Implementing Two Generalizations of the Friis Transmission Formula

Two generalizations of the Friis transmission formula are based on the concept of unnamed power gain, defined as the ratio of the available power at the port(s) of one or more receiving antennas to the average power received by the port(s) of one or more transmitting antennas. The first generalization is about one transmitting antenna and one receiving antenna, at any distance, in any environment. The second generalization encompasses the first one. It is about two multiport antenna arrays, one used for emission and the other for reception, at any distance, in any environment. Both generalizations say that the unnamed power gains have two properties, referred to as "symmetry under link direction reversal" and "vanishing sensitivity to terminations for small coupling". The definitions of these properties for multiport antenna arrays are somewhat more involved than the ones applicable to the two-antenna case. We implement these generalizations in numerical experiments comprising two or six antennas, to observe and analyze the behavior of the unnamed power gains and these properties. We also define and investigate a new concept: the rank measure of the unnamed power gain.