Time Reversal-MUSIC and degrees of freedom of scattered field

It is investigated how Time Reversal MUSIC behaves when the number of scatterers is more than two. It is shown that if a little amount of noise corrupts data there is an intrinsic limit on the number of scatterers that can be successfully detected. This number turns to be the so-called number of degrees of freedom of the scattered field. Therefore, it is found that Time Reversal MUSIC works well as long as the number of scatterers does not exceeds the degrees of freedom corresponding to the spatial region within they reside.