Polynomial matrix decompositions and semi-blind channel estimation for MIMO frequency-selective channels

Polynomial eigenvalue decomposition (PEVD) and polynomial QR decomposition (PQRD) are generalisation of eigenvalue decomposition (EVD) and QR decomposition (QRD), and they are suitable for decoupling and precoding of frequencyselective (FS) multiple-input multiple-output (MIMO) channels. Precoding and decoding of communication channels however require reliable estimation of the channel which is normally achieved through use of pilot signals. The pilot transmission will reduce spectral efficiency due to lower data throughput – not particularly attractive for FS-MIMO channels. In this paper, we therefore introduce a new method that utilises a semi-blind channel estimation (semi-BCE) scheme coupled with PQRD/PEVDbased MIMO-channel decomposition to enable efficient communications over wireless MIMO channels. The proposed semi-BCE algorithm is a generalisation of a recently developed single-input single output (SISO) BCE method to MIMO systems. A new class of PQRD algorithms is introduced, which is based on the recently-developed sequential matrix diagonalization (SMD). The decoders produced by the proposed SMD-based PQRD algorithm are shown to be more suitable (efficient) for MIMO-channel equalisation than those generated by the prior art. Computer simulations show that the proposed MIMO-channel coding strategy compares favourably to state-of-the-art MIMO systems, in terms of bit error rate (BER) performance, while reducing the overhead.