Efficient postcoding filter in LU-based beamforming scheme

This paper considers time-domain beamforming in MIMO convolutive systems, using the classical LU-based (Gauss elimination) polynomial matrix decomposition. As the pre- and postfilters are not paraunitary, the output signal-to-noise ratio is degraded compared to QR-based beamforming. We investigate the role of the postfilter on the noise enhancement and propose a simple and efficient solution. We show that a simple normalisation of the postfilter, using row balancing, is sufficient to significantly improve the conditioning of the system and thereby, the performance of the system. With the resulting performance increase, the LU-based polynomial matrix decomposition for MIMO beamforming becomes competitive as compared to its QR-based counterparts, in terms of bit error rate, for medium input SNR.