LU-Based Beamforming Schemes for MIMO Systems

We present a time-domain broadband beamforming based on a unimodular-upper polynomial matrix decomposition. The unimodular factor is the product of elementary J-orthogonal matrices and a lower-triangular matrix with 1's on the diagonal, as in the constant matrix lower upper (LU) decomposition. This leads to a J-orthogonal LU polynomial matrix decomposition, as a combination of two classical matrix factorization methods: Smith canonical form and LU Gaussian elimination. The inversion of the unimodular factor, for use as a pre/postfilter in the beamforming scheme, is immediate and can be achieved with O(1) complexity. The resulting reduced multiple-input multiple-output (MIMO) channel is exactly diagonal, leading to separate single-input single-output (SISO) channels with no cochannel inteference. There is no need to model the MIMO channel as a Laurent polynomial as usual, thus introducing unnecessary delays just for technical reasons. In addition, it turns out that each of the resulting SISO channels, except to the last channel, reduces to a simple additive noise channel, with no intersymbol interference (ISI), except for unprobable original MIMO channels. However, these very interesting features are to be balanced with the possible noise enhancement in the postfiltering step. The performance in terms of bit error rate (BER) is studied and compared with the QR-based frequency-domain and time-domain broadband beamforming. In particular, the proposed beamforming scheme can be used both in orthogonal frequency-division multiplexing (OFDM) and in single-carrier MIMO systems, without a cyclic prefix (CP). Meanwhile, the QR-based scheme requires a CP extension.