Bounding the Peak Sidelobe Level of Binary Sequences of All Lengths
Idris Mercer · IEEE Transactions on Information Theory · 2016
Improving upon 2010 results of Alon et al., it was shown in 2014 by Schmidt that asymptotically, almost all binary sequences of length n have peak sidelobe level close to (2n log n)1/2. One specific result of Alon et al. is that if we fix ε > 0, then almost all binary sequences of length n have peak sidelobe level at most (2n(log n - (1.5 - ε) log log n))1/2, in the sense that the probability of not satisfying that bound approaches 0 as n approaches infinity. In this note, we prove that for all sequence lengths n > 1, there is a binary sequence of length n with peak sidelobe level at most (2n(log n - log log n + 0.862))1/2.