随机调制信号参数的统计Cramer-Rao下限及其最大似然估计

摘要

The processing of both random frequency-hopping and random pulse repetition interval signals can be translated into the parameter estimation of random modulated signals. For random modulated complex sine wave (RMCSW) the Cramer-Rao lower bound of the complex amplitude and modulated coefficient is deduced via a Fisher information matrix, and their statistic characteristics are analyzed. Then the maximum likelihood estimations of the parameters are calculated for single and multiple RMCSWs, the resolution and ambiguity performances are researched via the generalized periodogram, which provides theoretic reference for the subsequent signal design and processing. Some simulations are performed to verify the related conclusions.%随机跳频和随机脉冲重复间隔等随机调制信号的处理可以等价为随机调制信号中的参数估计问题.针对抽象的随机调制复正弦信号模型,借助Fisher信息矩阵推导了其复幅度和调制系数估计的Cramer-Rao下限并分析了其统计特性.求解了单个和多个随机调制复正弦信号的最大似然估计,利用“广义周期图”研究了其分辨及模糊性能,为后续的信号设计与处理提供了理论参考.计算机仿真实验验证了相关结论.