The effect of imperfect carrier synchronization on the performance of multi-tone DSSS

Compared with single-carrier DSSS, multi-tone DSSS (MT) obtains larger processing gain with equal spectrum efficiency, but it is more sensitive to imperfect carrier synchronization due to much spectral overlap on non-orthogonal subcarriers. In this paper, the carrier synchronization errors of MT system, including frequency offset and phase noise, were modeled as slowly varying Gaussian random processes with little variance. The coherent decision statistics and bit error rate (BER) were theoretically derived with imperfect carrier synchronization, which were verified by numerical simulations. The results show that, in the presence of synchronization errors, the BER performance of MT with same spreading codes on subcarriers is not determined by processing gain, while for different code case the performance could be improved since inter-subcarrier interference is suppressed by larger processing gain at the cost of bandwidth efficiency.