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

Constant-modulus algorithms try to separate linear mixtures of sources with modulus 1. We study the identifiability of this problem: how many samples are 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, we provided a sub-exponentialy decaying upper bound on the probability of non-identifiability. Here, we provide an improved exponentialy decaying upper bound, based on Chernoff bounds. We show that under practical assumptions, this upper bound is much tighter than previously known bounds.