I really don’t know what you’re trying to do.
The constraint trace(X’X) <= S would not be accepted in that form by CVX, due to appearance of X'*X, which violates CVX’s DCP rules. But it can be reformulated as norm(X,'fro') <= sqrt(S) , which CVX will accept,l presuming thatX is a variable or affine expression which you seem to violate)…
Your last constraint can be written as norm(v(i,:)) <= sqrt(Q)
As for C = [sqrt(P1)*c1;....sqrt(PT)*vT),], you’ll have to explain to me how that is consistent with the overall problem being a convex optimization problem. I’ll assume it’s not unless you show otherwise.
Perhaps you need to more carefully read the following link, which you were previously provided.