The anomalous Doppler resonance is an instability that occurs due to coupling between an electromagnetic wave and a negative harmonic of the electron cyclotron frequency, as such this regime is only achievable in slow-wave media, including plasma.[1-2]In magnetic confinement fusion experiments the generation of fast electrons by Lower Hybrid Current Drive can lead to the criterion for which the anomalous Doppler resonance is fulfilled.A simulation of non-thermal electrons drifting at relativistic velocities along a magnetic field with a background plasma has been developed in the 3D Particle-in-Cell code VORPAL. By tailoring the fast electron distribution so that the number density decreases as the velocity of the electrons increases suppression of the two-stream and Cherenkov instabilities can be achieved. From these experiments indications of the anomalous Doppler instability have been observed. An experiment to test the prediction of simulations is being developed at University of Strathclyde, with current work focussing on the production of energetic electrons to mimic the energetic tail critical to the anomalous Doppler instability. The results of the experiment will benchmark the code and be used to inform further simulations which will have parameters relevant to magnetic confinement fusion and astrophysical phenomena.