QR Decomposition of Laurent Polynomial Matrices Sampled on the Unit Circle

• Published in: IEEE transactions on information theory Vol. 56; no. 9; pp. 4754 - 4761
• Main Authors: Cescato, Davide, Bölcskei, Helmut
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-09-2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Context; Exact sciences and technology; Frequency division multiplexing; Information theory; Information, signal and communications theory; Interpolation; Laurent polynomial (LP) matrices; Mapping; Matrix; Matrix decomposition; MIMO; Miscellaneous; Multiplexers; Multiplexing; OFDM; Polynomials; QR decomposition; sampling; Sampling, quantization; Signal and communications theory; Signal processing; Signal processing algorithms; Telecommunications and information theory; Wireless communication; MIMO system; Interpolation; Telecommunication system; Wireless telecommunication; QR decomposition; QR factorization; Orthogonal frequency division multiplexing; Signal processing; Mapping; Sampling; Laurent polynomial (LP) matrices
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2010.2054454

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).