Regular synthesis of pairs of phase-keyed binary minimax signals

A regular method is proposed for synthesizing pairs of phase-keyed binary signals with minimum values of maximum autocorrelation and crosscorrelation peaks. The method is based on the mutual energy spectrum of two code sequences and representation of the corresponding polynomial as the product of two. It involves selection of + and - signs in one sequence to minimize the maximum of the crosscorrelation function and to derive the second sequence from the first one to minimize the side peaks of the autocorrelation function. The method is demonstrated on pairs of Barker sequences, of M-sequences, and of sequences which with any given autocorrelation function have the minimax of the crosscorrelation functions. The method yields a smaller minimax than the Gold method, only very long sequences obtained by both methods have similar characteristics.