Partial period autocorrelations of geometric sequences

For a binary pseudorandom sequence {Si} with period N , the partial period autocorrelation function AS(τ, k,D) is defined by correlating the portion of the sequence within a window of size D, and start position k, with the portion in another window of the same size but starting τ steps later in the sequence. A distribution of possible partial period autocorrelation values is obtained by allowing the start position k to vary over all possible values 0 ≤ k < N . The expectation value is proportional to the periodic autocorrelation function AS(τ). In this paper the variance in the partial period autocorrelation values is estimated for a large class of binary pseudorandom sequences, the so-called “geometric sequences ”. An estimate is given for the minimum window size D which is needed in order to guarantee (with probability of error less than ), that a signal has been synchronized, based on measurement of a single partial period autocorrelation value.