The impact of imperfect code synchronization on bit error rate in DS-SS systems: upper and lower bound

The impact of code synchronization error (CSE) on bit error rate (BER) in direct-sequence spread-spectrum (DS-SS) communications with binary phase-shift keying (BPSK) is analyzed. Under the assumption that CSE is constant, an exact analytical expression for BER, which takes into account the structure of the pseudonoise code, is derived. It is shown that the approximate expression of R.L. Pickholtz et al. (see IEEE Trans. Commun., vol.com-30, no.5, p.855-83, 1982) is a special case of the general formula. Since in CSE is a time-dependent function in practical DS-SS receivers, the upper and lower bounds to BER are derived. The difference between the upper and lower bounds to BER increases with the standard deviation of CSE.