Acquisition of PN sequences in chip synchronous DS/SS systems using a random sequence model and the SPRT

The use of a sequential probability ratio test (SPRT) for the acquisition of pseudonoise (PN) sequences in chip syn- chronous direct-sequence spread-spectrum (DS/SS) systems is considered. The out-of-phase sequence is modeled as a random sequence and the probabilities of error and expected sample sizes for the corresponding test are derived. A different (and very commonly used) test is obtained if the out-of-phase sequence is modeled as a zero sequence. The probabilities of error and the expected sample sizes of both SPRT's are compared, and it is shown that the latter test has a significantly larger probability of type I error. Numerical evaluation of the performance of both tests applied to a PN sequence of period 21° - 1 gives results in agreement with the analytical results. We conclude that a random sequence is an excellent model for a PN sequence, and that significant degradation in performance can be expected if the test design is based on the zero sequence model rather than on the random sequence model.