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

The authors propose a semi‐blind channel estimation (semi‐BCE) and precoding/decoding technique for frequency selective (FS) multiple‐input multiple‐output (MIMO) channels. A FS MIMO channel can be represented using a matrix whose elements are polynomials; hence their method is based on polynomial matrix decomposition. Polynomial eigenvalue decomposition (PEVD) and polynomial QR decomposition (PQRD) are the generalisation of eigenvalue decomposition and QR decomposition; they are suitable for decoupling and precoding of FS MIMO channels. As the coding of communication channels requires reliable estimation of the channel, a semi‐BCE scheme, coupled with PQRD/PEVD‐based MIMO‐channel decomposition, is attractive since this reduces training overhead (pilot transmission) considerably, resulting in higher spectral efficiency. The proposed semi‐BCE algorithm is a generalisation of a recently developed single‐input single output BCE method to MIMO systems. A new class of PQRD algorithms is introduced, which is based on the recently‐developed sequential matrix diagonalisation (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 performance, while reducing the overhead.