Abstract
In this paper, we study the connectivity of multihop wireless networks under the log-normal shadowing model by investigating the precise distribution of the number of isolated nodes. Under such a realistic shadowing model, all previous known works on the distribution of the number of isolated nodes were obtained only based on simulation studies or by ignoring the important boundary effect to avoid the challenging technical analysis, and thus cannot be applied to any practical wireless networks. It is extremely challenging to take the complicated boundary effect into consideration under such a realistic model because the transmission area of each node is an irregular region other than a circular area. Assume that the wireless nodes are represented by a Poisson point process with densitynover a unit-area disk, and that the transmission power is properly chosen so that the expected node degree of the network equals lnn + ξ (n), where ξ (n) approaches to a constant ξ as n → ∞. Under such a shadowing model with the boundary effect taken into consideration, we proved that the total number of isolated nodes is asymptotically Poisson with mean e$ {-ξ}. The Brun’s sieve is utilized to derive the precise asymptotic distribution. Our results can be used as design guidelines for any practical multihop wireless network where both the shadowing and boundary effects must be taken into consideration.
Highlights
Connectivity is one of the most fundamental properties of multi-hop wireless networks
Approaches to a constant ξ as n → ∞. Under such a shadowing model with the boundary effect taken into consideration, we proved that the total number of isolated nodes is asymptotically
To the best of our knowledge, there are no theoretical results on asymptotic distribution of the number of isolated nodes in the network obtained by rigorous analytical studies with the realistic log-normal shadowing model when the complicated boundary effect is taken into consideration
Summary
Connectivity is one of the most fundamental properties of multi-hop wireless networks. The path-loss model ( known as the unit-disk communication model) of wireless networks assumes that the received signal strength at a receiving node from a transmitting node is only determined by a deterministic function of the Euclidean distance between the two nodes. It has been shown that a more accurate and realistic modeling of the physical layer is important for better understanding of wireless multi-hop network characteristics [8] [9] This generalized radio propagation model is referred to as the log-normal shadowing model which has been widely used in the literature [10]-[15]. We derive the precise asymptotic distribution of the number of isolated nodes in the network under the log-normal shadowing model, taking the complicated boundary effect into consideration.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
