Clear-air analytical and empirical K-Factor determination and characterization for terrestrial microwave LOS link applications.

Abstract

The transmission media, that is, the atmosphere, through which terrestrial and satellite signals traverse, is irregular. Thus, one requires proper knowledge on how variations in atmospheric refractive conditions will affect the optimal performance of terrestrial and satellite links. Under clear-air conditions, atmospheric changes will mainly involve variations in atmospheric pressure, relative humidity and temperature, which are the key to defining the way signals are refracted as they travel from the transmitter to the receiver. Accurate knowledge of these variations can be acquired through proper modeling, characterization and mapping of these three atmospheric quantities, in terms of the refractive index, refractivity gradient or the effective earth radius factor (k-factor). In this dissertation, both parametric and non-parametric modeling and characterizing, interpolation and mapping of the k-factor for South Africa is done. Median (k50%) and effective (k99.9%) k-factor values are the ones that determine antenna heights in line of sight (LOS) terrestrial microwave links. Thus, the accurate determination of the two k-factor values is critical for the proper design of LOS links by ensuring that adequate path clearance is achieved, hence steering clear of all obstacles along the radio path. Thus, this study is critical for the proper design of LOS links in South Africa. One parametric method (curve fitting) and one non-parametric method (kernel density estimation) are used to develop three-year annual and seasonal models of the k-factor for seven locations in South Africa. The integral of square error (ISE) is used to optimize the model formulations obtained in both cases. The models are developed using k-factor statistics processed from radiosonde measurements obtained from the South African Weather Service (SAWS) for a three year period (2007-2009). Since the data obtained at the seven locations is scattered, three different interpolation techniques are then explored to extend the three-year annual and seasonal discrete measured k-factor values for the seven locations studied to cover the rest of the country, and the results of the interpolation are then presented in the form of contour maps. The techniques used for the interpolation are kriging, inverse distance weighting (IDW) and radial basis functions (RBFs). The mean absolute error (MAE) and the root mean square error (RMSE) are the metrics used to compare the performance of the different interpolation techniques used. The method that produces the least error is deemed to be the best, and its interpolation results are the ones used for developing the contour maps of the k-factor.