Steepest descent method for minimizing the peak sidelobe level of hopped-frequency waveform

Hopped-frequency waveform achieves high range resolution by transmitting a burst of narrowband pulses spanning the desired bandwidth. As its frequencies are irregularly or even sparsely distributed, hopped-frequency waveform could obtain a wider bandwidth with fixed pulses number and shows stronger anti-jamming ability than the linear stepped-frequency waveform; however, an undesired attribute associated is its high range sidelobe which would mask weak echo. In this paper, we optimally design the transmitted frequencies of the hopped-frequency waveform to suppress the peak sidelobe level (PSL). The considered design problem is formulated into a finite minimax optimization and a gradient-based descent method is proposed to solve this problem. This descent method uses the gradients of the largest several sub-functions of the considered minimax problem to fix a descent direction, and computes the step-length under the greedy criterion. Through iterative operation, this method reduces the function value monotonically and thus guarantees the convergence. Numeric results indicate that the proposed method can effectively suppress the PSL of the hopped-frequency waveform.