宽带频率步进信号参数估计的克拉美罗界研究

On the Cramer-Rao Bound of Parameter Estimation for Wideband Stepped Frequency Signal

随着宽带雷达技术的发展,经典窄带信号参数估计的克拉美罗(CR)界已经不能再作为参数估计算法的评估标准。该文以宽带频率步进雷达为应用背景,首先推导了宽带频率步进信号参数估计的CR界,给出了Fisher信息阵元的闭合表达式。然后深入揭示了宽带CR界的特性,证明了频率步进信号参数估计的性能不仅与信号带宽、信噪比有关,还会受到相对带宽的影响。最后验证了窄带CR界只是宽带CR界的一个特例,宽带CR界综合考虑了宽带模型下各种因素的影响,在理论分析中有更加全面的指导意义。

With the development of wideband radar technology,classic narrowband Cramer-Rao（CR） bound can not be used as the criteria for the parameters estimation.Based on the application of Wideband Stepped Frequency Signal（WSFS）,the wideband CR bound for WSFS parameters estimation is firstly derived in this paper,and the complete expression of Fisher information matrix is provided.Then an insight into theoretical performance of the wideband CR bound is given,from which it can be known that the estimated performance of stepped frequency signal is not only determined by the signal bandwidth and signal-to-noise ratio,but also affected by the relative bandwidth.Finally,it is proved that the narrowband CR bound is just a special case of wideband CR bound.All factors of wideband model are fully considered in the wideband CR bound,which make it more comprehensive in the theoretical analysis.