Position Error in SGP4

Is there any literature about how much position error there is in SGP4 estimations? I was thinking that someone on my team could make a particularly high gain antenna for our ground station but I don’t want to introduce any pointing losses. Ideally I want to have know how position error is distributed.

Also, can anyone think of a highly directional antenna that wouldn’t be too hard to modify to get a main lobe with a particular width and minimal side-lobes.

The positions provided by the SGP4 model are typically accurate to the order of a km. See the analysis by Vallado (celestrak.com/publications/AIAA/2008-6770/AIAA-2008-6770.pdf). However, this is only true if the age of the orbital elements is not large. Deviations from the predicted orbit can be minimal for orbits that suffer minimally from drag and lunisolar perturbations. For very low orbits the drag will make the elements less accurate very quickly.