A Triad of Cardioid Sensors in Orthogonal Orientation and Spatial Collocation—Its Spatial-Matched-Filter-Type Beam-Pattern

This paper proposes a new configuration of acoustic sensors—the collocation of three cardioid sensors in perpendicular orientation, in order to increase the mainlobe-to-sidelobe height ratio (possibly to <inline-formula> <tex-math notation="LaTeX">$\infty$</tex-math></inline-formula>). This paper will analyze such a proposed triad's “spatial matched filter” beam-pattern that is independent of the frequency/spectrum of the incident signals. Specifically, this paper will analytically derive the mainlobe's pointing error in azimuth-elevation, the mainlobe's two-dimensional beam “width,” the necessary and sufficient conditions for a sidelobe to exist, the mainlobe-to-sidelobe height ratio, and the array gain. These above characteristics depend on the cardioids’ “cardiodicity parameter” and on the beam's nominal “look direction.”

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