Wireless Ad Hoc and Sensor Networks

Adaptive and Probabilistic Power Control Scheme 475As shown in Figure 10.4, Beta(0.1, 0.1) renders 30% probability in selectingeither high or low power. On an average, a third of the total readerswill not operate in each time slot, and therefore the interference levelswill be reduced. Such a distribution is expected to perform well in densenetworks, because it works similar to a time-slotting method. For sparsernetworks in which the target SNR is achievable for all readers, powerdistribution Beta(0.1, 0.1) will degrade the performance as readers will beoff 30% of the time. Meanwhile, the distribution generated by Beta(2, 2)will result in higher probability being in the medium-power range, andit will achieve better results as higher output power can overcome theinterference produced in sparser networks. It is important to note thatdense RFID networks involve 30 to 40 readers whereas sparse networksmay involve 5 to 10 readers unlike in wireless ad hoc and sensor networks,where dense networks may involve several hundred to thousand sensornodes.10.4.2 Distribution AdaptationEquation 10.26 represents the relationship between the cumulative densityfunction of read range and output power of all readers. However, in adistributed implementation, operation parameters such as the power distributionand location of a reader are not known to the other readers.Hence, these parameters have to be reflected in a measurable quantity;Equation 10.5 provides such a representative quantity in the form ofinterference, which leads to Equation 10.28 asFr ( ) l( FP ( ), FI ( ))i = i 1 i(10.29)Substituting Equation 10.27 and Equation 10.28 into Equation 10.29,g( µ , τ ) = l( H( α, β), F( I ))i r r i i(10.30)Transforming Equation 10.30, we can represent α and β in terms of µ r , ρ,and FI ( i ) as[ αβ , ] = h( µ , ρ, F( I ))i r i(10.31)where FI ( i ),the cumulative density function of interference, can be statisticallyevaluated by observing the interference level at each reader overtime. It can also be interpreted as the local density around the reader.The function represented by Equation 10.31 involves joint distributionsof multiple random variables, and it is complex and difficult to extract.However, it is easy to obtain numerical data sets of this function fromsimulation. Such data sets can be used potentially to train a neural networkthat could provide a model of the function. In this chapter, we do