Maximum likelihood DSSS code acquisition in the presence of multipath propagation, Doppler shift and data modulation

During the initial synchronisation in a direct sequence spread spectrum system the time and frequency uncertainty contained in the received signal have to be estimated. In this paper, maximum likelihood (ML) acquisition is investigated in the presence of multipath propagation, Doppler shift, data modulation and noise. The resulting ML acquisition detector is given. It is shown, how the ML acquisition detector is related to the matched filter (MF) principle, which is better suited for implementations. The performance of both approaches is compared and it is shown, that the ML acquisition detector outperforms the MF acquisition detector in the investigated cases. Finally, the mean acquisition time of the ML acquisition detector is derived and compared to the well known threshold detector.