A hyperplane-based algorithm for the digital co-channel communications problem

The relationship between the blind digital co-channel communications problem and the problem of finding a separating hyperplane in IR^d is explored. A simple model for the blind digital co-channel communications problem is X=AS, where X is a known IR ^d×N matrix. A is an unknown full-rank IR^d×d matrix, and S is an unknown full-rank d×N matrix with elements drawn from a multiple-amplitude-shift-keying (M-ASK) alphabet S. An algorithm with proof is given that solves for A and S up to a simple matrix factor. The algorithm is extended to the complex quadrature-amplitude modulation (QAM) alphabet. The key step in this algorithm involves finding a separating hyperplane parallel to one of the hyperplanes defining the received signal vectors. The geometric interpretation of this relationship is discussed. Examples with noisy data are presented and refinements to the algorithm are discussed