Fast algorithms for sparse frequency waveform design with sidelobe constraint

Sparse frequency waveform (SFW) is widely used in wideband systems (for instance, radar and communication systems) to suppress the narrowband interferences or avoid the reserved frequency bands. However, it suffers high autocorrelation sidelobes due to the discontinuous spectrum. In this paper, we aim at designing waveforms with low autocorrelation sidelobes and arbitrary frequency stopbands. After formulating this design as an unconstrained minimization problem, two algorithms based on the majorization-minimization method and a gradient-based algorithm are derived to deal with this problem. The proposed algorithms can be easily implemented by the fast Fourier transform (FFT) operations and thus are computationally efficient for long waveform design with good sidelobe and stopband suppression. In addition, they can handle both the design problem of low sidelobe waveform and the design problem of sparse frequency waveform with low sidelobes. Numerical experiments show that the proposed algorithms can provide better performance than the existing ones on the running time.