Novel Method for Designing Waveform With Good Correlation Properties Based on High-Order Norm Unified Representation

This study exploits high-order p-norm to uniformly represent the peak sidelobe level (PSL) and integrated sidelobe level (ISL) commonly used in waveform optimization, and presents a unified optimization objective function by considering the requirement that waveforms have good correlation properties in radar and communication systems. A novel and efficient waveform optimization algorithm is then proposed, which tackles the waveform and waveform set optimization of the PSL, the weighted sidelobe level, the ISL, and the weighted ISL. Applying the unified optimization objective function, the iteration factors are dynamically adjusted based on the quasi-Newton algorithm; in addition, the objective function is optimized with the gradient descent search algorithm and includes the optimization of autocorrelation and cross-correlation. Because certain application scenarios involve the Doppler sensitivity of waveforms, the problem is converted to cross-correlation optimization via channel division of Doppler frequency, and waveform with anti-Doppler sensitivity can be obtained. Multiple numerical simulations illustrate the positive performance of the proposed method. Furthermore, compared with certain traditional algorithms, the waveforms designed by this algorithm demonstrate improved correlation properties.