Wireless Ad Hoc and Sensor Networks

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Distributed Power Control and Rate Adaptation 261power limitations of the hardware. In Subsection 6.8.2, we present thedetails of how the scheme uses the channel-state estimator provided bythe DPC algorithm. Next, the lower limit of the set is identified as themost energy-efficient rate. The underlying DPC implementation is takeninto account, because the train of pulses used during transmission of theMAC frames introduces the energy overhead.Subsequently, the selection of the most suitable modulation rate from theset is presented in Subsection 6.8.5. The buffer utilization at the transmitterdictates the selection of a particular modulation rate from the set of ratescalculated in Subsections 6.8.6. Next, the transmission power is adjusted forthe selected rate such that a corresponding target SNR is achieved. Here, thebuffer utilization at the receiving node dictates a suitable value for the backoffinterval. Finally, changes needed to the MAC layer as the result of the proposedprotocol implementation are discussed in Subsection 6.8.8.REMARK 2In this scheme, we assume that all nodes are capable of handling the sameset of N modulations. In the case of a heterogeneous network, the nodeswill have to exchange the rate information by using the control packetstransmitted at the lowest rate. To simplify the description of the problem,the modulation schemes are sorted by rate.6.8.2 Channel-State EstimationThe proposed protocol uses a threshold method similar to Holland et al.(2001) to determine the maximum rate possible for the given SNR. Themaximum SNR that corresponds to the maximum transmission power isalso to be determined. In the proposed scheme, the DPC is used to predictthis maximum SNR for transmitting the next frame.THEOREM 6.8.1 (MAXIMUM SNR PREDICTION)Given the maximum transmission power defined for the network, and information(Zawodniok and Jagannathan 2005) for the lowest supported rate through DPC,the maximum possible SNR for subsequent transmission can be predicted usingSNR () t = SNR ∗ Pt / Pt () tMAX 0 MAX 0(6.21)where SNR 0 is the target SNR for the lowest supported rate, Pt0( t)is theestimated power value for the lowest supported rate, and Pt MAX is the maximumtransmission power defined for the network.PROOF First, let us consider the SNR ratio of a received signal expressed asSNR() t = Pr()/() t I t =Ptt () ⋅Gi()/()t I t(6.22)
262 Wireless Ad Hoc and Sensor Networkswhere Pr( t)is a received signal strength, Pt()t is the transmission power,Gi( t) is a gain (loss) experienced by the signal, and It () is an interferenceplus a noise level.It is important to note that the SNR depends upon transmitted power.Furthermore, we can calculate the ratio of two SNR values using thecorresponding transmission power values. This ratio is equal toSNRl()t Ptl() t ∗Gi()/ t I()t ()=SNR () t Pt () t ∗ Gi(t)/ It ( )= Pt l tPt () tkkk(6.23)where SNRl( t) and SNRk( t) are the measured SNRs, and Pt1( t)andPtk( t)are the corresponding transmission powers used in each case,respectively.Let the value of Pt0( t) needed to meet the target SNR 0 along with themaximum power Pt MAX be known. The maximum SNR, when the maximumpower is used, can be calculated from Equation 6.23 asSNR / SNR ( t) = Pt ( t)/Pt0 MAX 0MAX(6.24)Equation 6.24 can be rewritten as Equation 6.21.6.8.3 Maximum Usable RateNext, the maximum achievable rate is selected using a thresholdingmethod similar to the case of RBAR protocol (Holland et al. 2001). However,in the proposed scheme, the current SNR value is an estimated valueof the SNR for the next transmission, while in the case of RBAR, the SNRis an outdated value measured from the reception of the previous frame(i.e., a half loop-delay before the DATA frame). Hence, the proposedprotocol will be able to accurately select the rate taking into account thechannel state. The highest rate, m, is selected fromSNRm/ SNRMAX( t)< SNRm+1(6.25)where SNRMAX( t)is the estimated SNR ratio if the maximum power isused for transmission, and SNR m is the lower threshold for the mth rate.All modulation schemes that render rates up to the mth rate are consideredusable because, the transmission power for these rates, is below the maximumnetwork threshold.6.8.4 Minimum Usable RateThe most energy-efficient rate will become the optimal rate that can beused. Under the ideal circumstances, energy efficiency decreases with an
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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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Page 326 and 327: 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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