QR decomposition of Laurent polynomial matrices sampled on the unit circle

Authors

Davide Cescato and Helmut Bölcskei

Reference

IEEE Transactions on Information Theory, Vol. 56, No. 9, pp. 4754-4761, Sept. 2010.

DOI: 10.1109/TIT.2010.2054454

Abstract

We consider Laurent polynomial (LP) matrices defined on the unit circle of the complex plane. QR decomposition of an LP matrix A(s) yields QR factors Q(s) and R(s) that, in general, are neither LP nor rational matrices. In this paper, we present an invertible mapping that transforms Q(s) and R(s) into LP matrices. Furthermore, we show that, given QR factors of sufficiently many samples of A(s), it is possible to obtain QR factors of additional samples of A(s) through application of this mapping followed by interpolation and inversion of the mapping. The results of this paper find applications in the context of signal processing for multiple-input multiple-output (MIMO) wireless communication systems that employ orthogonal frequency-division multiplexing (OFDM).

Keywords

Interpolation, Laurent polynomial (LP) matrices, QR decomposition, sampling

Download this document:

Copyright Notice: © 2010 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.