On the Analytic Performance of Differential Spread Spectrum Code Acquisition

Spread spectrum code acquisition methods based on differential correlation are interesting alternatives to conventional non-coherent acquisition. Differential correlation can be seen simply as a correlation between two consecutive outputs of a coherent integrator. A differential acquisition variable is then obtained by averaging these correlation variables which results in an attenuation of any time-uncorrelated (or weakly time-correlated) interference components in a received signal. An existing analysis on the differential methods is mainly numeric or at least approximative in its nature. In this paper, we carry out rigorous analytic performance comparison of differentially coherent and conventional, non-coherent acquisition in terms of probabilities of detection and false alarm. First, we derive an exact probability distribution for the differential method from which we, then, evaluate the needed probabilities. In addition, we give a theoretical discussion about differentially noncoherent code acquisition which provides more reliable detection under residual frequency errors. Finally, we also give numerical examples to illustrate a suitability of the differential methods in Galileo-satellite positioning system