Min-max metric for spectrally compatible waveform design via log-exponential smoothing

To ensure the proper functioning of active sensing systems in the presence of interferences from other electromagnetic equipment in a spectrally crowded environment, we devise four new solutions for spectrally compatible waveform design based on the min-max metric, namely, minimum modulus dynamic range, min-max spectral shape, minimum weighted peak sidelobe level, and minimum similarity. To address the resultant nonconvex and nonsmooth optimization problems, a unified algorithm framework is proposed. That is, we first approximate the min-max metric by using the 'log-exponential smoothing' technique, then apply majorization-minimization to smooth and simplify the approximate optimization formulations, and finally use the Karush-Kuhn-Tucker theory to tackle the majorized problems. Besides, we develop an adaptive approximation parameter selection scheme, which monotonically decreases the approximation error at each iteration. The proposed algorithms are computationally efficient as they can be realized via fast Fourier transform. Finally, numerical examples are presented to demonstrate their excellent performance.