Wireless Ad Hoc and Sensor Networks

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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
476 Wireless Ad Hoc and Sensor Networksnot attempt to provide the interference-based adaptive distribution tuningscheme for the PPC. We only implement PPC using fixed power distributionsfor all scenarios to observe the overall performance patterns andto understand the differences between the DAPC and PPC. The twodistributions, Beta(0.1, 0.1) and Beta(2, 2) used in Figure 10.4 are chosenfor the simulation and compared for performance evaluation.In terms of implementation, PPC only requires a power control blockthat selects output power based on predefined probability distributions.However, a more complex model of PPC can be generated provided therelationship in Equation 10.31 can be obtained. This PPC requires interferencemeasurement and dynamically adjusts the power distributionbased on interference to maximize µ r and ρ .10.5 Simulation ResultsThe simulation environment is set up in MATLAB. Full model of DAPCand PPC are implemented for comparison. Both algorithms are testedunder the same configuration.10.5.1 Reader DesignReader power is implemented as a floating point number varying from0 to 30 dBm (1 W) as per FCC regulations. For error-free detection, thereader should maintain a target SNR of 14 (~11 dB). Other system constantsare designed so that the maximum read range of a reader in anisolated environment is 3 m. Interference experienced at any reader iscalculated based on a matrix consisting of power and positions of all otherreaders plus the channel variation g ij . A desired range of 2 m is specifiedbased on the worst case analysis.For the proposed DAPC, power update parameters Kv and s are bothset to 0.001. For proposed PPC, both Beta(0.1, 0.1) and Beta(2, 2) areimplemented.10.5.2 Simulation ParametersFor both models, random topologies are generated in order to emulatedenser networks with a suitable number of readers. The RFID networkwith a suitable density for a given scenario is created by placing thereaders with the minimum distance between them and the maximum areaunder test. The minimum distance between any two readers is varied
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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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Wireless Ad Hoc and Sensor Networks

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