Wideband MIMO channel diagonalization in the time domain

Methods for spatially diagonalizing wideband multiple-input multiple-output channels using linear finite impulse response (FIR) filters are investigated. The PSVD approach by applying the PQRD-BC algorithm for approximate singular value decomposition (SVD) of polynomial matrices is compared to the approach of performing a set of conventional SVDs in the Discrete Fourier Transform (DFT) domain, in terms of complexity and approximation error. Reduced order filters, based on the DFT-SVDs, are then obtained by optimizing the phases of the filters. Applying the phase optimized filters as linear filters then forms a benchmark on the accuracy attainable for any PSVD factorization, for the given filter length. Simulations show that the DFT-SVD method has significantly lower complexity than the PSVD by PQRD-BC, but results in higher order filters. On the other hand, the PSVD by PQRD-BC yields filters which are close to being perfectly unitary for all frequencies. To achieve good performance, the reduced order filters are around one order of magnitude longer than the channel impulse response length. Therefore there is no gain in performing time domain diagonalization using a polynomial SVD, compared to using a multicarrier solution.