On the number of samples needed to identify a mixture of finite alphabet constant modulus sources

Abstract

Constant modulus algorithms try to separate linear mixtures of sources with modulus 1. We study the identifiability of this problem: the number of samples needed to ensure that in the noiseless case we have a unique solution. For finite alphabet (L-PSK) sources, finite sample identifiability can hold only with a probability close to but not equal to 1. In a previous paper (Leshem, A. et al., Proc. IEEE Workshop on Sensor Array and Multichannel Signal Processing, 2002), we provided a subexponentially decaying upper bound on the probability of non-identifiability. Here, we provide an improved exponentially decaying upper bound, based on Chernoff bounds. We show that, under practical assumptions, this upper bound is much tighter than previously known bounds.