Optimization methods for solving the low autocorrelation sidelobes problem

In this paper, a discussion is made on the optimization methods that can solve the low autocorrelation sidelobes problem for polyphase sequences. This paper starts with a description and a comparison of two algorithms that are commonly used in the literature: a stochastic method and a deterministic one (a gradient descent). Then, an alternative method based on the Random Walk Metropolis-Hastings algorithm is proposed, that takes the gradient as a search direction. It provides better results than a steepest descent alone. Finally, this autocorrelation question is handled differently, considering a mismatched filter. We will see that a mismatched filter performs impressively well on optimized sequences.