Perspective effects are tied to the field of view (FOV) of the camera, whether it be a real or a virtual camera. One of the key considerations in creating a scene that matches the FOV of a real camera is getting the scale of the model correct. If your model is very small, then you need a very low lens setting (wide FOV) to imitate the effects of a wide angle lens. If you scale the model up some, you can use a somewhat higher lens setting (narrower FOV) and get similar effects without the distortion of the extremely low Lens settings.
I haven’t used it yet but v2.48, just released, has some atmospheric haze features that might be useful for you. Not sure if they work with the backbuffer, though If you want to fake it, try using the Mist function and tweaking the backbuffer image by lowering its contrast and saturation by small amounts (this could perhaps be done in the Compositor by using the BG image on billboard plane, btw, in which case the Mist would affect the billboard rendering).