A recursive all-lag reference-code correlator for generating odd correlations

An all-lag reference-code correlator generates an all-lag even- or odd-correlation vector at a rate equal to the rate of incoming data samples. Direct implementation of an all-lag reference-code correlator requires N parallel correlators, and the resultant degree of complexity is of the order N², where N is the length of the reference code. In a previous paper, a recursive form for generating all-lag even correlations was derived. In this paper, we derive the recursive form for generating all-lag odd correlations. It is shown that the corresponding correlator can be implemented with a complexity approximately equal to that of a single parallel correlator. That is, the degree of complexity of the proposed recursive all-lag reference-code correlator is of the order N. Thus, substantial reduction in the implementation complexity is achieved