Wireless Ad Hoc and Sensor Networks

236 Wireless Ad Hoc and Sensor NetworksTherefore, the decision-making is fully distributed at the link level. Consequently,the overhead due to the feedback control is minimal in DPCcompared to its counterpart for centralized operations. Because eachreceiver provides feedback to the transmitter, the DPC presented in theprevious chapter can be extended to ad hoc wireless and sensor networks.The goal of transmitter power control is to maintain a target SIR thresholdfor each network link although the transmitter power is adjusted so thatthe least possible power is consumed in the presence of channel uncertainties.Suppose there are N ∈ Z + links in the network. Let g ij be thepower loss (gain) from the transmitter of the jth link to the receiver of theith link. The power attenuation is considered to follow the relationshipgiven in the following paragraph.Calculation of SIR, R i (t), at the receiver of ith link at the time instant t,is given bygii() t Pi() tRi()t = = gii() t Pi () t gij() t Pj( t) + ηi( t)I () t(6.1)where i, j {1, 2, 3,…, n}, I i (t) is the interference, P i (t) is the link’s transmitterpower, P j (t) are the transmitter powers of all other nodes, and i (t) > 0 isthe variance of the noise at its receiver node. For each link i, there is alower SIR threshold i and upper threshold i *. Therefore, we require(6.2)for every i = 1, 2, 3,…, n the lower threshold value for all links can betaken equal to for convenience, reflecting a certain QoS that the link hasto maintain to operate properly. An upper SIR limit is also set, to managethe interference.6.2.2 Radio Channel Model with UncertaintiesiThe radio channel places fundamental limitations on wireless communicationsystems. The path between the transmitter and the receiver canvary from clear line-of-sight to one that is severely obstructed by buildings,mountains, and foliage. In ad hoc wireless networks, channel uncertaintiessuch as path loss, shadowing, and Rayleigh fading can attenuatethe signal power during transmission and thus cause variations in thereceived SIR which degrades the performance of any DPC scheme. Theeffect of these uncertainties (see Chapter 5) is represented via a channelloss (gain) factor that typically multiplies the transmitter power. Therefore,the channel loss or gain, g, can be expressed as (Rappaport 1999,Canchi and Akaiwa 1999)∑j≠i*γ ≤R () t ≤ γi i ing= f( d,n,X, ζ)=d − ζ⋅ ⋅X10 0.1 2(6.3)