Optimal search resolution for single dwell serial-search code phase acquisition in DS-SpSp

We address the problem of optimal search granularity for a code phase acquisition system in direct-sequence spread-spectrum communication (DS-SpSp). We do this by testing the acquisition systems\´ performance in terms of the mean acquisition time and variance as a function of the search step size. Apparently, the following tradeoff exists: in a code sequence of length N chips, chip duration, T_c, and search step size, ΔT, reducing ΔT usually improves the detector performance, while delaying the whole search process (acquisition time), due to the higher number of hypotheses (m=┌N/ΔT┐) to be tested, and the processing time required for each hypothesis. This tradeoff points towards the existence of an optimal setting of ΔT that minimizes the mean acquisition time. An analytical derivation of the mean acquisition time and variance as a function of ΔT for a coherent acquisition system is carried out. It is shown that, in contrast to some conventional approaches that choose ΔT=T_c/2^k, k=1,2,3... to increase the search granularity, the optimal ΔT that minimizes the acquisition time is ∼T_c. Furthermore, choosing ΔT=T_c/2^k, k = 1,2,3.... might severely degrade the mean acquisition time and variance by up to a factor of three.