Designing Low Side-Lobe Level-Phase Coded Waveforms for MIMO Radar Using <i>P</i>-Norm Optimization

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.