## 5 Numerical Results  
This section presents the analysis and simulation results for our system. We focus on evaluating our proposed performance metrics, which include the system reliability, packet timeout probability, and outage probability for both the HHT and HDT protocols. Due to the randomness of the channel state, we use Monte Carlo simulation technology for our analysis. To ensure accuracy, we sample a total of \(10^{5}\) loops, and the system parameters are set according to Table 1. \begin{table}
\begin{tabular}{c c} \hline The packet size of HDT protocol & \(L_{1}=K*512\) bits \\ \hline The packet size of HHT protocol & \(L_{2}=512\) bits \\ \hline The time of timeout threshold & \(t_{out}=0.864\) ms [22] \\ \hline Bit error rate & \(BER=10^{-2}\)[22] \\ Channel mean gains & \(\omega_{k}=\Theta_{k}=\Phi_{k}=1\)[22] \\ \hline The locates of BS & \((x_{0},y_{0})=(0,0)\) \\ \hline The pathloss exponent of channel & \(\lambda=4\)[22] \\ \hline \end{tabular}
\end{table} 
Table 1: The default parameters employed in this paper to simulate the system we consider. In Figure 4, we analyze the impact of different distances between the BS and the sensor nodes on the packet timeout probability. We set the coordinates of the four nodes as \((x_{1},y_{1})=(0.6,0.6)\), \((x_{2},y_{2})=(0.55,0.55)\), \((x_{3},y_{3})=(0.5,0.5)\), and \((x_{4},y_{4})=(0.45,0.45)\). The energy-harvesting time of the HHT protocol is \(\alpha_{0k}=0.05\), while that of the HDT protocol is \(\alpha_{0}=0.2\). The packet transmission time for both protocols is \((1-\alpha)_{k}=0.2\). According to our observation, node 4 performs the best out of all nodes, due to its lowest packet timeout probability. This is the case since node 4 can harvest the most energy and has more energy available for packet transmission because of the fact that the distance between it and the BS is the shortest. Furthermore, we note that the packet timeout probability under the HHT protocol is consistently lower than that under the HDT protocol for all nodes. At the same time, under the same conditions, the packet timeout probability using MRC technology is lower than that using SC technology. This is because MRC selected the maximum value of channel gain, which has a higher channel gain than the average value of channel gain selected by SC. Additionally, the packet timeout probability of the MRC technology in the HHT protocol is lower than that of the SC technology in the HHT protocol, and the system performance of the HHT protocol using MRC technology is the best under the same distances. In Figure 5, we examine the impact of energy harvesting effectiveness between single sensors on the packet outages probability for the system. According to [22], we set the coordinates of the sensor nodes to a fixed point \((x_{k},y_{k})=(0.6,0.6)\). We adopt the univariate research concept and set the number of antennas and nodes as \(M=2\) and \(K=4\), respectively. We assign four different energy harvesting efficiencies to four sensor nodes, namely \(\eta_{1}=0.2\), \(\eta_{2}=0.3\), \(\eta_{3}=0.4\), and \(\eta_{4}=0.5\). Additionally, the energy-harvesting times for the HDT protocol and the HHT protocol are denoted as \(\alpha_{0k}=0.05\) and \(\alpha_{0}=0.2\), respectively. Our observations indicate that increasing the energy harvesting efficiency leads to a decrease in the packet timeout probability for both the HHT and HDT protocols. This is because higher energy-harvesting efficiency allows sensor nodes to harvest more energy, which in turn enables them to use more energy for information transmission. This reduces the packet loss rate and leads to improved system performance. Moreover, we have observed that the packet timeout probability of the HHT protocol is consistently lower than that of the HDT protocol under the same energy harvesting efficiency conditions. This can be attributed to the fact that the HHT protocol uses a more refined time slot division and is therefore more sensitive to channel variations.