Analysis of non-coherent correlation in DS/BPSK spread spectrum acquisition

Non-coherent detectors for initial code synchronization (acquisition) of BPSK direct sequence spread spectrum signals on an AWGN channel are analyzed. In addition to the thermal noise, in many applications such detectors are faced with the "self-noise", due to the partial period correlations. Under the random code sequences assumption, in this paper an exact analysis of the non-coherent correlator\´s detection performance is carried out by using the theory of circularly symmetric random variables. The exact analysis shows that the familiar Gaussian approximation to the distribution function of the code self-noise is justified for all cases of practical interest. Furthermore, the overall detection performance was found to be determined asymptotically by the sum of the thermal and correlator\´s self-noise. In most cases of practical interest, this asymptotic result provides a very good approximation to the actual detection performance of a non-coherent correlator, improving the approximations devised previously.<>