## 4 Outage Performance
With the increase of the number of relays, the gap between the outage probability of U\({}_{2}\) caused by these two schemes gradually becomes smaller, because the existence of the link U\({}_{1}\)\(\rightarrow\)U\({}_{2}\) is harmonized by the excessive number of relays. Figures 3 and 4 show the impact of the transmit power of the primary and the interference threshold on the secondary outage performance for the different number of relays, respectively. Obviously, the impact of the transmit power constraint and interference constraint imposed by the primary on the secondary cannot be ignored. On the one hand, too high transmit power of the primary can significantly degrade the signal quality of the secondary network; on the other hand, a lower interference threshold, while ensuring QoS in the primary, may cause the secondary to adjust to a suitable (lower) transmit power. However, if the interference threshold constraint is relaxed, the outage probability of U\({}_{1}\) and U\({}_{2}\) will stabilize when \(I_{th}>35\) dB. This result shows that the outage performance improves until a certain lower limit of the outage probability determined by the interference constraint of the primary network. Figure 2: Outage probability of U\({}_{1}\) and U\({}_{2}\) versus \(P_{0}\) with different number of relays, where \(P_{t}=30\) dB, \(I_{th}=25\) dB, \(\alpha_{2}=0.8\), \(R_{2}=1.2\) bps\(/\)Hz and \(R_{1}=1.0\) bps\(/\)Hz. Figure 5 plots the outage probability of \(\mathrm{U}_{2}\) versus the maximum transmit power \(P_{0}\) for different signaling. At the end of the first slot, \(\mathrm{U}_{1}\) sends four kinds of signaling to the relays according to its decoding results. When \(\Theta\in\{11,01\}\), the optimal relay assists \(\mathrm{U}_{2}\) with full power. In particular, when \(\Theta\) = '11', \(\mathrm{U}_{1}\) will give aid to \(\mathrm{U}_{2}\) as much as possible if there is no relay that satisfies the condition. However, when \(\Theta\in\{10,00\}\), the optimal relay allocates power to \(\mathrm{U}_{1}\) and \(\mathrm{U}_{2}\) with adaptive power allocation strategy, and opportunistically serves \(\mathrm{U}_{2}\) while satisfying the QoS of \(\mathrm{U}_{1}\). Therefore, the outage performance of \(\Theta\in\{11,01\}\) is better than that of \(\Theta\in\{10,00\}\), and \(\mathrm{U}_{2}\) has the best outage performance when \(\Theta\) = '11'. As shown in Figure 3, The outage probability is the lowest when \(\Theta\) = '11', followed by  
\(\Theta\) = '01', and similar when \(\Theta\) = '10' and \(\Theta\) = '00', which just verifies the correctness of the above analysis. In Figure 6, we investigate how the power allocation factor \(\alpha_{2}\) at BS affects the outage probability of the secondary users for different target rates. As \(\alpha_{2}\) increases, the outage probability decreases and then increases for both U\({}_{1}\) and U\({}_{2}\), which implies that an optimal \(\alpha_{2}\) can be found to optimize the outage performance of the secondary. Compared to the cooperative scheme without the link U\({}_{1}\)\(\rightarrow\)U\({}_{2}\), the proposed cooperation achieves optimal outage performance by allocating less power to U\({}_{2}\) since the presence of the link U\({}_{1}\)\(\rightarrow\)U\({}_{2}\) improves the diversity gain. It can also be observed that the outage performance is enhanced significantly with low target rates, indicating that the high target data rate of the user side will adversely affect the system outage performance. When decreasing the target rate, the gap between the outage probability of two users gradually decreases, because the achievable rate at the far user is maximized through adaptive power allocation. Figure 5: Outage probability of U\({}_{2}\) versus \(P_{0}\) in different cases \(\Theta\), where \(P_{t}=30\) dB, \(I_{th}=25\) dB, \(\alpha_{2}=0.8\), \(R_{2}=1.2\) bps\(/\)Hz and \(R_{1}=1.0\) bps\(/\)Hz. Figure 7 shows the impact of target rate \(R_{2}\) on the secondary outage performance for different \(R_{1}\).