On signal processing and electromagnetic modelling applications in antennas and transmission lines

Abstract: This doctoral thesis is comprised of five parts. The first three parts concern signal processing and electromagnetic modelling of multiport antennas. The last two parts concern signal processing and transmission line theory applied to wave splitting on transmission lines. In Part I, the spherical vector wave expansion of the electromagnetic field is used to completely characterize a multiport antenna. A general framework for modelling an antenna configuration based on measurement data and numerical computation is obtained. The generic electromagnetic model for arbitrary multiport antennas or vector sensors is applied in direction of arrival (DOA) estimation. Next, in Part II using the generic electromagnetic model (from Part I), we obtain the Cramér–Rao bound (CRB) for DOA and polarization estimation using arbitrary multiport antennas. In the Gaussian case, the CRB is given in terms of the transmission matrix, the spherical vector harmonics and its spatial derivatives. Numerical examples using an ideal Tripole antenna array and a non-ideal Tetrahedron antenna array are included. In Part III, the theory of optimal experiments is applied to a cylindrical antenna near-field measurement setup. The D-optimal (determinant) formulation using the Fisher information matrix of the multipole coefficients in the spherical wave expansion of the electrical field result in the optimal measurement positions. The estimation of the multipole coefficients and corresponding electric field using the optimal measurement points is studied using numerical examples and singular value analysis. Further, Part IV describes a Digital Directional Coupler (DDC), a device for wave splitting on a transmission line. The DDC is a frequency domain digital wave splitter based on two independent wide-band measurements of the voltage and the current. A calibration of the digital processor is included to account for the particular transmission line and the sensors that are employed. Properties of the DDC are analyzed using the CRB and an experiment where wave splitting was conducted on a coaxial–cable is accounted for. Finally, in Part V the DDC has been designed and implemented for wave splitting on a medium voltage power cable in a power distribution station using low cost wide–band sensors. Partial discharge measurements are conducted on cross–linked polyethylene insulated power cables. The directional separation capabilities of the DDC are visualized and utilized to separate multiple reflections from partial discharges based on the direction of travel.