Adaptive Relay Selection Protocol for the Parallel Hybrid RF/FSO Relay Channel

Transcription

1 Adaptive Relay Selectio Protocol for the Parallel Hybrid RF/FSO Relay Chael Marzieh Najafi, Vahid Jaali, ad Robert Schober Abstract Hybrid radio frequecy RF)/free space optical FSO) systes are aog the cadidate eablig techologies for the ext geeratio of wireless etworks sice they beefit fro the advatages of both the FSO subsyste, e.g. high data rates, ad the RF subsyste, e.g. high reliability i ters of lik coectivity. I this paper, we focus o the proble of throughput axiizatio i the parallel hybrid RF/FSO relay chael. I the parallel hybrid RF/FSO relay chael, a source ode seds its data to a destiatio ode with the help of ultiple relay odes. Thereby, the source-relay ad the relay-destiatio FSO liks are orthogoal with respect to each other due to the arrow bea eployed for FSO trasissio whereas the RF liks are half duplex with respect to each other due to the broadcast ature of RF sigals. We derive the optial relay selectio policies for trasissio ad receptio for the RF ad FSO liks ad the optial tie allocatio policy to the RF relay receptio ad trasissio liks. Siulatio results deostrate that a cosiderable gai ca be achieved by the proposed adaptive protocol i copariso with bechark schees fro the literature. I. INTROUCTION The ever-growig dead for higher data rates observed over the last few decades has becoe the ai challege ad research focus for the desig of the ext geeratio of wireless couicatio systes [1]. I particular, it is expected that the uber of devices which will use the fifth geeratio 5G) of wireless couicatio techology will reach tes or eve hudreds of billios [2] ad the total data rate requireets will exceed 500 exabytes by 2020 [3]. Free space optical FSO) systes have bee cosidered as a poweul copleetary ad/or alterative eablig techology to the curret radio frequecy RF) systes i order to achieve the data rate requireets of ext geeratio wireless etworks [1]. I additio to the huge usable badwidth, FSO systes are iheretly secure ad eergy efficiet [4]. The aforeetioed beeficial properties of FSO systes coe at the expese of soe drawbacks ad challeges icludig the requireet of havig a lie of sight LOS) betwee trasitter ad receiver, the adverse effects of atospheric turbulece, ad upredictable coectivity ad teporary lik outages due to visibility liitig coditios icludig sow, fog, ad dust [4], [5]. Relay-based cooperatio has bee proposed as a effective strategy to facilitate a LOS betwee trasitter ad receiver [6], [7]. Thereby, the parallel relayig etwork, where ultiple relay odes assist trasissio fro a source ode to a destiatio ode, is of particular iterest [6] [10]. I particular, this etwork architecture provides spatial diversity which ca be exploited to itigate the fadig iduced by atospheric turbulece. Moreover, i cotrast to the upredictable coectivity of FSO systes, RF systes are reliable i ters of preservig coectivity albeit for lower data rates. Therefore, hybrid RF/FSO systes, where a additioal RF lik is eployed to support the FSO lik, have bee proposed as they ca beefit fro both the high data rates provided by the FSO lik ad the reliability of the RF lik [11], [12]. The parallel FSO relay chael without RF backup liks was cosidered i [6] [9] ad the parallel ixed RF/FSO relay chael with source-relay RF liks ad relay-destiatio FSO liks was studied i [10]. However, to the best of the authors kowledge, the parallel hybrid RF/FSO relay chael, which is cosidered i this paper, has ot yet bee ivestigated i the literature. Here, we cosider relay selectio sice it efficietly exploits the diversity that idepedet fadig realizatios offer ad sigificatly reduces coplexity copared to the case whe all relays are active siultaeously [9], [10], [13]. Furtherore, we assue full-duplex trasissio for the FSO liks owig to the arrow-bea property of FSO couicatio, whereas due to the broadcast ature of RF couicatio, half-duplex trasissio is assued for the RF liks for siplicity ad feasibility reasos 1. We derive the optial relay selectio policies for trasissio ad receptio for the RF ad FSO liks such that the ed-to-ed throughput is axiized. Thereby, we show that depedig o which relays are selected for RF ad FSO receptio/trasissio, there are three possible optial protocol odes aely the hybrid ode, the idepedet ode, ad the cross ode. To further iprove the throughput, the tie allocatio betwee RF trasissio ad receptio for the selected relays is optiized. Siulatio results deostrate that a cosiderable gai ca be achieved by the proposed optial protocol i copariso with bechark schees fro the literature. Notatios: We use the followig otatios throughout this paper: E deotes expectatio, represets the agitude of a coplex uber, e ) is the Gauss-error fuctio, ad PrA deotes the probability of the occurrece of evet A. Moreover, 0 deotes a vector with all eleets equal to zero. Additioally, RiceΩ, Ψ) ad GGaaΘ, Φ) deote a Ricia rado variable RV) with paraeters Ω ad Ψ ad a Gaa-Gaa RV with paraeters Θ ad Φ, respectively. For otatioal coveiece, we use the defiitio [x] b a ib, axa, x for a b. II. PRELIMINARIES AN ASSUMPTIONS I this sectio, we preset the cosidered syste odel, the chael odels for the RF ad FSO couicatio liks, ad the assuptios regardig the required chael state iforatio CSI). A. Syste Model The syste odel uder cosideratio is scheatically depicted i Fig. 1. I particular, source S wishes to sed its 1 Full-duplex RF relays have bee reported i the literature [14]. However, they etail high hardware coplexity for efficiet self-iteerece suppressio. Hece, i this paper, we focus o half-duplex RF relayig.

2 S g 11[b] h 11[b] g 1[b] h 1[b] g 1M [b] h 1M [b] R 1 R R M g 21[b] h 21[b] g 2[b] h 2[b] g 2M [b] h 2M [b] idepedet, ergodic, ad statioary rado processes with cotiuous probability desity fuctios pdfs). We adopt the widely-accepted Gaa-Gaa distributed turbulece odel [4], [12], [15]. Thereby, h l [b], l = 1, 2, is odelled as h l [b] = h l hl [b], where h l ad h l [b] are the average gai ad the fadig gai of the FSO liks, respectively, ad are give by [4], [12], [15] [ h l = R e h l [b] GGaaΘ, Φ), πr 2φdl )] 2 10 kd l/10 2) FSO Lik RF Lik Fig. 1. Parallel hybrid RF/FSO relay chael. iforatio to destiatio via M iterediate relay odes deoted by R, 1,..., M. We assue that there is o direct lik betwee S ad. Moreover, the S R ad R liks are hybrid RF/FSO where each FSO lik is supported by a RF lik. The etire tie of operatio is divided ito B equal-legth blocks satisfyig B. Fially, we assue that each relay ode has to forward the data received fro the source i the sae RF lik) or the ext FSO lik) block to the destiatio. This is a practical costrait for applicatios with striget delay requireets. B. Couicatio Liks I the followig, we describe the adopted chael odel for the FSO ad RF liks. 1) FSO Liks: We assue that the FSO syste eploys o-off keyig OOK) with itesity-odulatio ad directdetectio IM/). Here, S is equipped with a ulti-aperture trasitter poitig i the directios of the relays. Each relay has a aperture directed towards ad a photodetector i order to detect the optical sigal received fro S. Furtherore, is equipped with a photodetector detectig the optical sigals received fro the relays. Let y1[b] ad y2[b] deote the itesities of the optical sigals received at R ad i the b-th block, respectively. Thereby, after reovig the abiet backgroud light itesity, yl [b] ca be odelled as [4], [5] y l[b] = h l [b]x l[b] + z l[b], l = 1, 2, 1) where x 1[b] 0, PS ad x 2[b] 0, PR deote the itesities of the optical sigals trasitted by S ad R i the b-th block, respectively. The axiu allowable itesities of the FSO sigals, i.e., PS ad PR, are aily liited by restrictios iposed by eye safety regulatios [4]. Moreover, z1[b] ad z2[b] are the itesities of the shot oises caused by abiet light at R ad i the b-th block, respectively. Noises z1[b] ad z2[b] are odelled as zero-ea real-valued additive white Gaussia oises AWGNs) with variaces σ1 2 ad σ2, 2 respectively, ad are idepedet fro each other ad fro the FSO trasitted sigals. Furtherore, h 1 [b] ad h 2 [b] deote the chael gais of the S R ad R FSO liks i the b-th block, respectively, ad are odelled as utually where R deotes the resposivity of the photodetector, r is the aperture radius, φ is the divergece agle of the bea, d 1 ad d 2 are the distaces betwee the trasitters ad the receivers of the S R ad R liks, respectively, ad k is a weather-depedet atteuatio coefficiet. Paraeters Θ ad Φ of the Gaa-Gaa distributio deped o physical paraeters such as the wavelegth λ ad the weatherdepedet idex of refractio structure paraeter C, 2 cf. [12, Eqs. 3) ad 4)]. Fro a iforatio theoretical poit of view, FSO liks ca be odelled as biary iput-cotiuous output AWGN chaels where the axiu iforatio rate is achieved by uiforly distributed biary iputs [16]. Thereby, i the b-th block, the capacities of the S R ad R FSO liks, deoted by C1[b] ad C2[b], respectively, for OOK iputs are give by [16] C l [b] = W [ 1 1 2π [ exp 2tp l [b] 2σ 2 l ) + exp exp t 2 )log exp p2 l [b] 2σ 2 l ) 2tp l[b] + exp p2 l [b] ) ] ] 2σ 2 l 2σl 2 dt 3) where p 1 [b] = PS h 1[b], p 2 [b] = PR h 2 [b], ad W is the badwidth of the FSO sigal. 2) RF Liks: We cosider a stadard AWGN chael for the RF liks. Moreover, we assue that all RF trasitters ad receivers are equipped with a sigle atea. Let y1[b] ad y2[b] deote the RF sigals received at R ad i the b-th block, respectively, which are odelled as [17] y l[b] = g l [b]x l[b] + z l[b], l = 1, 2, 4) where x 1[b] ad x 2[b] are the RF sigals trasitted by S ad R, respectively. Additioally, z1[b] ad z2[b] deote the receiver oises at R ad i the b-th block, respectively. We assue z1[b] ad z2[b] are odelled as zero-ea coplex AWGNs with variaces δ1 2 ad δ2, 2 respectively. The RF oise variaces are give by [δl 2 ] db = W N l,0 +N l,f, where W is the badwidth of the RF sigal, N l,0 deotes the oise power spectral desity i db/hz), ad N l,f is the oise figure i db) of the RF receivers. Furtherore, g 1 [b] ad g 2 [b] are utually idepedet, ergodic, ad statioary rado processes with cotiuous pdfs specifyig the chael coefficiets of the S R ad R RF liks i the b- th block, respectively. For the hybrid RF/FSO lik, a LOS has to be available for the applicability of the FSO syste [12], [15]. Therefore, we assue Ricia fadig for the RF liks which icludes the effects of both scattered ad LOS )

3 paths. Takig ito accout the effect of path-loss, g l [b] is odelled as g l [b] = ḡ l g l [b], where ḡ l ad g l [b] deote the average gai ad the fadig coefficiet of the RF liks, respectively, ad are give by [12], [18] [ λ ] 2 [ ] ν G ḡ l = txg rx d ref 4πd ref d l 5) g l [b] RiceΩ, Ψ), where λ is the wavelegth of the RF sigal, G tx ad G rx are the trasit ad receive RF atea gais, respectively, ad d ref deotes a referece distace for the atea far-field. Paraeters Ω ad Ψ of the Rice distributio deote the ratio betwee the power i the direct path ad the power i the scattered paths ad the total power i both paths, respectively. Moreover, the capacities of the S R ad R RF liks i the b-th block, deoted by C1[b] ad C2[b], respectively, are give by where q 1 [b] = Cl[b] = W log q2 l [b] ), l = 1, 2, 6) C. CSI Requireets δ 2 l P S g 1[b] ad q 2 [b] = P R g 2 [b]. Throughout this paper, we assue that a cetral ode, e.g., the destiatio, kows the istataeous CSI of all FSO ad RF liks ad is resposible for deteriig the optial trasissio strategy ad coveyig it to all odes. Moreover, we assue that the chael states chage slowly eough such that the sigalig overhead caused by chael estiatio ad feedback is egligible copared to the aout of iforatio trasitted i oe block. III. THROUGHPUT MAXIMIZATION I this sectio, we first preset the proposed protocol, ad subsequetly, we derive the optial throughput axiizig policy as a fuctio of a give fadig state. Fially, we itroduce the cosidered peorace etrics for the evaluatio of the proposed protocol i a slowly tie-varyig eviroet. A. Proposed Protocol For the cosidered couicatio syste, our goal is to derive a optial relay selectio policy which axiizes the throughput based o the CSI of all RF ad FSO liks. To this ed, let α 1 [b], 1,..., M, deote biary selectio variables where α 1 [b] = 1 if relay R is selected for FSO receptio i the b-th block ad α 1 [b] = 0 if relay R is ot selected. Siilarly, α 2 [b] = 1 idicates that relay R is selected for FSO trasissio i the b-th block ad α 2 [b] = 0 if relay R is ot selected. Aalogously, β 1 [b] ad β 2 [b], 1,..., M, deote biary selectio variables for RF relay receptio ad trasissio i the b-th block, respectively. Moreover, sice i each block oly oe of the relays is selected for RF ad FSO receptio/trasissio, respectively, α l[b] = 1, l, b, ad β l[b] = 1, l, b, have to hold. Assuig relay R ad relay R are selected for FSO receptio ad trasissio, respectively, they ca siultaeously trasit over both the S R ad R FSO Lik 1 2 b B RF Lik S R ρ 1[b] S R R R Fig. 2. Proposed trasissio protocol for the cosidered parallel hybrid RF/FSO relay chael. FSO liks, i.e., the FSO liks are orthogoal with respect to each other. However, due to the broadcast ature of RF sigals, siultaeous activatio of the selected relays creates iteerece fro the trasittig relay to the receivig relay. I particular, self-iteerece occurs if the sae relay is selected for both trasissio ad receptio ad iter-relay iteerece occurs if the relays selected for trasissio ad receptio are differet. Therefore, for the sake of siplicity of ipleetatio ad practical feasibility, we assue that the RF liks are half-duplex with respect to each other. I other words, assuig relay R ad relay R are selected for RF receptio ad trasissio, respectively, both the S R ad R RF liks caot be active at the sae tie. Hece, we activate the S R RF lik i the ρ 1 [b] [0, 1] fractio of the b-th block ad the R RF lik i the reaiig ρ 2 [b] [0, 1] fractio of the b-th block, respectively, where ρ 1 [b] + ρ 2 [b] = 1, b, holds. The trasissio protocol is scheatically illustrated i Fig. 2. ρ 2[b] B. Optial Throughput Maxiizig Policy I this subsectio, we derive adaptive RF/FSO relay selectio ad RF trasissio tie allocatio policies such that, i each trasissio block, the iforatio rate fro the source to the destiatio, deoted by τ[b], is axiized. Sice the optial throughput axiizig policy depeds oly o the fadig states of the RF ad FSO liks, ad ot o the trasissio block idex, we drop the block idex i the reaider of the paper for otatioal siplicity. The resultig throughput axiizatio proble ca be forulated as axiize τ α A,β B,ρ C,τ 0 7) subject to τ α 1 C1 + β 1 ρ 1 C1, τ α 2 C2 + β 2 ρ 2 C2,, where α, β, ρ, ad τ are the vectors cotaiig the relay selectio variables of the FSO liks, the relay selectio variables of the RF liks, the tie sharig variables of the RF liks, ad the relays throughputs, respectively. Moreover, A = α α l 0, 1, l, α l = 1, l, B = β β l 0, 1, l, β l = 1, l, ad C = ρ ρ l [0, 1], l l ρ l = 1 are the feasible sets of α, β, ad ρ, respectively. The costraits i 7) follow fro the ax-flow i-cut theore [17], accordig to which the throughput of relay R is liited by the capacities of the S R ad R liks, respectively. I the followig theore, the optial solutio to the optiizatio proble i 7) is provided.

4 Theore 1: The optial policies for FSO ad RF relay selectio ad optial trasissio tie allocatio to the RF liks for the cosidered parallel hybrid RF/FSO relay chael are give by α l = β l = 1, if Case 1 = argax Case 2 = argax τ hyb τ Case 3 l = 1, ) = argax,) Case 3 l = 2, ) = argax,) 0, otherwise 1, if Case 1 = argax Case 2 = argax 0, otherwise ρ 1 = 1 ρ 2 = where τ hyb τ hyb = τ id τ hyb τ Case 3 l = 1, ) = argax,) Case 3 l = 2, ) = argax,) = τ τ = [ C 2 +C 2 C 1 C 1 +C 2 ] 1 0 C 2 C 1 +C C 2, C 1, τ τ τ τ if Case 1 = argax, if Case 2 = argax 2 + τ, where τ hyb τ if Case 3, ) = argax,), τ, id ad τ are give by C2 + C2, if C 2 +C 2 < 1 C1 C1 + C1, if C 1 +C 1 < 1 C2 C 2 +C 2 C 1 C C1 +C 1 + C1, otherwise 2 τ = i C C 1 + C 2, τ if C 2 0, otherwise. ax > ax Case 2 Idepedet Mode): = C 1 C 2 +C 2 + C 1 1 C2 Moreover, Cases 1-3 are defied as follows Case 1 Hybrid Mode): τ hyb ax ax τ + ax τ > ax Case 3 Cross Mode): ax τ > ax,) ax 1, C2 τ + ax τ, ax τ,) ax τ hyb, ax Proof: Please refer to Appedix A. τ hyb, ax τ,) τ + ax τ τ 8a) 8b) 8c) 9a) 9b) 9c) 10) The feasible sets A ad B of the relay selectio variables allow the selectio of at ost four differet relays for RF/FSO receptio ad trasissio. However, due to the costraits i 7), the optial relay selectio policy ca select at ost two differet relays for RF/FSO receptio ad trasissio i order to esure that the data which is trasitted fro the source to a certai relay is actually forwarded to the destiatio. Moreover, the optial throughput axiizig policy i Theore 1 reveals that the optial relay selectio policy α l, β l ) belogs to oe of the followig three cases, see Fig. 3. Case 1 Hybrid Mode): The sae relay R is selected for S Hybrid Mode Idepedet Mode Cross Mode R FSO Lik S RF Lik R Fig. 3. The three differet possible optial operatioal odes i the cosidered parallel hybrid RF/FSO relay chael. FSO/RF trasissio/receptio, i.e., the RF liks serve as support liks for the FSO liks. Case 2 Idepedet Mode): Relay R is selected for FSO receptio ad trasissio ad a differet relay R is selected for RF receptio ad trasissio, i.e., the FSO ad RF liks are used idepedetly. Case 3 Cross Mode): Relays R ad R,, are selected for FSO receptio ad trasissio, respectively, ad relays R ad R are selected for RF trasissio ad receptio, respectively. The optial trasissio tie allocatio to the RF liks give i 8c) is foud such that the bottleeck throughput of the S R ad R liks is axiized. Thereby, depedig o whether R uses both the RF ad FSO liks, i.e., the hybrid ad cross odes, or oly the RF liks, i.e., the idepedet ode, the resultig optial RF tie allocatio policy depeds o both the RF ad FSO fadig states or oly the RF fadig state, respectively. Sice our goal is to axiize the throughput, we select the optial ode aog the hybrid, idepedet, ad cross odes, which provides the highest throughput, cf. 10). Thereby, the axiu throughput achieved by the protocol i Theore 1, deoted by τ opt, is give by ax τ opt = ax ax R τ hyb for Case 1 τ + ax τ for Case 2 for Case 3,) τ S R R 11) Reark 1: As etioed before, the restrictio that the optial relay selectio policy as the solutio of 7) ca select at ost two differet relays, ad ot four differet relays, is caused by the requireet that the selected relay has to forward the received data to the destiatio iediately. This is a practical costrait for applicatios with striget delay requireets. If this costrait is relaxed ad the relays are equipped with buffers for teporary data storage, it is potetially possible to select four differet relays for RF/FSO trasissio/receptio depedig o the qualities of the RF/FSO liks. This additioal degree of freedo ay provide further throughput iproveet at the expese of a icreased ed-to-ed delay. I particular, such buffer-aided protocols have bee widely ivestigated i the literature o pure RF wireless couicatio, cf. [19], [20], ad the refereces therei. Studyig a buffer-aided relayig protocol for the parallel hybrid RF/FSO relay chael is a iterestig proble for future research, but is beyod the scope of this paper.

5 C. Peorace Metrics for Tie-Varyig Fadig The protocol i Theore 1 provides the optial trasissio policy for a give set of the fadig states of the FSO ad RF chaels. For peorace evaluatio i a tie-variat fadig eviroet, we cosider the ergodic throughput ad the outage probability as peorace etrics for the protocol proposed i Theore 1 [21]. 1) Ergodic Throughput: The ergodic throughput is the expectatio of the achievable throughput over all possible fadig states [21]. The ergodic throughput is a appropriate peorace etric if the source has eough data for trasissio i each trasissio block ad the odes are able to adapt their trasissio rates to the uderlyig chael capacities. Thereby, the ergodic throughput of the protocol i Theore 1 is forally give by τ erg = Eτ opt [h, g], 12) where h ad g are the vectors of all fadig gais of the FSO ad RF liks, respectively, ad τ opt [h, g] is the achievable throughput of the protocol i Theore 1 for give fadig states h ad g, cf. 11). 2) Outage Probability: I ay couicatio scearios, the source is expected to covey a costat iforatio rate R req i bits/secod) to the destiatio. Thereby, a relevat peorace etric is the outage probability [21] which is defied as the probability that the axiu achievable throughput τ opt [h, g] falls below the costat iforatio rate R req. The outage probability of the protocol i Theore 1 is forally give by P out = Prτ opt [h, g] < R req. 13) IV. NUMERICAL RESULTS I this sectio, we evaluate the peorace of the proposed protocol ad copare it with several bechark schees. I particular, we cosider the well-kow ax-i protocol [9] as bechark schee where for each fadig state, the relay with the axiu bottleeck capacity, i.e., the iiu of the capacities of the S R ad R liks, is selected. Thereby, we cosider the ax-i protocol for the followig scearios: i) FSO ax-i: Max-i relay selectio for the FSO liks without RF liks as backups [8], [9], ii) Idepedet RF/FSO ax-i: Max-i relay selectio ad data trasissio are peored idepedetly for the RF ad FSO liks, ad iii) Hybrid RF/FSO ax-i: Max-i relay selectio is peored for hybrid RF/FSO liks, i.e., a sigle relay is selected for trasissio over both the RF ad FSO liks. For the RF liks i the bechark schees, we assue that each block is divided ito two subblocks of equal legth for the S R ad R RF trasissio. Uless otherwise stated, the values of the paraeters for the RF ad FSO liks used for the uerical results reported i this sectio are give i Table I. Reark 2: It is clear that the idepedet ad hybrid RF/FSO ax-i protocols outpeor the FSO ax-i protocol. However, the peorace copariso betwee the idepedet RF/FSO ax-i protocol ad the hybrid RF/FSO ax-i protocol is ot straightforward ad depeds o the Ergodic Throughput, τ erg i Mbits/secod) TABLE I EFAULT VALUES FOR SYSTEM PARAMETERS [12], [15] RF Lik FSO Lik Paraeter Value Paraeter Value G tx, G rx 10 dbi R V N0 114 db/mhz σ A 2 λ GHz) λ THz) W 20 MHz W 1 GHz Ω, Ψ) 4, 1) Θ, Φ) 2.23, 1.54) ν 3.5 k 0.03 light-oderate fog) NF 5 db r 10 c d ref 80 φ 2 rad Proposed Protocol, Optial Hybrid RF/FSO Max-Mi Protocol, Hybrid RF/FSO Max-Mi Protocol, Idepedet RF/FSO Max-Mi Protocol, FSO Oly k = k = k = RF Trasit Power, P i db) Fig. 4. Ergodic throughput, τ erg, i Mbits/secod vs. RF trasit power, PS = P R = P, i db for M = 3, k 0.43, 32, , PS = P R = 20 W 13 db), ad d 1 = d 2 = 800 syetric etwork). syste paraeters. I particular, the advatage of the idepedet RF/FSO protocol over the hybrid RF/FSO protocol is that two differet relays ca be selected for the RF ad FSO subsystes whereas i the hybrid RF/FSO protocol, oly oe relay ca be selected for both RF ad FSO. O the other had, i the hybrid RF/FSO protocol, the RF liks are eployed as backups to iprove the bottleeck throughputs of the S R ad R liks, whereas, i the idepedet RF/FSO protocol, the FSO ad RF subsystes operate idepedetly. I Fig. 4, we show the ergodic throughput, τ erg, cf. 12) versus the RF trasit power, PS = PR = P, for k 0.43, 32, correspodig to clear air, lightoderate fog, ad oderate fog weather coditios, respectively. We assue d 1 = d 2 = 800 for each relay which leads to a syetric syste with respect to the first ad secod hops, i.e., the statistical chael coditios of the S R FSO RF) lik ad the R FSO RF) lik are idetical. We observe fro Fig. 4 that except for the parallel FSO relay chael without RF backup liks, the ergodic throughput iproves as the RF power icreases. Moreover, the proposed optial protocol outpeors the bechark schees particularly for o-clear weather coditios, which cause ipairet to the FSO liks. Furtherore, for the cosidered set of paraeters, the throughputs of the hybrid ad idepedet ax-i protocols are siilar but ot idetical, see Reark 2). I Fig. 5, we show the outage probability P out, cf. 13), versus the FSO trasit power, PS = P R = P, ad we choose the distace betwee the trasitters ad the receivers

6 Outage Probability, P out M = 5 FSO Trasit Power, P i db) M = 3 M = 1 Proposed Protocol, Optial Hybrid RF/FSO Max-Mi Protocol, Hybrid RF/FSO Max-Mi Protocol, Idepedet RF/FSO Max-Mi Protocol, FSO Oly Fig. 5. Outage probability, P out, vs. FSO trasit power, PS = P R = P, i db for M 1, 3, 5, R req = 128 Mbits/secod, PS = P R = 0.2 W 23 db), ad [d 1, d 2 ] = [1000, 800] asyetric etwork). of the S R ad R liks as d 1 = 1000 ad d 2 = 800, respectively, which results i asyetric chael coditios for each relay. We observe that a cosiderable peorace gai is achieved by the proposed protocol copared to the bechark schees. This gai stes fro the optial selectio of the trasissio odes, i.e., the hybrid, idepedet, ad cross odes i Fig. 3, as well as optial RF tie allocatio, cf. Theore 1. Furtherore, we observe that the idepedet ax-i protocol slightly outpeors the hybrid ax-i protocol for M = 3, 5 for the asyetric chaels cosidered i Fig. 5, see Reark 2. Fially, as expected, the diversity gais of all protocols icrease with the uber of relay odes. V. CONCLUSIONS We cosidered the proble of throughput axiizatio for the parallel hybrid RF/FSO relay chael. I particular, we derived the optial relay selectio policies for trasissio ad receptio for the RF ad FSO liks ad the optial tie allocatio policy for RF trasissio ad receptio. Siulatio results verified the superiority of the proposed adaptive protocol copared to bechark schees fro the literature, especially whe the FSO liks suffered fro severe atospheric ipairets. APPENIX I this appedix, we derive the solutio to the optiizatio proble i 7). To this ed, we first specify the potetial cadidates for the optial relay selectio policy aog all possible relay selectio policies α l, β l ). Subsequetly, we derive the optial RF tie allocatio policy ρ l for each of the potetial cadidates for the optial relay selectio policy. Fially, the relay selectio policy which yields the axiu ed-to-ed throughput aog the cadidate relay selectio policies is chose as the optial relay selectio policy αl, β l ). 1) Cadidate Policies: The feasible sets A ad B of the relay selectio variables allow the selectio of at ost four differet relays for RF/FSO receptio ad trasissio. Therefore, there are i total M 4 possibilities for the optial biary values of α l ad β l i the feasible set A B. However, due to the costraits i 7), the optial relay selectio policy ca select at ost two differet relays for RF/FSO receptio ad trasissio i order to esure that the data which is trasitted fro the source to a certai relay is actually forwarded to the destiatio. Thereby, there are MM 1) 2 possibilities to select two relays out of M relays. Moreover, for a give selected relay pair, there are 2 4 = 16 possibilities to assig the selected relays to RF/FSO receptio ad trasissio, respectively. I the followig, we show that oly 6 aog these 16 possibilities are cadidates for the optial relay selectio policy. To this ed, let ad be the idices of the selected relays. Cosiderig the feasible sets A ad B, we ivestigate the followig 2 2 = 4 possibilities for the RF/FSO receptio relays: i) Relay is selected for both RF/FSO receptio, i.e., α 1 = β 1 = 1. I this case, relay is the oly optio for RF/FSO trasissio, i.e., α 2 = β 2 = 1 has to hold hybrid ode). ii) Relay is selected for RF receptio ad relay is selected for FSO receptio, i.e., α 1 = β 1 = 1. Here, there are two optios, relays ad are chose either for RF ad FSO trasissio, respectively, i.e., α 2 = β 2 = 1 idepedet ode), or for FSO ad RF trasissio, respectively, i.e., α 2 = β 2 = 1 cross ode). Cases iii) ad iv) are idetical to Cases i) ad ii), respectively, after chagig the roles of relays ad. To suarize, aog the M 4 possibilities for α l ad β l i the feasible set A B, oly 3MM 1) possibilities have to be ivestigated for the optial relay selectio policy. 2) Optial RF Tie Allocatio: I the followig, the optial RF tie allocatio policy ρ l ad the resultig throughput are derived for the aforeetioed 3MM 1) possibilities depedig o their odes of trasissio, aely hybrid, idepedet, ad cross odes. Case 1 Hybrid Mode): Suppose relay R is selected for both RF/FSO trasissio/receptio. Thereby, the optial ρ l is foud such that the differece betwee the trasissio rates of the S R hybrid RF/FSO lik ad the R hybrid RF/FSO lik is iiized, i.e., ρ 1 = 1 ρ 2 = [ C 2 + C 2 C1 C 1 + C 2 ] 1, 14) 0 which leads to the overall throughput τ hyb give i 9a). Moreover, the optial relay for RF ad FSO trasissio is the oe which leads to the axiu value of τ hyb i 9a), i.e., the idex of the optial relay is give by = argax τ hyb. Case 2 Idepedet Mode): Let relay R be selected for both FSO receptio ad trasissio ad a differet relay R be selected for RF receptio ad trasissio. The optial ρ l which akes the RF trasissio rates of the S R ad R liks equal is foud as ρ 1 = 1 ρ 2 = C ) C 2 This leads to the overall throughput τ id give i 9b). Moreover, i this case, we ca idepedetly select the relay which axiizes the throughput of FSO trasissio, i.e.,

7 = argax throughput of RF trasissio, i.e., = argax τ, ad the relay which axiizes the τ. Case 3 Cross Mode): Here, differet relays R ad R are selected for FSO receptio ad trasissio, respectively. Moreover, for this case to be optial, relays R ad R have to be selected for RF trasissio ad RF receptio, respectively. For this case, we ca distiguish the followig four subcases depedig o which liks are the bottleeck of data trasissio. Subcase 1: The bottleeck liks for both relays R ad R are the FSO liks. Hece, the RF tie sharig variables have to be chose to support the FSO liks, i.e., ρ 1 C 2 ad ρ 2 C 1. Therefore, a ecessary coditio for this subcase C2 to be optial is that C 2 + C 1 1 holds. Without loss of C2 geerality ad sice ρ 1 + ρ 1 = 1 has to hold, we choose the followig solutio ρ 1 = 1 ρ 2 = C 2. 16) This subcase leads to throughput τ = C1 + C2. Subcase 2: The bottleeck liks for both relays R ad R are the RF liks. This leads to throughput τ = ρ 1 +ρ 2 C2. Hece, we obtai ρ 1 = 1 ρ 2 = 1, if C2 0, otherwise. 17) However, the RF trasissio tie allocatio policy i 17) eas that the RF lik is selected to support either FSO trasissio or receptio, i.e., oly oe of the relays is active. Therefore, this subcase caot be optial sice Case 1 always yields a higher throughput. Subcase 3: The bottleeck liks for relays R ad R are the FSO ad RF liks, respectively. This leads to throughput τ = C1 + ρ 1. Here, the throughput ca be always iproved by icreasig ρ 1 ad decreasig ρ 2 util the S R FSO lik is o loger the bottleeck. This cotradicts the earlier assuptio of this subcase, i.e., Subcase 3 caot occur for the optial solutio. Subcase 4: The bottleeck liks for relays R ad R are the RF ad FSO liks, respectively. Siilar to Subcase 3, Subcase 4 caot occur for the optial solutio. To coclude, aog the four possible subcases for Case 3, oly Subcase 1 ca be the optial solutio for soe fadig realizatios. Hece, without loss of geerality, we defie the throughput of Case 3, deoted by τ, i 9c) as the throughput of Subcase 1 if the ecessary coditio for this subcase, C i.e., 2 + C 1 1 holds, ad zero otherwise. The idices C2 of the optial relays are give by, ) = argax τ.,) 3) Optial Policy: Now, the reaiig questio is i which ode the RF ad FSO liks should operate for a give chael realizatio. Sice our goal is to axiize the throughput, we have to select the case which yields the axiu achievable throughput, i.e., the axiu value aog τ hyb, τ + τ, ad τ. This leads to the relay selectio policy give i Theore 1 ad copletes the proof. REFERENCES [1] F. eers, H. Yaikoeroglu, ad M. St-Hilaire, A Survey of Opportuities for Free Space Optics i Next Geeratio Cellular Networks, i Proc CNSR, May 2011, pp [2] M. Corso, R. Laroia, J. Li, V. Park, T. Richardso, ad G. Tsirtsis, Toward Proxiity-Aware Iteretworkig, IEEE Wireless Cou., vol. 17, o. 6, pp , ec [3] Aalysys Maso Report S. Hilto, Machie-to-Machie evice Coectios: Worldwide Forecast , Aalysys Maso Report, [4] M. Khalighi ad M. Uysal, Survey o Free Space Optical Couicatio: A Couicatio Theory Perspective, IEEE Cou. Surveys Tutorials, vol. 16, o. 4, pp , [5] H. Kaushal ad G. Kaddou, Free Space Optical Couicatio: Challeges ad Mitigatio Techiques, Olie versio available at arxiv, Ju [Olie]. Available: [6] C. Abou-Rjeily, All-Active ad Selective FSO Relayig: o We Need Iter-Relay Cooperatio? J. Lightw. Techol., vol. 32, o. 10, pp , May [7] M. Kashai, M. Safari, ad M. Uysal, Optial Relay Placeet ad iversity Aalysis of Relay-Assisted Free-Space Optical Couicatio Systes, IEEE/OSA J. Opt. Cou. Net., vol. 5, o. 1, pp , Ja [8] C. Abou-Rjeily, Peorace Aalysis of FSO Couicatios with iversity Methods: Add More Relays or More Apertures? IEEE J. Sel. Areas Cou., vol. 33, o. 9, pp , Sep [9] N. Chatzidiaatis,. Michalopoulos, E. Kriezis, G. Karagiaidis, ad R. Schober, Relay Selectio Protocols for Relay-Assisted Free-Space Optical Systes, IEEE/OSA J. Opt. Cou. Net., vol. 5, o. 1, pp , Ja [10] M. Petkovic, A. Cvetkovic, G. jordjevic, ad G. Karagiaidis, Partial Relay Selectio with Outdated Chael State Estiatio i Mixed RF/FSO Systes, J. Lightw. Techol., vol. 33, o. 13, pp , Jul [11] M. Usa, H. Yag, ad M.-S. Alouii, Practical Switchig-Based Hybrid FSO/RF Trasissio ad its Peorace Aalysis, IEEE Photoics J., vol. 6, o. 5, pp. 1 13, Oct [12] B. He ad R. Schober, Bit-Iterleaved Coded Modulatio for Hybrid RF/FSO Systes, IEEE Tras. Cou., vol. 57, o. 12, pp , ec [13] J.-Y. Wag, J.-B. Wag, M. Che, ad X. Sog, Peorace Aalysis for Free-Space Optical Couicatios usig Parallel All-Optical Relays over Coposite Chaels, IET Cou., vol. 8, o. 9, pp , Ju [14] M. uarte, C. ick, ad A. Sabharwal, Experiet-rive Characterizatio of Full-uplex Wireless Systes, IEEE Tras. Wireless Cou., vol. 11, o. 12, pp , ec [15] W. Zhag, S. Hrailovic, ad C. Shi, Soft-Switchig Hybrid FSO/RF Liks Usig Short-Legth Raptor Codes: esig ad Ipleetatio, IEEE J. Sel. Areas Cou., vol. 27, o. 9, pp , ec [16] P. McIllree, Calculatio of Chael Capacity for M-ary igital Modulatio Sigal Sets, i Proc. IEEE Sigapore It. Cof. If. Egieerig, Cou., Net., vol. 2, Sep. 1993, pp vol.2. [17] T. M. Cover ad J. A. Thoas, Eleets of Iforatio Theory. Wiley, Joh ad Sos, Icorporated, [18] N. Vaiopoulos, H. Sadalidis, ad. Varoutas, WiMAX o FSO: Outage Probability Aalysis, IEEE Tras. Cou., vol. 60, o. 10, pp , Oct [19] V. Jaali, N. Zlataov, A. Ikhlef, ad R. Schober, Achievable Rate Regio of Bidirectioal Buffer-Aided Relay Chael with Block Fadig, IEEE Tras. If. Theory, vol. 60, o. 11, pp , Nov [20] N. Zlataov, V. Jaali, ad R. Schober, Achievable Rates for the Fadig Half-uplex Sigle Relay Selectio Network Usig Buffer- Aided Relayig, IEEE Tras. Wireless Cou., vol. 14, o. 8, pp , Aug [21] A. Maaref ad S. Aissa, Closed-For Expressios for the Outage ad Ergodic Shao Capacity of MIMO MRC Systes, IEEE Tras. Cou., vol. 53, o. 7, pp , Jul