  This paper presents an iterative geometric mean decomposition (IGMD)
algorithm for multiple-input-multiple-output (MIMO) wireless communications. In
contrast to the existing GMD algorithms, the proposed IGMD does not require the
explicit computation of the geometric mean of positive singular values of the
channel matrix and hence is more suitable for hardware implementation. The
proposed IGMD has a regular structure and can be easily adapted to solve
problems with different dimensions. We show that the proposed IGMD is
guaranteed to converge to the perfect GMD under certain sufficient condition.
Three different constructions of the proposed algorithm are proposed and
compared through computer simulations. Numerical results show that the proposed
algorithm quickly attains comparable performance to that of the true GMD within
only a few iterations.
