Wireless Ad Hoc and Sensor Networks

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Distributed Power Control and Rate Adaptation 263increase in rate. Hence, the lowest rate should be the most energy-efficient.However, in the proposed protocol, the train of pulses in DPC (Zawodniokand Jagannathan 2004) used to overcome the hidden-terminal problemintroduces an additional energy OH and becomes an important factor tobe considered for rate adaptation. Hence, the lowest rate is not alwaysenergy efficient. Consequently, the most energy-efficient rate is found bycomparing the energy consumed at each rate for a given packet underthe current channel state. The rate with lowest energy consumption thattakes into account the channel state and energy overhead due to thehidden-terminal problem will be selected as the minimum usable rate asdiscussed next.Normally, the energy consumed for transmission is equal toE=D⋅Pt(6.26)where E is the energy consumed, D is the duration of transmission, andPt is the current transmission power. For the case of the DPC algorithmwith the train of pulses illustrated in Figure 6.14, the energy consumedduring transmission is equal toE =E +ETOTAL DPC PULSES(6.27)E TOTALEDPCwhere is the total energy consumed on transmission of the packetwith pulses, represents the energy consumed for the transmission ofthe packet using the power selected by the DPC algorithm, andTx powerP MAXD PULSEpulsedurationD 1pulsesintervalE PULSESP DPCE DPCD PPacket durationTimeFIGURE 6.15Energy consumption during packet transmission.
264 Wireless Ad Hoc and Sensor NetworksE PULSES denotes the additional energy consumed for the generation ofpulses. Therefore, E DPC and E PULSES can be expressed using Equation 6.26 asE DPC =PtDPC ∗ Pktsize/R(6.28)andE = ( Pkt / R) ∗( D / D ) ∗(Pt −PtC)PULSES size PULSE I MAX DP(6.29)After substituting Equation 6.28 and Equation 6.29 into Equation 6.27we get,E TOTAL = ( Pktsize/ R) ∗Pt DPC + ( Pktsize/R) ∗(DPULSE/ DI) ∗( PtMAX −PtDPC)(6.30)It is important to note that for the given packet size and rate, the totalenergy consumed varies linearly with transmission power. Also, the DPCscheme increases the transmission power for a given rate proportional tothe target SNR as per Equation 6.23. Thus for a rate k, Equation 6.30 isexpressed asE = ( Pkt / R )[( D / D ) ∗Pt + ( Pkt / R )TOTAL,k size k PULSE I MAXsize× ( SNR / SNR ) ∗( 1 −( D / D )) Pt ( t)]k 0 PULSE I 0k(6.31)The upper and lower thresholds of the DPC power (calculated forthe lowest supported rate) need to be found so that the most energyefficientrate can be selected. By equating Equation 6.31 for the twosuccessive rates, the threshold values for the rate adaptation aredetermined asE =ETOTAL,kTOTAL,k+1( Pkt / R )[( D / D )∗Pt + ( SNR / SNR ) ∗( 1 −( D / D )) Pt ( t)]size k PULSE IMAX k 0 PULSE I 0= ( Pkt / R )[( D / D ) ∗ Pt + ( SNR / Ssize k+ 1 PULSE I MAX k+1 NR0∗( 1 −( D / D )) Pt ( t)]PULSE I 0(6.32)Using Equation 6.31, the rate’s upper threshold using power as a constraintis given by)ϕ 1 αkPt O,k = Pt1 − ϕ∗ −∗γ −α ∗γk k k+ 1MAX(6.33)where α k =R k / R k+ 1, γ k =SNR k / SNR 0 and ϕ =DPULSES/DI.
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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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4Admission Controller Design for Hi
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Admission Controller Design for Hig
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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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10Adaptive and Probabilistic Power
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Adaptive and Probabilistic Power Co
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