It appears that you have copied a problem out of the paper https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=7990198 without understanding it.
Apparently, you are trying to solve the paper’s problem (33), which is proven to be a convex optimization problem in the paper’s Appendix B. The proof of convexity in that appendix provides a road map for how to formulate the problem in CVX, with use of log_sum_exp being the key.
You will need to read the paper more carefully in order to understand how the solution to problem (33) fits into a larger algorithm (algorithm 1) for solving a higher level non-convex problem of interest.
Your use of rel_entr is as a substitute for log, as described in 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 . In your case, I don’t recommend distracting yourself with that until you get a formulation which is accepted by CVX. Also niote that instances of log occurring in what will need to be handled via log_sum_exp, should indeed be handled by log_sum_exp, without use of rel_entr.
Also note that terms of the form 2^x will need to replaced by exp(log(2)*x) when determining the argument for log_sum_exp.