Cramer-Rao Lower Bound for DOA Estimation Using Vector and Higher-Order Sensor Arrays

The Cramer-Rao lower bound for estimating the azimuth and elevation angles of multiple planewave sources using a line array of general n^th-order sensors is derived, generalizing the results of Nehorai and Paldi (1994) [1] for vector (first order) sensors. An analytical framework using spherical harmonics is used to derive the bound and the MVDR estimator for the higher order sensor array. Theoretical and simulation results for both a single higher-order sensor and a vertical line array are presented.