Probability of error for diversity combining in DS CDMA systems with synchronization errors

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Abstract
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. Three types of diversity schemes are considered: selection diversity, equal gain diversity combining and maximal ratio diversity combining. The error probability derivation does not resort to the widely used Gaussian approximation for the intersymbol interference and multiple access interference and is very accurate. The derived series for probability of error calculations is used to assess the reduction in the system capacity due to different levels of synchronization errors. For all three diversity combining schemes considered, the degradation in the system performance is expressed as an effective reduction in the system processing gain. Systems of 1.25 MHz, 5 MHz and 10 MHz are considered for different number of diversity branches and it is shown that the percentage reduction in the system capacity due to synchronization errors is approximately the same for all these systems.

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