I use the MUSIC and ESPRIT algorithm to estimate the AoA and try to derive the CRLB to analyze its performance. Therein, the derivation of CRLB is based on this reference :
P. Stoica and A. Nehorai, "MUSIC, maximum likelihood, and Cramer-Rao bound," in IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 37, no. 5, pp. 720-741, May 1989. doi: 10.1109/29.17564.