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

Abstract

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.

Polynomial GSVD Beamforming for Two-User Frequency-Selective MIMO Channels

“…We assume block fading and perfect knowledge of channel-state information. Convolutional source coding with the code rate of 1 2 was used along with appropriate equalization at the two receivers, as in [25]. The propagation environment was modeled using channels possessing an exponential powerdelay profile, which are typically seen in macro-cellular communications systems [25].…”

“…Convolutional source coding with the code rate of 1 2 was used along with appropriate equalization at the two receivers, as in [25]. The propagation environment was modeled using channels possessing an exponential powerdelay profile, which are typically seen in macro-cellular communications systems [25]. A five-path fading model was used for the frequency-selective channel from the nth source antenna element to the mth/pth antenna sensor of U 1 /U 2 , where m = 1, .…”

“…Elimination of CCI is to be expected given exact knowledge of the two MIMO-channel polynomial matrices. Perfect channel knowledge is typically assumed, in the literature, when evaluating channel coding schemes [1], [2], [25]. However, in practice, the channel state information may have to be estimated and tracked, especially in a fast varying environment.…”

“…This performance degradation highlights the reliance of PGSVD-based beamforming on MIMO-channel estimation accuracy. The semi-blind broadband MIMO-channel estimator of Hassan et al in [25] can be used to provide good channel estimates when considering such MIMO systems; the investigation of which is left for future work as it would detract from the main goals of this work.…”

A robust LU polynomial matrix decomposition for spatial multiplexing

“…In this paper, we revisit the LU-based factorization in [11], in combination with the row balancing trick in [14]. We show that the resulting transformations solve the illconditioning problem and lead to a MIMO spatial multiplexing scheme that is robust to noise and channel estimation errors (see also [15] for a combination of spatial beamforming and channel estimation). In the latter context, the proposed LU-based beamforming compares favorably to the QR-based counterpart in terms of both complexity and bit error rate.…”