Qr Decomposition Based Matrix Inversion Technique

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  • Topic: Matrix, Triangular matrix, QR decomposition
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Evaluation Of A High Performance Qr Decomposition-Based Matrix Inversion Technique For Embedded Mimo Receivers

P.G.C. VIKRAM
M.Tech Student Scholar, DECS,
Dept of Electronics and Communication Engineering,
Nalanda Institute of Engineering and technology,
Sattenapalli (M); Guntur (Dt); A.P, India

N.GOPI CHAND
M.Tech, Asst Professor
Dept of Electronics and Communication Engineering,
Nalanda Institute of Engineering and technology,
Sattenapalli (M); Guntur (Dt); A.P, India

Abstract
Matrix inversion is an essential computation for various algorithms which are employed in multi antenna wireless communication systems. FPGAs are ideal platforms for wireless communication; however, the need for vast amounts of customization throughout the design process of a matrix inversion core can overwhelm the designer. Decomposition methods provide the analytic simplicity and computational convenience necessary for computationally intensive matrix inversion. Real-time matrix inversion is a key enabling technology in multiple-input multiple-output (MIMO) communications systems, such as 802.11n. To date, however, no matrix inversion implementation has been devised which supports real-time operation for these standards. In this paper, we overcome this barrier by presenting a novel matrix inversion algorithm which is ideally suited to high performance floating-point implementation. We show how the resulting architecture offers fundamentally higher performance than currently published matrix inversion approaches and we use it to create the first reported architecture capable of supporting real-time 802.11n operation. Specifically, we present a matrix inversion approach based on modified squared Givens rotations (MSGR). This is a new QR decomposition algorithm which overcomes critical limitations in other QR algorithms that prohibits their application to MIMO systems. In addition, we present a novel modification that further reduces the complexity of MSGR by almost 20%. This enables real-time implementation with negligible reduction in the accuracy of the inversion operation, or the BER of a MIMO receiver based on this.

Keywords: BLAST, matrix inversion, multiple-input multiple-
output (MIMO) , QR decomposition.

Introduction

Matrix inversion is a common function found in many algorithms used in wireless

communication systems. For example MIMO-OFDM systems use matrix inversion in equalization algorithms to remove the effect of the channel on the signal [1], minimum mean square error algorithms for pre-coding in spatial multiplexing [2] and detection-estimation algorithms in space-time coding [3]. These systems often use a small number of antennas (2 to 8) which results in small matrices to be inverted and/or decomposed. For example the 802.11n standard specifies a maximum of 4 antennas on the transmit/receive sides and the 802.16 standard specifies a maximum of 16 antennas at a base station and 2 antennas at a remote station. Matrix inversion is a computationally intensive calculation. Decomposition methods provide a means to simplify this computation. There are different decomposition methods, such as QR, LU and Cholesky, that solve matrix inversion. The selection of the decomposition method depends on the characteristics of the given matrix. For non-square matrices or when simple inversion to recover the data performs poorly, the QR decomposition is used to generate an equivalent upper triangular system, allowing for detection using the sphere decomposition or M-algorithm. For simpler detection via inversion of square channel matrices, the LU and Cholesky decompositions are compatible with positive definite and nonsingular diagonally dominant square matrices, respectively[4].

FPGAs are an ideal platform for wireless communication due to their high processing power, flexibility and non recurring engineering (NRE) cost. However, FPGAs require vast amounts of...
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