Binary Sequences With Small Peak Sidelobe Level
A binary sequence of length n is an n-tuple with elements in {-1, 1} and its peak sidelobe level is the largest absolute value of its aperiodic autocorrelations at nonzero shifts. A classical problem is to find binary sequences whose peak sidelobe level is small compared to the length of the sequence. Using known techniques from probabilistic combinatorics, this paper gives a construction for a binary sequence of length n with peak sidelobe level at most root 2n log (2n) for every n > 1. This improves the best known bound for the peak sidelobe level of a family of explicitly constructed binary sequences, which arises for the family of - sequences. By numerical analysis, it is argued that the peak sidelobe level of the constructed sequences grows in fact like order root n log log n and, therefore, grows strictly more slowly than the peak sidelobe level of a typical binary sequence.
binary sequence peak sidelobe level aperiodic autocorrelation derandomization