the following three equations $$\begin{aligned}
\label{eqn : strong interference condition 1}
h_{12}^2 \geq p^2 \frac{P_1 + \sigma_1^2}{\sigma_2^2}, \quad h_{13}^2 \geq \frac{P_1 + \sigma_1^2}{\sigma_3^2}\nonumber\\
h_{21}^2 \geq q^2 \frac{P_2 + \sigma_2^2}{\sigma_1^2}, \quad h_{23}^2 \geq \frac{P_2 + \sigma_2^2}{\sigma_3^2}\\
h_{31}^2 \geq \frac{P_3 + \sigma_3^2}{\sigma_1^2}, \quad h_{32}^2 \geq \frac{P_3 + \sigma_3^2}{\sigma_2^2}\nonumber\end{aligned}$$ (or) $$\begin{aligned}
\label{eqn : strong interference condition }
h_{12}^2 \geq \frac{P_1 + \sigma_1^2}{\sigma_2^2}, \quad h_{13}^2 \geq \frac{P_1 + \sigma_1^2}{\sigma_3^2}\nonumber\\
h_{21}^2 \geq \frac{P_2 + \sigma_2^2}{\sigma_1^2}, \quad h_{23}^2 \geq p^2 \frac{P_2 + \sigma_2^2}{\sigma_3^2}\\
h_{31}^2 \geq \frac{P_3 + \sigma_3^2}{\sigma_1^2}, \quad h_{32}^2 \geq q^2 \frac{P_3 + \sigma_3^2}{\sigma_2^2}\nonumber\end{aligned}$$ (or) $$\begin{aligned}
\label{eqn : strong interference condition 3}
h_{12}^2 \geq \frac{P_1 + \sigma_1^2}{\sigma_2^2}, \quad h_{13}^2 \geq q^2 \frac{P_1 + \sigma_1^2}{\sigma_3^2}\nonumber\\
h_{21}^2 \geq \frac{P_2 + \sigma_2^2}{\sigma_1^2}, \quad h_{23}^2 \geq \frac{P_2 + \sigma_2^2}{\sigma_3^2}\\
h_{31}^2 \geq p^2 \frac{P_3 + \sigma_3^2}{\sigma_1^2}, \quad h_{32}^2 \geq \frac{P_3 + \sigma_3^2}{\sigma_2^2}\nonumber\end{aligned}$$ then, the users can achieve rates given by $$R_i \leq \frac{1}{2}\log\left(\frac{P_i}{\sigma_i^2}\right), \quad i\in\{1,2,3\}.$$ That is, each user can achieve rates within half a bit of their maximum possible rates.

The proof of the lemma is very similar to the proof of [@Sridharan-Globecom Theorem 2]. We describe below a brief outline of the proof.when the channel gains satisfy (\[eqn : strong interference condition 1\]).

*Outline of the Proof:* The 