On the Optimality of Spectrally Notched Radar Waveform & Filter Designs

Designing radar waveforms with notched spectral regions can mitigate mutual interference with other proximate RF users. However, this capability comes at the cost of degraded range-Doppler sidelobe performance. To evaluate the limitations of correlation-based processing, the null-constrained power spectral density that minimizes correlation sidelobe levels is determined for comparison with waveform and pulse compression filter design methods. Existence of the least-squares (LS) global optimum indicates a fundamental dynamic range limitation for notched power spectra (notwithstanding further receive compensation or range resolution spoiling). Recent work investigated spectrally notched random FM (RFM) waveform design where ad-hoc tapering was incorporated into the null shape as a heuristic means of reducing range sidelobes. Here, waveforms designed according to the optimal null-constrained spectral template are demonstrated to have improved sidelobe performance after pulse compression and slow-time processing. Further, because these waveforms are designed according to the LS optimal spectral template, application of the LS mismatched filter provides additional sidelobe reduction (toward the global limit) with minimal mismatch loss.