In the case of a frequency flat multiple-input multiple-output (MIMO) system, QR decomposition can be applied to reduce the MIMO channel equalization problem to a set of decision feedback based single channel equalization problems. Using a novel technique for polynomial matrix QR decomposition (PMQRD) based on Givens rotations, we extend this work to frequency selective MIMO systems. A transmitter design based on Diagonal Bell Laboratories Layered Space Time (D-BLAST) encoding has been implemented. Turbo equalization is utilized at the receiver to overcome the multipath delay spread and to facilitate multi-stream data feedback. The effect of channel estimation error on system performance has also been considered to demonstrate the robustness of the proposed PMQRD scheme. Average bit error rate simulations show a considerable improvement over a benchmark orthogonal frequency division multiplexing (OFDM) technique. The proposed scheme thereby has potential applicability in MIMO communication applications, particularly for TDMA systems with frequency selective channels.
"Typical areas of application include broadband adaptive sensor array processing  , MIMO communication channels   , and digital filter banks for subband coding  or data compression . Just as orthogonal or unitary matrix decomposition techniques such as the QR decomposition (QRD), eigenvalue decomposition (EVD), and singular value decomposition (SVD)  are important for narrowband adaptive sensor arrays , corresponding paraunitary polynomial matrix decompositions are proving beneficial for broadband adaptive arrays    and also for filterbank design  . In a previous paper , we described a generalisation of the EVD for conventional Hermitian matrices to para-Hermitian polynomial matrices. "
[Show abstract][Hide abstract] ABSTRACT: An algorithm is presented for computing the singular value decomposition (SVD) of a polynomial matrix. It takes the form of a sequential best rotation (SBR) algorithm and con-stitutes a generalisation of the Kogbetliantz technique for computing the SVD of conventional scalar matrices. It avoids "squaring" the matrix to be factorised, uses only uni-tary and paraunitary operations, and therefore exhibits a high degree of numerical stability.
[Show abstract][Hide abstract] ABSTRACT: An algorithm has been recently proposed by the authors for calculating a polynomial matrix singular value decomposition (SVD) based upon polynomial matrix QR decomposition. In this work we examine how this method compares to a previously proposed method of formulating this decomposition. In particular, the performance of the two methods is examined when each is used as part of a broadband multiple-input multiple-output (MIMO) communication system by means of average bit error rate simulations. These results confirm a clear advantage of using the new polynomial matrix SVD method over the existing technique. This paper also discusses the possible errors that are encountered when formulating the SVD of a polynomial matrix and investigates how these errors affect the error rate performance of both SVD methods within the proposed application.
Acoustics Speech and Signal Processing (ICASSP), 2010 IEEE International Conference on; 04/2010
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