Wireless Ad Hoc and Sensor Networks

180 Wireless Ad Hoc and Sensor Networks5.2 Distributed Power Control in the Presence of Path LossThe wireless network can be considered a collection of radio links. Eachlink in the network is connected between a pair of nodes, which correspondto a single-hop radio transmission. The transmission is intendedfrom the transmitter via the link to its corresponding receiver. A collectionof consecutive links corresponds to a multihop communication path.Many communication channels may be present simultaneously in thenetwork, but it is considered that these channels are orthogonal. However,links operating in the same channel experience interference fromother channels. We can, therefore, model the wireless network as acollection of interfering links for each channel. “Distributed” implies perindividual link. Each receiver of the link measures the interference it isfaced with and communicates this information to its transmitter. Eachlink decides autonomously how to adjust its power, based on exclusiveinformation that is collected. Therefore, the decision-making is fullydistributed at the link level. The overhead due to the feedback controlis minimal in DPC compared with its counterpart when centralizedoperations are used.Whereas a link in the peer-to-peer networking scenario corresponds tosingle-hop transmissions, in cellular communication network, a linkcorresponds to up- and downstream transmission between the users andbase stations. In spread-spectrum systems, the whole spectrum can beviewed as a single channel, and interference can be attributed to the crosscorrelationeffects between codes in code division multiple access (CDMA)transmission.Our goal in both peer-to-peer and cellular network paradigms is tomaintain a required SIR threshold for each network link while the transmitterpower is adjusted so that the least possible power is consumed.Suppose there are N∈ Z + links in the network. Let G ij be the power loss(or gain) from the transmitter of the jth link to the receiver of the ith link.It involves the free space loss, multipath fading, shadowing, and otherradio wave propagation effects, as well as the spreading or processinggain of CDMA transmissions (Grandhi et al. 1994). The power attenuationis taken to follow the inverse fourth power lawGij= gr, αij(5.1)where g is a constant usually equal to 1, r ij is the distance between transmitterand receiver, and α is a constant that varies with the environment.Typically, α = 2 to 4.