Research Article Analysis of Wireless Energy Harvesting Relay Throughput in Rician Channel

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1 Moble Informaton Systems Volume 16, Artcle ID , 9 pages Research Artcle Analyss of Wreless Energy Harvestng Relay Throughput n Rcan Channel Yfan Hu, 1 Nng Cao, 1 and Yunfe Chen 1 School of Computer and Informaton, Hoha Unversty, Xkang Road 1, Nanjng 198, Chna School of Engneerng, Unversty of Warwck, Coventry CV4 7AL, UK Correspondence should be addressed to Yfan Hu; hhu huyfan@yeah.net Receved 14 June 16; Revsed 1 October 16; Accepted 3 October 16 Academc Edtor: Francesco Grngol Copyrght 16 Yfan Hu et al. Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. Cooperatve communcaton uses dle nodes to acheve performance gans. Energy harvestng allows cooperatve communcaton to be less dependent on batteres. In ths paper, the performance of energyharvestng()amplfy-and-forwardrelayngsanalyzed for Rcan fadng channels, n contrast to prevous works that focused on Raylegh fadng channels. Contnuous tme protocol and dscrete tme protocol are consdered. Analytcal expressons for the average throughput are derved. Numercal results are presented to show the good performance of the system n Rcan fadng channels by examnng varous system parameters usng the analytcal expressons. 1. Introducton Amplfy-and-forward (AF) relayng s wdely used n communcaton systems to extend network coverage or acheve dversty gan. In AF relayng, the nformaton from the source node s receved and amplfed by the relay node before t s forwarded to the destnaton node. On the other hand, wreless energy harvestng has an mportant applcaton n relayng. The relay node may be lmted by ts battery lfe so that t may count on some external power source to reman actve n the network. In ths case, energy harvestng s partcularly useful, as the source node can act as an external power source for the relay node by transmttng energy wrelessly. Several works have been done on ether energy harvestng technque or amplfy-and-forward relayng technque, to name a few. References [1 3] consdered the use of energy harvestng from ambent rado frequency sgnals to power a wreless sensor network. References [4, 5] studed the transmsson strateges for nodes. In these cases the nodes harvest energy at some tme nstant and transmt the harvested energy at some other tme nstants. In [4], the transmsson tme mnmzaton was consdered. Reference [5] studed the maxmzed short-tme throughput for systems. Reference [6] also studed ambent RF energy harvestng, but nstead of usng the harvested energy to power the wreless sensor network drectly, t consdered the opton of storng the harvested energy n a capactor or battery to power the wreless sensor network. In [7], a rado frequency energy harvestng model was analyzed by consderng a recevng antenna part, a rectfyng part, and an energy storage n the crcut. In [8], the optmum samplng of a random feld was studed. Reference [9] studed the best-effort sensng wth fnte battery. The optmum estmaton of a contnuous tme random process usng dscrete tme samples taken by a sensor wth wreless power was studed n [1]. Ths work showed that, for the sensng of a tme-varyng random event wth wreless power, the optmum performance s acheved when the energy-harvestng-consumpton-rato s 1. In other studes, the optmal placement of the relay node was also studed. For example, [11] consdered a dual-hop energy transfer scheme, whle [1] presented a novel optmzaton problemfortwo-hoprfenergytransfertomprovewreless energy transfer effcency. In [13], artfcal nose was added to reducethenformatonleakagerateforenergyreceverswhle satsfyng ts energy harvestng requrements. Reference [14] consdered a wreless energy harvestng enabled massve multple-nput-multple-output relayng system n order to provde wreless securty. A protocol usng one part of each

2 Moble Informaton Systems frame for energy harvestng and the other part for message transmsson was consdered n [15]. In [16], the optmum performance boundares of a two-hop multantenna AF relayng system wth a multantenna energy harvestng () recever were studed. Also, energy harvestng technques for practcal devces n low-power applcatons were studed usng energy harvestng relayng n [17 19]. Reference [] studed the dfferent rate-energy trade-offs n order to acheve the optmal source and relay codng n a multple-nputmultple-output relay system. Reference [1] proposed two protocols of energy harvestng AF relayng and analyzed the throughput of each protocol (contnuous tme protocol and dscrete tme protocol). All the above works have been conducted for Raylegh fadng channels. However, t s well known that Raylegh fadng channel s only a specal case of the Rcan fadng channel when the lne of sght s. Thus, the Rcan fadng channel s more general and useful than the Raylegh fadng channel, and t s of great nterest to nvestgate the performance relayng n Rcan fadng channel. In ths paper, we fll ths gap by analyzng the performance of energy harvestng AF relayng n Rcan fadng channels. We consder two protocols, smlar to [1], as contnuous tmeprotocolanddscretetmeprotocol.basedon these protocols, we derve the analytcal expresson for the throughput n the Rcan fadng channels, whch s more challengng due to the Bessel functon n ts probablty densty functon. Numercal results are presented to compare the Rcan fadng channel wth the Raylegh fadng channel. They show that the performance n Rcan fadng channel s better than that n Raylegh fadng channel and ths performance gan can be quantfed usng our results. The rest of ths paper s organzed as follows. Secton presents the system model of AF relayng system wth energy harvestng. In Secton 3, we derve the analytcal expresson for the throughput of each protocol n Rcan fadng channel. InSecton4,weshowthenumercalexamplesobtaned from the analytcal expressons and verfy ts accuracy usng computer smulaton. Secton 5 concludes the paper.. System Model We consder a cooperatve communcaton scenaro consttuted by a source node (S), a destnaton (D), and an ntermedate relay node (R). The source node and the destnaton node are not energy-constraned, but the relay node s energy-constraned. We assume that the destnaton node can not communcate drectly wth the source because of physcal obstacles. Ths s a vald assumpton n some communcaton scenaros. Then, deployng relay nodes wll be a good soluton to make the communcaton between source and destnaton work effectve. The followng assumptons of relayng model are used n ths work. (1) The processng power used for the crcut at the relay s neglgble compared wth the transmsson power requred by the relay. () The energy-constraned relay node frst harvests suffcent energy from the source and then the relay node relays the source nformaton to the destnaton usng theharvestedenergy.thebatterycapactyattherelay s much larger than the requred transmsson power. (3) The relay adopts the tme-swtchng (TS) archtecture. It spends a porton of tme for energy harvestng () and the remanng tme for nformaton transmsson (). (4) The S R and R D channels are composed of Rcan fadng and large-scale path loss. We denote the dstances between S R and R D as d 1 and d, respectvely. The channel fadng gans between S R and R D are denoted, respectvely, as h and g. The fadng channel gans are assumed to be constant over a perod of T seconds and are ndependent and dentcally dstrbuted from one block to the other. (5) Assume that the communcaton happens n blocks of T seconds, each of whch s composed of two parts: part and part. We denote the fracton of tme allocated for n the th block as α.thus,part takes α T seconds, S R part takes (1 α )T/ seconds, and R D part takes (1 α )T/ seconds. For contnuous tme, the relay harvests energy and transmts nformaton wthn each block. Thus, α (, 1) [1]. For dscrete tme, the relay uses the whole block for energy harvestng or transmsson. When the relay harvests energy, α =1,whlewhen the relay transmts the nformaton, α =[1]. (6) For contnuous tme, an - block contans part and part, where occupes a porton of the block and occupes the rest. For dscrete tme, an - pattern contans (X+1)blocks, where there are X blocks and one block (X=,1,,...). Also, we defne the followng symbols: E : the avalable energy at the start of an - pattern E (): the avalable energy at the start of the th block E (t): the harvested energy at the tme nstant t n the th block E T : the energy harvested n an block t : - pattern start tme X: the number of blocks of dscrete tme protocol..1. Sgnal Model. For the th block, the source node sends the normalzed nformaton sgnal s wth E{ s }=1through the S R channel, whch s receved at the relay node as y r,. y r, = h d m 1 P s s +n r,, (1) where h s the S R fadng channel gan, d 1 s the dstance from source to the relay, m s the path loss exponent, P s s

3 Moble Informaton Systems 3 the source transmsson power, and n r, s the addtve whte Gaussan nose (AWGN) wth mean zero and varance σ nr. Then, the AF relay harvests enough energy to guarantee the requred transmsson power P r n the part. For the general case, P r canbeanyvaluesetbytherequrementsofthe applcaton QoS, whch wll produce dfferent throughput. After the part, the relay amplfes the receved sgnal and forwards t to the destnaton node. The sgnal sent by relay s P x r, = r y r,, P s h () /d1 m +σ nr where P s h /d m 1 +σ nr s the average power of y r, such that E { y r, } = P s h d1 m +σ nr. (3) Fnally, the sgnal y d, receved by the destnaton node s gven by y d, = g d m x r, +n d, P = r P s h g s d m P s h +d1 mσ nr P r d1 mg n r, + +n d,. d m P s h +d1 mσ nr In (4), g s the R D fadng channel gan, d s the dstance of the R D lnk, and n d, s the AWGN at the destnaton node. From (4), we can dstngush the sgnal part and the nose part, where P r P s h g s / d m P s h +d1 mσ nr s the sgnal part and P r d m 1 g n r, / d m P s h +d m 1 σ nr +n d, s the nose part. Thus we can get the sgnal-to-nose rato (SNR) at the destnaton node as γ d, = (4) P s P r h g /d m (P s h +d m 1 σ nr ) σnd +P r g d1 mσ nr /dm (P s h (5) +d1 mσ nd ), where agan σ nd sthevaranceofawgnatr node. For the th block, f the SNR s less than the threshold SNR (γ )therewllbeoutage.sowegettheoutagendcatori, as I, = L (γ d, <γ ), (6) where L( ) s an ndcator functon whch s equal to 1 f ts argument s true; otherwse t s... Relay Protocols..1. Contnuous Tme Protocol. In ths protocol, the relay harvests the energy just enough to transmt the nformaton sgnal.thecontnuoustmerelaymakessurethattherelay can harvest the requred amount of energy wthn each block and transmt t to the destnaton node. The - pattern only has one block [1]. As Fgure 1 shows, frstly the relay spends α T seconds on harvestng energy, where α (,1). Then, n the part, half of the tme (1 α )T/ s for S R transmsson and the other half tme (1 α )T/ s for R D transmsson. The energy harvested n the tme wll be consumed n the tme, so that the accumulated harvested energy s. Thus, E =E () =. In ths case, the harvested energy durng α T seconds s gven by E (α T) = ηp s h α T, (7) where <η<1s the energy converson effcency. The relay needs to forward the source message to the destnaton node wth a transmsson power P r for a tme of (1 α )T/.Wecan get the relaton as (1 α E (α T) =P )T r. (8) So, combnng (7) and (8), we can get d m 1 d m 1 α = P r ηp s h +d1 mp. (9) r In ths paper, throughput means the proporton of the effectve communcaton tme to the total tme when the relayng transmsson succeeds. As (1 α )T/ s the effectve communcaton tme wthn one block of tme T, the throughput τ s calculated as τ =(1 I, ) (1 α ) T/ T = (1 I,)(1 α ). (1) The throughput n (1) s a functon of the channel gans h and g. They are random varables. Thus, the average throughput s τ=e h g {τ }=E h g { (1 I,)(1 α ) }. (11)... Dscrete Tme Protocol. In ths protocol, each block s used ether for or for. If E () < P r T/, theblocks used for. Otherwse, t s used for. Wthn the part, T/ s used for S R transmsson, and the rest s for R D transmsson. In Fgure, f E <P r T/,therewllbeX blocks, and wll contnue untl E () > P r T/. Then,therelaystarts the. However, f E >P r T/ atthebegnnng,therewllbe no part (X = ), andtherelaywllstartmmedately. Inthscase,wecanseethattheharvestedenergymaynotbe completely consumed, so that E canbebggerthanzero[1]. In ths case, when a block s used for, the harvested energy wll be E T =η P s h T. (1) d m 1

4 4 Moble Informaton Systems T S R R D d1 m α = P r ηp s h +d1 mp r E(t) P r (1 α ) T α T (1 α ) T (1 α ) T E o = t to t o +α T t o +T Fgure 1: The TS protocol for and n AF relayng wth contnuous tme [1]. T (a) X blocks α {, 1} (b) (a) (b) E(t) P r T E o t o t o +XT P r T t E(t) E o > P rt P r T t o t t o +T Fgure : The TS protocol for and n AF relayng wth dscrete tme [1]. Then { 1, E () < P rt α =, {, E { () > P rt, { E () +E T, E () < P rt E (T) =, { E { () P rt, E () > P rt. (13) 3. Performance Analyss n Rcan Fadng Channels In ths secton, we wll derve the analytcal expresson for the throughput of each protocol n Rcan fadng channels Average Throughput of Contnuous Tme Protocol. Snce h and g are ndependent, (11) can be wrtten as τ=e h { E g {1 I, }(1 α ) }. (15) Smlarly, the throughput of the dscrete tme s also τ =(1 I, )(1 α )/, and the average throughput s where h {h,h 1,h,...}. τ=e h,g {τ }, (14) The functon of I, s gven by I, = L ( <γ ). P s P r h g P r g d1 mσ nr +dm σ nd (P s h +d1 mσ nr ) (16)

5 Moble Informaton Systems 5 For convenence, we defne a = P s d m σ nd γ, b = d m σ nd dm 1 σ nr γ, c=p s P r,andd=p r d m 1 σ nr γ.thenwehave L ( { g < a h +b c I, = h d ), h > d c, { L ( g > a h +b { c h d )=1, h < d (17) c. We assume the channel gan s Rcan dstrbuted. Thus, the PDF of h or g s gven by p h (x) = x +V )/σ σ e (x I ( Vx ), x>, (18) σ where σ s the power of the cluttery component and V s the ampltude of the lne-of-sght component. Usng the transformaton z=x, h or g has the PDF of p h (z) = 1 σ e V /σ e z/σ I ( V z), z >. (19) σ Then, we get that E g {1 I, } s E g {1 I, }=1 1 σ (a h +b)/(c h d) e V /σ e z/σ I ( V z) dz, σ h > d c. () Here,wecanseethatwhen h <d/c, E{1 I, }=. Fnally we get the average throughput by takng the PDF of h nto the formula as 1 d m 1 τ= P r/(ηp s z+d m 1 P r) [1 d/c (az+b)/(cz d) 1 σ e V /σ e x/σ I ( V x) dx] σ 1 σ e V /σ e z/σ I ( V z) dz. σ (1) One sees that ths s a two-dmensonal nested ntegral, whch s not easy to be computed numercally due to convergence ssue. So we should do some smplfcatons. We notce that, n (), we can get (ax + b)/(cx d) = (a/c)(1 + (ad + bc)/c x).for(ad + bc)/c,tsd m σ nd dm 1 σ nr γ γ /P rp s = γ /SINR nrsinr nd. In general cases, the SINR wll not be very small, so (ad + bc)/c smuchsmallerthan1.so()canbe approxmated as (az+b)/(cz d) 1 a/c 1 1 σ e V /σ e z/σ I ( V z) dz σ () 1 σ e V /σ e z/σ I ( V σ z) dz. Also, a/c 1 σ e V /σ e z/σ I ( V z) dz σ 1 σ e V /σ e z/σ I ( V (3) σ z) dz. =1 a/c On the other hand, for (1/σ ) /σ a/c e V e z/σ I ((V/ σ ) z)dz,weusethesubsttutonx =z/σ to have 1 σ a/c = e V /σ σ = e V /σ σ e V /σ e z/σ I ( V z) dz σ e z/σ I ( V z) dz a/c σ e x / I ( V dz x) ( a/c/σ σ dx )dx = xe (x+(v/σ) )/ I ( V x) dx, a/c/σ σ where Q functon s defned as (4) Q m (a, b) = x( x b a )m 1 e (x +a )/ I m 1 (ax) dx. (5) Then, (5) can be xe (x+(v/σ) )/ I ( V a/c/σ σ x) dx=q 1 ( V σ, a/c σ ). (6) So we get E g {1 I, } Q 1 ( V σ, a/c σ ). (7) Combnng (1) and (7), we get τ Q 1 ( V σ, a/c σ ) Then we have (8) 1 α σ e V /σ e z/σ I ( V σ z) dz. τ Q 1 (V/σ, a/c/σ) (1 dm 1 P r σ u), (9)

6 6 Moble Informaton Systems where u = (e V /σ e x/σ I ((V/σ ) x)/(ηp s x + d m 1 P r))dx. As we can see (9) s a one-dmensonal ntegral from to, and due to the exponental functon and the Bessel functon, the ntegrand of ths ntegral converges very quckly. 3.. Average Throughput of Dscrete Tme Protocol. Snce =(P s h η/d m 1 )T and h has the PDF of (19), one has E T p E T (ε) = 1 σ ρ e V /σ e ε/ρσ I ( V σ ε ), (3) ρ where ε s the dummy varable for the random varable E T, ρ=p s ηt/d m 1,andthemeanofE T s (σ + V )ρ. In the above, the harvested energy s X =1 E T.The leftover energy at the end of the frst - pattern after consumng P r T/ n the part s X =1 E T P r T/. Afterwards, for the second - pattern, f the leftover energy of the frst - pattern s smaller than P r T/, t wll be E for the second - pattern, but f t s larger than P r T/,tsalsoE of the second - pattern and wll consume another P r T/ energy wthout energy harvestng. Ths process contnues. We can deduce that the leftover energy at the end of any - pattern, n a sequence of - patterns, can be transformed to the same form as E T whch s a functon of ρ, V,andσ. Consequently, the harvested energy avalable at the start of any - pattern, E,wll have the PDF: We have p E (ε) = 1 σ ρ e V /σ e ε/ρσ I ( V σ ε ). (31) ρ Atthesametme,wesetXasthe number of the total blocks. Then we denote X = X 1asthenumberofblocks just before the energy arrves P r T/.IfE >P r T/,therewll be X=.WhenE <P r T/, wehaveknownthatthemean of E T E )/(σ + V )ρ. So we have s (σ + V )ρ. Then we can get E{X E }=(P r T/ {, E > P rt, E X {X E }= P { r T/ E {(σ + V )ρ +1, E < P (35) rt. Thus E X {X} = E E {E X E {X E }} So we have P r T/ E X {X} = P r T/ = (1 + E X {X E }) p E (ε) dε P r T/ + p E (ε) dε. 1 ( (σ + V )ρ (P rt ε)+1) p E (ε) dε + p E (ε) dε P r T/ P r T/ = 1 ( (σ + V )ρ (P rt ε)+1) 1 σ ρ e V /σ e ε/ρσ I ( V σ ε ρ ) dε. (36) (37) τ=e h,g {τ } = E h,g { (1 I,)(1 α ) }. (3) In ths case, I, s ndependent of the tme, α,butt depends on the fadng channels, h and g ;alsoα depends on theaccumulatedharvestedenergyatthestartoftheth block, E ().Thus,E () depends on S R fadng channels of the prevous blocks, or h\h ={h 1,h,...}.Sothethroughput τ canbewrttenas We use Q functon consdered before agan, to get E X {X} P =(1+ r T (σ + V )ρ )(1 Q 1 ( V σ, P rt/ρ )) σ 1 (σ + V )ρ ω, (38) τ= 1 E h,g {1 I, } E h\h {1 α }. (33) Usng the results of () and (7), we can get E h,g {1 I, } Q 1 ( V σ, a/c ). (34) σ where ω= P rt/ (ε/σ ρ)e V /σ e ε/ρσ I ((V/σ ) ε/ρ)dε. From the defnton of throughput we have E h\h {1 α }= 1/ E X {X+1}. (39) Combnng (34) and (39), the average throughput s τ Q 1 (V/σ, a/c/σ) ((1+P r T/ (σ + V )ρ)(1 Q 1 (V/σ, P r T/ρ/σ)) (1/ (σ + V )ρ)ω+1). (4)

7 Moble Informaton Systems 7 Throughput.5.45 Dscrete tme Contnuous tme P r (dbm) Throughput Dscrete tme Contnuous tme P r (dbm) Analyss of dscrete tme n Rcan fadng channel Analyss of contnuous tme n Rcan fadng channel Smulaton of dscrete tme n Rcan fadng channel Smulaton of contnuous tme n Rcan fadng channel Fgure 3: Comparson of the analytcal and smulaton results for the throughput of dscrete tme and contnuous tme n Rcan fadng channel. 4. Numercal Result and Dscusson In ths secton, numercal results are presented to show the throughput of the system n Rcan fadng channels. The source transmsson power s set to P s =46dBm. The path loss exponent s set to m = 3. The dstance from source to relay s set to d 1 = 35 meters and the dstance from relay to destnaton s set to d = 1 meters. The energy converson effcency s set to η=.5. The threshold SNR s set to γ = 55dB. The nose varances at the relay and the destnaton nodes are set to σ nr = 8dBm and σ nd = 11 dbm. Also, σ =.5, whchsthesameasσ n the Raylegh fadng channel. We also obtan the smulaton results to verfy the analytcal results obtaned n Secton 3. In the smulaton, 1 blocks are used, where we generate ndependent fadng channels h and g for each block. We assume fxed power transmsson at the relay so that P r s fxed whle α changes wth h, smlar to [1]. Fgure 3 shows the comparson of analytcal and smulaton results for the throughput of dscrete tme and contnuous tme n Rcan fadng channel. From Fgure 3 we can see that the smulaton and analytcal result of the throughput of contnuous tme and dscrete tme n Rcan fadng channel match well. Ths shows the accuracy of the approxmaton we used. In addton, we can fnd that there s a peak n the curve. It s because the throughput s relatedtoboththefnalsnrandthetmefor.when P r ncreases the fnal SNR wll be larger so that the outage probablty wll decrease, whch makes the throughput larger. On the other sde, when P r becomes bgger, the tme for wll be more, whch can decrease the throughput. Therefore, there wll be P r that makes the throughput the bggest, whch s the optmal. Moreover, we can see that the performance of dscrete tme protocol s better than that of contnuous tme protocol. There s energy left after a - pattern of dscrete tme protocol wll harvest more energy when h s larger. Then t makes the tme of the followng - pattern smaller, so that the throughput wll be larger. Analyss of dscrete tme n Rcan fadng channel Analyss of contnuous tme n Rcan fadng channel Smulaton of dscrete tme n Rcan fadng channel Smulaton of contnuous tme n Rcan fadng channel Smulaton of dscrete tme n Raylegh fadng channel Smulaton of contnuous tme n Raylegh fadng channel Fgure 4: Comparson of throughput versus P r for dscrete tme and contnuous tme n Raylegh and Rcan fadng channel. Optmal throughput.5.45 Dscrete tme Contnuous tme C nd (dbm) Analyss of dscrete tme n Rcan fadng channel Analyss of contnuous tme n Rcan fadng channel Smulaton of dscrete tme n Rcan fadng channel Smulaton of contnuous tme n Rcan fadng channel Smulaton of dscrete tme n Raylegh fadng channel Smulaton of contnuous tme n Raylegh fadng channel Fgure 5: Optmal throughput versus σ nd for dscrete tme and contnuous tme n Raylegh and Rcan fadng channel. In Fgure 4, the value of P r ncreases from 5 dbm to 5 dbm. The performance of the throughput of dscrete tme and contnuous tme n Raylegh and Rcan fadng channels can be compared. From the result, we can see that the throughput n Rcan fadng channel s hgher than that n Raylegh fadng channels under the same other condtons. It conforms to the physcal truth that the Rcan fadng channel s a better fadng channel than Raylegh fadng channel, such thatperformancenrcanfadngchannelshouldbebetter than that n the Raylegh fadng channel. Fgure 5 plots the optmal throughput when the nose varance at the destnaton nodes ncreases form 13 dbm to 7 dbm, so that the throughput also changes when the nose varance changes. The optmum throughput decreases when the nose varance ncreases. When the nose becomes bgger, P r needs to be bgger to satsfy the outage condton,

8 8 Moble Informaton Systems Optmal throughput Contnuous tme Dscrete tme Threshold SNR (db) Analyss of dscrete tme n Rcan fadng channel Analyss of contnuous tme n Rcan fadng channel Smulaton of dscrete tme n Rcan fadng channel Smulaton of contnuous tme n Rcan fadng channel Smulaton of dscrete tme n Raylegh fadng channel Smulaton of contnuous tme n Raylegh fadng channel Fgure 6: Optmal throughput versus threshold SNR for dscrete tme and contnuous tme n Raylegh and Rcan fadng channel. Throughput Contnuous tme Dscrete tme P r (dbm) Rcan true dscrete tme, v = 1 Rcan true contnuous tme, v = 1 Rcan dscrete tme, v =.5 Rcan contnuous tme, v =.5 Rcan dscrete tme, v = 1 Rcan contnuous tme, v = 1 Rcan true dscrete tme, v =.5 Rcan true contnuous tme v =.5 Fgure 7: Throughput versus P r for dfferent V n dscrete tme and contnuous tme n Rcan fadng channel. whch wll make the tme longer, and fnally, makes the throughput decrease. Fgure 6 shows the optmal throughput versus the threshold SNR when t ncreases from 3 db to 7 db. We can see that when the threshold SNR ncreases the throughput decreases. The hgher threshold SNR needed, the hgher fnal SNR should be, and t wll requre hgher P r,whchwll make the tme longer to decrease the throughput. When the threshold SNR ncreases, the gap between the smulaton and analytcal results ncreases, because when the threshold SNR ncreases the sensblty to σ nr wll be bgger, so the approxmaton becomes naccurate n ths case. In Fgure 7, we examne the lne of sght effect. The throughput when V = 1 s larger than that when V =.5. When the lne of sght ncreases, that s, the channel becomngbetter,thethroughputwllncrease. 5. Concluson In ths paper, we have derved the analytcal throughput of contnuous tme and dscrete tme protocols used n AF relay n Rcan fadng channel and have proved the accuracy of the analytcal throughput by computer smulaton. In addton, we also dscussed the performances n dfferent stuatons for dfferent transmt power of the relayng node, nose at the receve node, and threshold SNR. Moreover, the performance of the - protocols n Rcan fadng channel s better than that n Raylegh fadng channel, because of the channelmprovementfromthelneofsght.inaddton,the throughput wll change whle P r changes and there s a peak to attan the optmal throughput, and the optmal throughput wll decrease when the nose and threshold SNR ncreases. Competng Interests The authors declare that they have no competng nterests. References [1] A. M. Zungeru, L. M. Ang, S. Prabaharan, and K. P. Seng, Rado frequency energy harvestng and management for wreless sensor network, n Green Moble Devces and Networks: Energy Optmzaton and Scavengng Technques, pp ,CRC Press, 1. [] D.Bouchoucha,F.Dupont,M.Latrach,andL.Ventura, Ambent RF energy harvestng, n Proceedngs of the Internatonal Conference on Renewable Energes and Power Qualty (ICREP 1),Granada,Span,March1. [3] H. Jabbar, Y. S. Song, and T. T. Jeong, RF energy harvestng system and crcuts for chargng of moble devces, IEEE Transactons on Consumer Electroncs,vol.56,no.1,pp.47 53, 1. [4] J.YangandS.Ulukus, Optmalpacketschedulngnanenergy harvestng communcaton system, IEEE Transactons on Communcatons,vol.6,no.1,pp. 3,1. [5] K. Tutuncuoglu and A. Yener, Optmum transmsson polces for battery lmted energy harvestng nodes, IEEE Transactons on Wreless Communcatons, vol. 11, no. 3, pp , 1. [6]T.BengLm,N.M.Lee,andB.K.Poh, Feasbltystudyon ambent RF energy harvestng for wreless sensor network, n Proceedngs of the IEEE MTT-S Internatonal Mcrowave Workshop Seres on RF and Wreless Technologes for Bomedcal and Healthcare Applcatons (IMWS-BIO 13), pp.1 3,Sngapore, December 13. [7] H. ElAnzeery and R. Gund, Frequency survey smulaton for developng novel rado frequency energy harvestng model, n Proceedngs of the 14th Internatonal Conference on Modellng and Smulaton (UKSm 1), pp , March 1. [8] K. Rtter, G. W. Waslkowsk, and H. Woznakowsk, Multvarate ntegraton and approxmaton for random felds satsfyng Sacks-Ylvsaker condtons, The Annals of Appled Probablty, vol. 5, no., pp , [9] J. Yang, X. Wu, and J. Wu, Adaptve sensng schedulng for energy harvestng sensors wth fnte battery, n Proceedngs of

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