What do you plan to do with Sigma_i? In order fro CVX to be applicable, the problem needs to be a convex optimization problem.
If what you need is the trace, you can reformulate using
trace(H*V*V'*H') = square_pos(norm(H*V,'fro')), and make use of trace being linear to build up the trace of the overall thing.
Or if you only need to use this for a quadratic form, you can form each individual quadratic form, then take the sum of the quadratic forms.