An Efficient Algorithm for Designing Long Aperiodic Binary Sequences With Low Auto-Correlation Sidelobes

Sequences with low auto-correlation sidelobes are important in diverse fields, including communications, radar, sonar, and medical imaging. The task of finding binary sequences with low auto-correlation is known as a difficult optimization problem. Recently, many computational methods have been proposed for designing long binary sequences with good auto-correlation properties. In this paper, we present a new algorithm to generate long aperiodic binary sequences with low peak sidelobe levels. Our algorithm combines the Legendre sequence to seed an initial binary sequence, and an efficient stochastic search method with a dynamic fitness function mechanism to generate a final binary sequence. Numerical examples of the obtained binary sequences with a length N up to
$2^{20}-1$
and a peak sidelobe level lower than
$0.8\sqrt {N}$
are provided, to demonstrate the efficiency of the proposed stochastic algorithm, that can outperform existing computational methods for designing long aperiodic binary sequences.