Perturbation analysis of conjugate MI-ESPRIT for single acoustic vector-sensor-based noncircular signal direction finding

The closed-form conjugate multiple-invariance ESPRIT (CMI-ESPRIT) algorithm herein analyzed: (1) makes use of redundancy in the nonvanishing conjugated second- and fourth-order cumulants of noncircular signals; (2) recognizes the real-valued two-dimensional directivity inherently achieved by an acoustic vector-sensor in a free-space. It is provided in this correspondence the perturbation analyses on both the norm-penalized and the subspace-constraint ESPRIT matrices that play the key role in the CMI-ESPRIT. It is shown that the norm-penalized ESPRIT matrix is biased (but bounded) and has a minimal mean-squared-error (MSE) for some finite regularization factor, whereas the subspace-constraint ESPRIT matrix is unbiased and its MSE approaches minimum when the regularization factor becomes infinite. These observations are potentially useful for the determination of the regularization parameters which is significant for the performance of CMI-ESPRIT. The results also contribute to the ultimate study of direction-finding accuracy. Simulation results are presented to validate the given analyses.