Because of the sunrise simulation, the housing, or a least a major part of it must be translucent or transparent. Translucent materials are preferred as the diffusion of the light will make the housing light up as a whole. It's an option to use transparent materials for the housing and stick a translucent film onto it.
- Acrylic : can be laser cut
There's a chance that the electronics of the generate too much EM-noise, so that the antenna and receiver need to be placed in a separate housing.
A suitable housing is the Hammond 1593NBK (Farnell €2.75).
If you want to build a really cheap enclosure for your antenna with hot glue and some scrap piping, have a look here.