1. LU-Based Beamforming Schemes for MIMO Systems
- Author
-
Mamadou Mboup, Moussa Diallo, Moustapha Mbaye, Université Cheikh Anta Diop [Dakar, Sénégal] (UCAD), Centre de Recherche en Sciences et Technologies de l'Information et de la Communication - EA 3804 (CRESTIC), Université de Reims Champagne-Ardenne (URCA), Non-Asymptotic estimation for online systems (NON-A), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), and Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Beamforming ,Polynomial Matrix Decomposition ,Computer Networks and Communications ,MIMO ,Aerospace Engineering ,02 engineering and technology ,Topology ,Precoding ,MIMO system ,law.invention ,Matrix decomposition ,symbols.namesake ,[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing ,0203 mechanical engineering ,Gaussian elimination ,law ,Control theory ,0202 electrical engineering, electronic engineering, information engineering ,Orthogonal matrix ,Electrical and Electronic Engineering ,Computer Science::Information Theory ,Mathematics ,020206 networking & telecommunications ,020302 automobile design & engineering ,LU decomposition ,Polynomial matrix ,Automotive Engineering ,symbols - 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 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.
- Published
- 2017