The best achievable performance for DOA estimation using ESPRIT arrays

This paper studies the Cramer-Rao (CR) bound for the problem of estimating the directions of arrival of narrow-band plane waves impinging on an ESPRIT array with multiple displacement invariances. We call this bound the MI-CR bound. The CR bound for ESPRIT arrays with a single invariance was derived by Ottersten, Viberg and Kailath (see IEEE Trans. on Signal Processing, vol.39, p.1122-35, May 1991), and called the ESPRIT-CR bound. The difference between the ESPRIT-CR bound and the MI-CR bound can be large, especially for highly correlated sources. We give examples to show that an algorithm called WSE achieves the MI-CR bound derived in this paper