Phase-Coded Sequence Design for Local Shaping of Complete Second-Order Correlation

The auto-correlation is not sufficient for the complete statistical characterization of a complex sequence, especially in applications involving nonlinear systems. Therefore, this letter addresses the sequence design problem considering the local shaping of complete second-order correlation, which controls the sidelobe level for both auto-correlation and conjugate correlation over specific lags. An efficient algorithm based on the Majorization-Minimization technique is proposed, which only consists of close-form iterations with full fast Fourier transform (FFT) operations. Numerical simulations indicate that the proposed algorithm significantly outperforms the existing gradient method in terms of the achieved objective and runtime. The application in nonlinear radar is also presented.