Optimizing V antenna arrays using a Bayesian DOA estimation criterion

Experimentations have shown V-shaped uniform antenna arrays to be near-optimum for estimating the direction of arrival of a far-field source, whether the source position is fixed or random. We consider, as performance measure, the expected Cramer-Rao bound, normalized (for comparison purposes) to that of the commonly used uniform circular arrays. We study in details the behavior of V arrays in this context. For large-sized V arrays, the performance measure shows a simple expression, enabling analytical solution of the subsequent array-geometry optimization problem. We obtain closed-form expressions of the orientation, shape and performance of optimal V arrays and learn about their ability to benefit from the available prior about the source direction.