# Hybrid NOMA Protocol with Relay Adaptive AF/DF Collaboration and Its Modeling Analysis in NB-IoT
## 3 Performance Modeling Analysis of H-NOMA Protocol
### Relay-Based Adaptive Collaboration and H-NOMA Signal Transmission Process
#### 3.1.2 Collaboration Stage

Table 2: Three different cases representing the distance between the device and the relay. Figure 8: Throughput at different distances between the two devices and the relay (\(\alpha_{2}=0.4,\beta_{2}=0.3\), \(T=1\)). Figure 7: Throughput of system with different power allocations (\(\beta_{2}=0.3\)). The Figure 9 discusses the effect of giving different power allocation factors to the two users on the system outage probability. As can be seen in the figure, when \(\alpha_{1},\alpha_{2}\) is fixed, changing \(\beta_{1},\beta_{2}\) does not have a significant impact on the outage probability of the system. We believe that this is related to the high probability that the system can successfully receive signals during the broadcast phase. Therefore, the power allocation of the relay transmission power is not a key factor that influences the outage probability of the system. However, different values of \(\alpha_{1},\alpha_{2}\) can greatly affect the outage probability. It can be seen that when \(\beta_{2}=0.3\), the closer the power allocation factor given to \(U_{2}\) is to 0.5, the smaller the outage probability of the system for a given transmission power. Next, we analyze \(\alpha_{2}\) to improve system performance. In cases where the system can make multiple retransmissions, we use (44) as an example to analyze what value of \(\alpha_{2}\) can minimize the outage probability. In (44), when \(\alpha_{2}\in\left(0,\frac{1}{2^{R_{th}}+1}\right)\), \(P_{BU_{2}}^{tN}=\Gamma(T,\frac{2^{R_{th}}-1}{\alpha_{2}\cdot\alpha_{2}\mu_{2} \beta_{5}})\), which is a monotonically decreasing function of \(\alpha_{2}\), and when \(\alpha_{2}\in\left(\frac{1}{2^{R_{th}}+1},0.5\right)\), \(P_{BU_{2}}^{tN}=\Gamma\left(T,\frac{2^{R_{th}}-1}{\rho_{5}\lambda_{42}\left(1- \alpha_{2}2^{R_{th}}\right)}\right)\), which is a monotonically increasing function of \(\alpha_{2}\). Thus, the minimum value of the outage probability will be obtained at \(\alpha_{2}=\frac{1}{2^{R_{th}}+1}\). \(\frac{1}{2^{R_{th}}+1}\) is a decreasing function of variable \(R_{th}\), i.e., \(\sup\frac{1}{2^{R_{th}}+1}=\lim\limits_{R_{th}\to 0}\frac{1}{2^{R_{th}}+1}=0.5\). Therefore, it can be obtained that when \(\alpha_{2}\) is closer to 0.5, the system performance is better. In Figure 10, it can be found that as \(\alpha_{2}\) gets closer to 0.5, the system throughput is higher, which verifies our analysis. Figure 10: System throughput with different power allocation factors (\(P_{s}=12\) dB). Figure 9: System outage probability with SNR (\(T=1\)). ## 7 Conclusions

In this paper, we focus on solving the problem of low relay utilization and overuse of resources by users in NB-IoT due to a single relay collaboration mode and a single-user reception mode. In particular, we design a hybrid NOMA protocol for relay adaptively selecting collaboration mode to compensate for the shortcomings of using only AF and DF, as well as only NOMA and OMA. In addition, considering the problem that the transmitted signals want to be received as successfully as possible, we design a mechanism by which the eNB can retransmit the superimposed signals several times during the broadcast phase, extending the hybrid NOMA protocol with relay adaptive selection collaboration approach proposed in this paper. By comparing the performance of the model proposed in this paper with the pure OMA model, we show that the system is more advantageous when two devices are close to the eNB and have higher transmission power while allowing multiple retransmissions from the eNB also improves the system's performance. In the future, we will further investigate the approach proposed in this paper to improve the energy efficiency of this system in NB-IoT.