Is there anyway to specify that the solution to a convex optimization problem must be a white noise?

is there anyway to specify that the solution to a convex optimization problem must be a white noise

Invoke CVX’s white noise mode:
cvx_begin white_noise

No, seriously, what specifically does it mean that the solution of a convex optimization problem is a white noise? Do you have a concrete definition of what that would be for your problem, and can you specify that in such a way that your entire optimization problem, including the white noise “constraint”, is convex? If so, and you are having difficulty figuring out how to formulate that in CVX, then perhaps forum readers can provide assistance.