Distributed Scheduling in Wireless Powered Communication Network: Protocol Design and Performance Analysis
aa r X i v : . [ c s . N I] M a r Distributed Scheduling in Wireless PoweredCommunication Network: Protocol Design andPerformance Analysis
Suzhi Bi ∗ , Ying Jun (Angela) Zhang † , and Rui Zhang ‡∗ College of Information Engineering, Shenzhen University, Shenzhen, Guangdong, China 518060 † Department of Information Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong SAR ‡ Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583E-mail: [email protected], [email protected], [email protected]
Abstract —Wireless powered communication network (WPCN)is a novel networking paradigm that uses radio frequency (RF)wireless energy transfer (WET) technology to power the informa-tion transmissions of wireless devices (WDs). When energy andinformation are transferred in the same frequency band, a majordesign issue is transmission scheduling to avoid interference andachieve high communication performance. Commonly used cen-tralized scheduling methods in WPCN may result in high controlsignaling overhead and thus are not suitable for wireless networksconstituting a large number of WDs with random locations anddynamic operations. To tackle this issue, we propose in this papera distributed scheduling protocol for energy and informationtransmissions in WPCN. Specifically, we allow a WD that isabout to deplete its battery to broadcast an energy request buzz(ERB), which triggers WET from its associated hybrid accesspoint (HAP) to recharge the battery. If no ERB is sent, the WDscontend to transmit data to the HAP using the conventional p -persistent CSMA (carrier sensing multiple access). In particular,we propose an energy queueing model based on an energydecoupling property to derive the throughput performance. Ouranalysis is verified through simulations under practical networkparameters, which demonstrate good throughput performance ofthe distributed scheduling protocol and reveal some interestingdesign insights that are different from conventional contention-based communication network assuming the WDs are poweredwith unlimited energy supplies. I. I
NTRODUCTION
The recent development of RF-enabled WET technol-ogy provides a new solution to continuously power energy-constrained wireless devices (WDs) over the air [1], [2].Wireless power in tens to several hundred of microwatts canbe effectively transferred to WDs within ten meters distance,making self-sustainable network operation truly feasible andefficient for many low-power wireless applications, e.g., wire-less sensor networks and RF identity (RFID) systems with alarge number of WDs. The application of WET to wirelesscommunications spurs a novel networking structure namedwireless powered communication network (WPCN), wherethe WDs transmit information using the energy harvested bymeans of WET [3]. WPCN removes the need of frequent
This work was supported in part by the National Natural Science Foundationof China (Project number 61501303), and the Foundation of Shenzhen City(Project numbers JCYJ20160307153818306). The work of Y. J. Zhang wassupported in part by General Research Funding (Project number 14209414)from the Research Grants Council of Hong Kong and by the National BasicResearch Program (973 program Program number 2013CB336701).
WD1
EnergyTransmitter
HAP
Data flowEnergy flow
WD2
CommunicationCircuit
EnergyReceiver
CommunicationCircuit
WD3
EnergyTransmitter
CommunicationCircuit
Fig. 1. A TDD based wireless powered communication network [1]. battery replacement/recharging and reduces the probabilityof energy outage. The network lifetime can thus be largelyextended and the communication performance can also beimproved with more sustainable power supply.As shown in Fig. 1, we consider a single-cell WPCN wherea hybrid access point (HAP) is responsible for transmittingwireless energy to and receiving wireless information transmis-sion (WIT) from a set of distributed WDs [1]. In practice, WETand WIT are desired to operate in the same frequency bandto achieve higher spectrum efficiency and cost effectiveness.In this case, time-division-duplexing (TDD) circuit structuresare applied at both HAP and WDs to switch between WETand WIT modes to avoid the harmful interference from WETto information decoding [4]. While a major design challengeis transmission scheduling for WET and WIT to achieve bothefficient communication and energy harvesting. Most of theexisting studies in WPCN have assumed the HAP to centrallycoordinate the WET and WIT with the WDs. For instance, [5]proposes a round-robin based scheduling, where the HAP andWDs take turns to transmit energy or data. The duration ofeach WD’s transmission is optimized by the HAP accordingto the global instantaneous channel state information (CSI)and then sent to all the WDs. [6] later extends [5] to thecase with a multi-antenna HAP that enables more efficientenergy beamforming technique for WET and SDMA (spatialduplexing multiple access) for WIT. A similar round-robinbased scheduling method is considered in [7], where each energy-harvesting WD can be either active or inactive in atime slot to achieve a balance between communication delayand energy consumption. In addition, [8] considers a polling-based method that the HAP periodically inquires the WDsabout their residual energy levels and performs WET wheneversome WDs are in low battery state.In practice, the above centralized methods often incur con-siderable signaling overhead on channel estimation, control,synchronization, etc. This could be costly in networks witha large number of WDs (e.g., sensors) that are randomlydeployed and switch on/off over time for energy saving. In thiscase, distributed scheduling of WET and WIT is of high prac-tical interests. Although distributed wireless charging controland data transmissions have been well investigated separately(e.g., [9]–[12]), there are only few studies integrating them inthe design of WPCN. For instance, [13] proposes an energy-adaptive CSMA-type MAC (medium access control) method,where the access probability of a WD decreases with its energyharvesting rate. However, it assumes that WET is independentof WIT, and thus no joint WET and WIT scheduling isconsidered. [14] proposes a RF-MAC scheme that multipleHAPs are divided into groups to perform WET in respond toWDs’ energy request, and the WDs use CSMA-type randomaccess control to coordinate the data exchange among eachother. The RF-MAC method, however, requires the WDs tobear complicated computation and channel estimation tasks.Further, [15] considers a simplified version of RF-MAC, wherethe throughput performance of a WPCN using a single HAPis evaluated via simulations. Nonetheless, the analysis of bothworks is limited and does not capture the important couplingbetween energy and information transmissions.In this paper, we present a practical distributed schedulingprotocol for WPCN. Similar to the idea of RF-MAC, we alloweach WD that is about to deplete its battery to broadcastan energy request buzz (ERB) signal in order to trigger theWET by the HAP to recharge its battery. If no ERB is sent,the WDs then contend to transmit data to the HAP basedon the conventional p -persistent CSMA. In particular, wepropose an energy queueing model to analyze the throughputperformance of the proposed distributed scheduling protocol.Simulation results are provided to verify our analysis andshow that the proposed method can achieve good throughputperformance as compared to a benchmark p -persistent CSMAnetwork assuming always sufficient energy supply. In addition,an interesting energy decoupling property is revealed, which isuseful in deriving the throughput and understanding the insighton designing distributed scheduling in WPCN.II. S YSTEM M ODEL
As shown in Fig. 1, we consider a WPCN consisting ofa HAP and N WDs, where all the devices each have onesingle antenna. We assume that WET and WIT are performedover the same frequency band, such that each WD’s antenna is p -persistent CSMA achieves similar performance as the exponential back-off scheme in [10] when the transmit probability p t of the WDs is proportionalto the user number [16]. In practice, the HAP is aware of the number ofassociating WDs and thus can calculate p t and broadcast its value to theWDs. WD/HAPchannel sensingEnoughenergy?SendERB NO Harvestenergy WD HAPAny ERBsent?Idle forDIFS?Generate X ~U(0,1) X ≤ P t ? YES
WIT WET
YES
StartIdle forPIFS?
NO NOYES
Datacorrectlydecoded? SendACK
YESNONOYES NO
BroadcastNAKAny datasent?
YES NO, idle slot
Fig. 2. A diagram illustrating the distributed information and energy schedul-ing in WPCN. used for both energy harvesting and communication in a TDDmanner (see WD1 in Fig. 1). The energy harvesting circuitconverts the received RF signal to DC energy and stores ina rechargeable battery. The energy is then used to power theWIT. The HAP also has a similar TDD circuit structure (seeFig. 1) to switch between energy transfer and communicationswith the WDs.We assume that all the N WDs are continuously back-logged, i.e., they always have packets to transmit. Besides,the network is fully connected, such that the transmission ofone device (WD or HAP) can be overheard by all the otherdevices. Meanwhile, all devices are assumed to have carriersensing capability, such that they remain silent when sensingany ongoing energy/information transmission and attempt totransmit only after the channel becomes idle. The proposeddistributed scheduling mechanism is illustrated in Fig. andexplained as follows. A. Distributed WET and WIT Scheduling
In the proposed distributed scheduling mechanism, eachWD continuously monitors its residual battery level. If it isabove a predetermined threshold, the WD waits for the channelto be continuously idle for a DIFS (distributed inter-framespacing) time and then transmits independently a payloadpacket with probability < p t < to the HAP. The durationof DIFS is much larger than the signal round-time-delay(RTD) of the network, such that a WD’s data transmissionwill not interfere with the potential data transmissions of theother WDs due to signal prorogation delay. The packet headercontains the identity of the transmitting WD, such that theHAP can identify the sender if the packet is successfullydecoded. Otherwise, if a WD finds its residual battery levelbelow the threshold, it waits the channel to be continuouslyidle for a PIFS (priority inter-frame spacing) time and then sends a short energy request buzz (ERB) signal. The durationof the PIFS is smaller than that of DIFS (but still muchlarger than the RTD), such that a higher priority is assignedto sending an ERB than a data payload.From the HAP’s perspective, it can identify the current timeslot as a WET slot when sensing any ERB sent, either by oneor multiple WDs, and respond by performing WET for T et amount of time. Meanwhile, all the WDs sensing the ERBsignal switch to energy harvesting mode. Otherwise, if noERB signal is sensed, the HAP identifies the current time slotas a WIT slot and switches to information receiving mode.Due to the close communication range (say, within meters)typically for WPCN, we assume the receiver signal-to-noiseratio (SNR) is sufficiently high and thus neglect the decodingerrors caused by channel fading and receiver noise during datatransmissions. Accordingly, a WIT slot may correspond to oneof the following three scenarios:1) success: if only one WD transmits data, the transmittedpacket can be successfully decoded by the HAP, whichthen responds to the transmitting WD by sending anACK message (containing the ID of the transmitter) aftersensing the channel to be idle for SIFS (short inter-framespacing) time. Notice that SIFS is shorter than the DIFSand PIFS such that no WD will transmit before the HAPsends the ACK;2) collision: if more than one WDs transmit data in thesame time slot, the multiple packets will collide andnone of then can be correctly decoded by the HAP. Inthis case, the HAP broadcasts a NAK message aftersensing the channel to be idle for SIFS. By doing so,the transmitting WDs can identify collision and scheduledata retransmission;3) idle: otherwise, no WD transmits data and all WDs keepsilent for a mini slot of duration σ . Notice that the WDsdo not need to wait for another DIFS time to transmitdata after an idle time slot. Instead, they can persistentlyaccess the channel with probability p t in the followingmini slots until some WD transmits. Therefore, we mayobserve consecutive idle mini slots.After the current time slot, either for WET or WIT, all thedevices continue to sense the wireless medium, and the aboveiteration repeats itself.We use an example to illustrate the operation of the pro-posed protocol in Fig. 3. Initially, the WDs have sufficientenergy to transmit and WD1 transmits successfully. After thechannel becomes idle for DIFS, no WD transmits in twoconsecutive idle time slots each of duration σ , until they bothtransmit data in the third attempt and cause a collision. Then,after transmitting data, WD is lack of energy and sends anERB signal after a PIFS. Upon detecting the ERB signal, theHAP starts WET for the WDs to harvest energy. B. Wireless Energy and Information Transfer Model
For a WET time slot, we assume channel fading effect isaveraged out over the duration of energy transmission suchthat the received energy by the n -th WD is only related toits distance d n to the HAP. Due to the broadcasting nature DIFS Payload(success) DIFS
HAPWD1WD2
ACK ERBPayload(collision)SIFS SIFSNAKPIFS WETSIFSPayload(collision)(idle)(idle)
Fig. 3. A -node example of the distributed scheduling protocol operation. of wireless channels, all the N WDs can harvest energy in aWET time slot. We also assume that the WDs cannot harvestenergy from WIT, as transmit power of WD is significantlylower than that of WET by the HAP, e.g., mW versus W.Thus, the received energy by the n -th WD in a WET slot is R n = ηA d P h T et (cid:18) · πf d d n (cid:19) υ , n = 1 , · · · , N, (1)where η ∈ (0 , denotes the energy harvesting efficiency, A d denotes the antenna gain, P h denotes the power of WET, f d denotes the carrier frequency and υ ≥ denotes the path lossexponent, which is assumed equal for all the WDs.For a WIT slot, we assume that all the WDs transmit withconstant power P w . For the simplicity of analysis, we assumethat each WD transmits a payload of fixed duration T pl ina WIT slot, such that it consumes V n = P w T pl amount ofenergy regardless of that the transmission is successful orresults in a collision. Nonetheless, our analysis can also beextended to the case that the payload lengths are differentin a success and a collision slot, such as a CTS/RTS-likescheme in 802.11 WLAN [10]. With channel error neglected,the decoding failure is only caused by transmit collisions. C. Device Battery Model
In this paper, we consider a discrete energy model andassume that the transmission of each fixed-length payloadconsumes unit of energy and the battery capacity of eachWD is C units, where C >> is a positive integer. Besides,we assume that the n -th WD harvests fixed e n units ofenergy in each WET slot. Here, e n << C is a positiveinteger, n = 1 , · · · , N , depending on the distance betweenthe WD and the HAP. This may correspond to a practicaldesign requirement that e n ≥ , ∀ n , to avoid frequent energytransmissions, which is achievable through either setting along enough T et or preventing ineffective far-away WDs fromassociating with the HAP. We denote B ln as the battery level(in units) of the n -th WD at the end of the l -th time slot,and E ln and Q ln as the number of units of energy harvested Here it means the energy harvested minus that spent on sending ERBsignal. The energy consumption on channel sensing is also neglected forsimplicity. and consumed during the l -th time slot, respectively. Then, thebattery dynamics of the n -th WD can be expressed as B ln = min (cid:8) max (cid:0) B l − n + E ln − Q ln , (cid:1) , C (cid:9) , (2)where l = 1 , , · · · and B n denotes the initial energy level.Depending on the type of the l -th transmission slot, E ln and Q ln can be categorized as follows:1) WET slot: E ln = e n and Q ln = 0 for all the WDs;;2) Success/collision WIT slot: E ln = 0 and Q ln = 1 fortransmitting WDs, and E ln = Q ln = 0 otherwise;3) Idle WIT slot: E ln = Q ln = 0 for all the WDs.Without loss of generality, we assume that a WD sends ERBsignal when B ln = 0 . D. Performance Metric
In this paper, a key performance metric is the normalizednetwork throughput, defined as the percentage of air timeoccupied by successful data transmissions expressed as ψ = P suc · T suc P suc T suc + P col T col + P idl T idl + P ene T ene , (3)where { P suc , P col , P idl , P ene } and { T suc , T col , T idl , T ene } de-note the probabilities of a successful packet transmission slot,a packet collision slot, an idle slot, and an energy transfer slot,respectively. By assuming the durations of ACK and NAK areequal, we can see from Fig. 3 that T suc = T col = DIF S + T pl + SIF S + ACK,T idl = σ, T ene = P IF S + ERB + SIF S + T et . In the next section, we analyze the throughput performance ofthe distributed energy and information scheduling algorithm.III. T
HROUGHPUT P ERFORMANCE A NALYSIS
A. Energy Queueing Model
We start with modeling the battery dynamic of each WDas a B-D queueing process. As shown in Fig. 4, we drop thesuperscript l for simplicity of expression and use B n to denotethe residual energy of the n -th WD at the beginning of a timeslot. We refer to the WD as in the i -th energy state if B n = i , i ∈ { , , · · · , C } . In particular, we use p en ( i ) to denote theprobability of the n -th WD in the i -th energy state observinga WET slot, i = 1 , · · · , C . Therefore, we can express the statetransition probability p n ( i → j ) , which denotes the probabilitythat the n -th WD changes from the i -th to the j -th energy state,as follows: p n ( i → max { i + e n , C } ) = p en ( i ) , (4a) p n ( i → i −
1) = p t (1 − p en ( i )) , (4b) p n ( i → i ) = (1 − p t ) (1 − p en ( i )) , (4c)for intermediate states with < i < C . Besides, the other twoboundary states and C satisfy p n (0 → e n ) = 1 , (5a) p n ( C → C −
1) = p t (1 − p en ( i )) , (5b) p n ( C → C ) = 1 − p t (1 − p en ( i )) . (5c) C-1 3 2 1 0C C-2 C-3 (cid:258) (cid:258) Fig. 4. Energy queueing model of the n -th WD ( e n = 2 ). Here, (4a)-(4c) correspond to a WET slot, a success/collisionWIT slot, and an idle slot, respectively. In addition, (5a) holdsbecause a WD with B n = 0 will immediately send ERB andreceive energy in the current time slot. (5b) and (5c) holdbecause the energy of a fully-charged WD will reduce onlywhen it transmits data, and remain unchanged otherwise.It is evident that the occurrence of an energy transfer slot isrelated to the energy states of all the WDs, where a WET slotoccurs when B n = 0 for some WD n . Accordingly, precisesystem-level analysis requires a high-dimensional Markovsystem that jointly considers the energy states of all the WDs.This, however, renders the problem analytically intractable dueto the large number of inter-connected states. For tractableanalysis, we make in this paper the following energy decou-pling assumption . Energy decoupling assumption (EDA):
In the consideredenergy queueing system (4) and (5), the limiting probabilitiesof the N WDs are independent and each WD n observes aconstant probability of WET in a time slot independent of itscurrent energy state, i.e., p en ( i ) = p en , i = 1 , · · · , C . Remark 1 : The EDA assumption considered in this paperis analogous to the well-known mean-field decoupling assump-tion made in the seminal work on performance analysis of802.11 DCF medium access control [10], where WDs withunlimited energy supply transmit data following a randombackoff mechanism. Specifically, it assumes that when thenumber of WDs in a 802.11 network is large enough, each WDobserves a constant collision probability upon transmission,which is independent of (but in fact related to) the currentbackoff stages of itself and the other WDs.As an initial attempt to investigate the performance ofdistributed scheduling of WET and WIT in WPCN, we leavethe proof of the above EDA assumption in our future work. Forthe time being, the EDA is verified using simulations later inSection V, where we show that this assumption approximatelyholds when the number of WDs is not too small, e.g., N ≥ . B. Queueing Analysis
With the EDA assumption, we can replace p en ( i ) ’s with p en in (4) and (5). We denote the steady-state limiting probabilitiesof the n -th WD as w in , i = 0 , · · · , C . For such a birth-death (B-D) queueing process in Fig. 4, its limiting probabilities satisfythe following equalities by establishing “flow conservation”conditions between two adjacent states, i.e., p t (1 − p en ) w n = w n , (6a) p t (1 − p en ) w in = w n + p en P i − j =1 w jn , i = 2 , · · · , e n , (6b) p t (1 − p en ) w in = p en P e n j =1 w i − jn , i = e n + 1 , · · · , C. (6c) The above C equations, combined with the total probabilitycondition P Ni =0 w in = 1 , can be expressed as H n w n = b , (7)where w n = (cid:0) w n , · · · , w Cn (cid:1) T , b = (0 , · · · , , T , with ( · ) T denoting the matrix transpose and H n = − α n · · · p ne − α n · · · p ne p ne − α n · · ·
00 0 p ne p ne − α n · · · ... . .. . . . . . . . . . . . . ... · · · p ne p ne − α n · · · . Here, α n , p t (1 − p en ) . Because H n is a full-rank squarematrix, we can obtain the steady state limiting probabilitiesas w n = H − n b , with ( · ) − denoting the matrix inverse. Inparticular, we can infer that w n = (cid:2) H − n (cid:3) ,C +1 , (8)where [ · ] i,j denotes the ( i, j ) -th entry of a matrix.Notice that the value of H n is determined by p en and e n for the n -th WD. Therefore, when e n is a fixed parameter, wecan expressed w in (8) as a function of p en , denoted by w n = f n ( p en ) , n = 1 , · · · , N. (9)In general, f n ( p en ) is a polynomial function of p en . For instance,when e n = 2 and C = 3 , f n ( p en ) can be expressed as p t (1 − p en ) p t (1 − p en ) + 2 p t (1 − p en ) + 3 p t p en (1 − p en ) + ( p en ) . Besides, we show in the appendix that f n ( x ) is a decreasingfunction for x ∈ (0 , . C. Throughput Derivation
Notice that each WD n with B n > observes an ongoingERB signal when at least one of the other ( N − WDs is inthe -th energy state. Accordingly, we can express p en as p en = 1 − Q i = n (cid:0) − w i (cid:1) , g n ( w ) , n = 1 , · · · , N, (10)where w = (cid:2) w , · · · , w N (cid:3) T . (10) implies that g n is a non-decreasing function of each entry in w . By stacking the N equations in (9) and N equations in (10), we have w = f (cid:0) g (cid:0) w (cid:1)(cid:1) , Ψ( w ) , (11)where g ( w ) = [ g ( w ) , · · · , g N ( w )] T and f ( x ) =[ f ( x ) , · · · , f N ( x N )] T . Evidently, Ψ is a non-increasing func-tion of w ∈ (0 , N due to the monotonic property of f n . Forinstance, when the WDs are homogeneous, i.e., e n ’s are equalfor all the WDs, we can denote by symmetry that w , w n and p e , p en = 1 − (cid:0) − w (cid:1) N − , ∀ n . In this case, as Ψ( w ) isa non-decreasing function, w can be obtained using simple bi-section search over w ∈ (0 , until w = Ψ( w ) is satisfiedwithin a given precision level. In general, w n ’s can be obtainednumerically, e.g., using the quasi-Newton method. TABLE IS
IMULATION P ARAMETERS
HAP power W Path-loss exponent WD Tx power mW Carrier frequency MHz
DIF S ms P IF S ms SIF S ms ERB ms σ ms ACK ms T pl ms T et . sTransmit antenna gain . Receive antenna gain Given w , we are ready to derive the throughput perfor-mance. Specifically, the probability of a WET slot is P ene = 1 − Q Ni =1 (cid:0) − w i (cid:1) , (12)i.e., at least one of the WDs sends ERB. Accordingly, theprobability of an information transmission slot is P it = 1 − P ene . Then, the probability of a successful transmission is P suc = P it N p t (1 − p t ) N − , (13)i.e., exactly one WD transmits information. Besides, the prob-abilities of an idle slot and a collision slot are respectively P idl = P it (1 − p t ) N ,P col = P it − P suc − P idl . (14)By substituting (12)-(14) into (3), we can obtain the through-put ψ . We notice that each WD has the equal probability totransmit information in a WIT slot. Therefore, the N WDshave the same average data rate ψ/N . From (12), if someWD n has very high probability of energy outage, i.e., large w n , the data rates of all the WDs can be very low. Therefore,our proposed method should be applied to a network withlimited WET range, e.g., the maximum WD-to-HAP distanceis less than meters to ensure that all WDs can be effectivelycharged by the HAP.IV. S IMULATION R ESULTS
In this section, we use simulations to verify the analysisand evaluate the performance of the distributed schedulingprotocol proposed. In all simulations, we use the PowercastTX91501-3W transmitter as the energy transmitter at the HAPand P2110 Powerharvester as the energy receiver at each WDwith η = 0 . energy harvesting efficiency. Unless otherwisestated, the simulation parameters are listed in Table I, whichcorrespond to a typical outdoor sensor network. We considertwo types of WDs, where type-I WDs are located around meters away from the HAP, while type-II WDs are locatedaround . meters away. From Table I, each WD consumesaround mJ energy to transmit a payload. From (1), type-Iand type-II WDs harvest and units of energy, i.e., e n = 1 and , respectively. Unless otherwise stated, we consider WDs with type-I WDs and type-II WDs. Besides, thebattery capacity is set as C = 30 . Each point in the figuresshown in this section is obtained from simulating the WPCNfor time slots. Battery state (i) P en ( i ) (a) P en (i), e n =1 satisfying EDAnot satisfying EDA Battery state (i) -2 l og ( w n i ) (b) log(w ni ), e n =1 Fig. 5. Verification of the EDA assumption for WDs with e n = 1 . Sub-figures(a) and (b) show P ne and w in (in log-scale), respectively. We first verify in Figs. 5 and 6 the proposed energydecoupling assumption (EDA). In particular, for each WD n , we calculate P ne ( i ) by dividing the number of ET slotsobserved at each battery state i and the number of occurrencesof battery state i , i = 1 , · · · , C . In Fig. 5, we plot P ne ( i ) ’sand the limiting probabilities of battery states ( w in ’s) of type-I WDs. We can see that p ne ( i ) ’s are approximately constantfor i = 2 , · · · , C , which matches the statement of EDA.The only exception is the -st battery boundary state, where p ne (1) is significantly lower than the other p ne ( i ) ’s and w n is much higher than the other states. This is mainly due toits close connection with the -th battery state, where a WDimmediately enters the -st battery state when it reaches the -th battery state. We also plot in Fig. 6 the P ne ( i ) ’s and w in ’s of type-II WDs. Interestingly, we can see that p ne ( i ) ’s areapproximately equal as long as sufficient samples are collectedat energy state i , e.g., ≤ i ≤ . For states and , no sampleor very few samples are collected due to the extremely lowprobabilities of the two states, thus the samples collected forthe two states are ignored. From the above discussion, we cansee that the proposed EDA approximately holds, which servesas the basis of our analysis.In Fig. 7, we compare the throughput analysis in (12)-(14)with simulations when the number of WDs changes from N = 6 to . Without loss of generality, we assume N WDsare type-I and the rest N WDs are type-II, and p t = N . Forbrevity, we only present the results for the probability of aWET slot ( P ene in (12)) and that of a successful transmissionslot ( P suc in (13)). We can see that the simulation and analysismatch well, which validates our proposed analytical method.Besides, P ene decreases with the number of WDs, N . Thisis because, by setting p t = N , the successful transmissionprobability keeps almost unchanged but each WD transmitsless frequently. This reduces the overall energy consumptionand the need for energy transfer. We can also infer from Fig.7 that the proposed distributed scheduling method can achievestable throughput performance against the variation on the Battery state (i) P en ( i ) (a) P en (i), e n =2 satisfying EDAnot satisfying EDA Battery state (i) -10 -5 l og ( w n i ) (b) log(w ni ), e n =2 Too few samples collected for states 1 and 2
Fig. 6. Verification of the EDA assumption for WDs with e n = 2 . Sub-figures(a) and (b) show P ne and w in (in log-scale), respectively. Number of WDs P ene (a) P ene AnalysisSimulation
Number of WDs P s u c (b) P suc AnalysisSimulation
Fig. 7. Comparisons of analytical and simulation results. Sub-figures (a) and(b) show the probabilities of an energy transmission slot ( P ene ) and successfultransmission slot ( P suc ), respectively. number of WDs, as long as the transmit probability p t is setproportionally to the number of WDs. In practice, the HAPcan calculate p t by counting the number of associating WDsand broadcast its value to the WDs either periodically or whenthe number of associating WDs varies.At last, we investigate the impact of data transmit proba-bility ( p t ) to the throughput performance. Here, we considera performance benchmark with unlimited battery supply, i.e.,no need of WET. This may correspond to the conventional p -persistent CSMA WLAN network without device energyconstraint. Evidently, the benchmark method produces a per-formance upper bound of the energy-constrained scheme con-sidered in this paper. All the points in Fig. 8 are calculated nu-merically based on the proposed analytical model. In Fig. 8(a),we consider N = 18 and compare P suc achieved by the twomethods when p t = 1 /m , m = 12 , · · · , . We can see that
12 14 16 18 20 22 24 26 28 30 m P s u c (a) P suc v.s. P t = 1/m Unlimited batteryProposed
10 20 30 40 50 60 70 80 90 100 m T h r oughpu t (b) Normalized Throughput v.s. P t = 1/m Unlimited batteryProposed maximum at Pt=1/18 maximum at Pt=1/19maximum at Pt=1/44 maximum at Pt=1/56
Fig. 8. Impact of p t = 1 /m to the throughput performance. Sub-figures (a)and (b) show P suc and normalized throughput ψ , respectively. the benchmark method achieves the maximum P suc ≈ e − when m = N = 18 . The considered distributed scheduling,however, achieves the maximum P suc at a smaller p t when m = 19 . Besides, we also plot in Fig. 8(b) the throughputperformance comparison. Similarly, we can see that the max-imum throughput of the proposed wireless-powered schemeis achieved at a smaller p t than that with unlimited energysupply, i.e., p t = versus . This is because a larger p t would induce high collision probability in both networks, butin WPCN, it also causes higher device energy consumption,and thus inducing more frequent WET and on average shorterairtime of WIT. Overall, the throughput of the WPCN isaround lower than the case with unlimited energy supply,e.g., conventional WLAN. The performance loss is acceptableconsidering the additional overhead for WET in WPCN.V. C ONCLUSIONS
In this paper, we presented a fully distributed schedulingprotocol for energy and information transmissions in RF-enabled WPCN. An energy queueing model was proposedto analyze the throughput performance, which leverages aninteresting and novel energy decoupling property in the consid-ered WPCN. Simulation results have verified our analysis andshowed that the proposed distributed scheduling can achievesustainable and efficient operation of WPCN.A
PPENDIX P ROOF OF THE MONOTONIC PROPERTY OF f n ( x ) Proof : Without loss of generality, we denote w in = λ i w n when p en = a , and w in = β i w n when p en = b , where < a ≤ b < and i = 1 , · · · , C . Evidently, we can see from (6a) that λ = 1(1 − a ) p t < − b ) p t = β . (15) Similarly, by substituting w n into w n in (6b), we have λ = 1(1 − a ) p t + a (1 − a ) p t λ ≤ − b ) p t + b (1 − b ) p t λ ≤ − b ) p t + b (1 − b ) p t β = β . (16)By repeatedly substituting w in into w i +1 n in either (6b) or (6c),we have λ i ≤ β i , i = 1 , · · · , C. (17)Therefore, we have f n ( a ) = 11 + P Ci =1 λ i ≥
11 + P Ci =1 β i = f n ( b ) , (18)which leads to the proof of the desired result. (cid:4) R EFERENCES[1] S. Bi, C. K. Ho, and R. Zhang, “Wireless powered communication:opportunities and challenges,”
IEEE Commun. Mag. , vol. 53, no. 4,pp. 117-125, Apr. 2015.[2] X. Lu, P. Wang, D. Niyato, D. I. Kim, and Z. Han, “Wireless networkswith RF energy harvesting: a contemporary survey,”
IEEE Commun.Surveys Tuts. , vol. 17, no. 2, pp. 757-789, 2015.[3] S. Bi, Y. Zeng, and R. Zhang, “Wireless powered communication net-works: an overview,”
IEEE Wireless Commun. , vol. 23, no. 2, pp. 10-18,Apr. 2016.[4] X. Zhou, R. Zhang, and C. K. Ho, “Wireless information and power trans-fer: architecture design and rate-energy tradeoff,”
IEEE Trans. Commun. ,vol. 61, no. 11, pp. 4754-4767, Nov. 2013.[5] H. Ju and R. Zhang, “Throughput maximization in wireless poweredcommunication networks,”
IEEE Trans. Wireless Commun. , vol. 13, no. 1,Jan. 2014.[6] L. Liu, R. Zhang, and K. C. Chua, “Multi-antenna wireless powered com-munication with energy beamforming,”
IEEE Trans. Commun. , vol. 62,no. 12, pp. 4349-4361, Dec. 2014.[7] D. Niyato, P. Wang, and D. I. Kim, “Performance analysis and opti-mization of TDMA network with wireless energy transfer,”
IEEE Trans.Wireless Commun. , vol. 13, no. 8, pp. 4205-4219, Aug. 2014.[8] V. B. Misic and J. Misic, “A polling MAC for wireless sensor networkswith RF recharging of sensor nodes,” in
Proc. IEEE QBSC , pp. 76-80,Jun. 2014.[9] S. Bi and R. Zhang, “Distributed charging control in broadband wirelesspower transfer networks,”
IEEE J. Sel. Areas Commun. , vol. 34, no. 12,pp. 3380-3393, Dec. 2016.[10] G. Bianchi. “Performance analysis of the IEEE 802.11 distributedcoordination function,”
IEEE J. Sel. Areas Commun. , vol. 18, no. 3, pp.525-547, Mar. 2000.[11] G. Bianchi and I. Tinnirello, “Remarks on IEEE 802.11 DCF per-formance analysis,”
IEEE Commun. Lett. , vol. 9, no. 8, pp. 765-767,Aug. 2005.[12] S. Bi and Y. J. Zhang, “The cost of mitigating power law delay inrandom access networks,”
IEEE Trans. Wireless Commun. , vol. 12, no. 9,pp. 4612-4625, Sep. 2013.[13] J. Kim and J. W. Lee, “Performance analysis of the energy adaptiveMAC protocol for wireless sensor networks with RF energy transfer,” in
Proc. ICTC , pp. 14-19, pp. 4205-4219, Sep. 2011.[14] M. Y. Naderi and P. Nintanavongsa, “RF-MAC: a medium access controlprotocol for re-chargeable sensor networks powered by wireless energyharvesting”,
IEEE Trans. Wireless Commun. , vol. 13, no. 7, pp. 3926-3937, Jul. 2014.[15] P. Tamilarasi and B. Lavenya, “Energy and throughput enhancement inwireless powered communication networks using RF-MAC and CSMA,”in
Proc. ICIIECS pp. 1-4, Mar. 2015.[16] S. Bi, L. Qian, and Y. J. Zhang, “Monotonic optimization method forgeneral utility maximization in random-access networks,” in