Higher-order figure-8 sensors in a pair, skewed and collocated-Their azimuthal "spatial matched filter" beam-pattern

Two figure-8 sensors, differently oriented but collocated, can facilitate azimuth- elevation two-dimensional beamforming that is invariant of the frequency spectrum of the incident signal. For such a pair of identical figure-8 sensors of any arbitrary directivity-order, their spatial matched filter beam-pattern is characterized analytically here in this paper. This paper shows that the beamformer would suffer a high pointing bias if the figure-8 sensors' directivity-order exceeds one. Other characteristics of the beam-pattern are also analytically explained herein.