Sequence design to minimize the peak sidelobe level

Sequences with low aperiodic autocorrelation sidelobes are well-known to have extensive applications in active sensing and communication systems. In this paper, we consider the sequence design problem of minimizing the ℓp-norm of the autocorrelation side-lobes, which can then be used to minimize the peak sidelobe level (PSL) criterion. An algorithm based on the general majorization-minimization method is developed to tackle the problem. The proposed algorithm can be implemented by means of fast Fourier transform (FFT) operations and thus is computationally efficient in practice. Numerical experiments show that the proposed algorithm can produce very long sequences with impulse-like autocorrelation and with much smaller PSL compared with some well-known analytical sequences.