ON THE PERFORMANCE OF DIRECTION FINDING WITH TIME-VARYING ARRAYS

This paper considers the problem of finding the directions of narrow-b and signals using a time-varying array whose elements move during the observation interval in an arbitrary but known way. We derive the cond itional maximum likelihood (CML) estimator for the directions-of-arriv als, and the corresponding Cramer-Rao bound (CRB). Using small-error a nalysis we derive analytical expressions for the bias and variance of the estimates. The CML is derived using a deterministic signal model. Its performance for Gaussian signal is, therefore, suboptimal. However , we demonstrate that for the case of two uncorrelated sources, and su fficiently high signal-to-noise ratio, the accuracy of the CML is clos e to the CRB derived for Gaussian signals. Thus, the closed-form expre ssions for the performance of the CML are useful for evaluating the pe rformance of time-varying arrays. For uncorrelated sources, these expr essions are significantly simpler than the corresponding expressions f or the Gaussian signal model, and provide more insight into the proble m. Furthermore, these expressions provide a simple quality measure for time-varying arrays which depends only on the time-varying geometry o f the problem.