Abstract-Unimodular sequences with low autocorrelations are desired in many applications, especially in the area of radar and code-division multiple access (CDMA). In this paper, we propose a new algorithm to design unimodular sequences with low integrated sidelobe level (ISL), which is a widely used measure of the goodness of a sequence's correlation property. The algorithm falls into the general framework of majorizationminimization (MM) algorithms and thus shares the monotonic property of such algorithms. In addition, the 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 algorithms in terms of both the quality of designed sequences and the computational complexity.

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 ℓp-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.

Sets of sequences with good correlation properties are desired in many active sensing and communication systems, e.g., multiple-input-multiple-output (MIMO) radar systems and code-division multiple-access (CDMA) cellular systems. In this paper, we consider the problems of designing complementary sets of sequences (CSS) and also sequence sets with both good auto-and cross-correlation properties. Algorithms based on the general majorization-minimization method are developed to tackle the optimization problems arising from the sequence set design problems. All the proposed algorithms can be implemented by means of the fast Fourier transform (FFT) and thus are computationally efficient and capable of designing sets of very long sequences. A number of numerical examples are provided to demonstrate the performance of the proposed algorithms.