Estimation accuracy of maximum likelihood direction finding using large arrays

The authors analyze the performance of methods for estimating the parameters of narrowband signals arriving at an array of sensors. The deterministic and stochastic maximum likelihood (ML) methods are considered. A performance analysis is carried out for a finite number of snapshots but assuming that the array is composed of a sufficiently large number, m, of sensors. Strong consistency of the parameter estimates is proved and the asymptotic covariance matrix of the estimation error is derived. Unlike the previously studied large (time) sample case, the present analysis shows that the accuracy is the same for the two ML methods. The covariance matrix of the estimation error attains the Cramer-Rao bound. For many array geometries of practical interest, the array propagation vectors become orthogonal as m as increased. It is shown that the traditional beamforming method provides consistent (but not necessarily efficient) estimates under the assumption. This is true also in the presence of perfectly correlated emitters