MAP estimator for code-directed spread spectrum

The coherent maximum a posteriori probability (MAP) estimator of the codeword transmitted by a remotely-monitored site using binary phase-shift keying (BPSK) for a set of nonequiprobable codewords is derived. Although codewords are transmitted at pre-arranged intervals, the receiver must accommodate some uncertainty in the time of reception. Unlike the maximum likelihood (ML) case, the received signal amplitude and noise covariance matrix must either be known in advance or estimated simultaneously. We present simulation results for two cases in which one codeword is more probable than the rest, and illustrate that the increased receiver complexity is warranted only at sufficiently low signal-to-noise ratio (SNR) and sufficiently high imbalance between codeword probabilities