Cramér-Rao Bound for Joint Angle and Delay Estimators by Partial Relaxation

Abstract

Novel Fisher-Information Matrix (FIM) and Cramér-Rao Bound (CRB) expressions for the problem of the "partially relaxed" Joint Angle and Delay Estimation (JADE) are derived and analyzed in this paper. In particular, exact closed form expressions of the CRB on the Angles and Times of Arrival of multiple sources are presented. Furthermore, interesting asymptotic and desirable properties are demonstrated, such as high SNR behaviour and lower bound expressions on the CRBs of Angles and Times of Arrival of multiple sources. Computer simulations are also given to visualize CRB behaviour in regimes of interest.