Wireless Ad Hoc and Sensor Networks

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Distributed Power Control and Rate Adaptation 267PROOF Recall the ratio of SNR values depending on the transmissionpower selected is expressed from Equation 6.22 asSNR l(t) / SNR k(t) = Pt l(t) / Pt k(t)(6.35)where SNRl( t) and SNRk( t) are the measured SNR values, and Ptl( t)andPtk( t)are the transmission powers used in each case, respectively. Assumethat value of Pt0( t) is known, which is needed to meet the target SNR 0 .Let the target SNR k for a different rate be provided beforehand. The transmissionpower Ptk( t) needed to meet the target SNR k can be obtainedfrom Equation 6.35 asSNR0/ SNR k = Pt0( t)/ Ptk( t)(6.36)Equation 6.36, after rewriting becomes Equation 6.34. Error in estimationfor the kth rate is bounded provided the power calculated by DPCis bounded. Because the power for the lowest supported rate is estimatedusing the DPC algorithm, the power for the kth rate is also an estimate.ε Assume that is the maximum error in estimation of power by the DPC0algorithm. Applying this to Equation 6.34, the maximum error in estimationfor the kth rate ε k is given asSNR SNR = Pt t Pt t0/ k 0( )/ k( )(6.37)It is important to note that the error in estimation for the kth rate isproportional to the error in estimation of the basic rate and the ratio ofthe two SNR values. Consequently, the proposed DPC protocol can beused to calculate transmission power although noting that the error inestimation is bounded.6.8.7 Backoff MechanismThe desired backoff mechanism should dictate the backoff interval.Higher queue utilization in the next-hop node indicates that a longerbackoff interval is needed for all the nodes in the region so that the nexthopnode will access the channel more often. A quadratic relationship forbacking off is considered in this algorithm, with the intention that for highbuffer occupancy the backoff interval will be longer preventing bufferoverflowing, and that for low buffer occupancy the delay caused bybackoff will be low, thus not undermining throughput. The backoff intervalis calculated using( NEXT-HOP )2BI = ρ⋅SF ⋅ 1+ α⋅Q () t(6.38)
268 Wireless Ad Hoc and Sensor Networkswhere BI is the backoff interval, r is a random number, SF and a are the scalingfactors, Q NEXT-HOP(t)and is the utilization of queues at the next-hop node.6.8.8 MAC Protocol DesignThe DPC protocol presented in (Zawodniok and Jagannathan 2004)between a transmitting and receiving node is modified to accommodatethe rate adaptation. The DPC information is added to the MAC framessimilar to DPC for ad hoc wireless networks. To implement the rateadaptation, it must be incorporated with the MAC protocol along withthe necessary transformation required for the power and SNR valuesshown in Equation 6.34 and Equation 6.39. Additionally, the MAC frameshave to be modified to include the queue utilization for the proposedbackoff mechanism.The RTS, CTS, and ACK frames are transmitted using the lowest supportedrate whereas the DATA frames are transmitted at the rate selected by thealgorithm. The 802.11 frame header contains a standard field, which indicatesthe rate used for payload transmission. We use this field to indicate the rateof transmission to the receiver so that it can correctly decode the payload.The DPC requires that the input value of the SNR corresponds to thetransmission power calculated by the DPC algorithm. However, in theproposed scheme, the power value is modified according to Equation6.34. Hence, the received SNR will be invalid for the DPC algorithm. Insuch a case, the measured SNRk( t)needs to be scaled to correspond tothe lowest supported rate. Multiplying both sides, of Equation 6.36 byG i (t)/I(t) we get,SIR () t = SIR () t ∗SNR / SNR0 k 0 k(6.39)where SNR 0 and SNR k are target values for the lowest supported rate andkth rate, respectively, SNR k( t ) is the measured SNR ratio, and SNR 0 (t) isthe SNR value that would be measured if the lowest supported rate (andadequate power) was used. Now, the SNR0( t)value can be used in the DPCalgorithm to calculate the transmission power for the lowest supported rate.6.9 Dynamic-Programming-Based Rate AdaptationThe second proposed rate adaptation scheme based on dynamic programmingminimizes energy consumption, while providing required level ofservice. Recall that this scheme, in contrast to the heuristic one, is able to
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Wireless Ad Hocand SensorNetworksPr
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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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