ACQUISITION OF TIMING AND DOPPLER-SHIFT IN A DIRECT-SEQUENCE SPREAD-SPECTRUM SYSTEM

This paper presents a model for acquisition of a spread-spectrum signal distorted by Doppler shifts. Previous analyses of acquisition have been concerned primarily with obtaining a coarse estimate of the time delay of the received signal. Herein, we attempt a joint acquisition of both the time delay and the distorting Doppler velocity. Most previous studies have been restricted to carrier Doppler only. Here we consider the case where the ratio of platform to propagation velocity, v(r)/c is large enough to generate time compression of the pseudo-noise (PN) sequence itself. A Doppler effect of this type may be encountered in underwater acoustic or intersatellite communications. It is pointed out that the simultaneous presence of the unknown Doppler shift and timing necessitates a substantial modification of conventional acquisition strategies. A two-dwell system, using a short duration correlation to acquire the timing information, with a subsequent longer correlation to acquire the Doppler velocity is proposed. The joint acquisition process is modeled by a finite state Markov chain, and the performance of the system is characterized by the mean and variance of the acquisition time. Two systems of linear equations that can be solved for the mean and variance, respectively, are developed. The matrices specifying the systems are large but very sparse and thus can be solved efficiently. As a particular example, we analyze the performance of systems with spread-spectrum signals having sequence lengths of 15 and 63 chips. It is shown that the two-dwell system can acquire timing and Doppler in a reasonable time period. Although the system studied is not well-suited to multiple-access or antijam applications, the analysis techniques developed here may prove useful in evaluating the performance of more complex acquisition techniques.