EM-ESPRIT ALGORITHM FOR DIRECTION FINDING WITH NONUNIFORM ARRAYS

International audienceThis paper deals with the problem of the Direction Of Arrival (DOA) estimation with nonuniform linear arrays. The proposed method is a combination of the Expectation Maximization (EM) and the ESPRIT methods. The EM algorithm interpolates the nonuniform array to an equivalent uniform array, and then, the application of ESPRIT is possible, in order to estimate the DOA. One of this method novelties lies in its capacity of dealing with any nonuniform array geometry. This technique manifests significant performance and computational advantages over previous algorithms such as MUSIC, specially in the preasymptotic domain, and the comparison with the theoretical Cramer-Rao Bounds (CRB) shows its efficiency

Advantages of nonuniform arrays using Root-MUSIC

In this paper, we consider the Direction-Of-Arrival (DOA) estimation problem in the Nonuniform Linear Arrays (NLA) case, particularly the arrays with missing sensors. We show that the root-MUSIC algorithm can be directly applied to this case and that it can fully exploit the advantages of using an NLA instead of a Uniform Linear Array (ULA). Using theoretical analysis and simulations, we demonstrate that employing an NLA with the same number of sensors as the ULA, yields better performance. Moreover, reducing the number of sensors while keeping the same array aperture as the ULA slightly modifies the Mean Square Error (MSE). Therefore, thanks to the NLA, it is possible to maintain a good resolution while decreasing the number of sensors. We also show that root-MUSIC presents good performance and is one of the simplest high resolution methods for this type of arrays. Closed-form expressions of the estimator variance and the Cramer–Rao Bound (CRB) are derived in order to support our simulation results. In addition, the analytical expression of the CRB of the NLA to the CRB of the ULA ratio is calculated in order to show the advantages of the NLA