This paper introduces a robust waveform design method aimed at reducing the impact of electromagnetic interference in radar systems, thereby enhancing target detection accuracy. We propose utilizing a high-order p-norm to characterize the peak sidelobe level (PSL) of the waveform. Additionally, the method incorporates spectral zero-trapping within known interfering frequency bands to mitigate interference effects. A unified optimization objective function is developed to ensure optimal correlation properties of waveforms for dual-use in radar and communication systems. By employing the AdamW algorithm for dynamic adjustment of the iteration factor, combined with a gradient descent search, this method refines both the autocorrelation of the waveform and its resilience to known disturbances. Experimental results demonstrate that our approach significantly improves autocorrelation performance over randomly generated initial waveforms. Moreover, the introduction of spectral zero-trapping notably enhances interference suppression in targeted frequency bands, thereby boosting overall signal performance. Our method effectively balances interference rejection with the minimization of sidelobe levels, offering a pragmatic waveform solution for complex radar environments.