# Brain-Inspired Data Transmission in Dense Wireless Network
## 4 Network Reliability Assessment through the Percolation Theory
### Experiment Setup  
To evaluate the investigated concept of highly simplified transmission in dense wireless networks, we conducted extensive computer experiments. The whole simulator was prepared using Matlab version 9.4.0.813654 (R2018a) with standard libraries, and all simulation runs were carried on the standard personal computer PC with specification i7-6500u, 12 GB RAM, under Windows 10 system. In our experiment analysis, we apply normalized values to generalize it and make it independent from the applied physical values. Thus, the analyzed system consists of a network of \(N=\{30\}\) randomly distributed neuron-nodes. These devices mirror neurons in the nervous system, i.e., they are designed to transmit information to each other. Moreover, once the neuron-nodes are deployed, \(M=0.1N\) microglia-nodes are added, deployed also uniformly in the same area. (Please note that in this investigation phase we intentionally do not deploy astrocyte-nodes.) The analyzed area is a square with the side \(D=10\). The devices are characterized by the transmitting power \(P_{0}=P_{l}\) and the range \(r=1\). The required signal to noise and interference level was set at \(\theta^{*}=1\) (in a linear scale) and the noise level at \(\sigma_{n}^{2}=1\). All simulation parameters used in this part of our work are summarized in Table 1. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Description** & **Value** \\ \hline \(N\) & number of the neuron nodes & 30 \\ \hline \(M\) & number of the microglia nodes & \(M=0.1\cdot N=3\) \\ \hline \multirow{2}{*}{\(D\)} & size of the considered area & \multirow{2}{*}{10 [distance units]} \\  & (related to the cell range size) & \\ \hline \(r\) & transmission range (cell range) & 1 [distance unit] \\ \hline \(P_{0}=P_{l}\) & transmit power of any node & 1, 10, 30, 40 or 50 [power units] \\ \hline \(\sigma^{2}\) & noise power & 1 [power units] \\ \hline \(\theta^{*}\) & required SINR level & 1 [linear scale] or 0 [dB] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters used in the first phase of the study. During the experiment, we assume that the simulations searches for the percolation threshold value that ensures correct operation of the network. The simulations were averaged (repeated) over different topologies and different device operation probability levels. An example of the analyzed topology is shown in Figure 2. One may observe the presence of wireless nodes (corresponding to neurons, denoted by black dots), the source, and the destination. In the following results, we show the size of the SG cluster as the function of the probability \(p_{c}\), which is the probability of proper functioning of any wireless node. Each simulation result is presented as a solid line and the additional dashed line is a fourth-degree polynomial approximation. As mentioned above, the greatest value of SG is achieved at the percolation threshold, i.e., \(p_{T}=\arg\max_{p_{c}}SG(p_{c})\). The smaller is the \(p_{T}\), the better is the reliability of the network (i.e., fewer nodes are required to guarantee permeability). In other words, when the percolation threshold decreases, the network will be able to operate in heavier conditions (with greater error probability at a certain link). In Figures 3 and 4, one may observe the changes of SG as function of different transmit power levels and for different number of neuron-nodes. One may observe that when the transmit power increases (so the coverage area increases as well, and, in consequence, for the fixed node density the number of nodes located in interference areas increases) the percolation threshold slightly shifts left, but the minimum is achieved for \(p_{c}\approx 0.25\). However, the change in node density not only shifts the curves left, but also emphasizes the effect that for higher transmit power the percolation threshold also decreases. In Figure 5, one may observe the changes of SG as function of different number of nodes.