I have an optimization problem in the form of

\max\hspace{3mm}R=\sum_{k=1}^K\log_2(1+\gamma_k)

\text{subject to}

\log_2(1+\gamma_k)\ge R\beta_k,\hspace{4mm}\forall k

where \gamma_k is given by

\gamma_k=\frac{|h_{b_k,k}f_k|^2}{1+\sum_{i=1,i\neq k}^K|h_{b_i,k}f_i|^2}

Note that this problem comes with other constraints, which I can express easily in CVX.