An algorithm for generating low autocorrelation‐sidelobe skew symmetric binary sequences based on complex exponential functions

Abstract

AbstractIn the smearing process to suppress impulse noises and the pulse compression in long‐range radar, it is crucial to employ the finite binary sequence which minimizes the sidelobe of the autocorrelation function.This paper proposes a new generation algorithm for the finite binary sequence with a sharp autocorrelation function. The method is based on the fact that the autocorrelation function θ(n) of skew‐symmetric sequence is always zero when n is odd, and the Fourier expansion coefficient sequence of the complex exponential function is an uncorrelated sequence.First, the generating function is derived for the skew‐symmetric real‐valued sequence, for which the Fourier expansion coefficient sequence is an uncorrelated sequence. An algorithm is presented in detail, where the foregoing real‐valued sequence is quantized into a binary sequence, and the binary sequence minimizing the autocorrelation is derived with the finite delay coefficients of the generating function as the variables.In the past, no generation algorithm has been found which can derive the optimal skew‐symmetric binary sequence. It is shown that the proposed generation algorithm can derive all of the optimal skew‐symmetric binary sequence derived by Golay using the exhaustive method. It is shown also that all Barker sequences with off length can be derived.