Vertical line arrays of vector sensors

A vertical line array (VLA) of vector sensors has a multi-component vector sensor at each sensor position. Vector sensors consist of an omni-directional receiver (Omni), two orthogonal horizontal dipoles, and possibly a vertical dipole. VLA beamforming may be factored into azimuthal processing at each sensor by using a weighted sum of the sensor components and vertical beamforming that combines the vector sensor outputs. Alternative sensor weights, which may depend on vertical steering angle, including cardioids, limacons, and the optimal weights for azimuthally symmetric noise are compared. The vertical dipole's usefulness is limited to sidelobe and grating lobe reduction. For steep vertical steering angles, the optimal weight on the horizontal dipoles becomes large, resulting in an undesirable sensitivity to white noise and tolerance errors. The optimum weights that minimize beam noise subject to an inequality constraint on sensitivity to white noise are derived. For non-symmetric noise, optimal beamforming may cause the mainlobe to squint in azimuth away from the steering direction in pursuit of reduction in directional noise. A simplified optimization approach is introduced that requires a global peak in the steering direction and completely prevents undesirable squinting. The performance of tilted dipoles in azimuthally symmetric noise is compared with other configurations.