Unimodular-Upper polynomial matrix decomposition for MIMO Spatial Multiplexing

International audienceWe present a simple algorithm to compute the factors of a Unimodular-Upper (UU) polynomial matrix decomposition. The algorithm relies on the classical LU factorization and the inverse of the unimodular factor is also provided. Such decomposition is useful for spatial multiplexing in MIMO channel transmission system since it enables to reduce the MIMO channel matrix into independent SISO channels by a pre- and post-filtering. Unlike the classical QR-based polynomial matrix Singular Values Decomposition (QR-PMSVD), the proposed UU method allows to completely cancel the co-channel interference (CCI). Moreover, most of the resulting independent SISO channels are likely to be reduced to simple additive noise channels, i.e. with no InterSymbol Interference. However, the noise is coloured and possibly enhanced due to the non unitary property of the corresponding post filter. The complexity and sum rate capacity performance of the proposed method are studied and compared with QR-PMSVD.Nous présentons un algorithme simple de décomposition d'une matrice polynômiale comme le produit d'une matrice unimodulaire et d'une matrice polynomiale triangulaire supérieur. L'algorithme repose sur la factorisation LU classique et l'inverse du facteur unimodulaire est également fourni. Une telle décomposition est utile pour un multiplexage spatial dans un système de transmission sur un canal MIMO convolutif, car elle permet de réduire ce dernier en des canaux SISO indépendants par un pré- et post-filtrage. Contrairement à la décomposition SVD classique à base de factorisation QR (QR-PMSVD), la méthode proposée ici permet d'annuler complètement l'interférence inter-canal (CCI). En outre, la plupart des canaux SISO résultants après pré- et post-filtrage sont vraisemblablement réduits à des canaux simples à bruit additif, c'est à dire sans interférence intersymbole. En l'occurrence, la fonction de transfert du premier canal réduit est une constante si, et seulement si, l'ensemble des polynômes formant la première colonne et la première ligne du canal MIMO original est irréductible. Cependant, les pré- et post filtres n'étant pas parauniitaires, le bruit résultant est coloré voire amplifié. La complexité et les performances en termes de débit global sont étudiées et comparées avec celles obtenues avec la décomposition QR-PMSVD

Polynomial matrix decomposition techniques for frequency selective MIMO channels

For a narrowband, instantaneous mixing multi-input, multi-output (MIMO) communications system, the channel is represented as a scalar matrix. In this scenario, singular value decomposition (SVD) provides a number of independent spatial subchannels which can be used to enhance data rates or to increase diversity. Alternatively, a QR decomposition can be used to reduce the MIMO channel equalization problem to a set of single channel equalization problems. In the case of a frequency selective MIMO system, the multipath channel is represented as a polynomial matrix. Thus conventional matrix decomposition techniques can no longer be applied. The traditional solution to this broadband problem is to reduce it to narrowband form by using a discrete Fourier transform (DFT) to split the broadband channel into N narrow uniformly spaced frequency bands and applying scalar decomposition techniques within each band. This describes an orthogonal frequency division multiplexing (OFDM) based system. However, a novel algorithm has been developed for calculating the eigenvalue decomposition of a para-Hermitian polynomial matrix, known as the sequential best rotation (SBR2) algorithm. SBR2 and its QR based derivatives allow a true polynomial singular value and QR decomposition to be formulated. The application of these algorithms within frequency selective MIMO systems results in a fundamentally new approach to exploiting spatial diversity. Polynomial matrix decomposition and OFDM based solutions are compared for a wide variety of broadband MIMO communication systems. SVD is used to create a robust, high gain communications channel for ultra low signal-to-noise ratio (SNR) environments. Due to the frequency selective nature of the channels produced by polynomial matrix decomposition, additional processing is required at the receiver resulting in two distinct equalization techniques based around turbo and Viterbi equalization. The proposed approach is found to provide identical performance to that of an existing OFDM scheme while supporting a wider range of access schemes. This work is then extended to QR decomposition based communications systems, where the proposed polynomial approach is found to not only provide superior bit-error-rate (BER) performance but significantly reduce the complexity of transmitter design. Finally both techniques are combined to create a nulti-user MIMO system that provides superior BER performance over an OFDM based scheme. Throughout the work the robustness of the proposed scheme to channel state information (CSI) error is considered, resulting in a rigorous demonstration of the capabilities of the polynomial approach

Integer-Forcing Linear Receivers

Linear receivers are often used to reduce the implementation complexity of multiple-antenna systems. In a traditional linear receiver architecture, the receive antennas are used to separate out the codewords sent by each transmit antenna, which can then be decoded individually. Although easy to implement, this approach can be highly suboptimal when the channel matrix is near singular. This paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer-valued entries. Rather than attempting to recover transmitted codewords directly, the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix. The codewords are all generated using the same linear code which guarantees that these integer combinations are themselves codewords. Provided that the effective channel is full rank, these integer combinations can then be digitally solved for the original codewords. This paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter(s), which corresponds either to a multi-user uplink scenario or to single-user V-BLAST encoding. In this setting, the proposed integer-forcing linear receiver significantly outperforms conventional linear architectures such as the zero-forcing and linear MMSE receiver. In the high SNR regime, the proposed receiver attains the optimal diversity-multiplexing tradeoff for the standard MIMO channel with no coding across transmit antennas. It is further shown that in an extended MIMO model with interference, the integer-forcing linear receiver achieves the optimal generalized degrees-of-freedom.Comment: 40 pages, 16 figures, to appear in the IEEE Transactions on Information Theor

From Linear Equalization to Lattice-Reduction-Aided Sphere-Detector as an Answer to the MIMO Detection Problematic in Spatial Multiplexing Systems

ISBN 978-953-307-223-4International audienc

Novel Efficient Precoding Techniques for Multiuser MIMO Systems

In Multiuser MIMO (MU-MIMO) systems, precoding is essential to eliminate or minimize the multiuser interference (MUI). However, the design of a suitable precoding algorithm with good overall performance and low computational complexity at the same time is quite challenging, especially with the increase of system dimensions. In this thesis, we explore the art of novel low-complexity high-performance precoding algorithms with both linear and non-linear processing strategies. Block diagonalization (BD)-type based precoding techniques are well-known linear precoding strategies for MU-MIMO systems. By employing BD-type precoding algorithms at the transmit side, the MU-MIMO broadcast channel is decomposed into multiple independent parallel SU-MIMO channels and achieves the maximum diversity order at high data rates. The main computational complexity of BD-type precoding algorithms comes from two singular value decomposition (SVD) operations, which depend on the number of users and the dimensions of each user's channel matrix. In this thesis, two categories of low-complexity precoding algorithms are proposed to reduce the computational complexity and improve the performance of BD-type precoding algorithms. One is based on multiple LQ decompositions and lattice reductions. The other one is based on a channel inversion technique, QR decompositions, and lattice reductions to decouple the MU-MIMO channel into equivalent SU-MIMO channels. Both of the two proposed precoding algorithms can achieve a comparable sum-rate performance as BD-type precoding algorithms, substantial bit error rate (BER) performance gains, and a simplified receiver structure, while requiring a much lower complexity. Tomlinson-Harashima precoding (THP) is a prominent nonlinear processing technique employed at the transmit side and is a dual to the successive interference cancelation (SIC) detection at the receive side. Like SIC detection, the performance of THP strongly depends on the ordering of the precoded symbols. The optimal ordering algorithm, however, is impractical for MU-MIMO systems with multiple receive antennas. We propose a multi-branch THP (MB-THP) scheme and algorithms that employ multiple transmit processing and ordering strategies along with a selection scheme to mitigate interference in MU-MIMO systems. Two types of multi-branch THP (MB-THP) structures are proposed. The first one employs a decentralized strategy with diagonal weighted filters at the receivers of the users and the second uses a diagonal weighted filter at the transmitter. The MB-MMSE-THP algorithms are also derived based on an extended system model with the aid of an LQ decomposition, which is much simpler compared to the conventional MMSE-THP algorithms. Simulation results show that a better BER performance can be achieved by the proposed MB-MMSE-THP precoder with a small computational complexity increase