On isotropic circular arrays of anisotropic sensors

Uniform circular arrays are popular in direction finding applications because they show to be isotropic, i.e. they exhibit the same accuracy (in terms of the Cramer-Rao bound) at all possible planar look directions. We prove that this is not absolutely true if the constituent sensors are not isotropic. For instance, we specify how the anisotropic sensors should be directed and how many are needed in order to ensure an isotropic behavior of the array. We study, in more details, the performance of arrays of cardioid sensors, including anisotropic arrays of cardioid sensors.