Pareto-optimal sparse frequency radar waveform design

To deal with the narrowband interferences in high frequency radar application, sparse frequency waveform allocates its energy into several disjointed bands to obtain a high signal to interference-plus-noise ratio (SIR). However, the spectrum discontinuity will result in high range sidelobes. The SIR and sidelobes are coupled in a conflicting way, and should be taken into account together in design, which boils down to multi-objective optimization. The analytical expression of integral sidelobe level (ISL) and SIR under a known interference environment is derived. Then a gradient-based iterative algorithm is proposed to obtain the optimum solution to the weighted sum of both metrics. By traveling the weight applied, the Pareto trade-off curve is obtained. Using the Pareto trade-off curve, waveform design results under different weights are analyzed. The simulation verifies flexibility the optimal design in practical applications.