Wireless information and power transfer in two-way relaying network with non-coherent differential modulation

Transcription

1 Xu et al. EURASIP Journal on Wreless Communcatons and Networkng :131 DOI /s RESEARCH Open Access Wreless nformaton and power transfer n two-way relayng network wth non-coherent dfferental modulaton Weka Xu 1*, Zheng Yang,ZhguoDng 3,LnWang 1 and Pngzh Fan Abstract In ths paper, we consder a denose-and-forward DNF two-way relay network TWRN wth non-coherent dfferental bnary phase-shft keyng modulaton, where a battery-free relay node harvests energy from the receved rado frequency RF sgnals and uses the harvested energy to help the source nodes for nformaton exchange. Based on the power splttng PS and tme swtchng TS recever archtectures, power splttng relayng PSR and tme swtchng relayng TSR protocols at relay are studed. In order to nvestgate the effect of power allocatons on two source nodes, power splttng coeffcent and tme swtchng factor at relay on performance, the two proposed protocols are analyzed and the bt error rate BER expressons of end-to-end system are derved. Based on these expressons, the optmal power of sources, the power splttng rato and the tme swtchng factor are obtaned va the numercal search method. The smulaton and numercal results provde practcal nsghts nto the effect of varous system parameters, such as the power splttng coeffcent, the tme swtchng factor, sources to relay dstances, the nose power, and the energy harvestng effcency on the performance of ths TWRN. In addton, the results show that the PSR protocol outperforms the TSR protocol n terms of throughput under varous network geometres. Keywords: Two-way relay network; Dfferental modulaton; Wreless nformaton and power transfer; Denose-and-forward, bt error rate Introducton As a common communcaton scenaro, two-way relayng realzes nformaton exchange between two nodes smultaneously. Recently, the two-way relay network TWRN has attracted many attentons from both academc and ndustral communtes [1-5], due to ts bandwdth effcency and potental applcatons to cellular networks and peer-to-peer networks. Generally, the data transmsson n TWRN can take place n ether three or two phases. For the three-phase TWRN, network codng NC s the most popular relayng protocol [6]. In NC, two source nodes S 1 and S transmt to the relay R separately over the frst two phases. After decodng the receved sgnals, the relay R performs bt-level exclusve OR XOR operatons and then broadcasts the XOR-coded bts to the two source nodes n the thrd phase. *Correspondence: xweka@xmu.edu.cn 1 Department of Communcaton Engneerng, Xamen Unversty, 4 Smng South Rd., Xamen, Fujan, Chna Full lst of author nformaton s avalable at the end of the artcle It shows that the two-phase TWRN protocol can acheve a maxmum throughput gan of one half over the three-phase TWRN. Therefore, varous protocols for twophase TWRN have been proposed n the lteratures. Two way amplfy-and-forward AF relayng was proposed n [7,8], where a relay drectly amplfes and forwards the sum of receved sgnals. Physcal-layer network codng PLNC was proposed n [9,10], where self-nformaton at source nodes s elmnated by XOR operatons. In [11], the denose-and-forward DNF protocol was proposed, where the relays apply a denosng functon to map the receve sgnal nto another quantzed symbol that can be used by each source node to unquely decode the symbol transmtted from the other end. The AF relayng protocol has less complexty than that of PLNC and DNF at the relay snce no decodng operaton s requred at the relay node. The AF relayng protocol requres perfect channel state nformaton CSI at the two source nodes to remove the self-nterference. Most of the exstng works assume that both the sources and the relay have perfect 015 Xu et al.; lcensee Sprnger. Ths s an Open Access artcle dstrbuted under the terms of the Creatve Commons Attrbuton Lcense whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly credted.

2 Xu et al. EURASIP Journal on Wreless Communcatons and Networkng :131 Page of 10 CSI knowledge of all lnks. In a practcal system, these CSIs need to be estmated at the recever. It s more dffcult to estmate the CSIs n two-way relay networks than that n conventonal pont-to-pont communcaton systems. To mtgate the dffcultes nvolved n estmatng the CSI n TWRN, non-coherent or dfferental transmsson schemes have been proposed for TWRN [1-14]. In [13], the AF and decode-and-forward DF TWRN protocols usng dfferental modulaton were proposed. It shows that these schemes suffer from more than 3 db performance loss compared wth ther coherent counterparts. In [14], Guan and Lu analyzed performance of TWRN wth DNF relayng protocol usng dfferental bnary phaseshft-keyng DBPSK modulaton over fadng channel. It s shown that the achevable dversty order of the proposed scheme s about half of the number of relays. The two-phase TWRN wth non-coherent recever not only acheve hgh spectral effcency but also reduce the overhead of estmaton of channel. Thus, t s a good opton of nformaton exchange for low cost wreless network, such as wreless sensor networks WSNs. The lfetme of the network s an mportant performance ndcator n energy-constraned wreless networks, such as WSNs, snce sensors are usually equpped wth lmted energy supples. Harvestng energy from the envronment s a promsng approach to prolong the lfetme of the energy-constraned wreless networks. The basc dea of smultaneous wreless nformaton and power transfer SWIPT was frst proposed n [15,16], and a general recever archtecture was then developed n [17]. Then, the SWIPT was extended to varous communcaton scenaros such as the cellular system [18], the broadcastng system [19,0] wth a sngle energy recever and a sngle nformaton recever when they are separately located or co-located, the cooperatve relay system [1-5], the two-way relayng system [6], and the nterference channel [7-9]. For broadcastng system, [19] nvestgated the R-E trade-off for a transmtter transferrng energy and nformaton to two separated/co-located nformatondecodng and energy harvestng recevers. And [0] optmzed the beamformng desgns of general broadcastng system where there are multple separated/co-located nformaton-decodng and energy harvestng recevers. For a DF cooperatve network, [1] derves the outage probablty of tme swtchng relay recever. In [], the authors studed the outage probablty and network capacty of end-to-end one-way relay system wth a battery-free relay. For multple source-destnaton pars communcaton system aded by a relay, [3] studed the relays strateges to dstrbute the harvested energy among the multple users and ther mpact on the system performance. For multple-nput multple-output relay channels, [4] proposed a low complexty dynamc antenna swtchng between nformaton decodng and energy harvestng based on the prncples of the generalzed selecton combner. In [5], the authors studed the relay selecton problem n AF relay network wth QoS and harvested energy constrants. In [6], the trade-off end-to-end outage probablty and power splttng coeffcent are studed n a two-way AF relay system where two source nodes exchange data va an energy harvestng relay. In [8] and [9], the authors nvestgated jont wreless nformaton and energy transfer n the two-user/multple-user MIMO nterference channel, n whch each recever ether nformaton decodng or energy harvestng. As s mentoned above, almost of the aforementoned SWIPT protocols assume that the transmtted sgnal satsfes Gaussan dstrbuton and do not consder the modulaton scheme. To the best of the authors knowledge, smultaneous wreless nformaton and power transfer n the two-phase TWRN wth dfferental modulaton has not been addressed so far. Here, we study a two-phase TWRN usng dfferental BPSK modulaton, where a battery-free relay node harvests energy from the receved RF sgnal and uses the harvested energy to exchange the two source nodes nformaton. The man contrbutons of ths paper are summarzed as follows: 1 Based on the power splttng PS and tme swtchng TS recever archtectures at relay node, we propose the PS-based relayng PSR and the TS-based relayng TSR protocols to enable wreless nformaton transferrng and energy harvestng at the battery-free relay n a DNF-TWRN. For PSR and TSR protocols, we deduce the maxmum lkelhood ML decodng algorthm at relay and source nodes. Then, we derve the end-to-end error performance and normalzed throughput of the two proposed protocols. These derved expressons provde practcal desgn nsghts nto the effect of varous parameters on the system performance. By maxmzng end-to-end throughput of system, we can optmze the power on two source nodes, power splttng coeffcent, tme swtchng factor, and other system parameters. 3 Dfferng from conventon two-way relayng network, the numercal results show that locatng the relay node closer to the source nodes yelds larger throughput for both the TSR and the PSR protocols. By comparng PSR and TSR protocols, the numercal results also show that the throughput performance of the PSR protocol s superor to the TSR protocol. The rest of ths paper s organzed as follows. The next secton presents system model of energy harvestng TWRN wth a battery-free relay. In secton Performance analyss, end-to-end BER expressons and throughput are derved. Numercal smulatons and

3 Xu et al. EURASIP Journal on Wreless Communcatons and Networkng :131 Page 3 of 10 dscussons are presented n Numercal results secton. Conclusons secton concludes the paper. System model Here, we consder two relayng protocols for separate nformaton decodng and energy harvestng at a batteryfree relay node, namely, PS-basedrelayngPSRprotocol and TS-based relayng TSR protocol []. In PSR protocol, the relay uses a facton of the receved power from twosourcenodesforenergyharvestngandtheremanng power for nformaton decodng. In TSR protocol, the relay use a fracton of tme for energy harvestng and the remanng tme for nformaton decodng. PSR protocol There are two sources S 1 and S that want to exchange nformaton wth the help of a relay R n a TWRN. The key parameters of PSR protocol and recever of relay are llustrated n Fgure 1. At the begn of multple access MA phase, S = 1, generates a sequence of uncoded BPSK symbols b n { 1, +1} of length L n = 1,,..., L. Then, these raw symbols are re-encoded through dfferental modulaton,.e., x n = x n 1 b n for n = 1,,..., L wth x 0 = 1 as the reference symbol. Two sources then smultaneously send the whole dfferental modulated block to the relay durng MA phase. At the end of MA phase, the nth n = 0, 1,,..., L symbol receved at the relay s y r n = P 1 h 1,r x 1 n + P h,r x n + w MA a,r n 1 where P = α P s power of the th = 1, source, P s total power, α s power rato of the th source. Assume that the channel gan s σ,r = 1/d μ,r,whered,r s dstance between source node to relay, μ s the path loss exponent. Thus, h,r CN 0, σ,r s the ndependent channel coeffcent from the th = 1, source to the relay durng MA phase. It s also assumed that the channels reman unchanged wthn one block of length L + 1. w MA a,r n CN 0, σa s the ndependent addtve whte Gaussan nose AWGN due to receve antenna at the relay wthn the nth n = 0, 1,..., L symbol nterval durng MA phase. We assume that relay knows channel gan σ,r but does not know channel coeffcent h,r. The basc dea of energy harvestng relayng s that an energy constraned relay rechargestsbatterybyusngtheenergyfromtsobservatons. For power splttng [17], let ρ denote the power splttng coeffcent for the relay,.e., ρ s the fracton of observatons used for energy harvestng. Thus, at the end of the MA phase, the relay s nformaton recever s based on the followng observaton ỹ r n = 1 ρ P1 h 1,r x 1 n+ P h,r x n + w MA a,r n + w MA c,r n where w MA c,r CN 0, σc sthesampledawgndueto RF band to base-band sgnal converson. The harvested energy n the frst L + 1 symbols s E h = L + 1ηρ α 1 Pσ1,r + α Pσ,r + σ a 3 where 0 <η 1 s the energy converson effcency whch depends on the rectfcaton process and the energy harvestng crcut. And power per symbol n the BC phase s P r = E h /L + 1 = ηρ α 1 Pσ1,r + α Pσ,r + σ a To facltate demonstratons, we defne a sequence of auxlary symbols bn = b 1 n b n { 1, +1} to ndcate whether the two raw BPSK symbols have the same sgns or not. Wth DNF [11,14], the relay just maps the nth receved symbol to a BPSK symbol ˆbr whch s used by each source to unquely decode the symbol transmtted from the other end. Here, t can be regarded as an estmate of the auxlary symbol bn. AsnoCSI s avalable, we use the sngle-symbol ML decoder n [14],.e., ˆb r n = sgn ln lrfỹ r n bn 5 4 Fgure 1 Power splttng protocol. a The parameters of the PSR protocol for energy harvestng and nformaton decodng at the relay n TWRN. b The block dagram of recever at relay.

4 Xu et al. EURASIP Journal on Wreless Communcatons and Networkng :131 Page 4 of 10 where ỹ r n = [ ỹ r n, ỹ r n 1 ] T,lrf ỹr n bn s the lkelhood rato functon LRF of ỹ r n condtonal on bn, lrfỹ r n bn = g ỹ r n, 1,r + g ỹr n,,r g ỹ r n, 3,r + g ỹr n, 4,r 6 where g y, s the probablty densty functon PDF of y CN0, s gven by g y, = 1 π exp y H y 7 Denote the channel sgnal-to-nose rato SNR,.e., γ,r = 1 ρα Pσ,r 1 ρσa +σ s from the th = 1, source to relay, c and I = [ ] 10, Î 01 = [ ] are two constant matrx. In the terms of reference [14], the condtonal covarance matrces are gven by b r 1n=1,b n=1 1,r = σ r γ1,r + γ,r + 1 I + σ r γ1,r + γ,r Î b r 1n= 1,b n= 1,r = σ r γ1,r + γ,r + 1 I σ r γ1,r +γ,r Î b r 1n=1,b n= 1 3,r = σr γ1,r + γ,r + 1 I + σr γ1,r γ,r Î b r 1n= 1,b n=1 4,r = σr γ1,r + γ,r + 1 I + σr γ,r γ,r Î 8 where σr = 1 ρ σa + σ c, t s the equvalent nose varance of nformaton decodng at relay. After decodng, the relay re-encode ˆb r n nto t r n = t r n 1 ˆb r n for n = 1,,..., L based on reference symbol t r 0 = 1. The relay then uses harvested energy n the MA phase for transmttng nformaton n the broadcastng BC phase. Wthout consderng the energy consumed by sgnal processng, from Equaton 3, the harvested energy per symbol duraton s P r, ths s energy constrant of the relay n the BC phase. Thus, at the end of BC phase, the th = 1, source wll receve from the relay, r n = P r h r, t r n + w BC n, n = 0, 1,,..., L 9 where P r s power per symbol gven by Equaton 4, h r, CN 0, σr, s the ndependent channel coeffcent from the relay to the th = 1, source. Durng BC phase, we assume h,r and h r, = 1, are ndependent but have the same varance, whch s determned by the dstance between two termnals. w BC n CN 0, σa + σ c ncludes the antenna and converson AWGNs at the th = 1, source wthn the nth n = 0, 1,,..., L symbol nterval n the BC phase. We agan use the sngle-symbol ML decoder n BC phase, the receved sgnalofthe th source s ˆb s n = sgn ln lrfr n bn 10 where r n = [r n, r n 1] T, r n br n CN 0, k, condtonal covarance matrces are gven by br n,s { r br n=1,s 1,s r = σa +σ c γr, +1 I + σa +σ c γr, Î b r r n= 1,s,s r = σa +σ c γr, +1 I σa +σ c γr, Î 11 where γ r, = ηρp α 1 σ1,r +α σ,r +σ a σr, σa +σ. The two knds of condtonal decodng error at the relay are assumed as c follow, and P M,r ˆb r n = 1 bn =+1 lnlrfỹ r n bn 0 bn =+1, 1 P F,r ˆb r n =+1 bn = 1 13 lnlrfỹ r n bn > 0 bn = 1 Thus, the LRF lnlrfr n bn s ln lrfr n bn 1 = ln g r n, 1,s r PM,r + g r n,,s r P M,r 1 g r n, r P 1,s F,r + g r n, r,s PF,r 14 TSR Protocol TSR protocol s shown n Fgure. We assume that data rate of drecton transmsson s ˆR.InPSR,thedatarates always ˆR.However,nTSR,datarateoftwo-waysystems dependent on the tme splttng factor α. In total symbol duraton L + 1, we also assume that the total power constrant s same as PSR protocol n L + 1 symbols,.e., L + 1P. Therefore, the power per symbol n energy harvestng and MA phase s P L + 1P = α + 1 αl + 1 = P 15 α + 1 At the end of MA phase, the nth n = αl + 1,α L+1 +1,...,α +1L+1 symbol receved at the relay s y r n = P 1 h 1,r x 1 n+ P h,r x n+w MA a,r n+wma c,r n 16

5 Xu et al. EURASIP Journal on Wreless Communcatons and Networkng :131 Page 5 of 10 Fgure Tme swtchng protocol. a The parameters of the TSR protocol for energy harvestng and nformaton decodng at the relay n TWRN. b The block dagram of recever at relay. where P = α P = α P 1+α = 1,. Denote the channel SNR,.e., γ,r = 1+ασa +σ c s from the th = α Pσ,r 1, source to the relay. The LRF of y r n condtonal on bn sthesameasequaton6wththesamecondtonal covarance matrces of PSR see Equaton 8 wth σr = σa + σ c. The harvested energy n the frst αl + 1 s EH r = ηαl + 1P α 1 σ1,r + α σ,r + σ a 17 whle the power per symbol n the BC phase s EH r P r = 1 αl + 1 = ηαl + 1P α 1 σ1,r + α σ,r + σ a 1 αl + 1 = ηαp α 1 σ1,r + α σ,r + σ a 1 α 18 Therefore, at the end of BC phase, the th = 1, source receves the sgnal from the relay s r n = P r h r, t r n + w BC n, n = 0, 1,,..., 1 αl 19 SmlartotheBCphaseofPSRprotocol,r n br n CN 0, rˆbrn,s wth the condtonal covarance matrx { r br n=1,s 1,s r = σa +σ c γr, +1 I + σa + σ c γr, Î b r r n= 1,s,s r = σa +σ c γr, +1 I σa +σ c γr, Î 0 where γ r, = ηαpα 1σ1,r +α σ,r +σ a σ,r 1 α σa +σ. c Performance analyss Utlzng Equaton 1 and 13, the relay decodng error can be evaluated as P e,r ˆbr n = bn = 1 PM,r + P F,r 1 The two knds of condtonal decodng error of n Equaton 1 and 13 are gven by[14] P M,r = h μ 1,r, μ,r, a r, b r, γth r, P F,r = 1 h μ 3,r, μ 4,r, a r, b r, γth r, and 4abt 1 t ht 1, t, a, b, γ= a t 1 t b t 1 + t exp t 1 + t ln γ, a 4γ 1,r γ,r γ1,r + γ,r + 1 a r = N 0 γ1,r + γ,r + 1 γ 1,r + 1 γ,r + 1, b r = 4γ 1,rγ,r γ1,r +γ,r +mn γ1,r, γ,r γ1,r +γ,r +1 N 0 γ1,r +γ,r +1 γ 1,r +1 γ,r +1, γ r th = γ1,r + γ,r + 1 γ1,r + 1 γ,r + 1, μ 1,r = μ,r = 1 N 0, μ 3,r = 1 N 0 γ1,r + γ,r + 1, 1 N 0 γ1,r + 1, 1 μ 4,r = N 0 γ,r + 1. In the BC phase, the two knds of condtonal decodng errors between the relay and the th source are noncoherent DBPSK decoder [30], they are gven by PD,S r ˆbr,S n = 1 ˆb r n = 1 ˆbr,S n = 1 ˆb r n = 1 γ r, + 1

6 Xu et al. EURASIP Journal on Wreless Communcatons and Networkng :131 Page 6 of 10 Smlar to Equaton 1 and 13, the two knds of condtonal decodng error at the th source are gven as, PM,S r ˆbS n = 1 bn = 1 ˆbr,S n = 1 ˆb r n, bn = 1 ˆb r n { 1,1} Pr ˆbr n bn = 1 ˆbr,S n = 1 ˆb r n ˆb r n { 1,1} Pr ˆbr n bn = 1 = P r D,S 1 PM,r + 1 P r D,S P M,r 3 PF,S r ˆbS n = 1 bn = 1 ˆbr,S n = 1 ˆb r n, bn = 1 ˆb r n { 1,1} Pr ˆbr n bn = 1 ˆbr,S n = 1 ˆb r n ˆb r n { 1,1} Pr ˆbr n bn = 1 = PD,S r 1 PF,r + 1 PD,S r P F,r 4 Therefore, the end-to-end error probablty of the th source node s P e,s ˆbS n = bn = 1 PM,S r + PF,S r = 1 [P r D,S 1 PM,r + 1 P D,S r P M,r +PD,S r 1 PF,r ] + 1 PD,S r P F,r = PD,S r 1 P M,r + P F,r + 1 PD,S r PM,r + P F,r = PD,S r 1 Pe,r + 1 PD,S r P e,r 5 Accordng to [14], the average BER of two sources can be approxmated at hgh SNRs as P e 1 P M,r + P F,r + PD,S r 1 + PD,S r 6 where P M,r c M,r γ, c M,r = PD,S r 1 mn α 1 σ1,r,α σ,r P F,r d F,r γ ln γ d F,r, d F,r = α 1σ1,r +α σ,r α 1 α σ1,r σ,r PD,S r 1 ηρ α 1 σ1,r +α σ,r +σ a 1 α 4ηα α 1 σ1,r +α σ,r +σ a σ,r γ for PSR for TSR σ,r 7 and { γ = 1 ρ γ for PSR γ = γ 8 1+α for TSR where γ = P σa +σ s system SNR. Substtutng Equaton 7 c and 8 nto Equaton 6, we can get the BER expresson of Pe PSR and Pe TSR for the PSR and TSR protocol, respectvely. We gnore the overhead of reference symbol n the dfferental modulaton. Thus, the end-to-end normalzed throughput are defned respectvely as follow, T PSR = 1 H Pe PSR, 9 T TSR = 1 α 1 H. P TSR e respectvely, where Pe PSR and Pe TSR are the end-to-end average error probablty of the PSR and TSR protocol, respectvely. The bnary entropy functon Hx s gven by Hx = xlog x 1 xlog 1 x 30 Therefore, through above expressons of throughput and BER, we are about to nvestgate that the power allocaton α 1 and α among the two sources, the energy harvestng factor ρ or α at the relay and other system parameters mpact on the performance. In the next secton, some numercal results wll be llustrated based on these analyzed formulas. Numercal results In ths secton, we use the derved analytcal results to provde nsghts nto the varous desgn choces. The optmal value of normalzed throughput for gven dstance between source and relay, optmal value of power splttng rato ρ n the PSR protocol and optmal value of tme swtchng factor α n the TSR protocol are nvestgated for dfferent values of the nose varances, the two source to relay dstances, d S1 R and d S R and energy harvestng effcency, respectvely. Unless otherwse stated, we set the energy harvestng effcency, η = 0.5, total source transmsson power, P = 0.1 mw, dstance between two source nodes, d = d S1 R + d S R and path loss exponent μ =.5. Fgure 3 shows the BER wth respect to ρ,0 ρ 1 for PSR protocol and α,0 α 1forTSRprotocol.The analytcal results for the BER as shown n Equaton 6 and 7 are examned and verfed through smulatons for both

7 Xu et al. EURASIP Journal on Wreless Communcatons and Networkng :131 Page 7 of 10 Fgure 3 BER versus PSR coeffcent ρ TSR coeffcent α. P = 0.1 mw, σ c = 80 dbm, σ a = 90 dbm, d S 1R = d SR = 7m,μ =.5, α 1 = α = 0.5, and η = 0.5. Fgure 4 Throughput versus PSR coeffcent ρ TSR coeffcent α. P = 0.1 mw, σ c = 80 dbm, σ a = 90 dbm, d S 1R = d SR = 7m, μ =.5, α 1 = α = 0.5, and η = 0.5. the PSR and the TSR protocols. The antenna nose varance, σ a, and converson nose varance, σ c,ssetto 90 and 80 dbm, respectvely. The two source nodes have the same power,.e., α 1 = α = 0.5, and d S1 R = d S R = 7 m. It can be observed from Fgure 3 that the analytcal and the smulaton results match well for all possble values of ρ and α for both the PSR and the TSR protocols. Fgure 3 also demonstrates that the PSR has a power splttng coeffcent to get mnmum BER, but the TSR has not a energy harvestng tme rato to get mnmum BER. The reason s that there s more energy harvestng tme durng MA phase, there s hgher transmtted power of relay durng the BC phase. In order to further observe the effect of power splttng coeffcent ρ and energy harvestng tme rato α on the two protocols, Fgure 4 shows the normalzed throughput of two protocols, whch s got by Equaton 8. Fgure 4 demonstrates that both PSR and TSR has the value of ρ and α to get maxmum normalzed throughput. We also can see that the maxmum throughput of PSR protocol s hgher than that of the TSR protocol. The throughput of TSR ncreases as α ncreases from 0 to maxmum pont, then starts decreasng quckly as α ncreases to 1. On the contrary, the throughput of PSR protocol change slowly wthρ.ths s becausethere s only 1 α tme for nformaton transmsson n the TSR protocol, but all tme s used for nformaton transmsson n the PSR protocol. Therefore, the TSR protocol acheves better BER performance, shown as n Fgure 3, but t has lower throughput. The optmal values n Fgures 5, 6, 7, 8, and 9 are obtaned through exhaustve search based on the expressons n the Performance analyss secton. Here, we set the step of parameters ρ, α and α 1 s Fgure 5 shows the optmal throughput for the PSR and the TSR protocols for dfferent values of the source node S 1 to relay dstance, d S1 R.ThesourcenodeS to destnaton dstance, d S R s set to d S R = d d S1 R where d = 14 m and the nose varances are kept fxed,.e., σa = 90 dbm and σc = 80 dbm. It can be observed from fgure 5 that for both the TSR and the PSR protocols, the optmal throughput decreases as d S1 R ncreases untl d S1 R = 7 m, whch s thehalfofdstancebetweensourcenodes 1 and S.From d S1 R = 7m,asncreasngofd S1 R, the throughput of two protocols are both ncreasng. It s mportant to note that, as llustrated n Fgure 5, the worst relay locaton of the two energy harvestng protocols s at the mddle of two source nodes. Fgure6showstheoptmalvaluesofρ and α for the TSR and the PSR protocols, respectvely, for dfferent values of the source node S 1 to relay dstance, d S1 R.Fgure6 states that both optmal power splttng coeffcent ρ and tme swtchng factor α are even symmetry wth d S1 R.The value of ρ and α both reach to maxmum when relay s at the mddle of two source nodes. It s shown that relay need more harvested energy to forward data when relay s at mddle of two source nodes. Fgure 6 also llustrates small α for all dstance area. Ths s because the parameter α mposes two sdes effect on throughput. On the one hand, throughput s ncreased wth more harvested energy lower end-to-end BER, on the other hand, throughput s decreased quckly wth ncreasng of α. Fgure 7 shows the optmal value of power allocaton coeffcent α 1 of source node S 1 of two protocols for dfferent values of the source node S 1 to relay dstance. The fgure demonstrates that optmal α 1 s odd symmetry wth dstance d S1 R for both PSR and TSR protocols.

8 Xu et al. EURASIP Journal on Wreless Communcatons and Networkng :131 Page 8 of 10 Fgure 5 Dstance source node S 1 to relay, d S1R, versus optmal throughput for PSR and TSR protocol. P = 0.1 mw, σc = 80 dbm, σa = 90 dbm, μ =.5, and η = 0.5. Fgure 7 Dstance source node S 1 to relay, d S1R, versus optmal power coeffcent of source node S 1. P = 0.1 mw, σc = 80 dbm, σc = 90 dbm, μ =.5, and η = 0.5. Fgures 8 and 9 show the optmal values of ρ and α for the PSR and the TSR protocols, respectvely, for dfferent values of antenna nose varance σa and dfferent values of converson nose varance σc. Fgure 8 llustrates that the optmal value of ρ ncreases by ncreasng σa and ρ decrease by ncreasng σ c.thereasons that for PSR protocol, the antenna nose w a,r n affects both the sgnal ρy r n used energy harvestng and the sgnal 1 ρy r n used nformaton decodng n MA phase, whle the converson nose w c,r n only affects the sgnal 1 ρy r n used nformaton decodng. In the BC phase, two noses mpose same effects on the recever. Thus, thetrend fortheoptmalvalueofρ s dfferent when curves are plotted wth respect to the nose varances σa or σc. However, t shows n Fgure 9 that the optmal value of α has the same trends by ncreasng σa or σ c.thss because for the TSR protocol, the antenna nose w a,r n and the converson nose w c,r n affect the receved sgnal n the same way. Fgures 10 and 11 show the maxmum throughput for the TSR and the PSR protocols, respectvely, for dfferent Fgure 6 Dstance source node S 1 to relay, d S1R, versus optmal PSR coeffcent ρ TSR coeffcent α. P = 0.1 mw, σc = 80 dbm, σa = 90 dbm, μ =.5, and η = 0.5. Fgure 8 Optmal values of ρ for the PSR protocol for dfferent values of antenna nose varance. σa and σ c = 80 dbm fxed. Other parameters: P = 0.1 mw, η = 0.5, and μ =.5.

9 Xu et al. EURASIP Journal on Wreless Communcatons and Networkng :131 Page 9 of 10 Fgure 9 Optmalvalues ofα for the TSR protocols for dfferent values of converson nose varance. σc and σ a = 80 dbm fxed. Other parameters: P = 0.1 mw, η = 0.5, and μ =.5. Fgure 11 Optmal throughput for the TSR protocol for dfferent values of converson nose varance. σc and σ a = 80 dbm fxed. Other parameters: P = 0.1 mw, η = 0.5, and mu =.5. The real lnes represent analytcal results, and markers represent smulatons. values of antenna nose varance, σa or converson nose varance σc. It can be observed from Fgures 10 and 11 that the analytcal results are agreement to the smulatons for both the PSR and the TSR protocols wth dfferent geometry scenaros. Fgures 10 and 11 also show that the antenna nose and converson nose have almost smlar effects on the two relayng protocols n dfferent geometrcal scenaro. Fnally, the optmal throughput for the PSR and the TSR protocols for dfferent values of energy harvestng effcency, η, are shown n Fgure 1. It llustrates that the PSR protocol outperforms the TSR protocol for all the values of η n varous geometry of the nodes. It also can be observed that the throughput of the two protocols s not senstve the changng of η when η s large enough. Conclusons In ths paper, we have nvestgated two SWIPT protocols, called by PSR and TSR, n TWRN wth non-coherent DBPSK modulaton, where a battery-free relay node harvests energy from the receved RF sgnal and uses that harvested energy to exchange nformaton between the two source nodes va the relay. We have developed ML decoder of ths TWRN and analyzed BER expressons of the two proposed protocols. Based on end-to-end BER Fgure 10 Optmal throughput for the PSR protocol for dfferent values of antenna nose varance. σa and σ c = 80 dbm fxed. Other parameters: P = 0.1 mw, η = 0.5, and mu =.5. The real lnes represent analytcal results, and markers represent smulatons. Fgure 1 Energy converson effcency versus optmal throughput. P = 0.1 mw, σc = σ c = 80 dbm, and μ =.5.

10 Xu et al. EURASIP Journal on Wreless Communcatons and Networkng :131 Page 10 of 10 and normalzed throughput expressons of the TWRN, we have nvestgated the effect of power allocaton on sources, tme swtchng factor, power splttng coeffcent, nose power, and other system parameters on the performance. Future work may focus on relay selecton and schedule for extended energy harvestng TWRN wth multple battery-free relays network. Competng nterests The authors declare that they have no competng nterests. Acknowledgements Ths paper s partally funded by the European Unon-FP7 CoNHealth, Grant No. 9493, the Natural Scence Foundaton of Fujan Provnce of Chna No. 013J0156, the Natonal Basc Research Program of Chna 973 Program No. 01CB316100, the Natonal Scence Foundaton of Chna NSFC, No , and the 111 Project No The authors would lke to express great apprecaton to the revewers of the paper for ther valuable comments on mprovng the qualty of ths paper. Author detals 1 Department of Communcaton Engneerng, Xamen Unversty, 4 Smng South Rd., Xamen, Fujan, Chna. Insttute of Moble Communcatons, Southwest Jaotong Unversty, 1 Jngqu Rd., Chengdu, Schuan, Chna. 3 School of Computng and Communcatons, Lancaster Unversty, InfoLab1, South Drve, LA1 4WA Lancaster, UK. Receved: 6 November 014 Accepted: 17 Aprl 015 References 1. B Rankov, A Wttneben, n Proceedngs of Internatonal Symposum on Informaton Theory. Achevable rate regons for the two-way relay channel IEEE, Seattle, 006, pp B Rankov, A Wttneben, Spectral effcent protocols for half-duplex fadng relay channels. IEEE J. Sel. Areas Commun. 5, T Cu, T Ho, J Klewer, Memoryless relay strateges for two-way relay channels. IEEE Trans. Commun. 57, M Da, H Wang, H Ln, S Zhang, B Chen, Opportunstc relayng wth analog and dgtal network codng for two-way parallel relay channels. IET Commun. 8, M Da, P Wang, S Zhang, B Chen, H Wang, X Ln, C Sun, Survey on cooperatve strateges for wreless relay channels. 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