Well, you have a non-convex problem. If the convex relaxation y^Hy <= N does not produce an acceptable solution, then you will need to use a non-convex solver, and CVX can not be used.
Edit. Erling posted seconds before me. Anyhow, you will not be able to prove your model is convex, because it is not*
*unless N = 0, in which case the problem is rather trivial