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Partial period autocorrelations of geometric sequences

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2 Author(s)
Klapper, A.M. ; Dept. of Comput. Sci., Kentucky Univ., Lexington, KY, USA ; Goresky, M.

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 O⩽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 ε), that a signal has been synchronized, based on measurement of a single partial period autocorrelation value

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Information Theory, IEEE Transactions on  (Volume:40 ,  Issue: 2 )