<title>Two-way beam patterns from ultrawideband arrays</title>

Abstract

For narrowband arrays, given the one way patterns (the transmit beam pattern and the receive beam pattern), the composite two way (transmit / receive) beam pattern may be found by beam pattern multiplication. However, as is shown, beam pattern multiplication does not generally hold for ultra-wideband arrays. Transmit beam patterns from ultra-wideband arrays have been described previously, and receive beam patterns are similar. Here examples (three dimensional plots) of two way, transmit / receive, beam patterns are given in which beam pattern multiplication does not hold. A theory and equations are given for mathematically deriving the two way patterns from the individual one way patterns. This theory uses the active imaging Green's function. The theory covers beam pattern multiplication as a special case, and the conditions required for beam pattern multiplication to hold are derived. For the far field two way linear array pattern, in the case of monochromatic transmission, the theory produces the familiar sinc squared function.