MIMO雷达相位编码波形集相关函数下界综述

MIMO雷达波形集的互相关函数峰值越低，则正交性越好，波形分集增益越高。非循环互相关函数下界的研究有助于确定波形分集增益的极限值，对MIMO雷达波形设计与应用有重要意义。相位编码波形集是目前被研究最多的MIMO雷达波形集，对其相关函数下界的研究较为深入。本文对目前相位编码波形集相关函数各类下界的研究进行归纳总结，包括相关函数峰值旁瓣下界、相关函数积分旁瓣下界、互相关内积下界、互补序列相关函数下界四大类。相关函数峰值旁瓣下界是影响MIMO雷达波形分集增益的关键指标，其他类型的下界与相关函数峰值旁瓣下界之间存在潜在联系，这可能有助于相关函数峰值旁瓣下界的确定。不同波形数，不同码长的典型相位编码波形相关函数指标与下界的对比结果表明，目前已有下界都不够紧，尤其在波形数较多时。因此，MIMO雷达相位编码波形集相关函数下界仍是一个值得研究的开放问题。 

Review of Lower Bounds on the Correlation Functions of MIMO Radar Phase Coded Waveform Set

? ?For multiple-input multiple-output （MIMO） radar waveform set， the lower the peak of the cross-correlation functions， the better the orthogonality， and the higher the waveform diversity gain. The studies of the lower bounds on aperiodic cross-correlation functions would help determine the limit value of waveform diversity gain， which is of great significance to the MIMO radar waveform designs and applications. At present， phase coded waveform sets are the most studied MIMO radar waveform sets. And the studies of the lower bounds on the correlation function of the phase coded waveform set are in-depth. This paper reviews the existing researches on the lower bounds， including lower bound on peak side-lobe level of correlation functions， lower bound on integral side-lobe level of correlation functions， lower bound on peak inner products and lower bound on correlation functions of complementary sequence set. Among them， the lower bound on peak side-lobe level of correlation functions is the key metric affecting the MIMO radar waveform diversity gain. There are intrinsic relationships among these bounds， which may help determine the lower bound on peak side-lobe level of correlation functions. Numerical results under different number of waveforms and sequence lengths show that the existing lower bounds are not tight compared with existing phase coded waveform sets with low cross-correlation functions. Particularly， the gap between them is obvious large when the number of waveforms is large. Hence， lower bound on the correlation function of the phase coded waveform set is still an open problem worthy of study.