The Study Of Capacity Of Wireless Ad Hoc Networks Based On Stochastic Geometry

The study of the capacity of wireless Ad Hoc networks is a very important problem in the network information theory. A key difference of the wireless Ad Hoc networks relative to the traditional wireless networks is that, each receiver(RX) in a wireless Ad Hoc network receives the aggregate interference from all other transmitters, which provides the spatially dependent relation of the interference. For this reason, the classic Shannon information theory can not be used to compute the capacity of wireless Ad Hoc networks, this motivates the pursuit of new definitions of the capacity of wireless Ad Hoc networks, which provide insight into the maximum data rates.Gupta and Kumar firstly put forward an important definition of capacity of wireless Ad Hoc networks, which is transport capacity. Transport capacity is defined as the end-to-end sum throughput of the network multiplied by the end-to-end distance. People use scaling laws to study how transport capacity grows with the network parameters. Unfortunately, they can not provide the exact relationship between the transport capacity and the network parameters, so people turn to using stochastic geometry to study the capacity of wireless Ad Hoc networks.This paper employs transmission capacity, SDP and random access transport capacity as the performance metrics. The research goal of this paper is to study how the capacity of wireless Ad Hoc networks grows with the network parameters, such as the power control strategies, the RX selection strategies, the effective transmission region, the overlaid networks, et.al. This paper includes several topics as the follow: 1, The n-th order approximate expression of transmission capacity in single-hop wireless Ad Hoc networks. The transmission capacity is defined as the number of successful transmissions taking place in the network per unit area, subject to a constraint on the network outage probability. For the closed-form expression of transmission capacity can not be obtained for general cases except for some special cases, people have to turn to study the bounds of transmission capacity. By using the Taylor series and Fourier transform, the n-th order approximate expression of transmission capacity is obtained. Furthermore, compared with the simulation results, the accuracy of the n-th order approximation has been studied. The numerical results show that the accuracy of the approximation is mainly determined by the order n, and high accuracy can be obtained when the node density or the outage constraint is close to zero.2,The transmission capacity of wireless Ad Hoc networks with signal-to-interference(SIR) based power control(SBPC). Under SBPC, the closed-form expression of transmission capacity is derived with the assumption that the small scale fading is Rayleigh fading. Based on the analysis of simulation results, using SBPC leads to reduced transmit power resulting in greatly reduced outage probability and increased transmission capacity.3,The effect of guard zone on the transmission capacity of wireless Ad Hoc networks. In wireless ad hoc networks, guard zone is helpful to suppress interference from the nodes around the desired RX in order to increase the likelihood of successful communication. A large guard zone naturally decreases the interference, but at the cost of inefficient spatial reuse. By quantifying the optimal tradeoff between interference and spatial reuse in terms of the system parameters, the optimal radius of guard zone is derived. According to the simulation results, using guard could increase the transmission capacity greatly, especially the optimal radius of guard zone, under which the maximum transmission capacity is obtained.4,The SDP of wireless Ad Hoc networks with different RX selection strategies. The SDP is defined as expectation of the product between the number of simultaneous successful transmission per unit area and the distance towards the destination. By considering three RX selection strategies, i.e., nearest RX selection strategy, random RX selection strategy and furthest RX selection strategy, closed-form expressions of SDP are derived. Numerical results show that, when the terminal density is small, the SDP with nearest RX selection strategy is nearly the same as that with furthest RX selection strategy, and the SDP with random RX selection strategy is the lowest; when the terminal density is larger, the nearest RX selection strategy has the largest SDP, and furthest RX selection strategy has the smallest SDP.5,The random access transport capacity in multi-hop wireless Ad Hoc networks. The random access transport capacity is used to quantify the end-to-end throughput in multi-hop wireless Ad Hoc networks, which is defined as the average maximum rate of successful end-to-end transmissions, multiplied by the communication distance, and normalized by the network area. The main contribution of this part is that, the effective transmission region is defined to guarantee that the data will be transmitted to the destination node within finite hops.6,The effect of power control strategies on the transmission capacities of overlaid wireless Ad Hoc networks. The primary network has a higher priority to access the spectrum without particular considerations for the secondary network, while the secondary network limits its interference to the primary network by carefully controlling its node density. Considering three power control strategies, i.e., no power control(NPC), channel inversion (CI) and SBPC, this paper derive the transmission capacities for both of the two networks. In terms of the transmission capacity gain of the overlaid network over that of a single network, the NPC has the largest capacity gain, the SBPC has the lowest gain, and the CI is in-between.The research above is helpful to understand the capacity of wireless Ad Hoc networks, and has certain significance to network engineering practice.