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.

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In this paper, we propose a generalized singular value decomposition (GSVD) for polynomial matrices, or polynomial GSVD (PGSVD). We then consider PGSVD-based beamforming for two-user, frequency-selective, multiple-input multiple-output (MIMO) multicasting. The PGSVD can jointly factorize two frequency-selective MIMO channels, producing a set of virtual channels (VCs), split into: private channels (PCs) and common channels (CCs). An important advantage of the proposed PGSVD-based beamformer, over the application of GSVD independently to each frequency bin of the orthogonal frequency division multiplexing (OFDM) scheme, is that it can facilitate different modulation and/or access schemes to various users. Using computer simulations, we characterize the bit error rate performance of our two-user MIMO multicasting system for different PCs/CCs configurations. Here, we also propose an OFDM-GSVD benchmark system, and show that our PGSVDbased beamformer compares favorably to this benchmark under erroneous and uncertain MIMO channel conditions, in addition to its advantage of facilitating heterogeneous modulation and access for various users.

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