  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 majorization-minimization (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.
