A Two-Step Optimization Framework for Low Sidelobe NLFM Waveform Using Fourier Series

The nonlinear frequency modulation (NLFM) waveform can achieve low sidelobes without loss of signal-to-noise ratio (SNR) by utilizing a nonlinear time-frequency structure. This letter presents a novel two-step progressive optimization framework for the NLFM waveform using Fourier series by exploiting the advantages of random searches and deterministic modifications. The modified GA is used for the preliminary design of the NLFM waveform, where random searches with waveform diversity and consideration of the signal's characteristic provide a rapid decrease of sidelobes in early iterations. When the descent speed of the sidelobes slows down, deterministic modifications in the gradient-based tuning are followed to further reduce the sidelobes. In the simulation, the peak-to-sidelobe level ratio (PSLR) is reduced by at least 5 dB with an almost equivalent normalized impulse response width (IRW) under the same time-bandwidth product (TBP) compared with other NLFM waveforms. Finally, the optimized NLFM waveform is implemented on hardware, which verifies its performance.