Adaptive gradient search for optimal sidelobe design of hopped-frequency waveform

Linear step frequency waveforms can achieve large time-bandwidth product by uniformly inter-pulse frequency stepping, but have limited anti-jamming ability. Hopped-frequency waveforms overcome the limitation by introducing irregularly or randomly stepped frequency. However, a challenge in hopped-frequency waveform design is that, given fixed pulse number and time-bandwidth product, the distribution of its autocorrelation sidelobe varies significantly under different frequency combinations. In this study, the authors propose an adaptive gradient search algorithm for optimal sidelobe design of hopped-frequency waveform. The method is iterative and applies a negative gradient adjustment adaptively according to sidelobe discrepancy between the current output of the matched filtering and the ideal expectation. As a result, it can be used to find optimal frequency combinations that produce hopped-frequency pulses with a prescribed sidelobe specification. Experimental evidence suggests that the proposed procedure gives promising results in terms of sidelobe level and it terminates in remarkably little time.