MSE Bounds for Phase Estimation in Presence of Recursive Nuisance Parameters

The mean squared error (MSE) is commonly used to measure and compare the performance of various phase estimation techniques in communications and signal processing systems. When the received signal contains recursive nuisance parameters, the MSE is extremely difficult to obtain and even the conventional modified Cramer-Rao bound (MCRB) can not be readily applied. In this paper, a recursive MSE bound and its simplified calculation method are proposed to solve the problem. As an application example, an adaptive hybrid antenna array and its associated angle-of-arrival (AoA) estimation technique are presented. The MSE of the AoA estimation is simulated and compared with the recursive MSE bound and MCRB. The results show that the proposed recursive MSE bound provides a tighter lower MSE bound than the recursive MCRB.