Effect of frequency offset on DS-SS acquisition in slowly fading channels

In practical direct sequence spread spectrum (DS-SS) receivers a frequency offset between the received carrier frequency and the receiver oscillator often exists. This offset is corrected after the DS-SS signal is acquired. This paper considers the effect of frequency offset on the acquisition performance of DS-SS systems in frequency non-selective fading channels. A rapid acquisition system employing sliding correlation (matched filter) is utilized. To combat the effect of frequency offset, the total length of the sliding correlator is divided into shorter sections. We derive analytical expression for the probability of detection when the fading process is constant across all the sections. This is the case in most practical channels. The squared magnitude of the correlation results of each section are added (which we denote as non-coherent combining). The effect of frequency offset on the the probability of detection, probability of false alarm and the mean acquisition time are analyzed, allowing the trade-off between coherent and non-coherent correlation to me optimized