\begin{align}
   \label{eqn:achievablerates}
&R\big(\beta^{\hat{k}_1}_1, \beta^{\hat{k}_2}_2\big) = \frac{T_D}{T}\log_2\bigg(1 +
\frac{P\big|H^{ff}(\beta^{\hat{k}_1}_1, \beta^{\hat{k}_2}_2)\big|^2}{\sigma^2}\bigg),
\end{align}
