Globally Convergent Algorithms for Blind Source Separation

We present a nobel class of adaptive algorithms for the blind separataion of non-Gaussian mutually independent source signals that can be modeled as independent identically distributed (i.i.d) discrete random processes. The signals are assumed to be transmitted through a m x p narrow-band (instantaneous linear mixture) channel. The original algorithm, called the Multi-User Kurtosis (MUK) algorithm was first presented in [1] and was derived from a set of conditions that were previously found to be necessary and sufficient for the recovery of all the sources [2]. The analysis presented in [1], [3] has shown that the MUK algorithm is globally convergent to a zero-forcing - ZF (decorrelating) solution both in the absence of noise and in the presence of additive white Gaussian noise (AWGN), provided that the received signals are perfectly pre-whitened. In this paper, we propose other constant-modulus (CM) type variants of the MUK algorithm. These inherit the global convergence behavior of the MUK due to its deflation structure and moreover, they allow for increased convergence speed. These variants of the MUK are particularly useful in cases where the number of received signal snapshots is limited, such as in wireless communication applications.