Two Figure-8 Sensors of Unequal Directivity in Perpendicular Colocation – “Spatial Matched Filter” Beam Steering

This paper is first in the research literature to analyze the “spatial matched-filter” beam-pattern of an array comprising solely of two figure-8 directional sensors at perpendicular colocation but (possibly) disparate “directivity orders”. This two-element array (strictly without any additional pressure sensor) entails the minimum number of constituent sensors capable of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">two</i>-dimensional spatial filtering over both the azimuth and the elevation. This paper analytically explores how <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">un</i>equal directivity orders between the two sensors would affect the pair's “spatial matched filter” beam steering. The resulting “action-able” insights show which directivity-order combinations grant full maneuverability for the spatial beam toward any azimuthal direction, and which directivity-order combinations can not.