially outperformed in the considered MIMO case.