A novel algorithm for calculating the QR decomposition of a polynomial matrix

A novel algorithm for calculating the QR decomposition (QRD) of polynomial matrix is proposed. The algorithm operates by applying a series of polynomial Givens rotations to transform a polynomial matrix into an upper-triangular polynomial matrix and, therefore, amounts to a generalisation of the conventional Givens method for formulating the QRD of a scalar matrix. A simple example is given to demonstrate the algorithm, but also illustrates two clear advantages of this algorithm when compared to an existing method for formulating the decomposition. Firstly, it does not demonstrate the same unstable behaviour that is sometimes observed with the existing algorithm and secondly, it typically requires less iterations to converge. The potential application of the decomposition is highlighted in terms of broadband multi-input multi-output (MIMO) channel equalisation.