A de-rotation approach to the blind separation of synchronous co-channel BPSK signals

We propose a simple algorithm for the blind separation of m synchronous co-channel BPSK signals by an array of n receiving antennas. We exploit the geometric implications of the finite alphabet property of BPSK signals. After a standard channel whitening step, the noiseless received data vectors describe an m-cube, which is a rotated version of the hypercube defined by the 2^m distinct vectors of ±1s corresponding to all the possible combinations of the states of the sources. We provide a simple procedure to estimate the vertices of this rotated hypercube in the noisy case and then show how the rotation matrix can be determined up to a sign and permutation of its columns. De-rotation of the channel-whitened data results in source separation. Simulations show the good performance of our proposed technique