On the finite sample behavior of the constant modulus cost function

We study the location of local minima of the finite sample approximation to the constant modulus cost function. This paper concentrates on source separation. The main result is a connection between the number of samples and the probability of obtaining a local minimum of the finite approximation within a given sphere around the local minimum of the CM cost function. The motivations for our study are two problems: equalization of communication signals, and blind separation of a desired signal in multiuser environment. In order to maintain simplicity we focus on the case of blind beamforming which is somewhat simpler to analyze