Capacity bounds for large scale wireless ad hoc networks under Gaussian channel model

We study the capacity for both random and arbitrary wireless networks under Gaussian Channel model when all wireless nodes have the same constant transmission power P. During the transmission, the power decays along path with attenuation exponent beta > 2. We consider extended networks, where n wireless nodes {v<sub>1</sub>, v<sub>2</sub>,hellip, v<sub>n</sub>} are randomly or arbitrarily distributed in a square region B<sub>a</sub> with side-length a. We randomly choose n<sub>s</sub> multicast sessions. For each source node v<sub>i</sub>, we randomly select k points p<sub>i,j</sub> (1 les j les k) in B<sub>a</sub> and the node which is closest to p<sub>i,j</sub> will serve as a destination node of v<sub>i</sub>. We derive the achievable upper bounds on unicast capacity and an upper bound (partially achievable) on multicast capacity of the wireless networks under Gaussian Channel model. We found that the unicast (multicast) capacity for wireless networks under Gaussian Channel model has three regimes.

[1]  J. Steele.  Growth Rates of Euclidean Minimal Spanning Trees With Power Weighted Edges , 1988 .

[2]  M. Penrose.  The longest edge of the random minimal spanning tree , 1997 .

[3]  Piyush Gupta,et al.  Critical Power for Asymptotic Connectivity in Wireless Networks , 1999 .

[4]  Panganamala Ramana Kumar,et al.  RHEINISCH-WESTFÄLISCHE TECHNISCHE HOCHSCHULE AACHEN , 2001 .

[5]  David Tse,et al.  Mobility increases the capacity of ad-hoc wireless networks , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[6]  Michael Gastpar,et al.  On the capacity of wireless networks: the relay case , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[7]  P. Viswanath,et al.  A deterministic approach to throughput scaling in wireless networks , 2002, Proceedings IEEE International Symposium on Information Theory,.

[8]  Xiang-Yang Li,et al.  Geometric spanners for wireless ad hoc networks , 2002, Proceedings 22nd International Conference on Distributed Computing Systems.

[9]  P. Kumar,et al.  Capacity of Ad Hoc Wireless Networks , 2002 .

[10]  Peng-Jun Wan,et al.  Distributed Construction of Connected Dominating Set in Wireless Ad Hoc Networks , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[11]  Xiang-Yang Li,et al.  Geometric Spanners for Wireless Ad Hoc Networks , 2003, IEEE Trans. Parallel Distributed Syst..

[12]  Murali S. Kodialam,et al.  Characterizing achievable rates in multi-hop wireless networks: the joint routing and scheduling problem , 2003, MobiCom '03.

[13]  Paolo Santi,et al.  The Critical Transmitting Range for Connectivity in Sparse Wireless Ad Hoc Networks , 2003, IEEE Trans. Mob. Comput..

[14]  Andrea J. Goldsmith,et al.  Large wireless networks under fading, mobility, and delay constraints , 2004, IEEE INFOCOM 2004.

[15]  Panganamala Ramana Kumar,et al.  The Number of Neighbors Needed for Connectivity of Wireless Networks , 2004, Wirel. Networks.

[16]  Nitin H. Vaidya,et al.  Capacity of multi-channel wireless networks: impact of number of channels and interfaces , 2005, MobiCom '05.

[17]  Philippe Jacquet,et al.  Multicast Scaling Properties in Massively Dense Ad Hoc Networks , 2005, 11th International Conference on Parallel and Distributed Systems (ICPADS'05).

[18]  Randeep Bhatia,et al.  Joint Channel Assignment and Routing for Throughput Optimization in Multiradio Wireless Mesh Networks , 2005, IEEE Journal on Selected Areas in Communications.

[19]  Alireza Keshavarz-Haddad,et al.  Broadcast capacity in multihop wireless networks , 2006, MobiCom '06.

[20]  Randeep Bhatia,et al.  Joint Channel Assignment and Routing for Throughput Optimization in Multiradio Wireless Mesh Networks , 2006, IEEE J. Sel. Areas Commun..

[21]  Bulent Tavli.  Broadcast capacity of wireless networks , 2006 .

[22]  Francesca Cuomo,et al.  Funneling-MAC: a localized, sink-oriented MAC for boosting fidelity in sensor networks , 2006, SenSys '06.

[23]  Rong Zheng,et al.  Information Dissemination in Power-Constrained Wireless Networks , 2006, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications.

[24]  Rudolf H. Riedi,et al.  Bounds for the capacity of wireless multihop networks imposed by topology and demand , 2007, MobiHoc '07.

[25]  Massimo Franceschetti,et al.  Closing the Gap in the Capacity of Wireless Networks Via Percolation Theory , 2007, IEEE Transactions on Information Theory.

[26]  Shaojie Tang,et al.  Multicast capacity for large scale wireless ad hoc networks , 2007, MobiCom '07.

[27]  Alireza Keshavarz-Haddad,et al.  Multicast capacity of large homogeneous multihop wireless networks , 2008, WiOpt 2008.

[28]  Yunhao Liu,et al.  Capacity of large scale wireless networks under Gaussian channel model , 2008, MobiCom '08.

[29]  Rong Zheng,et al.  Asymptotic Bounds of Information Dissemination in Power-Constrained Wireless Networks , 2008, IEEE Transactions on Wireless Communications.

[30]  Shaojie Tang,et al.  Multicast capacity for hybrid wireless networks , 2008, MobiHoc '08.

[31]  Changjun Jiang,et al.  Scaling Laws of Networking-Theoretic Capacity for Wireless Networks , 2009 .

[32]  R. Srikant,et al.  The Multicast Capacity of Large Multihop Wireless Networks , 2007, IEEE/ACM Transactions on Networking.

[33]  Shaojie Tang,et al.  Impact of deployment size on the asymptotic capacity for wireless ad hoc networks under Gaussian channel model , 2011, Wirel. Networks.