Super-directivity revisited

A special class of super-directive sensors consists of three orthogonal dipoles and an omni directional sensor, all collocated in small volume. A weighted sum of a dipole and the omni-directional sensor results in a cardioid or limacon. In acoustics, the omni-directional sensor measures the scalar pressure while the dipole measures a component of the velocity vector. The product of pressure and velocity is proportional to acoustic intensity. The performance of various approaches to processing vector sensor data is examined. The directional gain available through linear combining is obtained as a function of the combining weights in both two- and three-dimensional isotropic fields. The detection performance of additive processing and multiplicative (intensity) processing is compared for detection. Additive processing is found to be potentially superior. A discussion of null steering with vector sensors is also given. The classical problem of achieved super-directivity with short endfire linear arrays is examined and compared from two points of view.