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Wireless Ad Hoc and Sensor Networks

Wireless Ad Hoc and Sensor Networks

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262 <strong>Wireless</strong> <strong>Ad</strong> <strong>Hoc</strong> <strong>and</strong> <strong>Sensor</strong> <strong>Networks</strong>where Pr( t)is a received signal strength, Pt()t is the transmission power,Gi( t) is a gain (loss) experienced by the signal, <strong>and</strong> 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) <strong>and</strong> SNRk( t) are the measured SNRs, <strong>and</strong> Pt1( t)<strong>and</strong>Ptk( 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 (Holl<strong>and</strong> 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current SNR value is an estimated valueof the SNR for the next transmission, while in the case of RBAR, the SNRis an outdated value measured from the reception of the previous frame(i.e., a half loop-delay before the DATA frame).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, <strong>and</strong> 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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