# Brain-Inspired Data Transmission in Dense Wireless Network
## 1 Introduction
In order to correctly assess the reliability of the proposed solutions, deterministic methods such as Fault Trees, Reliability Block Diagrams (RBD), or Markov chains are often used [13]. Unfortunately, in the case of dense networks with a significant number of nodes, the problem of the high computational complexity of these methods becomes crucial. For this reason, the authors used stochastic geometry [16; 17], or more precisely the percolation theory, to assess the reliability of the dense wireless system. Particularly noteworthy here is the percolation threshold, which can be used to determine the critical number of nodes necessary for the correct operation of the assumed network. Initial results have been presented in [18; 19; 20], where in [18] the percolation was applied to evaluate the reliability of wireless network under different nodes density, in [19] the impact of microglia inspired nodes were tested in case of distributed antenna systems, and in [20] network nodes was evaluated in terms of reliability in the case of the limited lifetime of nodes. All mentioned initial works use an idealistic transmission model which omits a very important aspect in case of a dense wireless network - interference. In this research, we extend this work by including an analysis of interference impact on reliability. Moreover, in our prior works, we have applied two research methodologies to evaluate the performance of the biology-inspired dense wireless networks. In particular, we have adjusted the classic LOADng routing algorithm [21] and implemented it in the considered dense wireless transport network. In this case, four different types of HNS-based inspirations for dense wireless networks have been tested. Next, the theoretical analysis using percolation theory has been applied and verified by means of extensive computer simulations. However, in none of our prior work, we have evaluated the real impact of mutual (self-)interference on the overall performance of the system. As we consider a fully distributed system (i.e., the one with no central coordination), the probability of simultaneous data transmission by many nodes located in their close vicinity may be high. Thus, it is necessary to consider the presence of such phenomena. The main contribution of this paper is the evaluation of the impact of interference on the system performance. We did it in two ways, first, we verify the impact of interference in such a dense wireless systems by application of the percolation theory, and second, we carry out extensive computer simulations, where the LOADng algorithm is modified by adding a back-off procedure. In a nutshell, the novel contributions of this paper compared to all prior works, are the following:  
* in this paper, we have performed the final simulations where all previous findings have been jointly included in one computer experimentsnext, the detailed analysis of the self-interference between the nodes has been investigated
* a mathematical analysis of the percolation threshold for the dense wireless network has been provided
* the LOADng routing algorithm has been significantly improved to deal with self-interference. The structure of the manuscript is the following. First, we briefly overview the HNS and how it has inspired us in proposing new modifications in dense wireless networks. Next, we present our system model and scenarios selected for investigation and discuss the research problem, i.e., the evaluation of the expected impact of self-interference phenomena. The next section deals with the reliability analysis, including percolation theory and its implementation in dense wireless networks. Achieved simulation results are then discussed in the following section, and finally, the paper is concluded. * In this paper, we perform the final simulations where all previous findings are jointly included in one computer experiments. * A detailed analysis of the self-interference between the nodes is investigated. * A mathematical analysis of the percolation threshold for the dense wireless network is provided.