An Iterative Geometric Mean Decomposition Algorithm for MIMO Communications Systems

This paper presents an iterative geometric mean decomposition (IGMD) algorithm for multiple-input-multiple-output (MIMO) wireless communications. In contrast to the conventional geometric mean decomposition (GMD) algorithm, the proposed IGMD does not require the explicit Kth root computation in the preprocessing stage but depends on a carefully constructed iterative procedure that generates the GMD in its limit. We prove analytically that the proposed IGMD is guaranteed to converge to the exact GMD under certain sufficient conditions, and propose three different constructions achieving this condition. Both numerical simulations and complexity analysis of the proposed IGMD have been conducted and compared with the conventional GMD. Simulation results show that our new IGMD algorithm effectively reduces the complexity overhead and hence is more advantageous for low-complexity implementations.