Kk. Chawla et Dv. Sarwate, ACQUISITION OF PN SEQUENCES IN CHIP SYNCHRONOUS DS SS SYSTEMS USING ARANDOM SEQUENCE MODEL AND THE SPRT, IEEE transactions on communications, 42(6), 1994, pp. 2325-2334
The use of a sequential probability ratio test (SPRT) for the acquisit
ion of pseudonoise (PN) sequences in chip synchronous direct-sequence
spread-spectrum (DS/SS) systems is considered. The out-of-phase sequen
ce is modeled as a random sequence and the probabilities of error and
expected sample sizes for the corresponding test are derived. A differ
ent (and very commonly used) test is obtained if the out-of-phase sequ
ence 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 th
at the latter test has a significantly larger probability of type I er
ror. Numerical evaluation of the performance of both tests applied to
a PN sequence of period 2(10) - 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 performa
nce can be expected if the test design is based on the zero sequence m
odel rather than on the random sequence model.