Matrix decompositions for precoding and equalization of MIMO channel with ISI

This paper sets out a modification of algorithms for calculation QR and SVD decomposition of polynomial matrix into matrix with elements in the form of rational functions, which is equivalent to the use of IIR, instead of FIR filters in the suitable procedures of processing and generation of the signal. The proposed approach can reduce calculating cost of decomposition procedure and further signal processing, primarily by reducing the degree of polynomials, which form the elements of the resultant matrix, which is equivalent to the reduction of memory interval of virtual subchannels. This method is based on the polynomial version of QR algorithm and the procedure of Bauer factorization.