Performance analysis of multivariate complex amplitude estimators

We consider multivariate complex amplitude estimation in the presence of unknown interference and noise. Two multivariate approaches [Maximum Likelihood (ML) and Capon] are provided. We derive the closed-form expression of the Crame´r-Rao bound (CRB) for the unknown complex amplitudes. We also analyze the bias properties and Mean Squared Errors (MSE) of the two estimators. A comparative study shows that the multivariate ML estimator is unbiased, whereas the multivariate Capon estimator is biased downward for finite snapshots. Both estimators are asymptotically statistically efficient when the number of snapshots is large.