Performance Analysis Of Large Scale Wireless Sensor Networks Based On Random Geometry

With the rapid development of wireless sensor networks, its scenarios and applications are expanded. Nevertheless, the diversification of node distribution which make the network topology and network performance has become increasingly complex. Therefore, researching on the performance of large-scale wireless sensor network is of great significance.Energy consumption problem and network transmission capacity of wireless sensor network are the key performance indicators. This article around the energy consumption of wireless sensor network and transmission capacity, and selects hexagonal monitoring area which has the best coverage, and use stochastic geometry theory to study the distribution of nodes as follows:To begin with, this article introduces the concept of stochastic geometry theory and primary role. For random distribution node, we calculate the cumulative distribution function (CDF) and the probability density function (PDF) in a regular hexagon using stochastic geometry theory, and the functions are simulated by Monte Carlo method.In addition, according to the probability density function of the nodes which could be communicated with each other, we obtain the distance expectations of nodes. And we use the distance expectations to study network point average statistics energy consumption. Meanwhile, in order to reflect the network energy consumption better, node communication probability is proposed. And we use the communication probability to study the weighted network point average statistics energy consumption. Then we analysis these two energy consumption. Furthermore, considering the sparse network and intensive network, we also study the nearest neighbor point average statistical energy consumption and farthest neighbor point average statistical energy consumption. MATLAB simulation results show that the deployment of the network node has a great impact on energy consumption and the energy consumption in regular hexagon is lower than in rectangle or in circle.Finally, based on the star communication model, we study the network transmission capacity in CSMA protocol. In CSMA protocol, considering the space group density and backoff probability and retransmission probability, we can obtain the system outage probability. Meanwhile, combined with the coding strategy, considering the system maximum partition error probability, we study the relationship between coding efficiency and transmission capacity. MATLAB simulation results show that the space group density has a great impact on network interference and the level of coding efficiency determines the size of the transmission capacity. Furthermore, if the space group density is increasing, transmission capacity will increase in begin and reduce after exceeding the peak. Meanwhile, under the same conditions, the system outage probability in regular hexagon is lower than in rectangle or in circle, but the transmission capacity in regular hexagon is higher than in rectangle or in circle.After we study these performance of wireless sensor networks, they will provide theoretical basis and reference value to reduce the energy consumption and improve the lifetime and the transmission capacity.