Minimum local peak sidelobe level waveform design with correlation and/or spectral constraints

The problem of designing waveforms with specified aperiodic/periodic correlation and spectral properties has received much attention because of its wide applicability in sonar, radar, and communications. In particular, a waveform with low peak sidelobe level (PSL) of autocorrelation can improve the detection performance of a weak target masked by a nearby strong target in range compression radar systems, and that with adaptive spectrum nulls/notches can make the sensing systems not be interfered by other electromagnetic equipment. On the other hand, a constant modulus (CM) waveform can maximize the transmit power efficiency of the system. Whereas, it is difficult to design a CM waveform with minimum local PSL and specified autocorrelation and/or spectral properties due to numerous nonconvex inequality and equality constraints. To develop efficient algorithms for this problem, we first express the waveform autocorrelation in the frequency domain, then use the proximal method of multipliers to tackle the resultant nonconvex and nonsmooth constrained optimization. Numerical examples have shown that the proposed methods can produce the waveforms satisfying these challenging requirements.