Generalized geometric mean decomposition and DFE MMSE transceiver design for cyclic prefix systems

This paper considers the decomposition of a complex matrix as the product of several sets of semi-unitary matrices and upper triangular matrices in iterative manner. The innermost triangular matrix has its diagonal elements equal to the geometric mean of the singular values of the complex matrix. This decomposition, generalized geometric mean decomposition (GGMD), has one order less complexity than the geometric mean decomposition (GMD) if the target matrix is a diagonal matrix. GGMD can be used to design the optimal decision feedback equalizer (DFE) MMSE transceiver for arbitrary multi-input-multi-output (MIMO) channels. The GGMD transceiver shares the same performance as the transceiver designed by using GMD. For the applications over cyclic prefix system, the GGMD transceiver has K/ log2(K) times lower complexity¹ than the GMD transceiver, where K is the number of subchannels and is a power of 2.