LU based Beamforming schemes for MIMO systems
Résumé
—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 ones on the diagonal, as in the constant matrix 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/post filter in the beamforming scheme, is immediate and can be achieved with O(1) complexity. The resulting reduced MIMO channel is exactly diagonal, leading to separate single input single output (SISO) channels with no co-channel inteference. There is no need to model the MIMO channel as 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 the last one, reduces to a simple additive noise channel, with no intersymbol interference, 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 is studied and compared to the QR-based frequency-domain and time-domain broadband beamforming. In particular, the proposed beamforming scheme can be used both in OFDM and in single carrier MIMO systems, without cyclic prefix. Meanwhile, the QR based scheme requires a cyclic prefix extension.
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