BER Analysis of IM/DD FSO System with APD Receiver Over Gamma-Gamma Turbulence

Transcription

1 SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol. 11, No. 1, February 014, 61-7 UDC: : DOI: 10.98/SJEE P BER Aalysis of IM/DD FSO System with APD Receiver Over Gamma-Gamma Turbulece Milica I. Petković 1, Gora T. Đorđević 1, Deja N. Milić 1, Bata V. Vasić 1 Abstract: I this paper, the bit-error rate (BER) performace of itesitymodulated with direct detectio (IM/DD) free space optical (FSO) system usig the o-off keyig (OOK) ad avalache photodiode (APD) receiver is aalyzed. The itesity fluctuatios of the received optical sigal are modeled by gammagamma distributio, while both zero ad ozero ier scale models are observed. The total receiver oise icludes APD shot oise ad thermal oise. The BER expressio is theoretically derived ad umerical results are preseted. The results illustrate the BER depedece o the turbulece stregth, propagatio path legth, APD gai ad oise temperature. Keywords: Atmospheric turbulece, Avalache photodiode, Free space optical commuicatios, Gamma-gamma distributio, O-off keyig. 1 Itroductio Free space optical (FSO) commuicatio is licese-free techique, which offers may advatages such as: easy of deploymet, low cost, high security, wide badwidth. Also, FSO represets a good solutio for the last mile problem. Still, FSO deploymet is limited by the existece of atmospheric turbulece, which appears as result of the refractive idex variatios due to radom chages i atmospheric temperature, pressure ad wid speed. Atmospheric turbulece causes rapid itesity fluctuatios at the received sigal, also kow as fadig or scitillatio [1]. May statistical models have bee proposed i order to determie turbulece stregth. Sice the gammagamma model showed the good matchig betwee theoretical ad experimetal data, it has bee adopted as a appropriate model i wide rage of turbulece coditios [1 4]. Commercial FSO systems usually apply the itesity-modulatio with direct detectio (IM/DD) ad the o-off keyig (OOK) scheme, sice it is the simplest model for implemetatio ad desig. I [5], bit error rate (BER) of 1 Faculty of Electroic Egieerig, Uiversity of Niš, 14 Aleksadra Medvedeva, Niš, Serbia; s: milicapetkovic86@gmail.com; gora@elfak.i.ac.rs; deja.milic@elfak.i.ac.rs; bata.vasic@silico-studio.com 61

2 M.I. Petković, G.T. Đorđević, D.N. Milić, B.V. Vasić FSO system with IM/DD usig OOK over K-distributed atmospheric turbulece chael was derived, which is coveiet i strog turbulece coditios. The outage probability ad chael capacity of the same FSO system has bee aalyzed i [6]. After direct detectio at the receiver, a optical sigal is coverted to a electrical by photodetector. Above metioed papers aalyzed FSO systems with photodetectors usig PIN photodiodes. The avalache photodiodes (APDs) ca be also used i optical receiver desig sice they ca provide larger values of resposivity compared to PIN [7]. The FSO systems usig subcarrier biary phase-shift keyig ad APD photodiode at the receptio were observed i [8]. The BER performace of rectagular quadrature amplitude modulatio FSO system with APD receiver over log-ormal ad gamma-gamma chael has bee aalyzed i [9]. I this paper, we observe FSO system with IM/DD ad OOK i the case of APD receiver utilizatio. The atmospheric turbulece is modeled by gammagamma distributio. The effects of turbulece stregth, for both zero ad ozero ier scale, are observed. The BER expressio is theoretically derived ad umerical results are preseted. The impacts of APD shot oise ad thermal oise are take ito accout. The ifluece of turbulece stregth, APD s gai, trasmitted power, lik distace ad oise temperature are discussed. System Model Fig. 1 shows the FSO system usig IM/DD with OOK ad APD receiver. The iformatio bits are first modulated by IM with OOK. The output of modulator is the laser beam, whose directio ad size are determied by telescope at the trasmitter. The telescope output is optical sigal that is set through atmospheric chael to the receiver. Trasmissio over atmospheric chael is damaged by turbulece, atteuatio ad geometric loss. At the receiver, laser beam is arrowed by telescope ad forwarded to the APD photodetector. The APD coverts a optical sigal ito electrical [10]. The decisio which bit is set fially ca be made. The optical sigal at the iput of the APD photodetector ca be expressed as r = axi, (1) where x represets the iformatio o or off bit, a is the total lik loss ad I is ormalized irradiace accouted for the itesity fluctuatios due to atmospheric turbulece. Sice the FSO system with OOK scheme is assumed, x is either 0 or P t where P t is the average trasmitted optical power. The atmospheric atteuatio ad geometric loss are described by total lik loss give by [8, 9] 6

3 BER of IM/DD FSO System with APD Receiver Over Gamma-Gamma Turbulece A a= θl π e βv L, () where β v deotes the extictio coefficiet, L is the lik distace ad θ is the agle of divergece i radias. The area of the receiver A equals to A = πd /4 where D represets the diameter of the receiver s aperture. Fig. 1 Block diagram of the FSO system usig IM/OOK ad APD receiver. At the output of APD photodetector, electrical sigal is differet i o or off states ad it is give by gra PI t +, o re = (3), off where g ad R represet the average gai ad resposivity of APD, respectively. The total APD receiver oise is caused by shot oise, thermal oise ad dark curret. If dark curret is egligible, ca be expressed as [7 9] = ith + ish, (4) where i Th is the thermal oise ad i Sh the APD shot oise differet i o or off states. The thermal oise ca be modeled as statioary Gaussia radom process with zero-mea ad variace [7 9] T Th = 4kB F Δ f, (5) R where k B deotes the Boltzma costat, T is the receiver s temperature i degree Kelvi, R L deotes APD s load resistace, F is the amplifier oise L 63

4 M.I. Petković, G.T. Đorđević, D.N. Milić, B.V. Vasić figure ad f is the symbol s effective oise badwidth, here marked as Δf = R b /, where R b is the bit rate. I cotrast to thermal oise, the shot oise depeds o APD parts ad it is be differet i o ad off states. The shot oise ca be modeled as statioary zero-mea Gaussia radom process with variace [7] qg FARaI PtΔ f o Sh = (6) 0 off where q is a electro charge ad F A deotes the excess oise factor of the APD give by FA = kag + (1 ka)( 1 g), (7) where k A is the ioizatio factor. The variace of the total APD oise ca be expressed as [7] T 4kB FΔ f + qg FARaI PtΔf, o RL = (8) T 4 kb FΔf, off RL 3 Chael Model The atmospheric chael is uder the ifluece of atmospheric turbulece ad atteuatio ad geometric loss. The atmospheric turbulece is modeled by gamma-gamma distributio give by [1-4] 64 ( ) ( α+β)/ ( αβ) ( α+β)/ 1 pi ( I) = I Kα β αβi ΓαΓβ ( ) ( ), I 0, (9) where Γ(.) is the gamma fuctio [11, ( )], K v (.) is the vth-order modified Bessel fuctio of the secod kid [11, (8.43)] ad the parameters α ad β represet the effective umber of small-scale ad large scale cells ad ca be related to the atmospheric coditios. Free space optical sigal is trasmitted through medium, which ca be compreheded as plety of ustable idividual cells of air or eddies of differet diameters ad refractive idices. Accordig to theory about turbulece model, the atmospheric chael represets plety of ustable large turbulet eddies characterized by outer scale L 0. With icreasig wid speed, at a certai poit the kietic eergy from large eddies is trasferred without loss to smaller turbulet eddies, which are characterized by the ier scale l 0. If the ier scale is eglected, l 0 = 0, we have the zero ier scale. Whe ozero ier scale is cosidered (l 0 0), the model eeds to be modified i order to explai the slight

5 BER of IM/DD FSO System with APD Receiver Over Gamma-Gamma Turbulece chages i the power spectrum of the refractive idex variatios. The parameters α ad β ca be determied depedig o observed scale. I order to obtai their values, the stregth of the turbulece is explaied by the Rytov variace give by 7/6 11/6 R = 1.3Ck L, (10) where k=π/λ is the wave-umber, λ is the wavelegth, L is the propagatio distace, ad C deotes the weather ad altitude depedet idex of refractio structure. The idex C typically varies from to m /3 ad here it is used for determiatio of the turbulece stregth. Whe zero ier scale (l 0 = 0) ad plae wave propagatio are assumed, the parameters α ad β are foud as [1, 4] R α= exp 1, 1/5 7/6 ( R ) R β= exp 1. 1/5 5/6 ( R ) (11) I the case of ozero ier scale (l 0 0) ad plae wave propagatio, the parameters α ad β are [1, 4] where l X is give by [1, 4] ( ) l X 1 α= exp 1, p β= exp 1, 1/5 5/6 ( p ) 7 6 (1) ηxq l X = 0.16 R η x + Q 1 7. (13) η 1 x η x η x + Q η x + Q The remaiig required parameters ca be foud as [1, 4] L η x =, Q =, (14) 1/ kl R Q 0

6 M.I. Petković, G.T. Đorđević, D.N. Milić, B.V. Vasić 11/ P = 3.86 R ( 1+ 1/ Q ) si ta Q si ta Q 1/4 3 ( 1+ Q ) ( 1+ Q ) 4 1 5/6 si ta Q 3.5 Q. 7/4 (15) 4 BER Aalysis I practice, the FSO systems usually employ IM/DD with OOK because its simplicity i desig ad implemetatio. However, there is eed to set a threshold for detectio, which is a major problem i this system realizatio. The BER expressio of FSO usig IM/DD with OOK is calculated as [7] Pe = P() 1 P( 0 1) + P( 0) P( 1 0), (16) where P(1) ad P(0) represet the probabilities of trasmittig o ad off bits, respectively. The probability of detectig off bit whe o bit is set is P(0 1), ad P(1 0) is the otherwise. It is cosidered that P(1) = P(0) = 0.5. Sice the oise variace are differet i o ad off states, the probabilities P(0 1) ad P(1 0) are ot equal ad they deped o decisio threshold. So, the decisio threshold effects o BER. Uder coditio that P( 01) = P( 10), accordig to [7] the BER ca be expressed as 1 Q( I) PeI / = erfc, (17) where the parameter Q is grapi t 0 Q I =. (18) + ( ) o / off / The average BER over gamma-gamma fadig chael is coditioed o I, so ca be foud as 1 grapi erfc t Pe = ( )d pi I I. (19) 0 ( o / +off / ) After substitutig (9) ito (19) it follows: 66

7 BER of IM/DD FSO System with APD Receiver Over Gamma-Gamma Turbulece ( ) ( α+β)/ ( αβ) ( α+β)/ 1 Pe I Kα β I ΓαΓβ ( ) ( ) 0 = αβ grapi t erfc d I. T T 4kB FΔ f + qg FARaIPtΔ f + 4kB FΔf RL R L The fial BER expressio has o closed form ad it is evaluated umerically. 5 Numerical Results (0) Numerical results obtaied by derived expressio are preseted. The values of system parameters ad costats are give i Table 1 [8, 9]. Accordig to turbulece stregth, certai values of idex refractio are: C = i 14 weak, C = 10 i moderate ad C = i strog turbulece coditios [8]. The parameters α ad β are determied by (11) for zero ier scale, ad by (1) (15) whe ozero ier scale is cosidered. Table 1 Costats ad system parameters. NAME SYMBOL VALUE Optical wavelegth λ 1.55 μm Boltzma costat k B W/kHz Electro charge q C APD load resistace R L 1000 Ω Amplifier oise figure F Bit rate R b Gb/s Ioizatio factor k A 0.7 (IGaAs) Resposivity R 1 A/W Receiver s aperture diameter D 0.0 m Agle of divergece θ 10 3 rad Extictio coefficiet β v 0.1 db/km BER depedece o the average APD gai for differet propagatio distaces is show i Fig.. The ozero ier scale is cosidered. Whe propagatio distace is greater, BER performace is worse. The system performace ca be optimized by a proper selectio of APD gai because the BER miimum exists. The appropriate selectio of APD gai is very importat i receiver desig. 67

8 M.I. Petković, G.T. Đorđević, D.N. Milić, B.V. Vasić BER P t =0 dbm T=300 K C = m -/ 3 ozero ier scale l 0 =5 mm L=1000 m L=1500 m L=000 m L=500 m L=3000 m L=3500 m L=4000 m g Fig. BER depedece o the average APD gai for differet values of distace L whe ozero ier scale is cosidered. The effect of the receiver oise temperature T for zero ier scale ca be observed i Fig. 3. The system has better performace at lower temperatures T. With varyig the value of temperature T, the optimal gai is chagig rapidly. Whe T = 300 K the optimal gai is g = 6.1, ad whe T = 700 K we have g = 3.1. Also, whe higher values of g, the effect of the receiver oise temperature o performace becomes less expressed. T=100 K P t =0 dbm L=1000 m C = m -/3 zero ier scale T=300 K T=500 K T=700 K T=900 K 10 - BER g Fig. 3 BER depedece o the average APD gai for differet values of receiver oise temperature T whe zero ier scale is cosidered. 68

9 BER of IM/DD FSO System with APD Receiver Over Gamma-Gamma Turbulece 10 0 zero ier scale ozero ier scale (l 0 =5 mm) 10-3 BER C = m -/3 C =10-14 m -/ 3 C = m -/ 3 P t =0 dbm T=300 K L=1000 m Fig. 4 BER depedece o the average APD gai for differet values of turbulece stregth for both zero ad ozero ier scales. g I Fig. 4 BER depedece o g for differet values of parameter C is preseted. The zero ad ozero scales are cosidered. As expected, the results illustrated that the system has better performace for lower values of C (weak turbulece). The ifluece of APD gai is less expressed i strog turbulece coditios. Next, the BER depedece o average trasmitted power is preseted while the average gai is g = 10. I Fig. 5, BER depedece for differet values of propagatio distace L for zero ier scale is show. If the certai BER is wated, the greater trasmitted power is eeded. I Fig. 6, the same BER depedece is observed, while receiver oise temperature equals 300 K ad 700 K. The ozero ier scale is cosidered, whe the ier scale values are mm, 5 mm ad 10 mm. System has better performace whe the temperature is lower. Also, the degradatio of BER performace is oticed with icreasig ier scale value. The same depedece i differet atmospheric coditios is show i Fig. 7. To achieve a certai value of BER, the greater trasmitted power P t is eeded whe C is higher, i.e. i strog turbulece coditios. Besides the zero ier scale, ozero ier scales with differet values of ier scale are observed. With higher values of ier scale parameter, system has worse performace. The best performace are maifested whe l 0 = 0, i.e. zero ier scale. 69

10 M.I. Petković, G.T. Đorđević, D.N. Milić, B.V. Vasić BER L=1000 m L=1500 m L=000 m L=500 m L=3000 m L=3500 m L=4000 m g=10 T=300 K C = m -/ 3 zero ier scale P t [dbm] Fig. 5 BER depedece o the average trasmitted power P t for differet values of distace L whe zero ier scale is cosidered T=700 K l 0 = mm l 0 =5 mm l 0 =10 mm BER 10-3 T=300 K g=10 L=1000 m C = m -/3 ozerro ier scale P t [dbm] Fig. 6 BER depedece o the average trasmitted power P t for differet values of receiver oise temperature T whe ozero ier scale is cosidered. 70

11 BER of IM/DD FSO System with APD Receiver Over Gamma-Gamma Turbulece 10 0 C = /3 m g=10 L=1000 m T=300 K 10-3 BER C = m -/3 zero ier scale ozero l 0 = mm ozero l 0 =5 mm ozero l 0 =10 mm C =10-14 m -/ P t [dbm] Fig. 7 BER depedece o the average trasmitted power P t for differet values of turbulece stregth for both zero ad ozero ier scales. 6 Coclusio I this paper, we observe the BER performace of FSO system usig IM/DD with OOK ad APD receiver. The atmospheric turbulece is modeled by gamma-gamma distributio which is a appropriate model i wide rage of atmospheric coditios. Both zero ad ozero ier scales are cosidered. The receiver oise which icludes APD shot oise ad thermal oise is modeled as additive white Gaussia oise. The BER expressio is derived ad umerical results are preseted, while the effects of various lik coditios ad receiver cofiguratios are observed. With proper selectio of the optimal APD s gai which depeds o system coditios, system performace ca be sigificatly improved. 7 Ackowledgemet This paper was supported i part by the Miistry of Sciece of Republic of Serbia uder grats TR-308 ad III ad i part by the Norwegia Miistry of Foreig Affairs uder the project NORBAS (grat 011/1383) headed by NTNU. The authors also ackowledge the ICT COST Actio IC

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