Performance analysis of ESPRIT and TAM in determining the direction of arrival of plane waves in noise

The authors evaluate two subspace-based methods, ESPRIT and the Toplitz approximation method (TAM), for estimating the direction of arrival (DOA) of plane waves in white noise in the case of linear equispaced sensor array. It is shown that the least-squares versions of ESPRIT and TAM result in the same estimate and are statistically equivalent. It is also shown that, asymptotically, the estimates obtained using least-squares ESPRIT and total-least-squares ESPRIT have the same mean-squared error. Expressions for the asymptotic mean-squared error in the estimates of the DOA are derived for both methods. Simple closed-form expressions are derived for the one- and two-source cases to get further insight. Computer simulation results are provided to substantiate the analysis