Maximum likelihood estimation of constellation vectors for blind separation of co-channel BPSK signals and its performance analysis

In this paper, we present a method for blind separation of co-channel BPSK signals arriving at an antenna array. This method consists of two parts: the maximum likelihood constellation estimation and assignment. We show that at high SNR, the maximum likelihood constellation estimation is well approximated by the smallest distance clustering algorithm, which we proposed earlier on heuristic grounds. We observe that both these methods for estimating the constellation vectors perform very well at high SNR and nearly attain Cramér–Rao bounds. Using this fact and noting that the assignment algorithm causes negligble error at high SNR, we derive upper bounds on the probability of bit error for the above method at high SNR. These upper bounds fall very rapidly with increasing SNR, showing that our constellation estimation-assignment approach is very efficient. Simulation results are given to demonstrate the usefulness of the bounds.