## 2 Channel Reliability Modeling for 5G Communications
### Wireless Channel Model  
In wireless communication networks, to study the performance of the network, the most important thing is to test the reliability of the network communication channel, so it is necessary to establish a reasonable wireless channel model. Before studying the channel of the network, it is necessary to understand the propagation characteristics of electromagnetic waves in the wireless channel. The wireless channel is a very complex dynamic channel, electromagnetic wave propagation in space is mainly direct, reflective, scattered, diffracted, etc. Electromagnetic waves through the wireless channel will produce attenuation so that the signal strength received at the receiving end is weakened; this phenomenon is called fading. To provide a more intuitive explanation of the fading phenomenon in wireless channels, we created Figure 2. Figure 2 shows that the fading of wireless channels mainly includes large-scale fading and small-scale fading. Large-scale fading includes path loss and shadow fading, while small-scale fading mainly includes Rayleigh fading. Path loss is directly proportional to propagation distance and is influenced by the propagation environment. High path loss can lead to a decrease in the power of the received signal, thereby reducing the signal-to-noise ratio (SNR) and affecting signal demodulation and correct data reception. Shadow fading is a random signal attenuation caused by large obstacles (such as buildings) during the propagation of wireless signals, usually modeled as a log-normal distribution. This can lead to uneven signal coverage. Some areas may experience a significant decrease in signal strength due to signal obstruction, affecting communication quality. Rayleigh fading is a small-scale fading model used to describe the  
Figure 2: Various types of fading in wireless channels. rapid changes of wireless signals in multi-path environments, typically used to simulate wireless channels in urban environments. This kind of fading can lead to rapid fluctuations in the signal, affecting its stability and reliability, especially in high-speed data transmission. In this study, a composite channel fading model considering path loss and shadow fading was used to study the reliability of wireless networks. In a wireless communication network, all data packets are used to transmit information over a wireless channel. The source node and the nth (n \(\in\)\(\{1,2,\cdots,\text{N}\}\)) relay node are called node 0 and node n, respectively, and the destination node is called node N + 1. Suppose node n (n \(\in\)\(\{1,2,\cdots,\text{N}\}\)) sends a signal to node n + 1. The quality of the received signal can be measured by the SNR at the receiving end, which can be expressed as  
\[\Gamma_{\text{n}}=\frac{p_{\text{n}}^{t}h_{\text{n}}}{n_{0}},\forall\text{n} \in\{1,2,\cdots,\text{N}\} \tag{1}\]  
where \(p_{\text{n}}^{t}\) is the transmit power of node n. n\({}_{0}\) denotes the background noise power of the receiver. \(h_{\text{n}}\) denotes the channel gain of the wireless channel between node n and node n + 1, which, in dB form, can be expressed as  
\[\left[h_{\text{n}}\right]_{dB}=\left[G\right]_{dB}-\eta\left[\frac{d_{\text{n }}}{d_{ref}}\right]_{dB}-\left[\xi\right]_{dB} \tag{2}\]  
where \(\left[x\right]_{dB}\) means \(10\text{log}_{10}\)\(x\). \(G\) is a dimensionless constant indicating the path loss coefficient at the reference point \(d_{ref}\), the value of this parameter depends on the characteristics of the antenna as well as the average channel attenuation. \(\eta\) indicates the power loss index of the wireless channel, the value of which depends on the area and environment where the wireless channel is located, and its value usually ranges from 2 (in free space) to 6 (in the urban downtown area) [21]. \(d_{\text{n}}\) indicates the reference distance (the reference point must be in the far-field area of the antenna). \(d_{ref}\) indicates the straight line distance between node n and node n + 1 (the reference point must be in the far-field area of the antenna).