非圆信号的DOA与阵列误差参数的联合估计性能界

Cramer-Rao bound of estimations of DOA and sensor errors for noncircular sources

为了确定非圆信号波达方向(direction-of-arrival,DOA)估计中参数化校正的方差下限,基于阵列误差影响下的随机性非圆信号模型与联合信源时域自相关特性的非圆信号模型,分别推导了DOA参数与阵列误差参数的联合估计克拉美罗界(Cramer-Rao bound,CRB)。通过将推导的非圆性能界与未利用非圆特性的性能界进行对比分析,理论证明了非圆性能界比未利用非圆特性的性能界更低,且两者的差异在低信噪比和大非圆率信号入射的情况下较大。实验结果不仅验证了理论分析的正确性,同时表明信源时域自相关信息有助于进一步提升阵列误差的校正精度。

In order to determine the minimum variance of parameterization calibration for sensor errors are application to direction-of-arrival（DOA）estimation,the expressions of Cramer-Rao bound（CRB）matrices of estimations of DOA and sensor errors are derived based on the stochastic model of noncircular signals and the stochastic model of temporally correlated noncircular signals,respectively.Through the comparisons between the derived CRBs and the CRBs which do not take advantage of the noncircular feature,it is proved that the derived CRBs are lower than the CRBs which do not take advantage of the noncircular feature,and this difference is greater at low signal-to-noise ratio or when the sources have larger circularity rate.The simulation results not only verify the theoretical analysis,but also show that temporal correlation of the sources can enhance the accuracy of calibration.