Fast algorithm for designing periodic/aperiodic sequences with good correlation and stopband properties

Liang Tang,Yongfeng Zhu,Qiang Fu

doi:10.1186/s13634-018-0579-z

Abstract

Periodic/aperiodic sequences with low autocorrelation sidelobes are widely used in many fields, such as communication and radar systems. Besides the correlation property, the frequency stopband property is often considered in the sequence design when the systems work in a crowded electromagnetic environment. In this paper, we aim at designing periodic/aperiodic sequences with low autocorrelation sidelobes and arbitrary frequency stopbands, and propose an efficient algorithm named FFT (fast Fourier transform)-based conjugate gradient algorithm. To calculate the step size efficiently, a method based on Taylor series expansion is developed. By changing the number of FFT points, the proposed algorithm can be easily used to generate periodic/aperiodic sequences. Since the gradient and step size can be implemented by FFT operations and Hadamard product, the whole algorithm is computationally efficient and can be used to design very long sequences. Numerical experiments show that the proposed algorithm has better performance than the state-of-the-art algorithms in terms of the running time.

Highlights

Sequences with low periodic or aperiodic autocorrelation sidelobes have been studied for a long time since the 1950s
From (46), we can see that when the approximate step size can guarantee the direction dk+1 of the PRP-conjugate gradient algorithm (CGA) is descendant, the dk+1 is selected as the searching direction
The peak sidelobe level (PSL) of the sequences designed by the Stopband cyclic algorithm new (SCAN), Spectral-Monotonic minimizer for integrated sidelobe level (MISL), alternating direction method of multipliers (ADMM), gradient descent (GD), and fast Fourier transform (FFT)-based conjugate gradient algorithm (FCGA) algorithms are − 14.01 dB, − 14.09 dB, − 15.64 dB, − 13.80 dB, and − 15.81 dB, respectively

Summary

Introduction

Sequences with low periodic or aperiodic autocorrelation sidelobes have been studied for a long time since the 1950s. In [9], the CAN algorithm was proposed to design unimodular sequences of large length by minimizing a criterion which is “almost equivalent” to the integrated sidelobe level (ISL) metric. We consider the problem of designing periodic/aperiodic sequences with low autocorrelation sidelobes and arbitrary frequency stopbands. By using the relationship between the autocorrelation function and power spectrum density (PSD), the problem is formulated as an unconstrained minimization problem with respect to the sequence phase in frequency domain. To solve this problem, an efficient algorithm named FFT-based conjugate gradient algorithm (which we call FCGA) is proposed.

Phase gradient

Step size calculation via Taylor series expansion

Periodic sequence design with low autocorrelation sidelobes

Aperiodic sequences design with low autocorrelation sidelobes

Findings

Conclusions