Performance of selection diversity for a DS CDMA system with synchronization errors

Direct-sequence code division multiple access (DS CDMA), which was primarily used in military communications until the late 80s, has been the center of attention in cellular radio communications. An efficient series that is used to calculate the probability of error for a BPSK modulated DS CDMA system with chip timing and carrier phase errors in a slowly fading, multipath channel is derived. The receiver is assumed to be a coherent RAKE receiver that employs selection diversity. The error probability derivations require the characteristic functions of the intersymbol interference and the multiple access interference and these functions have been expressed in terms of the confluent hypergeometric function. The series is then used to assess the reduction in the system capacity due to different levels of synchronization errors. Systems of 1.25 MHz, 5 MHz and 10 MHz bandwidths are considered for different number of diversity branches