Statistical Analysis of Antenna Efficiency Measurements with Non-Reference Antenna Methods in a Reverberation Chamber

Reverberation chambers (RCs) have become a popular testing facility in antenna efficiency measurements. Unlike the standard reference antenna method, the non-reference antenna methods have been proposed to measure the antenna efficiency in the absence of a reference antenna. However, the statistical distributions of the measured (estimated) total antenna efficiencies using the non-reference antenna methods have not been derived before, making it difficult to perform a rigorous statistical analysis of the antenna efficiency measurement. In this paper, the distributions of the measured total antenna efficiencies using two non-reference antenna methods in an RC are derived, based on which the statistics (e.g., expectation and variance) of the measured total antenna efficiencies are also derived. It is shown that the original non-reference antenna methods (estimators) are only asymptotically unbiased and are biased with limited samples, thus corresponding unbiased estimators are proposed and analyzed. The derived analytical expressions of the statistics of the total antenna efficiency estimators are verified by simulations and measurements in an RC. The performances of different non-reference antenna methods are discussed.