about the strong interference condition at the cognitive receiver (Rx3).

-   **Strong interference at the primary users (Rx1 and Rx2):** We illustrate the condition for Rx1 and the one for Rx2 follows due to the symmetry. In the first scheme, condition at Rx1 is similar to Rx3 and it is assumed that $m_2$ and $m_3$ jointly cause strong interference, which is shown in the first terms of (\[eqn:set1\_I\]) and (\[eqn:set1\_III\]). Note that, the asymmetric nature of the conditions, compared to the one for Rx3, is due to the cognition capability of Tx3, i.e., $x_3$ depends on $m_1$ and $m_2$ in addition to $m_3$. However, in the second scheme, it is assumed that the interference caused by $m_2$ at Rx1 is stronger than the joint received signals of $m_1$ and $m_3$ (first term of (\[eqn:set2\_III\])). Therefore, it is possible to decode $m_2$ first. The second level for the strong interference condition at Rx1, assumes that after decoding $m_2$, the cognitive message ($m_3$) causes strong interference in comparison to the desired message ($m_1$) (first term of (\[eqn:set1\_III\])).

The above intuitions are summarized in Table \[tbl:str\_cond\].

                 Tx3 $\rightarrow$ Rx1             Tx3 $\rightarrow$ Rx2              Tx1 $\rightarrow$ Rx2               Tx2 $\rightarrow$ Rx1                                  Tx1 and Tx2 $\rightarrow$ Rx3
  