Wireless Ad Hoc and Sensor Networks

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Adaptive and Probabilistic Power Control Scheme 4733. R i−rd (l) is compared to R required , and percentage of time required forachieving required SNR, r is calculated and recorded.4. Based on Equation 10.24, the channel is estimated for the nexttime step l + 1, and the power for P(l + 1) is also calculated usingthe feedback control from Equation 10.21.5. P(l + 1) is then limited to maximum power P max ; if P(l + 1) isgreater than P max , the selective backoff scheme is triggered,otherwise P(l + 1) is used as the output power for the nextcycle.6. The selective backoff block follows the algorithm provided in thepreceding subsection and restricts the final output power for thenext cycle.Simulation and results of the preceding implementation are discussedin Section 10.5 and Section 10.6, respectively, along with those of PPC.Next, the PPC is discussed.10.4 Probabilistic Power ControlThe idea of PPC comes from simple TDM algorithms. If a reader isassigned a time slot to transmit in full power while others are turnedoff, it will achieve its maximum range. A round-robin assignment oftime slots can ensure that all readers operate with no interference.However, this is inefficient in terms of average read range, readerutilization, and waiting periods. It is obvious that more than one readercan operate in the same time slot but at different power levels toaccomplish better overall read range. If the power levels at all readerschange in each time slot following a certain distribution, over time,every reader will be able to achieve its peak range while maintaininga good average.For a distributed solution, this would involve setting a probability distributionfor power to be selected for each time step. Such a distributionwould need to be adapted based on the density and other parameters ofthe reader network.10.4.1 Power DistributionEquation 10.9 states that the read range of a particular reader is dependenton its transmission power and the interference experienced, which is afunction of powers of all other readers. If reader powers follow a certain
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.
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18. Chaos in Automatic Control, edi
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CRC PressTaylor & Francis Group6000
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Table of Contents1 Background on Ne
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3 Congestion Control in ATM Network
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5.4.2 Distributed Power Controller
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7.3 Adaptive and Distributed Fair S
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9.2.2 Overview.....................
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the number of connections in each l
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y Maheswaran Thiagarajan, and tirel
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2 Wireless Ad Hoc and Sensor Networ
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10 Wireless Ad Hoc and Sensor Netwo
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2BackgroundIn this chapter, we prov
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Background 51u(k)x n (k + 1)x n (k)
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Background 53with x( 0)being the in
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Background 55with tr(.) the matrix
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Background 57nGiven a function ft (
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Background 592.3.2 Lyapunov Stabili
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Background 61as well as Jagannathan
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Background 63The subsequent example
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Background 65Evaluating this along
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Background 67Now, select the feedba
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Background 69is SISL if and only if
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Background 71L 1 (x)L(x, t)L 0 (x)0
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Background 73for some R > 0 such th
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Background 75Evaluating the first d
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Background 77Section 2.4Problem 2.4
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100 Wireless Ad Hoc and Sensor Netw
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4Admission Controller Design for Hi
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Admission Controller Design for Hig
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7Distributed Fair Scheduling in Wir
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Distributed Fair Scheduling in Wire
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8Optimized Energy and Delay-Based R
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Optimized Energy and Delay-Based Ro
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