I think you can go with photoshop and draw the white circle in it in the size you need it, the other area should be black. Means finally you have a black sheet with a fat white circle in it ……THE RING…..(don't pick the phone if it is calling now, if you know what I mean heheh)
Then apply this picture file to the surface material you are going to use for the floor. I think you can then emit the particles from the white area, there are also tutorials in the net, how to do it. There is also a book….let me check….what describes exactly what you are looking for. Will come back!!!