Critical Power for Asymptotic Connectivity in Wireless Networks

Abstract

In wireless data networks each transmitter's power needs to be high enough to reach the intended receivers, while generating minimum interference on other receivers sharing the same channel. In particular, if the nodes in the network are assumed to cooperate in routing each others' packets, as is the case in ad hoc wireless networks, each node should transmit with just enough power to guarantee connectivity in the network. Towards this end, we derive the critical power a node in the network needs to transmit in order to ensure that the network is connected with probability one as the number of nodes in the network goes to infinity. It is shown that if n nodes are placed in a disc of unit area in ℜ2 and each node transmits at a power level so as to cover an area of πr 2 = (log n + c(n))/n, then the resulting network is asymptotically connected with probability one if and only if c(n) → +∞.

Keywords

Computer networkNode (physics)Wireless ad hoc networkWireless networkNetwork packetComputer scienceTransmitter power outputTopology (electrical circuits)Channel (broadcasting)WirelessTransmitterRouting (electronic design automation)Wireless mesh networkStochastic geometry models of wireless networksInterference (communication)Routing protocolMathematicsTelecommunicationsEngineeringOptimized Link State Routing ProtocolCombinatorics

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Publication Info

Year: 1999
Type: book-chapter
Pages: 547-566
Citations: 1139
Access: Closed

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APA Style

                            
                                    Piyush Gupta, 
                                
                                    P.R. Kumar
                                
                            (1999). 
                            Critical Power for Asymptotic Connectivity in Wireless Networks. 
                            Birkhäuser Boston eBooks
                            
                            , 547-566.
                            https://doi.org/10.1007/978-1-4612-1784-8_33

Identifiers

DOI: 10.1007/978-1-4612-1784-8_33