Effects of sensor placement on acoustic vector-sensor array performance

We consider the role played by the sensor locations in the optimal performa nce of an array of acoustic vector sensors. First we derive an expression f or the Cramer-Rao bound on the azimuth and elevation of a single far-field source for an arbitrary acoustic vector-sensor array in a homogeneous whole space and show that it has a block diagonal structure, i.e., the source loc ation parameters are uncoupled from the signal and noise strength parameter s. We then derive a set of necessary and sufficient geometrical constraints for the two direction parameters, azimuth and elevation, to be uncoupled f rom each other. Ensuring that these parameters are uncoupled minimizes the bound and means they are the natural or "canonical" location parameters for the model. We argue that it provides a compelling array design criterion. We also consider a bound on the mean-square angular error and its asymptoti c normalization, which are useful measures in three-dimensional bearing est imation problems. We derive an expression for this bound and discuss it in terms of the sensors' locations, We then show that our previously derived g eometrical conditions are also sufficient to ensure that this bound is inde pendent of azimuth. Finally, we extend those conditions to obtain a set of geometrical constraints that ensure the optimal performance is isotropic.