A Closed-Form Formula of Radiation and Total Efficiency for Lossy Multiport Antennas

This letter proposes a closed-form expression of the radiation and the total efficiency for the entire lossy multiport antenna system with simultaneous excitations. The equivalent circuit model and the detailed analysis process of the two-element lossy multiport antennas as well as a generalized expression for N-element lossy multiport antennas were considered. The required inputs to the closed-form expression are S-parameters, embedded radiation efficiency of each antenna element, and radiation efficiency of the entire antenna pair with identical simultaneous excitations. This method can be used for the analysis of multiple-input-multiple-output (MIMO) and antenna arrays, when the multiple elements are simultaneously excited with arbitrary amplitude and phase. To validate the proposed method, two different lossy MIMO antennas, namely, a pair of parallel end-fed dipoles and 4 × 1 layout printed bowtie antennas, were studied with various amplitude- and phase-feeding schemes. Full-wave numerical simulations were performed to provide inputs to the closed-form expression. Excellent agreement was observed between the radiation efficiencies of these antennas obtained through the closed-form expression and the full-wave numerical simulations, which demonstrates accuracy of the proposed closed-form expression. Furthermore, the proposed method can significantly reduce the total number of measurements for charactering the efficiency of the entire simultaneously excited lossy multiport antennas.