PERFORMANCE ANALYSIS OF DIRECTION FINDING WITH LARGE ARRAYS AND FINITE DATA

This paper considers analysis of methods for estimating the parameters of narrow-band signals arriving at an array of sensors. This problem has important applications in, for instance, radar direction finding a nd underwater source localization. The so-called deterministic and sto chastic maximum likelihood (ML) methods are the main focus of this pap er. A performance analysis is carried out assuming a finite number of samples and that the array is composed of a sufficiently large number of sensors. Several thousands of antennas are not uncommon in, e.g., r adar applications. Strong consistency of the parameter estimates is pr oved, and the asymptotic covariance matrix of the estimation error is derived. Unlike the previously studied large sample case, the present analysis shows that the accuracy is the same for the two ML methods. F urthermore, the asymptotic covariance matrix of the estimation error c oincides with the deterministic Cramer-Rao bound. Under a certain assu mption, the ML methods can be implemented by means of conventional bea mforming for a large enough number of sensors. We also include a simpl e simulation study, which indicates that both ML methods provide effic ient estimates for very moderate array sizes, whereas the beamforming method requires a somewhat larger array aperture to overcome the inher ent bias and resolution problem.