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Binary Sequences With Small Peak Sidelobe Level

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1 Author(s)
Schmidt, K. ; Dept. of Math., Simon Fraser Univ., Burnaby, BC, Canada

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 √2nlog(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 m-sequences. By numerical analysis, it is argued that the peak sidelobe level of the constructed sequences grows in fact like order √n log log n and, therefore, grows strictly more slowly than the peak sidelobe level of a typical binary sequence.

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Information Theory, IEEE Transactions on  (Volume:58 ,  Issue: 4 )