Sensitivity of a DS CDMA system with long PN sequences to synchronization errors

Use of direct sequence code division multiple access (DS CDMA) has been the object of much attention in the research and development of a multi-service personal communications network. The performance of such a system is usually given in terms of the bit error rate as a function of the number of active users for a given signal to noise ratio. We have investigated the degradation in the performance of a BPSK modulated, bi-phase spread DS CDMA system due to synchronization errors. A Fourier series approach has been used to find an infinite series representation for the probability of error when both chip timing and carrier phase errors are present. The analysis requires the characteristic functions of both the multiple access interference and self interference and these functions have been expressed in terms of the special functions of mathematical physics. Computation of the infinite series is very fast as a whole bit error curve can be generated in minutes on a Sparc IPX workstation. The infinite series is also compared with the standard Gaussian approximation and an alternative Gaussian approximation found in the literature. The series is then used to assess the reduction in system capacity when synchronization errors are present in the system. We have expressed this degradation in the system performance as an effective processing gain reduction.