LU-Based Beamforming Schemes for MIMO Systems

Abstract

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.

A robust LU polynomial matrix decomposition for spatial multiplexing

“…In this regard, a MIMO beamforming scheme based on a combination of the classical Smith canonical form and LU (Gauss elimination) was presented in [11] as alternative solution.…”

“…However, given a polynomial matrix, a PSVD factorization as described above does not exist in general [9]. By contrast, the MIMO spatial multiplexing scheme presented in [10], [11], completely eliminates the CCI. This beamforming method is inspired from a blind equalization method exploiting the Bezout identity [12], [13].…”

“…The decomposition method in [11], called LU-PMD (LU-Polynomial Matrix Decomposition), is effective and does not require any iteration: the algorithm ends up after a finite and prescribed number of steps, with a matrix Dpzq which is exactly diagonal. Moreover, it was shown in [11] that unless for some improbable original MIMO channel, all but except the last resulting independent SISO subchannels reduce to simple additive noise channels. Therefore, in addition to completely cancelling the CCI, this decomposition also inherently avoids the ISI problem.…”

“…In this paper, we revisit the LU-based factorization in [11], in combination with the row balancing trick in [14]. We show that the resulting transformations solve the ill-conditioning problem and lead to a MIMO spatial multiplexing scheme that is robust to noise and channel estimation errors.…”

Efficient Limited Feedback Technique for FDD MIMO Systems

“…Among these five technics, this is the Transmit Beamforming which can maximize the system capacity. Indeed, the Beamforming with precoding and postcoding eliminates the co-channel interferences (CCI) which are the fundamental problem faced by the practical MIMO system [6][7][8].…”