Many direction finding methods have been developed these last decades and the performance of some of the latter have been derived with or without modelling errors, jointly with some Cramer Rao bounds (CRB) on the estimated Direction of Arrival (DOAs). However, despite of these works, the link between the array geometry and these performances, or CRB, has been scarcely analyzed, which prevents from optimizing the array design to obtain a specified level of performance. We consider in this paper the general 2D DOA estimation problem from 3D, 2D or ID arrays and we limit the analysis to the single source case. In this context, the first purpose of this paper is to show that both the deterministic and the stochastic CRB, jointly with the variance of DOAs obtained from the MUSIC algorithm, with and without modelling errors, are proportional to the same term which depends on the sensors location. This term analysis allows to develop the second purpose of the paper, i.e. the first tools for an array design methodology for the performance optimization of DOA estimation methods.
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