Unimodular (i.e., constant modulus) sequences with good autocorrelation properties are useful in several areas, including communications and radar. The integrated sidelobe level (ISL) of the correlation function is often used to express the goodness of the correlation properties of a given sequence. In this paper, we present several cyclic algorithms for the local minimization of ISL-related metrics. These cyclic algorithms can be initialized with a good existing sequence such as a Golomb sequence, a Frank sequence, or even a (pseudo)random sequence. To illustrate the performance of the proposed algorithms, we present a number of examples, including the design of sequences that have virtually zero autocorrelation sidelobes in a specified lag interval and of long sequences that could hardly be handled by means of other algorithms previously suggested in the literature.
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