This is very similar to a problem by the same OP which was solved by @Bien at Let this function be supported by CVX by reparameterizing the key variables in terms of logs… In the previous problem, the OP did not provide the full optimization problem to Bien before his solution, which wound up not allowing its use.
I think Bien’s approach would work quite nicely in this problem if there were no “- 1” term. I don’t see how to deal with that in a way which would be acceptable to CVX.