Characterization of reverberation chambers for OTA measurements of wireless devices: Physical formulations of channel matrix and new uncertainty formula

The paper deals with reverberation chambers for over-the-air (OTA) testing of wireless devices for use in multipath. We present a formulation of the S-parameters of a reverberation chamber in terms of the free space S-parameters of the antennas, and the channel matrix in the way this is known from propagation literature. Thereby the physical relations between the chamber and real-life multipath environments are more easily explained. Thereafter we use the formulation to determine the uncertainty by which efficiency-related quantities can be measured in reverberation chamber. The final expression shows that the uncertainty is predominantly determined by the Rician K-factor in the reverberation chamber rather than by the number of excited modes, assumed by previous literature. We introduce an average Rician K-factor that is conveniently expressed in terms of the direct coupling between the transmitting and receiving antennas (corresponding to a line-of-sight contribution) and Hill's transmission formula (corresponding to a multipath or non-line-of-sight contribution). The uncertainty is expressed in terms of this average K-factor and geometrical mode stirring parameters, showing strong reduction by platform and polarization stirring. Finally the formulations are verified by measurements, and the new understanding of uncertainty is used to upgrade an existing reverberation chamber to better uncertainty.