CVX reported your problem to be infeasible (as seen in Status), not unbounded (it was solving the dual problem).
First: Rescale the input data so that all non-zero input data is within a small number of orders of magnitude of one.
Second: Use Mosek if available to you, otherwise follow the advice at CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions
Then see what happens. If the problem is still reported infeasible, follow the advice at https://yalmip.github.io/debugginginfeasible , all of which except for section 1 also applies to CVX. Of course if your problem really is infeasible, removing some constraints (for instance, the LMI constraints you mention) might make the problem feasible.