Mean effective gain of antennas in a wireless channel

The mean effective gain (MEG) is one of the most important parameters for the characterisation of antennas in wireless channels. An analysis of some fundamental properties of the MEG is provided and corresponding physical interpretations are given. Three points are analysed in detail: (i) closed-form expressions for MEG in a mixed environment with both stochastic and deterministic components are provided, showing that the MEG can be written as a sum of gains for the deterministic and stochastic components, (ii) it is shown that under some assumptions, the propagation channel and the antenna are equivalent in the sense that the impact of the channel cross-polarisation ratio (XPR) and the antenna effective cross-polar discrimination on the MEG are symmetrical, (iii) based on the fact that MEG depends on random variables, such as the XPR and antenna rotations because of user´s movements, the average, the minimum and maximum MEG of antennas are defined, respectively. Finally, the maximum effective gain of antennas is derived and shown that it is bounded by 4pieta_rad, where eta_rad is the radiation efficiency of the antenna.