Sequence Design to Minimize the Weighted Integrated and Peak Sidelobe Levels

TL;DR

This paper introduces efficient algorithms based on majorization-minimization and FFT to design sequences with minimal weighted integrated and peak sidelobe levels, enhancing autocorrelation properties for sensing and communication.

Contribution

The paper develops novel algorithms for minimizing WISL and PSL in sequence design, extending to $\, ext{l}_p$-norm optimization, with guaranteed convergence and computational efficiency.

Findings

Algorithms produce sequences with near-zero autocorrelation sidelobes.

Sequences have significantly lower peak sidelobe levels than existing sequences.

Methods are computationally efficient and scalable for long sequences.

Abstract

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 problem of minimizing the weighted integrated sidelobe level (WISL), which can be used to design sequences with impulse-like autocorrelation and zero (or low) correlation zone. Two algorithms based on the general majorization-minimization method are developed to tackle the WISL minimization problem and the convergence to a stationary point is guaranteed. In addition, the proposed algorithms can be implemented via fast Fourier transform (FFT) operations and thus are computationally efficient, and an acceleration scheme has been considered to further accelerate the algorithms. Moreover, the proposed methods are extended to optimize the $\ell_{p}$-norm of the autocorrelation sidelobes, which lead to a way to minimize the peak sidelobe level (PSL) criterion. Numerical experiments show that the proposed algorithms can efficiently generate sequences with virtually zero autocorrelation sidelobes in a specified lag interval and can also produce very long sequences with much smaller PSL compared with some well known analytical sequences.