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Incoherent acquisition of DSSS signals in presence of Doppler shifts

Code synchronization in direct-sequence spread-spectrum (DSSS) receivers can be divided into the acquisition and the tracking phases. Here we assume that the acquisition is performed with a periodic pseudo-random signal of period N. Acquisition of pseudo-random signals is similar to target detection with a pulse compression radar. The appropriate tool for the description of a pulse compression radars behaviour is the ambiguity function. The present paper describes the code acquisition in DSSS receivers in terms of cross ambiguity functions. Moreover the importance of the merit factor for incoherent acquisition is represented. The signal to interference ratio and an equation giving the optimum matched filter length as a function of the Doppler shift is derived.