Battery-Aware Relay Selection for Energy Harvesting Cooperative Networks
aa r X i v : . [ c s . I T ] A ug Battery-Aware Relay Selection for EnergyHarvesting Cooperative Networks
Yu-Hsien Lee and Kuang-Hao Liu
Institute of Computer and Communication EngineeringNational Cheng Kung UniversityTainan, Taiwan 701Email: { q36014413, khliu } @mail.ncku.edu.tw Abstract —The use of energy harvesting (EH) nodes as cooper-ative relays is an emerging solution for enabling green wirelesssystems. In this paper, we consider multiple EH relay nodesharvesting energy from the radio frequency (RF) signal receivedfrom the source and use that harvested energy to forward thesource information to the destination. Unlike conventional relayswith fixed power supplies, EH relays may not be permanentlyavailable to assist the source transmission due to the limitedenergy conversion efficiency, the mismatch between the chargingand discharging profiles, and the finite energy storage capacity.We propose the battery-aware relay selection (BARS) scheme,which jointly considers the channel condition and the batterystatus for relay selection. The outage probability of the proposedscheme is analyzed using a Markov chain model. Simulations areperformed to validate the analysis accuracy. Through numericalresults, we show that the proposed BARS scheme can achievefull diversity order equal to the number of relays without theneed of fixed power cables.
I. I
NTRODUCTION
Powering wireless devices by sustainable energy is anemerging solution to enable green wireless networks [1].Known as energy harvesting (EH), passively powered devicescollect energy from external power sources, such as vibration,solar, thermoelectric effects, ambient radio frequency (RF)radiation, and so forth, to maintain their physical operationswithout any wiring cost. In this work, we are interested in EHbased on RF signals [2].One of the potential applications of EH nodes is thecooperative relays, which are deployed to extend networkcoverage and improve transmission reliability between twodistant nodes. Traditionally, relays are powered by fixed powersupplies, leading to extra power consumption for informationrelaying. It is thus desirable to replace traditional relays byEH relays that power themselves by the energy harvestedfrom the source signal as a green communication solution.In this context, no additional power is consumed to performinformation relaying but the key challenge is that these EHrelays may not be permanently available to help as theirtraditional counterparts. When more EH relays are short ofenough energy to transmit, it implies less diversity branchescan be used to pass the source information, leading to lowdiversity gain.Several practical constraints hinder the EH relays from be-ing useful to cooperate. Firsly, only a portion of the harvested energy is available to use, because the energy collected by theenergy harvester circuit needs to be converted to DC voltagefirst. Depending on the conversion circuit design, the energyconversion efficiency reported in the literature varies from ∼ [3], [4]. Since the harvested energy from a singleshot may be far from enough to be used for transmission, itis desirable to accumulate the harvested energy by storing itin an energy storage such as a rechargable battery or a supercpacitor for the later use. In practice, the energy storage islimited in size, and thus EH relays may encounter energyshortage whenever the energy consumption rate is higher thanthe energy harvesting rate. One countermeasure is thus toselect those relays with sufficient energy to cooperate via acertain relay selection scheme.Relay selection has been extensively addressed for conven-tional relays. Previous research indicates that selecting onerelay with the superior channel condition than the othersis promising in achieving the same diversity-multiplexingtradeoff as that by using sophiticated space-time codingschemes [5], [6]. Such a relay selection scheme, referred tochannel state information (CSI)-based scheme, may fail tofully exploit the diversity gain if the selected relay lacks ofsufficient power to transmit and thus it is not suitable tocooperative networks with EH relays. In [7], the CSI-basedrelay selection is applied to cooperative networks where EHrelays are subject to finite energy storage and limited energyconversion efficiency. It is shown that the CSI-based relayselection scheme does not achieve any diversity gain evenwith a large battery. In [8], the authors consider two relayselection schemes, namely the random relay selection and thedistance-based relay selection schemes, in cooperative net-works with EH relays. Their analysis shows that the diversitygain achieved by these two methods is at most two. Theanalysis conducted in [9] further reveals that the diversity gainachieved by the CSI-based relay selection scheme using EHrelays is only half of that using traditional relays.In this work, we propose a new relay selection for EHrelays. The proposed scheme, referred to as battery-aware relayselection (BARS), employs both CSI and battery status formaking the relay selection decision. We analyze the outageprobability of BARS by developing a Markov-chain model thatcaptures the evolution of battery status at each relay selection r dr b r N Fig. 1. A two-hop cooperative communication network with multiple relayspowered by the energy harvested from the source signal. epoch. Numerical results are presented to validate the analysisaccuracy and demonstrate the performance of the proposedrelay selection scheme with EH relays subject to numeroussystem parameters. The rest of this paper is organized asfollows. Sec. II explains the system model. The traditionalCSI-based and the proposed relay selections schemes areintroduced in Sec. III. Performance analysis is conducted inSec. IV, followed by numerical results in Sec. V. Concludingremarks are drawn in Sec. VI.II. S
YSTEM M ODEL
Consider a multi-relay network with one source s , onedestination d , and N relays r , · · · , r N , as shown in Fig. 1.The communication between s and d relies on the intermediaterelays that perform decode-and-forward (DF) to forward thesource information, assuming that the direct link between s and d is not available. In this work, the RF signal emitted by s is the sole energy source for relays. The harvested energyis stored in a rechargeable battery of size B by convertingthe RF signal into the DC voltage. The conversion efficiencyis characterized by the parameter κ ∈ [0 , . The batterysize is assumed to be identical for all relays, and a discretebattery model is employed. Specifically, each relay battery isquantized into L levels. Let b l denote the i th quantization levelfor l = 0 , , · · · , L + 1 . The battery level associated with relay r i , denoted as V i , corresponds to level l if V i ∈ ( b l , b l +1 ] with b = 0 and b L +1 = B . The battery is assumed to be linearsuch that the charging and discharging rates are constant.The source transmit with a fixed power P , while relay r i transmit power P r i is adjusted to ensure the successfuldecoding at the destination. To support the transmission rateof R bits/sec/Hz, the decoding threshold T equals R − .Hence the minimum transmit power required for successfuldecoding by d is P r i = T /h i , where h i denotes the channelgain power between r i and d . The harvested energy fromthe source transmission at relay r i is E i = P g i κ , where g i is the channel gain power between s and r i . AssumingRayleigh fading channels, both g i ’s and h i ’s are exponentially distributed with mean ¯ g i and ¯ h i , respectively. In addition, thethermal noise power N at the receiving end is assumed tobe identical for all nodes. Therefore, the signal-to-noise ratio(SNR) P/N is a constant.III. R ELAY S ELECTION
We first review the CSI-based relay selection scheme forconventional relays. Considering DF relays, define the set ofrelays that can decode successfully as the decoding set, i.e., D ( s ) = { r i | P s g i N ≥ T } . From this decoding set, the best relay,denoted as r CSI b , is chosen as the one with the superior relay-destination channel condition than the others. Such a CSI-based relay selection scheme can be expressed as r CSI b = arg max r i ∈D ( s ) h i . (1)This is scheme is recognized as the optimal diversity-achievingrelay selection scheme because it achieves the same diversitygain as using multiple relays to forward the source signal butconsuming much less radio resources. For EH relays withfinite energy storage, however, the selected relay accordingto (1) might lack of enough power to transmit, yet its channelcondition is the best.To overcome this drawback, we propose to select thecooperating relay with battery status taking into account. Tothis end, we first define a subset of relays that not only candecode the source information but also has sufficient power totransmit. Such a set of relays is referred to as the forwardingset defined as F ( s ) = (cid:26) r i (cid:12)(cid:12)(cid:12) ( P s g i N ≥ T ) ∩ ( V i ≥ P r i ) (cid:27) , (2)where V i is the current battery level of relay r i at the selectionepoch. Given the forwarding set, the best relay selected by theproposed scheme, referred to as battery-aware relay selection(BARS), can be expressed as r BARS b = arg min r i ∈F ( s ) E i , (3)where E i = P s g i κ is the harvested energy by relay r i .The rational behind BARS is two-fold. Firstly, selecting thebest relay from the forwarding set ensures that the selectedrelay can successfully decode the source information andhas sufficient power to transmit. This is important to fullyexploit the selection gain provided by multiple relays basedon energy harvesting. Secondly, by choosing the relay withthe minimum harvested energy in the forwarding set, the ac-cumulated amount of harvested energy per source transmissionis maximized because there are always at least N − relaysperforming energy harvesting (it is possible that all the N relays will harvest energy if the forwarding set is empty).We note that although we do not have a rigorous proof forthe achievable diversity gain of BARS, the numerical resultsshown in Sec. V reveal that BARS is plausible to achieve fulldiversity order equal to the number of available relays. Thekey to this success lies in the consideration of the forwardingset F ( s ) in relay selection. If we replace the role of F ( s ) inhe selection rule (3) by D ( s ) , i.e., ignoring the battery status,full diversity gain is not guaranteed. The modified scheme,referred to the benchmark scheme, can be expressed as r Benchmark b = arg min r i ∈D ( s ) E i , (4)and its performance will be discussed in Sec. V.IV. P ERFORMANCE A NALYSIS
In BARS, the outage event occurs only when all the relaysare in the harvesting mode, i.e, the forward set F ( s ) is empty.From (2), whether a relay performs energy harvesting or dataforwarding depends on both its battery status and the channelconditions. Based on the discrete battery model, the battery ofan arbitrary relay may be in one of the L + 2 levels and thereare total of ( L + 2) N combinations of battery status for N relays. Denote s j = ( V , V , · · · , V N ) as the j th combination,where V i = { , · · · , L + 1 } for i = 1 , · · · , N . The outageprobability of BARS can be expressed in the following generalform as P out = ( L +2) N X j =1 Pr[ F ( s ) = ∅| s j ] Pr[ s j ] . (5)In (5), the conditional probability, Pr[ F ( s ) = ∅| s j ] dependson the specific configuration of s j and thus there is no generalform. On the other hand, the probability Pr[ s j ] can be obtainedby modeling the charging/discharging behavior of each relaybattery status as a discrete-time Markov chain (DTMC) withfinite states. The transition probability of the DTMC is definedas P = [ p j,k ] where p j,k denotes the transition probabilityfrom state s j to state s k . It can be verified that P is irreducibleand row stochastic, and thus there exists an unique steady-state probability vector π = { π j } ( L +2) N j =1 , where π j = Pr[ s j ] .Again, P does not have a general expression but can beobtained explicitly given the numbers of relays and batterylevels. In the following, we first derive the battery statetransitions of an arbitrary relay, which serve as the basis forconstructing P . To ease the presentation, F X ( · ) represents theCDF of a random variable X . A. Battery State Transitions of An Arbitrary Relay
For convenience, define A f ( m ) the event that a relay withbattery state V m is in the forwarding mode. According to (2), A f ( m ) , ( P g i /N ≥ T ) ∩ ( b m ≥ P r i ) with probability Pr[ A f ( m )] = (1 − F g i (cid:0) T N P (cid:1) )(1 − F h i (cid:0) Tb m (cid:1) ) (6)Similarly, denote the event of a relay with battery state V m isin the charging mode mode by A c ( m ) , ( b m < P r i ) ∪ [( b m ≥ P r i ) ∩ ( P g i /N < T )] with probability Pr[ A c ( m )] = F h i (cid:0) Tb m (cid:1) + h − F h i (cid:0) Tb m (cid:1)i F g i (cid:0) T N P (cid:1) . (7) m = n for ≤ m < L + 1 : The relay battery levelremains unchanged if the relay r i is in the charging mode but the collected energy does not increase the battery level withprobability p m,m = Pr[ A c ( m ) ∩ ( b m ≤ b m + P g i κ < b m +1 ]= Pr[( b m < P r i ) ∩ ( g i < b P κ )]+ Pr[ (cid:0) ( b m ≥ P r i ) ∩ ( P g i N < T ) (cid:1) ∩ ( g i < b P κ )]= F g i (cid:0) b P κ (cid:1) F h i (cid:0) Tb m (cid:1) + ( F g i (cid:0) T N P (cid:1) , T < b κ ,F g i (cid:0) b P κ (cid:1) , T ≥ b κ , Q ( m ) . (8) m = 0 , n = L + 1 : Given the battery is empty, relay r i must be in the charging mode. The probability that the relaybattery becomes fully charged is identical to p ,L +1 = Pr[ P g i κ ≥ B ] = 1 − F g i (cid:0) ακ (cid:1) , Q (0 , L + 1) . (9) m = 0 , < n < L + 1 : In this case relay r i withan empty battery harvests energy from the received signalsuch that its battery becomes partially charged. This transitionprobability is equal to p ,n = Pr[ b n ≤ P h i κ < b n +1 ] = F g i (cid:0) b n +1 P κ (cid:1) − F g i (cid:0) b n P κ (cid:1) , Q (0 , n ) . (10) < m ≤ L + 1 , n < m : The relay battery levelis reduced from level m to level n only if the relay is inthe forwarding mode. Hence, the transition probability can befound as p m,n = Pr[ A f ( m ) ∩ ( b n ≥ b m − P r i < b n +1 )]= h − F g i (cid:0) T N P (cid:1)ih F h i (cid:0) Tb m − b n +1 (cid:1) − F h i (cid:0) Tb m − b n (cid:1)i , Q ( m, n ) . (11) < m ≤ L + 1 , n = L + 1 : The partially chargedrelay battery becomes fully charged if the relay is in thecharging mode and the amount of harvested energy exceedsthe remaining space of the battery, whose probability is givenby p m,L +1 = Pr[ A c ( m ) ∩ ( P g i κ ≥ B − b m )]= F h i (cid:0) Tb m (cid:1)h − F g i (cid:0) αP − b m P κ (cid:1)i + ( , T ≤ αP − b m κ ,F g i (cid:0) T N P (cid:1) − F g i (cid:0) αP − b m P κ (cid:1) , T > αP − b m κ , Q ( m, L + 1) . (12) < m < n < L + 1 : This corresponds to the casethat the non-empty battery remains not full after harvestinghe energy, which takes place with probability p m,n = Pr[ A c ( m ) ∩ ( b n < b m + P g i κ < b n +1 )]= F h i (cid:0) Tκ (cid:1)h F g i (cid:0) b n +1 − b n P κ (cid:1) − F g i (cid:0) b n − b m P κ (cid:1)i + , T < b n − b m κ ,F g i (cid:0) T N P (cid:1) − F g i (cid:0) b n − b m P κ (cid:1) , b n − b m κ ≤ T < b n +1 − b m κ ,F g i (cid:0) b n +1 − b m P κ (cid:1) − F g i (cid:0) b n − b m P κ (cid:1) , T ≥ b n +1 − b m κ , Q ( m, n ) . (13) m = n = L + 1 : This case arises only when the relayis in the charging mode with probability p L +1 ,L +1 = Pr[ A c ( L + 1)] , Q ( L + 1) , (14)where Pr[ A c ( L + 1)] has been given in (7). B. Transition Probability Matrix
Based on the state transition probabilities obtained in theprevious subsection, the transition probability matrix of theDTMC can be constructed. Since the number of states growsexponentially with the number of relays, a systematic approachis provided below to facilitate the construction of the transitionprobability matrix.Step 1: Identify all the possible combinations of the for-warding set F ( s ) . Given N relays, there are N different configurations of F ( s ) .Step 2: For each F ( s ) , find the associated transition proba-bilities. For example, if L = 1 and N = 2 , there willbe combinations of F ( s ) . Consider F ( s ) = { r } ,one of the potential state transitions is from (1 , to (0 , where r ’s battery level is reduced by one levelwith probability Q (1 , and r ’s battery remainsempty with probability Q (0) .Step 3: Once the transition probability matrix P is obtained,the steady-state probabilities can be obtained bysolving the balanced equation π P = π along withthe normalized condition P ( L +2) N m =1 π m = 1 V. R
ESULTS AND D ISCUSSIONS
This section presents numerical results to demonstrate theperformance of the proposed BARS scheme. Unless specified,the following parameters are used throughout this section: R =1 bits/Sec/Hz, N = 1 , and ¯ g i = ¯ h i = 1 . In simulations, allrelay batteries are set to be full initially. Each curve in thefigure is obtained from independent runs. Besides, we use“Theo” and “Sim” to indicate the theoretical and simulationresults, respectively.Fig. 2 shows the outage probability of BARS versus SNRunder different number of relays N and the number of batteryquantization levels L . Here we fix the battery scaling factor α = 1 and the energy conversion efficiency κ = 0 . . For L =1 , both theoretical and simulation results are included whileonly simulation results are shown for L = 100 . It can be seenthat the theoretical results agree with the simulated ones well.When L = 1 , the outage probability decreases with N butincurs a severe error floor at high SNR. This is because a small SNR (dB) -5 -4 -3 -2 -1 O u t a g e p r o b a b ili t y L=1, N=2 (Theo)L=1, N=3 (Theo)L=1, N=4 (Theo)SimL=100, N=2 (Sim)L=100, N=3 (Sim)L=100, N=4 (Sim)
Fig. 2. Outage probability of BARS under varied L and N with fixed κ = 0 . . L implies a lossy quantization interval. In this case, the amountof stored energy can hardly reach the quantization thresholdand thus the battery is often at the low level. This problem canbe resolved by increasing L that in turns reduces the risk ofno relays eligible to help. As L increases to 100, the slope ofthe outage probability curve is equal to the number of relays N , which suggests that BARS can fully explore diversity gainprovided with sufficient battery quantization levels.Fig. 3 investigates the impact of energy conversion ef-ficiency κ for N = 3 . Intuitively, the outage probabilitydecreases with increasing κ , but the decreasing trend is lesssignificant when L is large. This is because a larger L impliesa finer granularity of the battery level such that the batterystatus is not sensitive to κ . For L = 10 and 100, the outageperformance of BARS is nearly saturated at κ = 0 . , whichis about the practical value of most RF energy harvesters.In other words, the room for further improvement by moresophisticated energy harvester might not be as notable asexpected.The impact of battery size to the outage performance isexplored in Fig. 4 by varying the battery scaling factor α .Here, we set L = 100 , κ = 0 . , SNR = 20 dB, R = 2 bits/sec/Hz, and only simulation results are shown. It followsthe intuition that increasing the battery size helps to reducethe outage probability, but the gain becomes diminished when α > . , regardless of the number of relays N . This can beexplained by the fact that when the battery is larger than acertain degree, it is less likely to be fully charged given alimited energy conversion efficiency. On the other hand, theimpact of battery size is more significant when N is larger, asa consequence of selection diversity.Finally, we compare the performance of BARS with theCSI-based relay selection scheme in (1) and the benchmarkscheme in (4). In Fig. 5, we fix κ = 0 . and consider N = 2 and 3. One can see the significant improvement of BARS overthe CSI-based and the benchmark relay selection schemes, .1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Energy conversion efficiency κ -4 -3 -2 -1 O u t a g e p r o b a b ili t y SNR=10 dB, L=1 (Theo)SNR=10 dB, L=10 (Theo)SNR=10 dB, L=100 (Sim)simSNR=20 dB, L=1 (Theo)SNR=20 dB, L=10 (Theo)SNR=20 dB, L=100 (Sim)
Fig. 3. Outage probability of BARS vs. energy conversion efficiency κ undervaried L and SNR for N = 3 . Battery scaling factor α -4 -3 -2 -1 O u t a g e p r o b a b ili t y N=2 (Sim)N=3 (Sim)N=4 (Sim)
Fig. 4. Outage probability of BARS vs. battery scaling factor α under varied N with L = 100 , κ = 0 . , SNR=20 dB, and R = 2 bits/sec/Hz. both failing to achieve full diversity gain. We note that thediversity order of BARS shown in the graph is slightly lessthan N primarily because a small quantization resolution ofthe battery is used ( L = 10 ). BARS can achieve full diversityorder provided with L = 100 , as shown in Fig. 2.VI. C ONCLUSION
In this paper, we proposed a relay selection scheme calledBARS for EH relays. BARS differs from traditional relayselection schemes based on CSI in that it takes into accountthe battery status of relays in order to prevent selecting therelay lacking of energy to forward the source signal, a keyfactor that deteriorates the performance of EH relays withfinite battery. In BARS, the relays that can decode the sourceinformation and have sufficient power to transmit are definedas the forwarding set. In this set, the best relay is chosen
SNR (dB) -5 -4 -3 -2 -1 O u t a g e p r o b a b ili t y CSI, N=2CSI, N=3Benchmark, N=2Benchmark, N=3BARS, N=2 (Theo)BARS, N=3 (Theo)Sim
Fig. 5. Comparison of outage probabilities for BARS and CSI-based relayselection with L = 10 and κ = 0 . . as the one that has the least harvested energy, depending onthe source-relay channel condition and the energy conversionefficiency of the energy harvester. Such a selection allows thenetwork to collect the largest amount of harvested energy persource transmission. The performance of BARS is analyzedtheoretically based on a discretized battery model. Our resultsreveal that BARS achieves full diversity order and significantlyoutperforms the traditional CSI-based relay selection scheme,which fails to fully exploit diversity gain provided by multipleEH relays. R EFERENCES[1] L. X. Cai, H. V. Poor, Y. Liu, T. H. Luan, X. S. Shen, and J. W. Mark,“Dimensioning network deployment and resource management in greenmesh networks,”
IEEE Wireless Commun. , vol. 18, no. 5, pp. 58–65, Oct.2011.[2] H. Ju and R. Zhang, “A novel mode switching scheme utilizing randombeamforming for opportunistic energy harvesting,”
IEEE Trans. WirelessCommun. , vol. 13, no. 4, pp. 2150–2162, Apr. 2014.[3] T. Le, K. Mayaram, and T. Fiez, “Efficient far-field radio frequency energyharvesting for passively powered sensor networks,”
IEEE J. Solid-StateCircuits , vol. 43, no. 5, pp. 1287–1302, May 2008.[4] M. T. Penella-Lopez and M. Gasulla-Forner,
Powering AutonomousSensors: An Integral Approach with Focus on Solar and RF EnergyHarvesting . Springer, 2011.[5] A. Bletsas, A. Khisti, D. Reed, and A. Lippman, “A simple cooperativediversity method based on network path selection,”
IEEE J. Select. AreaCommun. , vol. 24, no. 3, pp. 659–673, Mar. 2006.[6] E. Beres and R. Adve, “On selection cooperation in distributed networks,”in
Proc. 2006 Conference on Information Sciences and Systems (CISS2006) , Mar. 2006.[7] K.-H. Liu, “Selection cooperation using RF energy harvesting relays withfinite energy buffer,” in