Resolution performance analysis of cumulants-based rank reduction estimator in presence of unexpected modeling errors

Compared to the rank reduction estimator(RARE)based on second-order statistics(called SOS-RARE),the RARE employing fourth-order cumulants(referred to as FOC-RARE)is capable of dealing with more sources and mitigating the negative influences of the Gaussian colored noise.However,in the presence of unexpected modeling errors,the resolution behavior of the FOC-RARE also deteriorate significantly as SOS-RARE,even for a known array covariance matrix.For this reason,the angle resolution capability of the FOC-RARE was theoretically analyzed.Firstly,the explicit formula for the mathematical expectation of the FOC-RARE spatial spectrum was derived through the second-order perturbation analysis method.Then,with the assumption that the unexpected modeling errors were drawn from complex circular Gaussian distribution,the theoretical formulas for the angle resolution probability of the FOC-RARE were presented.Numerical experiments validate our analytical results and demonstrate that the FOC-RARE has higher robustness to the unexpected modeling errors than that of the SOS-RARE from the resolution point of view.

Compared to the rank reduction estimator （RARE） based on second-order statistics （called SOS-RARE）, the RARE employing fourth-order cumulants （referred to as FOC-RARE） is capable of dealing with more sources and mitigating the negative influences of the Gaussian colored noise. However, in the presence of unexpected modeling errors, the resolution behavior of the FOC-RARE also deteriorate significantly as SOS-RARE, even for a known array covariance matrix. For this reason, the angle resolution capability of the FOC-RARE was theoretically analyzed. Firstly, the explicit formula for the mathematical expectation of the FOC-RARE spatial spectrum was derived through the second-order perturbation analysis method. Then, with the assumption that the unexpected modeling errors were drawn from complex circular Gaussian distribution, the theoretical formulas for the angle resolution probability of the FOC-RARE were presented. Numerical experiments validate our analytical results and demonstrate that the FOC-RARE has higher robustness to the unexpected modeling en＇ors than that of the SOS-RARE from the resolution point of view.