Free Spce Opticl Communiction System ginst Chnnel Fding Prem.S 1, A.Elngovn 1 ME- 1 Applied Electronics, Aruni Engineering College, Tiruvnnmli, Tmil Ndu-6663, Indi Assistnt Professor of ECE Deprtment, Aruni Engineering College, Tiruvnnmli, Tmil Ndu-6663, Indi Abstrct A sttisticl chnnel model for multiple-input multipleoutput (MIMO) free-spce opticl (FSO) communiction systems is developed. It is impired by tmospheric nd mislignment fding. A slow-fding chnnel model is considered nd the outge probbility is derived s perforce mesure. The diversity gin defined s the Signl-to-Noise Rtio (SNR) exponent t high SNR is nlyzed. Interestingly in the presence of mislignment fding the diversity gin depends only on the mislignment vrince nd is independent of the number of trnsmitters M nd receivers N. Incresing the number of trnsmitters nd receivers only results in lower probbility of outge for given SNR, however, the rte of chnge is unffected. Contrry to this cse, the diversity gin of MIMO FSO systems in the presence of tmospheric fding nd no mislignment is shown to be proportionl to the number of trnsmitters nd receivers, in prticulr the product M N. Keywords: Signl to Noise Rtio (SNR), MIMO, Free- Spce Opticl (FSO). 1. Introduction The use of multiple ntenns t the trnsmitter nd receiver in wireless systems, populrly known s MIMO (multiple-input multiple-output) technology, hs rpidly gined in populrity over the pst decde due to its powerful perforce-enhncing cpbilities. Communiction in wireless chnnels is impired predominntly by multi-pth fding. Multi-pth is the rrivl of the trnsmitted signl t n intended receiver through differing ngles nd/or differing time delys nd/or differing frequency (i.e., Doppler) shifts due to the scttering of electromgnetic wves in the environment. Consequently, the received signl power fluctutes in spce (due to ngle spred) nd/or frequency (due to dely spred) nd/or time (due to Doppler spred) through the rndom superposition of the impinging multi-pth components. This rndom fluctution in signl level, known s fding, cn severely ffect the qulity nd relibility of wireless communiction. Additionlly, the constrints posed by limited power nd scrce frequency bndwidth mke the tsk of designing high dt rte, high relibility wireless communiction systems extremely chllenging. MIMO technology constitutes brekthrough in wireless communiction system design. The technology offers number of benefits tht help meet the chllenges posed by both the impirments in the wireless chnnel s well s resource constrints. In ddition to the time nd frequency dimensions tht re exploited in conventionl single-ntenn (single-input single-output) wireless systems, the leverges of MIMO re relized by exploiting the sptil dimension (provided by the multiple ntenns t the trnsmitter nd the receiver). The dvntges of multiple-input multiple-output (MIMO) systems hve been widely cknowledged, to the extent tht certin trnsmit diversity methods (i.e., Almouti signling) hve been incorported into wireless stndrds. Although trnsmit diversity is clerly dvntgeous on cellulr bse sttion, it my not be prcticl for other scenrios. Specificlly, due to size, cost, or hrdwre limittions, wireless gent my not be ble to support multiple trnsmit ntenns. Exmples include most hndsets (size) or the nodes in wireless sensor network (size, power). Fig.1. MIMO cellulr system Published by: PIONEER RESEARC & DEVELOPMENT GROUP (www.prdg.org) 1
exploiting the sptil dimension to increse the seprtion. MIMO Technology MIMO technology tht help chieve such significnt perforce gins re rry gin, sptil diversity gin, sptil multiplexing gin nd interference reduction. These gins re described in brief below.1 Arry gin Arry gin is the increse in receive SNR tht results from coherent combining effect of the wireless signls t receiver. The coherent combining my be relized through sptil processing t the receive ntenn rry nd/or sptil pre-processing t the trnsmit ntenn rry. Arry gin improves resistnce to noise, thereby improving the coverge nd the rnge of wireless network..1.1 Sptil diversity gin As mentioned erlier, the signl level t receiver in wireless system fluctutes or fdes. Sptil diversity gin mitigtes fding nd is relized by providing the receiver with multiple (idelly independent) copies of the trnsmitted signl in spce, frequency or time. With n incresing number of independent copies (the number of copies is often referred to s the diversity order), the probbility tht t lest one of the copies is not experiencing deep fde increses, thereby improving the qulity nd relibility of reception. A MIMO chnnel with M T trnsmit ntenns nd M R receive ntenns potentilly offers M T M R independently fding links, nd hence sptil diversity order of M T M R.1. Sptil multiplexing gin MIMO systems offer liner increse in dt rte through sptil multiplexing, i.e., trnsmitting multiple, independent dt strems within the bndwidth of opertion. Under suitble chnnel conditions, such s rich scttering in the environment, the receiver cn seprte the dt strems. Furthermore, ech dt strem experiences t lest the sme chnnel qulity tht would be experienced by single-input single-output system, effectively enhncing the cpcity by multiplictive fctor equl to the number of strems. In generl, the number of dt strems tht cn be relibly supported by MIMO chnnel equls the minimum of the number of trnsmit ntenns nd the number of receive ntenns, i.e., min [M T M R ]. The sptil multiplexing gin increses the cpcity of wireless network..1.3 Interference reduction nd voidnce Interference in wireless networks results from multiple users shring time nd frequency resources. Interference my be mitigted in MIMO systems by between users. For instnce, in the presence of interference, rry gin increses the tolernce to noise s well s the interference power, hence improving the signlto-noise-plus-interference rtio (SINR). Additionlly, the sptil dimension my be leverged for the purposes of interference voidnce, i.e., directing signl energy towrds the intended user nd minimizing interference to other users. Interference reduction nd voidnce improve the coverge nd rnge of wireless network. In generl, it my not be possible to exploit simultneously ll the benefits described bove due to conflicting deds on the sptil degrees of freedom. owever, using some combintion of the benefits cross wireless network will result in improved cpcity, coverge nd relibility..mimo in Cellulr Networks In cellulr wireless communiction network, multiple users my communicte t the sme time nd (or) frequency. The more ggressive the reuse of time nd frequency resources, the higher the network cpcity will be, provided tht trnsmitted signls cn be detected relibly. Multiple users my be seprted in time (timedivision) or frequency (frequency-division) or code (codedivision). The sptil dimension in MIMO chnnels provides n extr dimension to seprte users, llowing more ggressive reuse of time nd frequency resources, thereby incresing the network cpcity. Figure 1 is the schemtic of cell in MIMO cellulr network. A bse-sttion equipped with L ntenns communictes with P users, ech equipped with M ntenns. The chnnel from the bse-sttion to the users (the downlink) is brodcst chnnel (BC) while the chnnel from the users to the bse-sttion (the uplink) is multiple-ccess chnnel (MAC). The set of rte-tuples (R 1,R,..R P ) tht cn be relibly supported on the downlink or uplink constitutes the cpcity rte region for tht link. Recently, n importnt dulity hs been discovered between the rte regions for the downlink nd uplink chnnels. In order to understnd the possible gins from MIMO technology in multi-user environment, consider the uplink of cellulr MIMO system where ll the users simultneously trnsmit independent dt strems from ech of their trnsmit ntenns, i.e., ech user signls with sptil multiplexing. To the bse-sttion, the users combined, pper s multi-ntenn trnsmitter with PM ntenns. Thus the effective uplink chnnel hs dimension of L PM. This effective chnnel will hve considerbly different structure from the w MIMO single user chnnel due to pth-loss nd shdowing differences between users. Published by: PIONEER RESEARC & DEVELOPMENT GROUP (www.prdg.org)
The signl-to-noise rtio is defined s SNR = P/σ nd the chnnel gin N N n1 m1 ccounts for the combined effects of tmosphere nd mislignment fding where Fig. Distributed MIMO: multiple users cooperte to form virtul ntenn rry tht relizes the gins of MIMO in distributed fshion. owever, with rich scttering nd L PM, we cn expect tht the sptil signtures of the users re well seprted to llow relible detection. Using multi-user ZF receiver will llow perfect seprtion of ll the dt strems t the bse-sttion, yielding multi-user multiplexing gin of PM. The use of more complex receivers for multi-user detection nd the ssocited perforce trde-offs. A similr thought experiment cn be pplied for the downlink, where the bse-sttion exploits the sptil dimension to bem informtion intended for prticulr user towrds tht user nd steers nulls in the directions of the other users, thus completely eliminting interference. 3. Modules Explntion 3.1 Chnnel Model This section explins the MIMO FSO system nd chnnel fding. The model considers MIMO FSO system with M trnsmitters (lsers) nd N receivers (pertures). In ll cses, intensity modulted PAM signling with direct detection is considered. The received N 1 vector y = [y 1,..., y N ] T is given by where nd p p re independent rndom vribles representing the tmospheric nd time vrying mislignment (pointing) fding respectively between trnsmitter m nd receiver n. In the wek turbulence regime the chnnel gin due to tmospheric turbulence is well modeled by e where X is Gussin rndom vrible. Assume tht ll X re modeled s independent nd identiclly distributed (i.i.d) rndom vribles. For rdil displcement of R in the receiver plne between the center of trnsmitter bem m nd the center of perture n, the loss due to mislignment is A e X / p R w where A is the equivlent receiver re nd w is the equivlent bem wist t receiver. 3. Diversity Gin of MIMO FSO Chnnels These section three different mislignment scenrios will be nlyzed depending on the rndom displcements X nd Y Symmetric Mislignment in X nd Y Directions The displcements X nd Y hve i.i.d Gussin distributions with zero men nd vrince. Defining = w/(σs) the pdf of T = R /w is given by where is n M x N chnnel mtrix where the entry represents the chnnel gin from trnsmitter m to receiver n with m=1,...,m nd n = 1,...,N nd ( ) T is the trnspose opertor. The vector x = [x 1,...,x M ] T is the trnsmitted set of symbols nd z = [z 1,...,z N ] T is noise vector of independent components modeled s signl independent white nd Gussin distributed. nd hence Published by: PIONEER RESEARC & DEVELOPMENT GROUP (www.prdg.org) 3
where, nd. Substituting s = v + B the outge probbility cn be simplified to medium chrcterized by C n. Ech receiver hs circulr perture of rdius = 5 cm. The spcing between trnsmitters (s well s between receivers) is set to d = cm which is typicl vlue for commercil system nd results in independent X s shown. Typicl mislignment vrince of σ s =.1 m is considered nd rte R = 1 bits/chnnel-use is considered Substituting the results in the symptotic probbility of outge given s 1 ut o Probbility 1 - of outge P Numericl Simultion Closed-form expression 1-4 Unidirectionl Mislignment In this scenrio X ~ (, ) nd Y =. The probbility density functions of T = X /w is given by 1-6 The outge probbility is 1-8 5 1 15 (Log 1 (SNR)) 5 4. Conclusions 5 No Mislignment For comprison, the scenrio when X = nd Y =, i.e., no mislignment, is lso considered. The chnnel gin is given by modified version of the bove sttisticl chnnel model s eqution U A N N n1 m1 e X P m Pn w nd vrince U nd Go is Gussin with men The outge probbility is given s 3.3 Simultion Results In this section, we consider Gussin-bem of wvelength λ = 155 nm, bem wist wo = cm, nd rdius of curvture Fo = 1 m t the trnsmitter. The bem propgtes distnce L = 1 km through turbulent A novel generlized sttisticl model for MIMO FSO chnnels impired by tmospheric nd mislignment fding is developed. The derived model is utilized to study the outge probbility of FSO chnnels nd the diversity gin t high signl-to-noise rtio. Closed-form expressions for the outge probbility re derived tking into ccount different mislignment fding scenrios. It is shown tht, in the presence of tmospheric nd mislignment fding, the diversity gin depends only on the mislignment prmeters nd is independent of both the number of trnsceivers nd tmospheric fding prmeters. Contrrily, when tmospheric fding is the only chnnel impirment, i.e., no mislignment fding, the diversity gin depends on the number of trnsceivers. Thus lrger diversity gin cn be chieved by incresing the number of trnsmitters nd receivers. In ll cses incresing the number of trnsmitters nd receivers decreses the outge probbility for given SNR. owever, in order to hve independent chnnels gins it is required to sufficiently increse the spcing between receivers which is often prcticlly difficult. An lterntive pproch is to utilize lrge single-perture with the equivlent re of the N pertures. This pproch provides simple system structure nd reduces the fding vrince vi perture verging. Note tht, in this cse the fding is correlted cross the perture nd hence its vrince is lrger thn tht of system with multiple pertures nd independent fding t ech perture. Published by: PIONEER RESEARC & DEVELOPMENT GROUP (www.prdg.org) 4
Consequently, multiple-perture receiver systems chieve improved perforce t the cost of dditionl detector elements. Acknowledgments I thnk SPECTRUM SOLUTIONS, Pondicherry to help me for creting this pper with their Sincere Guidnce nd Technicl Expertise in the field of Communiction. References [1] J. M. Khn nd J. R. Brry, Wireless infrred communictions, Proc. IEEE, vol. 85, pp. 65 98, Feb. 1997. [] D. Tse nd P. Viswnth, Fundmentls of Wireless Communiction, 1st edition. Cmbridge University Press, 5. [3] M. Rzvi nd J.. Shpiro, Wireless opticl communictions vi diversity reception nd opticl premplifiction, IEEE Trns. Wireless Commun., vol. 4, pp. 975 983, My 5. [4] X. Zhu nd J. Khn, Free spce opticl communiction through tmospheric turbulence chnnels, IEEE Trns. Commun., vol. 5, pp.193 13, Aug.. [5] S. M. Nvidpour, M. Uysl, nd M. Kvehrd, BER perforce of free-spce opticl trnsmission with sptil diversity, IEEE Trns.Wireless Commun., vol. 6, pp. 813 819, Aug. 7. [6] T. A. Tsiftsis,. G. Sndlidis, G. K. Krginnidis, nd M. Uysl, Opticl wireless links with sptil diversity over strong tmospheric turbulence chnnels, IEEE Trns. Wireless Commun., vol. 8, pp. 951 957, Feb. 9. [7] N. Letzepis nd A. G. i Fábregs, Outge probbility of the Gussin MIMO free-spce opticl chnnel with PPM, IEEE Trns. Commun., vol. 57, pp. 368 369, Dec. 9. [8], Outge probbility of the free-spce opticl chnnel with doubly stochstic scintiltion, IEEE Trns. Commun., vol. 57, pp. 899 9, Oct. 9. [9] S. M. s nd J.. Shpiro, Cpcity of wireless opticl communictions, IEEE J. Sel. Ares Commun., vol. 1, pp. 1346 1356, Oct. 3. [1] S. G. Wilson, M. Brndt-Perce, Q. Co, nd J.. Leveque, Free-spce opticl MIMO trnsmission with Q- ry PPM, IEEE Trns. Commun., vol. 53, pp. 14 141, Aug. 5. [11] S. G. Wilson, M. Brndt-Perce, Q. Co, nd M. Bedke, Opticl repetition MIMO trnsmission with multipulse PPM, IEEE J. Sel. Ares Commun., vol. 3, pp. 191 191, Sep. 5. [1] G. A. Koepf, R. Peters, nd R. G. Mrshlek, Anlysis of brust error occurrence on opticl interstellite link (ISL) design, in Proc. SPIE Opt. Tech. Commun. Stellite Applictions, Jn. 1986, vol. 616, pp. 19 136. [13] S. Arnon, S. Rot, nd N. S. Kopeik, Bem width nd trnsmitter power dptive to trcking system perforce for free-spce opticl communiction, J. Appl. Opt., vol. 36, pp. 695 611, Aug. 1997. [14] S. Arnon, Optimiztion of urbn opticl wireless communiction systems, IEEE Trns. Commun., vol., pp. 66 69, Nov. 3. [15] C. C. Chen nd C. S. Grdner, Impct of rndom pointing nd trcking errors on the design of coherent nd incoherent opticl interstellite communiction links, IEEE Trns. Commun., vol. 37, pp. 5 6, Mr. 1989. [16] S. Arnon, Effects of tmospheric turbulence nd building swy on opticl wireless communiction systems, Optics Lett., vol. 8, pp. 19 131, Jn. 3. [17] K. Kisleh, On the probbility density function of signl intensity in free-spce opticl communictions systems impired by pointing jitter nd turbulence, Opt. Eng., vol. 33, pp. 3748 3757, Nov. 1994. [18] A. A. Frid nd S. rnilovic, Outge cpcity optimiztion for freespce opticl links with pointing errors, IEEE J. Lightwve Technol.,vol. 5, pp. 17 171, July 7. [19], Diversity gins for MIMO wireless opticl intensity chnnels with tmospheric fding nd mislignment, in Proc. 1 IEEE Globe-Com, pp. 115 119. [] J. A. Anguit, M. A. Neifeld, nd B. V. Vsic, Sptil correltion nd irrdince sttistics in multiplebem terrestril free-spce opticl communiction link, J. Appl. Opt., vol. 46, pp. 6561 6571, Sep. 7. Published by: PIONEER RESEARC & DEVELOPMENT GROUP (www.prdg.org) 5