An algorithm for calculating the QR and singular value decompositions of polynomial matrices

In this paper, a new algorithm for calculating the QR decomposition (QRD) of a polynomial matrix is introduced. This algorithm amounts to transforming a polynomial matrix to upper triangular form by application of a series of paraunitary matrices such as elementary delay and rotation matrices. It is shown that this algorithm can also be used to formulate the singular value decomposition (SVD) of a polynomial matrix, which essentially amounts to diagonalizing a polynomial matrix again by application of a series of paraunitary matrices. Example matrices are used to demonstrate both types of decomposition. Mathematical proofs of convergence of both decompositions are also outlined. Finally, a possible application of such decompositions in multichannel signal processing is discussed

A study of the effects of uncertainties when calculating the singular value decomposition of a polynomial matrix

An algorithm has been recently proposed by the authors for calculating a polynomial matrix singular value decomposition (SVD) based upon polynomial matrix QR decomposition. In this work we examine how this method compares to a previously proposed method of formulating this decomposition. In particular, the performance of the two methods is examined when each is used as part of a broadband multiple-input multiple-output (MIMO) communication system by means of average bit error rate simulations. These results confirm a clear advantage of using the new polynomial matrix SVD method over the existing technique. This paper also discusses the possible errors that are encountered when formulating the SVD of a polynomial matrix and investigates how these errors affect the error rate performance of both SVD methods within the proposed application