cvx_begin
variable y(3,1) complex
minimize (quad_form(y,RU))
subject to
y’y==N
cvx_end
y is a 31 complex vector，RU is a 3*3 comlpex matrix.N is a constant。

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