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Min-Max Metric for Spectrally Compatible Waveform Design via Log-Exponential Smoothing
IEEE Transactions on Signal Processing ( IF 5.4 ) Pub Date : 2020-01-01 , DOI: 10.1109/tsp.2020.2969043
Wen Fan , Junli Liang , Hing Cheung So , Guangshan Lu

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.

中文翻译:

通过对数指数平滑实现频谱兼容波形设计的最小-最大度量

为了确保有源传感系统在频谱拥挤的环境中存在来自其他电磁设备的干扰的情况下正常运行,我们设计了四种新的解决方案,用于基于 min-max 度量的频谱兼容波形设计,即最小模量动态范围,min -最大频谱形状、最小加权峰值旁瓣电平和最小相似度。为了解决由此产生的非凸和非光滑优化问题,提出了统一的算法框架。也就是说,我们首先使用“对数指数平滑”技术来近似最小-最大度量,然后应用专业化-最小化来平滑和简化近似优化公式,最后使用 Karush-Kuhn-Tucker 理论来解决专业化问题问题。除了,我们开发了一种自适应逼近参数选择方案,它在每次迭代时单调减少逼近误差。所提出的算法在计算上是高效的,因为它们可以通过快速傅立叶变换来实现。最后,给出了数值例子来证明它们的优异性能。
更新日期:2020-01-01
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