Design of spectrally compatible waveforms with low weighted sidelobe levels

The spectral compatibility of radar waveforms is crucial for mitigating mutual interference between radar and other electromagnetic systems. Additionally, the autocorrelation sidelobe level needs to be suppressed. Therefore, we formulate a weighted objective function for jointly optimizing sidelobe performance and spectral compatibility in this paper. Unlike existing constant modulus constraints, we establish the optimization problem under peak-to-average ratio (PAR) and energy constraints. To solve this resulting NP-hard problem, we propose the Fast Fourier Transform (FFT) Combined with Conjugate Gradient Method (CGM) under PAR Constraints (FCCPC) algorithm. We decompose the original problem into two subproblems and solve the waveform phases and amplitudes sequentially. The phases are iteratively solved via CGM. The waveform amplitudes are obtained using the Karush-Kuhn-Tucker (KKT) conditions. The proposed algorithm leverages FFT to significantly enhance computational efficiency. Furthermore, we develop a weighted value guided selection method based on different radar performance requirements. Numerical simulations verify the superiority of the FCCPC algorithm as well as the effectiveness of the proposed weighted value guided selection method.