Wireless Ad Hoc and Sensor Networks

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Distributed Power Control of Wireless Cellular and Peer-to-Peer Networks 185This is a stable linear system driven by a constant bounded input η i .Applying the well-known theory of linear systems (Lewis 1999), it is easyito show that xi( ∞ ) = η . In the absence of protection margin, the SIRkierror approaches to zero as t →∞.x iREMARK 1The transmission power is subject to the constraint pmin≤ pi≤ pmaxwherep min is the minimum value needed to transmit, p max is the maximumallowed power, and p i is the transmission power of the user i. Hence, fromEquation 5.11, pi( l+ 1)can be written as pi( l+ 1) = min( pmax, ( vi( l) Ii( l) + pi( l))).The power update presented in Theorem 5.2.1 does not use any optimizationfunction. Hence, it may not render optimal transmitter powervalues though it guarantees convergence of actual SIR of each link to itstarget. Therefore, in Table 5.2, an optimal DPC is proposed.THEOREM 5.2.2 (OPTIMAL CONTROL)Given the hypothesis presented in the previous Theorem 5.2.1, for DPC, with thefeedback selected as v() l =− k x() l +η , where the feedback gains are taken asi i i i( )−1k = H S H + T H S Ji i T ∞ i i i T ∞ i(5.14)TABLE 5.2Optimal Distributed Power ControllerSIR system state equationPerformance indexSIR errorAssumptionsFeedback controllerPower updateR( l+ 1) = R( l) + v () l∞∑i=1i i ixTx+vQvi T i i i T i ix () l = R()l −γi i iTi ≥ 0, Qi> 0 all are symmetricT−1TS = J [ S − SH ( H S H + T) H S ] J + Qiii i i iTi i i iT− Tk = ( H S H + T) 1 H S Jii∞v () l =− k x () l +ηi i i ii i ip( l+ 1) = ( v ( l) I ( l) + p( l))i i i i∞iiiwherek i, γ i , andηi are design parameters
186 Wireless Ad Hoc and Sensor Networkswhere is the unique positive definite solution of the algebraic Ricattiequation (ARE)S iS J S SH H S H T H S J Q( )⎡= − +⎣⎢⎤⎦⎥ +i i T i i i i T i i i i T i i−1(5.15)Then, the resulting time-invariant closed-loop system described byx( l+ 1) = ( J − HK ) x( l)+ Hηi i i i i i i(5.16)is asymptotically stable, if = 0.PROOF Follow the steps as in Lewis (1999).η iREMARK 2The proposed scheme minimizes the performance index∞∑ i=xTx i T i i + vQv i T i i where and are weighting matrices.The block diagram in Figure 5.1 explains the process of power controlusing SSCD/optimal schemes. The receiver as shown in the blockdiagram, after receiving the signal from the transmitter, measures theSIR value and compares it against the target SIR threshold. The differencebetween the desired SIR to the received signal SIR is sent to thepower update block, which then calculates the optimal power levelwith which the transmitter has to send the next packet to maintain therequired SIR. This power level is sent as feedback to the transmitter,which then uses the power level to transmit the packet in the next timeslot.1 T i Q iInterferenceTransmitter ∗ TPCP iFeedback∗ Transmitter power controlChannel with uncertaintiesTPC commandRadio channelReceiverDPCPower updateIEEE 802.11Target SIR (dB)Measured SIRFIGURE 5.1Block diagram representation of DPC.
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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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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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9Predictive Congestion Control for
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Predictive Congestion Control for W
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10Adaptive and Probabilistic Power
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Adaptive and Probabilistic Power Co
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