Optimal detection of a BPSK signal contaminated by interference and noise

The problem of detecting a desired binary phase-shift keying (BPSK) modulated bit in the presence of a second BPSK modulated interfering signal and additive white Gaussian noise is considered. Given knowledge of the amplitudes and phases of the unmodulated signals received from the two transmitters, the minimum achievable bit error rate is obtained and compared with that for a conventional matched filter detector. It is shown that the performance difference can be quite large when the interfering signal is strong.