A view of the input reflection coefficient of the N-port network model for MIMO antennas

The analysis of MIMO and other multiport antennas requires measurement of their efficiency, as well as other parameters. The total efficiency, as seen by each port, includes the impedance mismatch, i.e., input reflection coefficient, and this must be considered in a multiport context. The input reflection coefficient of a loaded N-port network can be derived with Mason´s rule and a signal flow graph. However, when N is larger than 3, this method becomes complicated. The approach presented in this paper is a matrix method which gives an insightful general expression for the input reflection coefficient for any N. The result is consistent with known results and the Mason´s rule. The makeup of the resulting formulation shows how the input reflection coefficient is impacted by the various scattering parameters of the multiport antenna and the load reflection coefficients at the other ports.