Additional Insights into Chamber Effects in the Gain Extrapolation Data using Empirical Mode Decomposition

Gain extrapolation data as a function of antenna distance is influenced by reflections in a chamber, manifested as ripples riding on otherwise smooth response data. A previous study introduced a method to analyze and remove the ripples by transforming the antenna response data to k-space via Fourier transform, and applying a filter in the k-space. The Fourier analysis assumes the antenna response is stationary as a function of its position. Because of the large travel distance in the gain extrapolation measurement, the stationary assumption cannot be guaranteed, especially for the influence from chamber reflections. As a result, in k-space, the reflected signals are smeared, making it difficult to identify and filter out the reflections. In this study, we apply the Empirical Mode Decomposition (EMD) and Hilbert-Huang Transform (HHT) to analyze the nonstationary antenna response data. The EMD is especially suited to analyze non-stationary empirical data. It decomposes the measurement data into intrinsic mode functions, from which localized spectrum at each antenna position can be derived using HHT. The position-based spectrum can provide additional insights into the reflection sources, such as how the spectral contents of the reflections vary as the antenna travels along the track. Unlike the Fourier method, EMD can operate on real valued data (e.g., the magnitude of the antenna response), so there is no need to obtain the vector response data. As a result of the EMD process, "clean" data with minimal chamber influence is obtained, which can be used to compute the far field gain. It provides yet another powerful post processing algorithm to reduce chamber effects in the gain extrapolation method.