How to solve a log{convex} problem??

Hello everyone, I am reproducing an article recently. Its constraints are as follows. When the constraint (37) is implemented, the log{convex} situation occurs.
This constraint only has two variables: gm,k[n] and wj.
Obviously, the first part Rm,k[n] is a quadratic term repect to wj. And the constant Im,kj[n] >= 0. Thus, the first part Rm,k[n] is concave. The second part which has the -log function is certainly concave. In conclusion, this constraint is convex.

But when I use cvx, it always says: Illegal operation: log( {convex} ). I understand that in cvx, we should make sure the formula within the log function should be concave. But I have no idea how to write the above convex constraint legally.

Thanks in advance!

5.2.7 Log-sum-inv of Mosek Modeling Cookbook

Mark, thank you so much for responding to my question. But I still have a doubt, that is, the second term (pk[n]β0/Kc+1)/σ2*(H2 + gm,k[n])α/2 is not a summation form, so it can also be used Log-sum-inv method?

That’s just another term being summed.