Wireless Ad Hoc and Sensor Networks

474 Wireless Ad Hoc and Sensor Networksprobability distribution, the distribution of read ranges for each reader isa function of these power distributionsFr ( ) = f( FP ( 1 ),…, FP ( ))i i n(10.26)where Fr ( i ) is the cumulative density function of the read range of thereader i, and FP ( i ) is the cumulative power density function of reader i.Performance metrics, including mean read range µ r and percentage oftime ρ the desired range r d was achieved, characterized the read rangedistribution Fr ( i ).Fr ( ) = g( µ , ρ)i i r(10.27)To achieve targeted characteristics on the read range distribution, weneed to modify the power distribution freely. Beta distribution, demonstratedin Figure 10.4, is specifically chosen for this reason: by specifyingthe shape variables α and β, one can change the cumulative density functionin the domain from 0 to 1 (0 to 100% power). By changing these twoparameters, we can control the power distribution and thus attempt toachieve desired targets on the read range distribution in Equation 10.26.Power using Beta distribution can be represented asFP ( ) = HP ( : αβ , )ii(10.28)10.90.80.70.6F(x)0.50.40.30.20.1(α = 2, β = 2)(α = 0.1, β = 0.1)00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1xFIGURE 10.4Cumulative density function of read range.