On statistics of the measured antenna efficiency in a reverberation chamber

In this paper, the distribution of the measured antenna efficiency in a reverberation chamber (RC) is derived, based on which the statistics (e.g., mean and variance) of the measured antenna efficiency are studied. It is shown that the standard method (proposed in IEC 61000-4-21) for measuring antenna efficiency results in a consistent estimate. However, the standard estimator is only asymptotically unbiased (as the independent sample number $N$ goes to infinity) and it is biased for a finite $N$. The derived analytical expressions for the statistics of the antenna efficiency estimator are verified by simulations as well as RC measurements. In order to use the analytical expressions of the estimation statistics in practice, one needs to estimate the independent sample number $N$ from the measurement. This can be done based on a single measurement. Thus, using the derived estimation statistics, one can characterize the measurement performance of the antenna efficiency based on a single measurement, instead of directly estimating the statistics by performing many independent measurements.