Suboptimum binary phase code search using a genetic algorithm

Abstract

Optimum binary phase codes of length L are characterized by an autocorrelation function R((tau) ) with uniform sidelobes of level 1/L with respect to the main lobe. These optimum binary codes are called Barker codes. Binary phase codes that exhibit minimum peak sidelobes above 1/L are called suboptimum. A genetic algorithm is implemented to conduct the search for optimum and suboptimum binary codes of a given length L. In this approach, several different fitness functions are considered. These fitness functions are based on sidelobe level (SLL) and generalized entropy measures. To verify that these are reasonable fitness functions, they are first applied to sequence lengths for which optimum codes are known to exist. It is shown that if L is such that a Barker code exists, and S is a generalized entropy measure, then the Barker codes are the only ones that give the minimum value for S. It is also shown that the proposed binary phase code search is efficient for large values of L.