Performance analysis of subspace based methods [plane wave direction of arrival estimation]

The authors analyze the performance of two subspace based methods, ESPRIT, and the Toeplitz Approximation Method (TAM), for estimating the direction of arrival (DOA) of plane waves in white noise. In the case of a linear equispaced sensor array, it is shown that ESPRIT, like TAM, can be treated via a state space formulation leading to interesting insights. The state transition matrix estimated by ESPRIT is shown to be related to that obtained by TAM by a diagonal similarity transformation. The performance of these methods is also analyzed. In particular, asymptotic results for the mean squared error in the estimates of the direction of arrival are derived for each of the above mentioned methods. Simple closed form expressions for the one source case are derived, and compared with the corresponding expressions for the Minimum-Norm method and MUSIC. Computer simulations are provided to substantiate the analysis