On the performance of direction finding with time-varying arrays

Abstract

This paper considers the problem of finding the directions of narrow-band signals using a time-varying array whose elements move during the observation interval in an arbitrary but known way. We derive the conditional maximum likelihood (CML) estimator for the directions-of-arrivals, and the corresponding Cramer-Rao bound (CRB). Using small-error analysis 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 sufficiently high signal-to-noise ratio, the accuracy of the CML is close to the CRB derived for Gaussian signals. Thus, the closed-form expressions for the performance of the CML are useful for evaluating the performance of time-varying arrays. For uncorrelated sources, these expressions are significantly simpler than the corresponding expressions for the Gaussian signal model, and provide more insight into the problem. Furthermore, these expressions provide a simple quality measure for time-varying arrays which depends only on the time-varying geometry of the problem.