Simulation of FSO Transmission Channel

Transcription

1 Simulaiof FSO Transmission Channel ZDENĚK KOLKA 1, VIERA BIOLKOVÁ 1, DALIBOR BIOLEK 1 Deparmen of Radio Elecronics, Deparmen of Microelecronics Brno Universiy of Technology urkyňova 118, 61 Brno CZECH REUBLIC Absrac: The paper deals wih he modeling and simulaiof amospheric Free-Space Opical (FSO) links. Due o he effec of amospheric urbulence he links are characerized by ouages in he order of ens of milliseconds, which are several orders of magniude longer han he duraiof frames (packes) being ransmied. For high ransmission raes he opical channel can be simply modeled as a slowly varying AWGN channel. I allows compuing he probabiliy of he occurrence of errors in each packe by means of analyical formulae. The mehod is demonsraed on he simulaiof channel coding for miigaing shor fades for unidirecional link using he OOK modulaion. Key-Words: Free-space opics, simulaion, channel coding 1 Inroducion The echnology of Free-Space Opical (FSO) links consiss in ransmiing informaion by means of ligh beams in space or in he amosphere. A presen, erresrial sysems up o 1.5 Gb/s wih a range of up o km are commercially available. The majoriy of he links are designed as simple proocolindependen repeaers on he physical layer, using on-off keying (OOK) of laser diode or LED in he ransmier. Oher ypes (ground-air, ground-space, and space-space) are sill in experimenal sage [1]. Amospheric links are influenced by amospheric aenuaion and urbulence. Aenuaion caused by scaering on paricles increases significanly during fog, rain, and snowfall and may cause a long ouage. Is a very slow process, which deermines he overall availabiliy of link [], [3]. Long-range links wih a igh power budge are, in addiion, influenced by amospheric urbulence. Inhomogeneiies in he amosphere cause power flucuaions a he receiver in he millisecond ime scale for saic erminals. These shor ouages increase he bi-error rae and inerfere wih communicaion proocols. General heory of urbulence can be found in he classical book [4]. Theoreical informaion capaciy of he channel for differen scinillaion models was analyzed, for example, in [5]. Many pracical experimens for erresrial and ground-space links have been conduced a DLR [1], [8]. Spaial diversiy has been sudied wih he aim of miigaing scinillaion effecs [6]. A millisecond ouage resuls in he loss of hundreds or housands of packes for high-speed neworks. The significan difference beween he packe duraion and he period of amospheric urbulence allows using analyic formulae for he calculaiof packe error probabiliy. The simulaion even rae is derived from he packe rae raher han from he bi rae. Secions and 3 of he paper provide a simple framework for FSO channel modeling, using samples of power received from a real link or from a model. Secion 4 deals wih an example simulaion of a coding scheme for miigaing shor-ime fades based on a combinaiof bi-level and packe-level coding. Model of Amospheric Channel Le us consider he OOK FSO amospheric link influenced by amospheric urbulence, Fig. 1. TX eddies urbulen amosphere L 1 Fig. 1 FSO link. ransversal wind v A amospheric urbulence jus redisribues energy in he beam wihou loss. Usually he receiving aperure is smaller han he beam crosssecion, which causes flucuaion in he received power, Fig.. ISSN: ISBN:

2 The ime scales of ransmied daa and power flucuaions can be described by he relaion τ DATA << τ TURB (1) wih ypical values τ DATA < 1ns, τ TURB 1ms. p () τ TURB Fig. Received opical power of amospheric FSO wih ON-OFF keying. Neglecing, and considering he equal probabiliy of he symbols and 1 and wih respec o (1) we can define he shor-ime mean power a he receiver m,. 5 1, =, () which flucuaes randomly due o amospheric urbulence. m, can be easily moniored and recorded a he receiver. The normalized received power is N m, =, (3) m, where he mean value, is compued for a m sufficienly long inerval. The normalized variance, called power scinillaion index (SI) p = N σ 1 (4) provides a measure of he scinillaion srengh. The scinillaion index is inversely proporional o he diameer D of receiving aperure due o he effec of averaging. Amospheric urbulence reduces he beam spaial coherence. The larger he receiver aperure he more uncorrelaed conribuions are summed a he phoodeecor. The effec can be expressed as [4]. σ p ( D1 ) A( D1 ), (5) σ ( D ) A( D ) p 1 shor-ime mean m, 1,, where D 1 and D are wo diameers of he receiving aperure and A(D) is he aperure-averaging facor 7 / 5 5 / 6 πd A ( D) = , (6) 1 L λ where λ is he wavelengh, and L 1 is he disance. On he assumpiof weak flucuaions and a small receiving aperure, N is heoreically lognormally disribued wih he probabiliy densiy funcion [4] f N, w ( p) [ ln p.5σ ] 1 + exp pσ p π σ =. (7) Analysis of experimenal daa showed ha he lognormal disribuion can be used wih a sufficien accuracy even in he case of srong urbulence [1]. The DF of received power does no describe he emporal behavior of he channel, which is crucial for simulaion. Using he Taylor principle of frozen urbulence, he frequency of scinillaions is proporional o he ransversal wind speed. The eddies in Fig. 1 can be hough of as wafed by he ransversal componen v of wind (or by relaive speed of mobile erminal) [4]. The average fade duraion is hen inversely proporional o v 1 τ. (8) v Changing he ime scale simply models differen wind condiions. 3 Model of Receiver Considering ransmission raes of 1Mb/s and above, an inerval of 1μs, during which he received power is pracically consan, corresponds o a block of more han 1 4 bis. Bi error probabiliy during he inerval depends on consan signal-onoise raio in he receiver. The opical amospheric channel can be modeled by a slowly varying probabiliy of independen single-bi error has called shor-ime bi error rae [9]. For On-Off Keying a realisic formula for shorime BER in AWGN channel was proposed in [9] p b = Q 1 + m, / 1 + ξ m, /, (9) where he empirically deermined parameers and ξ characerize he noise properies of he whole receiver, and Q is he sandard Gaussian ail inegral. The formula was derived for he adapive harddecision hreshold in he receiver and for he infinie ISSN: ISBN:

3 exincion raio of he ransmier. For a channel wih independen bi errors, he probabiliy of k errors occurring in a block of n bis is given by he Binomial disribuion n k n k n ( k) = pb pb k (1 ). (1) Fig. 3 shows he number of errors in a block of 15 bis as a funciof received power obained experimenally from an FSO link (λ = 155nm, L 1 = 5m, receiving aperure D = 5mm, R = 15Mb/s) [1]. The dashed curves represen he mean and 1- and 99- perceniles calculaed using (9) and (1). number of errors N / N [db] Fig. 3 Number of errors in block of 15 bis. Clock recovery circuiry of he receiver should be capable of operaing under frequen channel ouages, i.e. symbol and frame synchronizaion ime should be considerably shorer han periods of good channel sae. Fig. 4 shows he saisics of good channel ime when is lower han a chosen value. exceedance probabiliy <1-5 <1-4 < channel good ime [ms] Fig. 4 Saisics of good channel ime (for he link from Secion 4). Ehernes one of he echnologies suiable for applicaion in FSO links. There are readily available chipses as well as modules for implemenaion in FGA. Since he inroduciof Fas Eherne (1Mb/s) he frame preamble has no longer been used for clock synchronizaion. The clock recovery acquisiion ime is longer (e.g. 5 μs@1mb/s for D8384A from Naional Semiconducor). Fig. 5 shows a general model of receiver synchronizaion used for simulaions. Is parameers ( up, down, lock ) depend on receiver used. up p down Fig. 5 Model of receiver synchronizaion. Le us consider he applicaiof a correcing code a he receiver. Frames of lengh n conaining a mos bi errors are accepable. Frames conaining more errors are discarded. For he classic Eherne =. Wih regard o (1) he probabiliy of packe erasure is n i n i erasure = 1 pb (1 pb ). (11) i= i During simulaion, for a ransmied packe he insananeous shor-ime BER is deermined using (9) and he packe erasure probabiliy is deermined from (11). The packes discarded if > ξ, (1) erasure link-up level link-down level all frames los lock ime where ξ is he generaed random number wih uniform disribuion he inerval (, 1). Samples of received power for (9) can be obained eiher from a model or from an acual link. 4 Simulaiof Channel Coding The effec of amospheric urbulence presens almos no problem for very shor erresrial links. Their link margin, designed for high availabiliy, absorbs he power flucuaions. For longer links wih a igh power budge, amospheric urbulence causes shor ouages [6]. In his case he uilizaiof channel coding is advanageous. The channel model has been esed for he simulaiof FEC daa proecion suiable for long ISSN: ISBN:

4 unidirecional links wih no back channel for poenial ARQ procedures, Fig. 6. Is based on a combinaiof he correcing code on bi level wih he correcing code on packe level. ouer LDGM (,k o ) Fig. 6. Tesed coding scheme for long-range link. Each frame (packe) is proeced by an errorcorrecing inner block code (n i,k i, ), which is capable of correcing (n i -k i )/ errors. As shown in secion 3, he inpu power is almos consan during packe recepion, i.e. he channel is similar o he AWGN channel wih a flow of independen errors. Frames are eiher correced and passed o he ouer-code module or discarded. erasure [%] inner code (n i,k i ) FSO inner code LDGM = = b = 5b N / N [db] Fig. 7. Effec of inner coding for differen numbers of correcable bis (n i = 14B). Fig. 7 shows he effec of inner coding on he probabiliy of packe erasure. The saisics are he resul of channel simulaion (see secion 3) using samples of received power from a 7km saic es link (λ = 85nm, D = mm, sunny day 3 C, wind up o km/h, σ p. 5, rae 1Mb/s, 17. million packes simulaed). I can be seen ha correcing relaively small number of bis brings he gaif abou db. The ouer code should be capable of covering enmillisecond ouages, i.e. he erasure of hundreds or housands of packes. Fig. 8 shows he exceedance probabiliy of packe erasure in a block of size (up o 3 housands packes) for N /N = 8.1dB, where 3% of packes in average were erased for uncoded ransmission. The raio of erased packes in a block of packes approaches asympoically he average value of 3% for large. A suiable ouer code is he LDGM code (Low Densiy Generaor Marix Triangle or Saircase), which is capable of operaing on source blocks ha are composed of several ens of housands of packes [7], [8]. ackes ha are ransmied beween LDGM codecs should be eiher error-free or discarded by he lower layer [7]. A sofware implemenaiof LDGM aains a speed of.gb/s for encoding and 816Mb/s for decoding on a enium IV/3.6GHz/Linux (k =,, n = 3,, packe size 1kB) [11]. Higher speeds can be achieved using hardware acceleraion. exceedance probabiliy 1 - = k = 5k = 1k = 3k n erased / Fig. 8. Effec of block size of ouer code ( N /N = 8.1dB). LDGM is a block code generaing for k o informaion packes ( -k o ) pariy packes. I does no belong o he class of MDS codes. To reconsruc k o informaion packes is necessary o successfully ransmi slighly more han k o packes. The upper limi for he decoding delay is given as he ime needed o ransmi he whole block of packes (1, packes correspond o an inerval of.8s a 1Mb/s). The block size and he k o / raio is a subjec of radeoff beween packe loss and laency. For block size of 1, packes and for = 5 bis he coded packe erasure probabiliy will be decreased from uncoded 3% down o.1% for k o / =.65. erasure [%] = 5b = =, n e =b, n e =5b, n e =5b, n e =3k k o / Fig. 9. robabiliy of packe erasure as funciof ouer code rae ( N /N = 8.1dB, LDGM Triangle, degree 3). ISSN: ISBN:

5 4 Conclusions The paper presens a simple model for simulaing he FSO channel, using samples of opical power received from a real link or generaed by a urbulence model. The model was used o simulae he coding scheme for differen condiions. Ouages caused by urbulen amosphere require he use of large-block codes in combinaion wih error correcion codes on he packe level. The paper shows ha adding an error correcion capabiliy o he MAC layer can significanly improve he properies of FSO channel in he case of a igh power budge. 5 Acknowledgemens This research has been suppored by he Czech Science Foundaion under grans No. 1/8/851, No. 1/8/784 and No. 1/6/1358, and by he Czech Minisry of Educaion under research program No. MSM and research projec No. C61. References: [1] H. Henniger, B. Epple, and D. Giggenbach, Mobile FSO Aciviies in Europe and Fading Miigaion Approaches, roc. 17h In l. Conf. Radioelekronika, 7, p [] Z. Kolka, O. Wilfer, O. Fiser, Achievable qualiaive parameers of opical wireless links, J. Opoel. Adv. Ma., vol. 9, no. 8, Augus 7, p [3] I. I. Kim, B. McArhur and E. Korevaar, Comparisof laser beam propagaion a 785 nm and 155 nm in fog and haze for opical wireless communicaions, roc. of SIE, vol. 414, 1, p [4] L.C. Andrews, C.Y. hillips, J. Hopen, Laser Beam Scinillaion wih Applicaions, SIE ress, Bellingham (WA), USA, 1. [5] M. Uysal, J. Li, M. Yu, Error Rae erformance Analysis of Coded Free-Space Opical Links over Gamma-Gamma Amospheric Turbulence Channels, IEEE Trans. on Wireless Comm., vol. 5, no. 6, 6, pp [6] V.W.S. Chan, Free-Space Opical Communicaions, J. of Lighwave Techn., vol. 4, no. 1, 6, p [7] V. Roca and C. Neumann. Design, evaluaion and comparisof four large block FEC codes, LDC, LDGM, LDGM saircase and LDGM riangle, plus a Reed-Solomon small block FEC codec, Research Repor 55, INRIA, June 4. [8] H. Henniger, A. Gonzalez, Transmission Scheme and Error roecion for Simplex Long- Disance Amospheric FSO Sysems, Medierranean Journal of Elecronics and Communicaions, vol., no. 3, 6, pp, [9] N. erlo, Evaluaiof he scinillaion loss for opical communicaion sysems wih direc deecion, Opical Engineering vol. 46, no., 7, pp. 53. [1] M. Kubicek, H. Henniger, Z. Kolka, Bi error disribuion measuremens in he amospheric opical fading channel, roc. of SIE, vol. 6877, 8, p B. [11] hp://planeebcas.inrialpes.fr/aricle.php3?id_aricle=7 [1] D. Giggenbach, H. Henniger, Fading-loss assessmenn amospheric freespace opical communicaion links wih on-off keying, Opical Engineering vol. 47, no. 4, 8, pp ISSN: ISBN: