Wireless Ad Hoc and Sensor Networks

Distributed Power Control and Rate Adaptation 237where d −n is the effect of path loss and 10 0.1.ζ corresponds to the effect ofshadowing. For Rayleigh fading, it is typical to model the power attenuationas X 2 , where X is a random variable with Rayleigh distribution.Typically the channel gain, g, is a function of time.6.3 Distributed Adaptive Power ControlIn the previous DPC schemes (Bambos 1998, Janti and Kim 2000, Dontulaand Jagannathan 2004, Jagannathan et al. 2002), only path loss uncertaintyis considered. Moreover, the DPC algorithm proposed in (Bambos 1998)appears to be slow in convergence compared to (Dontula and Jagannathan2004) for cellular networks and the outage probability is slightly higher.Nevertheless, in the presence of other channel uncertainties, the performancesof these DPC schemes fail to render satisfactory performance asshown in (Jagannathan et al. 2004) for cellular networks. The work, presentedin this chapter, is aimed at demonstrating the performance of DPCin the presence of several channel uncertainties for wireless ad hoc networks,because there are significant differences between cellular and adhoc networks.However, the channel is time-varying when uncertainties are consideredand therefore g ij (t) is not a constant. In Lee and Park (2002), a newDPC algorithm is presented where g ii (t) is treated as a time-varying functiondue to Rayleigh fading by assuming that the interference I i (t) is heldconstant. Because this is an invalid assumption, in this paper, a novel DPCscheme is given where both g ii (t) and the interference I i (t) are time-varying,and channel uncertainties are considered for all the mobile users. In otherwords, in all existing works (Bambos et al. 2000, Janti and Kim 2000,Dontula and Jagannathan 2004), both g ij (t) and I j (t) are considered to beheld constant, whereas in our work, this assumption is relaxed. Moreover,the persistence of excitation condition requirement on the input signalsin (Jagannathan et al. 2004) is relaxed in this work.Following the work and similar notation from Chapter 5, the DPCcalculation for an ad hoc wireless network can be given for two scenarios.CASE 1 α i , β i , and r i are known. In this scenario, one can select thefeedback control as1v() l = β − ()[ l γ −α () l y() l −r() l ω () l +k e ( l)]iii i i i v i(6.4)where the error in SIR is defined as e i (l) = R i (l). This results ine ( l+ 1)=k e ( l)iv i(6.5)