Using a new framework for horn antenna optimization, a first frequency-independent horn antenna for a plasma positioning reflectometer (PPR) is designed. This hardware optimization is a new approach aiming on lowering the computational complexity of PPR interpretative models able to extract profiles and fluctuations of electron density and temperature from reflectometry measurements. PPR measurements are a strong candidate to provide real-time feedback for plasma position control in long-discharge fusion tokamaks such as ITER and DEMO, which requires fast interpretative models. Reducing the computational complexity of these models is therefore critical. In this paper, ray tracing simulations in the poloidal plane are used to compare different radiation patterns and evaluate them on multiple performance criteria. An antenna shape leading to a frequency-independent far-field radiation diagram is found with the PROFUSION optimizer and a prototype of this antenna is tested against an unoptimized conical reference antenna. The ray tracing performance criteria indicate that fundamental Gaussian frequency-independent antennas perform well, albeit in general worse than same-sized frequency-dependent antennas. Furthermore, it is seen that the pyramidal ITER gap 6 antenna performs well given the spatial constraints and that more performant antennas could be used, when more space was available. The prototype testing reveals challenges in obtaining frequencyindependent characteristics within a tokamak blanket environment, which is additionally complicated by misalignment risks.