Raio Range Ajustment for Energy Efficient Wireless Sensor Networks Q. Gao a,, K. J. Blow a 1, D. J. Holing a, I. W. Marshall b, X. H. Peng a a Electronic Engineering, Aston University, Birmingham B4 7ET,Unite Kingom b Computing Laboratory, University of Kent, Canterbury, Kent CT2 7NZ, Unite Kingom Abstract In wireless a hoc sensor networks, energy use is in many cases the most important constraint since it correspons irectly to operational lifetime. Topology management schemes such as GAF put the reunant noes for routing to sleep in orer to save the energy. The raio range will affect the number of neighbouring noes, which collaborate to forwar ata to a base station or sink. In this paper we stuy a simple linear network an euce the relationship between optimal raio range an traffic. We fin that half of the power can be save if the raio range is ajuste appropriately compare with the best case where equal raio ranges are use. Keywors: Sensor network; energy saving; range ajustment 1. Introuction Recent avances in micro-electro-mechanical systems (MEMS) technology, wireless communications an igital electronics have enable the evelopment of low-cost, low-power, multifunctional smart sensor noes. Smart sensor noes are autonomous evices equippe with heavily integrate sensing, processing, an communication capabilities. When these noes are networke together in an a-hoc fashion, they form a sensor network. The noes gather ata via their sensors, process it locally or coorinate amongst neighbors an forwar the information to the user or, in general, a ata sink. Since these integrate sensor noes have highly compact form factors an are wireless, they are highly energy constraine. Furthermore, replenishing energy via replacing batteries on up to thousans of noes (in possibly harsh terrain) is infeasible. Hence, it is well accepte that one of the key challenges in unlocking the potential of such ata gathering sensor networks is conserving energy so as to maximize their post-eployment active lifetime. In terms of energy consumption, the wireless exchange of ata between noes strongly ominates other noe functions such as sensing an processing. Moreover, actual raios consume power not only when sening an receiving ata, but also when listening. Stemm an Katz show ile:receive:transmit ratios are 1:1.05:1.4 by measurement [1], while more recent stuies show ratios of 1:2:2.5 [2] an 1:1.2:1.7[3]. Significant energy savings are only obtainable by putting as many noes as possible to sleep. Topology management provies the istribute resources to the overlying applications in an energy efficient manner to achieve the service requirements for the maximum possible time. Taking avantage of high-ensity eployment, each noe can assess its connectivity an aapts its participation in the multi-hop network topology base on local measurements to exten overall system lifetime. If we increase the raio range there are more noes in the collaborative area, which can ecie to go to sleep an therefore prolong the network s lifetime. So far, we have assume that the energy emane for transmission is inepenent of the istance. In fact, airborne raio transmissions are attenuate by a path loss in a power-law with istance. Since the path loss of raio transmission scales with istance in a greater-than-linear fashion [11], the total transmission energy can be reuce by iviing a long transmission path into several shorter ones. Now the problem is how can we reach the optimal range for energy efficient routing that uses the smallest amount of energy for ata transmission while simultaneously allowing many noes to be put into the sleep state. In this paper we euce the relationship between optimal raio range an traffic an fin that half of the power can be save if the raio range is ajuste accoring to the optimum strategy in a linear network compare with the best case where equal raio ranges are use. 2. Raio Power Moel an Characteristic Distance For a simplifie power moel of raio communication [4][5], the energy consume per secon in transmission is: 1 Corresponing author. Tel.: +44-0121-3596987; fax: +44-0121-3590156. E-mail aresses: qianggao@aston.ac.uk (Q. Gao), k.j.blow@aston.ac.uk (K. J. Blow), holinj@aston.ac.uk (D. J. Holing), i.w.marshall@kent.ac.uk (I. W. Marshall), x-h.peng@aston.ac.uk (X. H. Peng)
E t = e t r n (1) B where e t is the energy/bit consume by the transmitter electronics (incluing energy costs of imperfect uty cycling ue to finite startup time), an e accounts for energy issipate in the transmit op-amp (incluing op-amp inefficiencies). Both e t an e are properties of the transceiver use by the noes, r is the transmission range use. The parameter n is the power inex for the channel path loss of the antenna. This factor epens on the RF environment an is generally between 2 an 4. B is the bit rate of the raio an is a fixe parameter in our stuy. On the receiving sie, a fixe amount of power is require to capture the incoming raio signal E r =e r B (2) where e r is the energy/bit consume by the receiver electronics use by the noe. Typical numbers for currently available raio tranceivers are e t=50x10-9 J/bit, e r=50x10-9 J/bit, e =100x10-12 J/bit/m 2 (for n=2) an B=1Mbit/s [6]. Since the path loss of raio transmission scales with istance in a greater-than-linear fashion, the transmission energy can be reuce by iviing a long path into several shorter ones. However, if the number of intermeiate noes is very large then the energy consumption per noe is ominate by the term e t in equation (1) an the receiving energy consumption hence an optimum exists. Intermeiate noes between a ata source an estination can serve as relays that receive an rebroacast ata Let us consier multihop communication in a finite one imensional network from the source to the base station across a istance using k hops. The source at x= will generate traffic of A Erlang, so that each intermeiate noe receives an transmits the same traffic, A. The routing noes are assume to be regularly space an to consume no energy while ile. The power consume by this communication is then simply the sum of the transmit an receive energies multiplie by the effective bit rate, BA, an is given by k k (3) P= e t r i n+e r B A, r i = i=1 In orer to minimize P we note that it is strictly convex an use Jensen s inequality. Given an k then P is minimize when all the hop istances r i are mae equal to /k. The minimum energy consumption for a given istance has either no intervening hops or k opt equiistant hops where k opt is always one of, k opt = or k opt = char The istance char, calle the characteristic istance, is inepenent of an is given by, char = (5) n e t +e r e n 1 The characteristic istance epens only on the energy consumption of the harware an the path loss coefficient (i.e. it is inepenent of the traffic); char alone etermines the optimal number of hops. For typical COTS (commercial, off-the-shelf)-base sensor noes, char is about 35 meters. The introuction of relay noes is clearly a balancing act between reuce transmission energy an increase receive energy. Hops that are too short lea to excessive receive energy. Hops that are too long lea to excessive path loss. In between these extremes is an optimum transmission istance that is the characteristic istance. 3. Topology Management The traffic istribution through appropriate routing essentially exploits the macro-scale reunancy of possible routes between source an estination. However, on each route, there is also a micro-scale reunancy of noes that are essentially equivalent for the multi-hop path. In typical eployment scenarios, a ense network is require to ensure aequate coverage of both the sensing an multi-hop routing functionality, in aition to improving network fault-tolerance. Despite the inherent noe reunancy, these high ensities o not immeiately result in an increase network lifetime, as the raio energy consumption in ile moe oes not iffer much from that in transmit or receive moe. Only transitioning the raio into the sleep state can temporarily quiescent noes to conserve battery energy. However, in this state, noes cannot be communicate with, an have effectively retracte from the network, thereby changing the active topology. Thus, the crucial issue is to intelligently manage the sleep state transitions while maintaining robust unisturbe operation. This reasoning is the founation for topology management approach, which explicitly leverages the fact that in high noe ensity several noes can be consiere backups of each other with respect to i=1 char (4)
traffic forwaring. Achieving energy saving through activation of a limite subset of noes in an a-hoc wireless network has also been the goal of some recent research such as GAF [7], SPAN [3], ASCENT [8], CEC [9] an AFECA [10]. In SPAN, a limite set of noes forms a multi-hop forwaring backbone, which tries to preserve the original capacity of the unerlying a-hoc network. Other noes transition to sleep states more frequently, as they no longer carry the buren of forwaring ata of other noes. To balance out energy consumption, the backbone functionality is rotate between noes an therefore there is a strong interaction with the routing layer. In ASCENT, the ecision for being active is the courtesy of the noe. Passive noes keep listening all the time an assess their course of actions; stay passive or become active. Cluster-base Energy Conservation (CEC) an the Aaptive Fielity Energy-Conserving Algorithm (AFECA) are two other propose energy conserving topology management algorithms. CEC creates clusters an selects cluster-heas base on the highest avertise remaining energy. AFECA allows each noe to sleep for ranomize perios base on the number of (overhear) neighbors it has. The GAF algorithm is base on a ivision of the sensor network in a number of virtual gris of size R by R, see Figure 1. The value of R is chosen such that all noes in a gri are equivalent from a routing perspective. This means that any two noes in ajacent gris shoul be able to communicate with each other. By investigating the worst-case noe locations epicte in Figure 1, we can calculate that R shoul satisfy R r 5 For the one imension case, R shoul satisfy R r /2 (6) (7) 1 2 3 4 r 5 R Figure 1: GAF virtual gri structure Since all noes in a gri are equivalent from a routing perspective, we can use this reunancy to increase the network lifetime. GAF only keeps one noe awake in each gri, while the other noes put their raio in the sleep moe. To balance out the energy consumption, the buren of traffic forwaring is rotate between noes. For simplicity, we ignore the unavoiable time overlap of this process associate with hanoff. If there are m noes in a gri, the noe will (ieally) only turn its raio on for a fraction 1/m of the time an therefore will last m times longer. If we increase the raio transmission range, r, there will be more noes within each gri an hence more reunant noes can make the transition into the sleep state an therefore a longer network lifetime can be achieve. Since the energy consumption associate with transmission increases super-linearly with raio range, there will be an optimum range that provies the maximum energy saving. Topology management algorithms work well in high ensity sensor networks. They let reunant noes go to sleep an network life is prolonge while the connection an capacity of the networks are
preserve. For GAF there are many noes in a gri section when ensities are high an long lifetime can be achieve. Furthermore in high-ensity networks if some noes are transition into sleep state, collisions can be reuce when several neighboring noes compete to access the transmission meium. An overhearing energy waste can be reuce as well for topology management strategy. 4. Relationship between Range an Traffic In section 2 we introuce a simple energy moel in which no energy was consume while the noe was ile. This le to a characteristic istance that was inepenent of traffic. We now inclue the ile state energy an show how the characteristic istance is moifie. On one han a short range is preferre for energy efficient ata transmission as a result of the nonlinear path loss ratio. On the other han more reunant noes can be put into the sleep state to prolong the network lifetime if a long range is use in the topology management of sensor networks. So what is the optimal range from an energy efficiency perspective? Again, we consier a linear network of length in which the traffic carrie from en to en is A Erlang. If the transmission route is ivie into k gris an only one noe wakes up in each gri as relay noe, as in the GAF protocol, the total energy consumption per secon by k hops is P=k [ e r BA+e t BA 2 (8) n BA+ce r 1 2 A B ] k The last term ce r(1-2a)b in the equation (8) represents the energy consumption when the raio neither receives nor transmits, i.e. it is in the ile state. The energy consumption in the ile state is approximately equal to that in the receiving state, so that the parameter c is close to 1. Note that we are currently assuming that noes in the sleep state consume no energy. Also, we assume that the routing noe in each gri can be locate anywhere within that section an so the raio range is now twice the gri size. The energy efficient optimum size of the virtual gri can now be erive from equation (8) an is given by R opt =r opt /2= e n r +e (9) t A+ce r 1 2 A 2 n A n 1 e The minimum energy consumption characteristic range is no longer a constant an changes with the amount of traffic. Figure 2 shows the relationship between the traffic A an the optimal range r opt. The optimal range is ecreasing as the loae traffic increases. At the extreme point A=0.5, where the transmitter spens 50% of the time transmitting an 50% receiving (we assume the noe can only o one or the other), there is no ile time an so the optimal range converges to char. Uner conitions of light traffic the optimal range increases sharply as the loae traffic ecreases. When the ata transferre in the sensor network is low, the ile state ominates the energy consumption an hence the raio range can be relatively large. 2 5 0 Optimum range, r opt (m) 2 0 0 1 5 0 1 0 0 5 0 0 0 0. 0 5 0. 1 0. 1 5 0. 2 0. 2 5 0. 3 0. 3 5 0. 4 0. 4 5 0. 5 Traffic A(Erlang)
Figure 2: Optimum raio range as a function of the network traffic 5. Transmission Range Ajustment So far, we have only consiere ata in transit across a linear network of routing noes. In a real sensor network, the ata are generate internally. In many applications of wireless sensor networks, ata is gathere by multiple sensors at ifferent locations an transmitte to a single sink noe (such as a base station) where ata can be store an analyze. If the relay noe is close to the sink there is more traffic to be forware than for that of the relay noes far from the sink. For more energy efficient transmission this noe can use short range transmission accoring to the relationship between optimal range an loae traffic that we have euce above for the transport network. However, noes far from the sink have less ata to forwar an have longer ile times therefore they shoul use a longer raio range such that noes not involve in routing can be put into the sleep state. Thus we are le to consier a non-uniform gri covering the network. In this section we consier a sensor network collecting ata at all noes an forwaring all the ata to a base station. We will compare the normal uniform gri of the GAF protocol with non-uniform gris where the gri size is ajuste accoring to the local traffic level. We consier a linear network where the ensity of noes is uniform. The network contains a single sink on one ege at x=0. If each noe prouces a Erlang of ata then the traffic to be forware at a point that is x meters away from base station is A x = x n a (10) where is the size of the network an n is the noe ensity. Figure 3 shows a network that is covere by such a virtual gri. x r 3 =R 3 r 2 =R 2 + R 1 r 1 =R 1 R 3 R 2 R 1 Base station Figure 3: Linear network ivie by virtual gris of ifferent size We consier two heuristic algorithms base on the range-traffic relationship (9). In the first algorithm, the gri sizes for gri section-specific traffic levels are calculate iteratively as follows i (11) R 1 =R opt x=r 1,R 2 =R opt x=r 2 +R 1,,R i =R opt x= R j where R opt is the optimal gri size for the regular transport network erive in section 2, equation (9). To guarantee any noe in one gri section can connect to any noe in the immeiately ajacent ownstream gri section, the raio range in each section has been chosen as follows r 1 =R 1,r 2 =R 2 +R 1,,r i =R i +R i 1 (12) In the case where the length of the linear network is =600 m, noe ensity n =1/6 per meter an every noe prouces ata at a rate a=0.003 Erlang, the energy efficient optimal gri sizes are shown in table 1. i R i (m) 1 20.8 2 21.2 3 21.6 4 22.0 5 22.5 j=1
6 23.1 7 23.7 8 24.4 9 25.1 10 26.0 11 27.0 12 28.2 13 29.6 14 31.4 15 33.7 16 37.0 17 42.1 18 53.7 19 86.7 Table 1. Gri sizes calculate accoring to the algorithm of equations (11) for a 600m linear network. The traffic originating in section i of the gri is forware to the base station by the relay noe in section i-1 of the gri. The traffic hanle by the routing noe in any given section of the gri is passe irectly to the routing noe in the next section. The total power consumption ue to receiving bits in the i th gri section is given by P r i =e r R 1... R i n ab (13) Recall that the transmitte traffic in the ith gri, A t (i)=(-r 1 - -R i )n a, is ifferent to the receive traffic, A t(i)=(-r 1- -R i-1)n a, an so the power consume by transmission in the ith gri is (14) e E t i ={ t R 1 n n ab, i= 1 [ e t R i +R i 1 n ] R 1... r i 1 n ab, i> 1 The energy consumption of the relay noe uring the fractional ile time T ile(i)=1-2(-r 1- -R i)n a is P ile i =e r [1 2 R 1... R i n a ]B (15) Here we suppose the energy consumption in the ile state is the same as in the receiving state. The total power consumption of the whole network is k P= i=1 P r i +P t i +P ile i For the specific case represente by the network gri in table 1 we fin the total power consumption to be, P=9.51x10-4 J/s. However, we can improve still further on the total power consumption since the raio range r i =R i +R i+1, which we actually use in the i th gri, is not quite the same as the optimal range assume in calculating the gri size (r i=2r i, see equation (9)). To save a little more power we shoul choose the optimal raio range instea of optimal gri size as we have one. The gri sizes an raio ranges can then be calculate as follows R 1 =r opt x=r 1, R 2 +R 3 =r opt x=r 1 +R 3,,R i 1 +R i =r opt x= R j (17) The first gri, R 1, is no longer specifie by the algorithm (this is ue to a bounary conition effect so that the raio range require in the first an secon gri sections is etermine by ientical equations) an it can be chosen from the range 0 R 1 [R 1 r opt x=r 1 ]. The energy consumption of the whole network is almost invariant to the value of R 1 when R 1 is chosen from a large region aroun r opt(x=r 1)/2. To ensure the gri sizes change evenly an also that there is a high probability of fining a noe in the gris we aopt R 1 =r opt (x=r 1 )/2. The gri sizes calculate accoring to algorithm 2 are shown in table 2 (note that the number of gris is one fewer in this case). i R i (m) 1 21.2 i j=1 (16)
2 21.2 3 22.0 4 22.1 5 23.1 6 23.2 7 24.3 8 24.6 9 25.9 10 26.4 11 28.0 12 28.8 13 31.1 14 32.7 15 36.5 16 40.6 17 52.2 18 116 Table 2. Gri sizes accoring to the algorithm of equations (17) The total energy consumption is now P=9.01x10-4 J/s which is slightly better than the result we obtaine for algorithm 1. We now compare our range ajustment GAF algorithm with the unmoifie GAF protocol where a uniform gri solution is use as shown in Figure 4. r i =2R r 1 =R Base station Figure 4: Linear network ivie by equal size virtual gris The energy consumption in the transmission, receiving an ile states respectively are P t i ={ e t R n n ab, i= 1 [e t 2R n ] [ i 1 R ] n ab, i> 1 P r i =e r ir n ab P ile i =e r [1 2 ir n a ]B (18) (19) (20) The gri size R is unetermine an is chosen from 0<R. To obtain a more energy efficient GAF protocol, R shoul be etermine by some other methos. In Figure 5, the total energy consumption is plotte versus the number of gris for equal gri ivision. The energy consumption for the unequal gri ivision is also shown in Figure 5 as a single point since the number of gri sections is no longer a free parameter. We see that lower energy consumption has been achieve when the linear network is ivie into a virtual routing gri accoring to the new range-traffic relationship we have propose rather than using equal gri ivision. In our specific case, 50% of the total power is save compare with the best case of equal gri ivision where the total energy consumption is 2.1x10-3 J/s.
6 x 10-3 Energy consumption, P (J/s) 5 4 Equal range 3 2 Range ajustment: algorithm 1 1 0 Range ajustment: algorithm 2 10 20 30 40 50 60 70 80 90 100 Number of gri sections, K Figure 5: Total energy consumption of the network for the stanar uniform gri an the new non-uniform gri. 6. Conclusions In wireless a hoc sensor networks, energy use is in many cases the most important constraint since it correspons irectly to operational lifetime. Topology management such as GAF puts the noes not involve in forwaring to sleep to save energy. The raio range will affect the number of neighbour noes, which collaborate to forwar ata to the sink. In this paper we have euce the relationship between optimal raio range an traffic for a one imensional network an fin that half of the power can be save, if the raio range is ajuste, compare with the best case where equal raio ranges are use. This woul translate into a oubling of the network lifetime. We also showe that iviing the network into unequal gris accoring to the optimal range-traffic relationship can save a little more energy than by using the optimal size-traffic relationship. The concept of raio range ajustment can clearly be applie in other topology management algorithms to save energy. 7. Acknowlegements The authors woul lime to thank BT for financial support of this work. 8. References [1] M. Stemm, R. H. Katz, Measuring an reucing energy consumption of network interfaces in han-hel evices, IEICE Transactions on Communications E80-B (8) (1997) pp. 1125 1131. [2] O. Kasten, Energy consumption, Eth-Zurich, Swiss Feeral Institute of Technology, 2001. Available from <http://www.inf.ethz.ch/~kasten/research/bathtub/energy_consumption.html>. [3] B. J. Chen, K. Jamieson, H. Balakrishnan, R. Morris, Span: an energy-efficient coorination algorithm for topology maintenance in a hoc wireless networks, Wireless Networks 8 (5) (2002) 481-494. [4] M. Bharwaj, T. Garnett, A. P. Chanrakasan, Upper bouns on the lifetime of sensor networks, in: Proceeings of ICC 01, vol. 3, Helsinki, Finlan, June 2001, pp. 785-790. [5] R. Min, M. Bharwaj, N. Ickes, A. Wang, A. Chanrakasan, The harware an the network: total-system strategies for power aware wireless microsensors, in: Proceeings of IEEE CAS Workshop on Wireless Communications an Networking, Pasaena, USA, September 2002, pp. 36-12. [6] W. R. Heinzelman, A. C., H. Balakrishnan, Energy-efficient communication protocol for wireless microsensor networks, in: Proceeings of HICSS 00, vol. 2, Hawaii, USA, January 2000, pp. 4-7. [7] Y. Xu, J. Heiemann, D. Estrin, Geography-informe energy conservation for a hoc routing, in: Proceeings of ACMMobile 01, Rome, Italy, July 2001, pp. 70-84.
[8] A. Cerpa, D. Estrin, ASCENT: aaptive self-configuring sensor networks topologies, in: Proceeings of INFOCOM 02, vol. 3, New York, USA, June2002, pp. 1278-1287. [9] Y. Xu, J. Heiemann, D. Estrin, Energy conservation by aaptive clustering for a-hoc networks, in: Poster Session of MobiHoc 02, Lausanne, Switzerlan, June 2002, pp. 255-263. [10] Y. Xu., J. Heiemann, D. Estrin, Aaptive energy-conserving routing for multihop a hoc networks, USC/ISI Research Report TR-2000-527, 2000. Available from <http://www.isi.eu/~johnh/papers/xu00a.html>. [11] T. Rappaport, Wireless Communications: Principles & Practice, Prentice-Hall Inc., New Jersey, 1996.