Optimization Methods for Designing Sequences With Low Autocorrelation Sidelobes

Unimodular sequences with low autocorrelation are desired in many applications, especially in radar systems and code-division multiple access (CDMA) communication systems. In this paper, we propose a new algorithm to design unimodular sequences with low autocorrelation via directly minimizing the integrated sidelobe level (ISL) of the autocorrelation. The algorithm is derived based on the general framework of majorization-minimization (MM) algorithms and thus shares the monotonic property of such methods, and two acceleration schemes have been considered to accelerate the overall convergence. In addition, the proposed algorithm can be implemented via fast Fourier transform (FFT) operations and thus is computationally efficient. Furthermore, after some modifications the algorithm can be adapted to incorporate spectral constraints, which makes the design more flexible. Numerical experiments show that the proposed algorithms outperform existing ones in terms of both the merit factors of designed sequences and the computational complexity.