The Radiation and Transducer Efficiencies of a Multiport Antenna Array

We derive some general properties of generalized Rayleigh ratios, and use these properties to present a detailed theory of two efficiency metrics relevant to a specified excitation of a multiport antenna array (MAA) by a linear time-invariant (LTI) multiport generator. These efficiency metrics are the transducer efficiency and the radiation efficiency. To define the excitation and compute the transducer efficiency and the radiation efficiency, we consider six different variables. We then define and study four new efficiency metrics relevant to unspecified excitations: the minimum transducer efficiency, the transducer efficiency figure, the minimum radiation efficiency, and the radiation efficiency figure. We also look at their connection with the minimum power transfer ratio during emission and the power match figure. We discuss the relevance of the theory presented in this article to the design of an MAA, and to an actual configuration comprising a transmitter, the antenna outputs of which need not behave like an LTI multiport.