Recursive all-lag reference-code correlator and its efficient implementation

An all-lag reference-code correlator generates an all-lag 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 N 2 , where N is the length of the reference code. This paper derives a recursive form for the all-lag reference-code correlator. It is shown that the proposed recursive all-lag referencecode 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. lndex Terms All-lag reference-code correlator, Recursive relationship, Low-complexity implementation, Spread spectrum, Parallel correlator.