The high amount of scientific and communications data produced by low earth orbiting satellites necessitates economical methods of communication with these satellites. A volumetric phased array for demonstrating horizon-to-horizon electronic tracking of the NASA satellite EO-1 was developed and demonstrated. As a part of this research, methods of optimizing the elemental antenna as well as the antenna on-board the satellite were investigated. Using these optimized antennas removes the variations in received signal strength that are due to the angularly dependent propagation loss exhibited by the communications link. An exhaustive study using genetic algorithms characterized two antenna architectures, and included optimizations for radiation pattern, bandwidth, impedance, and polarization. Eleven antennas were constructed and their measured characteristics were compared to those of the simulated antennas. Additional studies were conducted regarding the optimization of aperiodic arrays. A pattern-space representation of volumetric arrays was developed and used with a novel tracking algorithm for these arrays. This algorithm allows high-resolution direction finding using a small number of antennas while mitigating aliasing ambiguities. Finally, a method of efficiently applying multiple beam synthesis using the Fast Fourier Transform to aperiodic arrays was developed. This algorithm enables the operation of phased arrays combining the benefits of aperiodic element position with the efficiency of FFT multiple beam synthesis. Results of this research are presented along with the characteristics of the volumetric array used to track EO-1. Experimental data and the interpretations of that data are presented, and possible areas of future research are discussed.