Designing Low Side-Lobe Level-Phase Coded Waveforms for MIMO Radar Using <i>P</i>-Norm Optimization
Tianqu Liu, Jinping Sun, Guohua Wang, Xiaoyong Du, Weidong Hu
Abstract
The detection performances of MIMO radar can be improved by waveform diversity technology. The waveform diversity gain depends on the correlation side-lobe level of the orthogonal waveform set. Generally, peak side-lobe level (PSL) and integrated side-lobe level (ISL) are two most important performance metrics of the correlation side-lobe level. Few existing orthogonal waveform set design algorithms can minimize PSL and ISL simultaneously. To tackle this problem, this article first proposes a correlation side-lobe performance metric in the form of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -norm, denoted by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -ISL. Then, in order to minimize the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -ISL, this article develops a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -MM algorithm based on majorization–minimization (MM) framework, which transforms the complex <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -order polynomial minimization problem into a series of low-order simple optimization problems. Numerical results show that the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -MM algorithm can effectively suppress the correlation side-lobe level and strike a good balance between the PSL and ISL metrics. Compared with the best PSL optimization algorithm based on primal dual method, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -MM obtains about the same PSL and lower ISL values. Compared with multi-CAN, MM-Corr, ISL-New,and the other state-of-the-art ISL minimization algorithms, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -MM obtains slightly higher ISL and much lower PSL. Briefly, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -MM is able to obtain almost the best PSL and relatively low ISL values.