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This article focuses on the estimation of the direction of Arrival based on the interpolation approaches of the sparse array. Such as the minimum redundancy array, co-prime array, and the nested array have attracted much attention, especially for a non-linear array antenna. We analyze the effect of antennas locations errors on overall estimation performance for deterministic and stochastic error models and to improve the estimator performance in the case of uncorrelated sources of signals in spatially-smoothed MUSIC scenarios. In two scenarios: we determine the Crame&#x0301;r-Rao bound in the case of the antennas locations are perfect, and in other cases, we take into account antennas locations errors. For the first scenario, the Crame&#x0301;r-Rao bound converges as the SNR increase. For the second scenario, the Signal-to-noise ratio increases to infinity, to achieve the same Crame&#x0301;r-Rao bound as in the first scenarios. There is a significant gap between the Crame&#x0301;r-Rao bound values in a situation where antennas locations errors are considered, and when other locations errors are not considered. This disparity shows that unknown antenna locations errors have a significant impact on the estimated achievable performance of the direction of Arriva of scattered linear matrices.

Stochastic and Deterministic Framework for Modeling the Effect of Antennas Location Error on DOA Estimation