The Performance of Error and Outage Capacity in SIMO and MISO FSO Links

Transcription

1 International Journal of Computer Science and Telecommunication [Volume 3, Iue 7, July ] 36 ISS The Performance of Error and Outage Capacity in SIO and ISO FSO Link. ofidi, A. Chaman-motlagh and. ofidi Abtract In pite of the everal technical advantage of a freepace optical (FSO communication, atmopheric turbulence can everely degrade the performance of a FSO link, becaue it create random fluctuation in the phae and the amplitude of the received ignal. The imultaneou uage of multiple tranmit/receive aperture (IO can mitigate the fading effect, that i particularly crucial for trong turbulent channel. However comparing to SIO and ISO cheme, IO ytem it ha more complexity and le applicability. In thi paper, we invetigate the performance of ymbol-error-rate (SE and outage capacity in FSO link with -Ary Pule Poition odulation (PP in thee cheme, both in the weak and trong turbulence condition. Our reult how that in a defined received energy per bit, employing diverity and adding the number of reource at the receiver end i more efficient than the tranmitter both in the weak and trong atmopheric turbulence cenario. Index Term Atmopheric Turbulence, Outage Capacity, Free-Space Optic, PP odulation and Symbol-Error-ate F I. ITODUCTIO EE-SPACE optical communication i an intereting alternative for a variety of application in telecommunication. FSO ha advantage over fiber-baed ytem uch a operating at unlicened optical wavelength, providing broadband capacity, high ecurity becaue of their direct line-of-ight, low cot of intallation and deployment, protocol tranparency, full-duplex tranmiion, and compact equipment ha emerged thee ytem a a complement to radio frequency (F counterpart. Depite their ignificant advantage, there are ome major undeirable effect that hamper the widepread deployment of FSO ytem. The main challenge lie in their high vulnerability to advere atmopheric condition. Even in a clear ky, FSO link uffer from random change of refractive index caued by the variation of air temperature and preure that caue rapid fluctuation of the received optical ignal, which i called ehdi ofidi i with the Electrical Engineering Department, Imam Hoein Univerity, Iran, (correponding author to provide phone: ; yahoo.com Abolfazl Chaman-motlagh, i with the Electrical Engineering Department, Imam Hoein Univerity, Iran, ( achaman@ihu.ac.ir afieh ofidi i with the Electrical and obotic Engineering Department, Shahrood Univerity of Technology, Iran, ( mofidi@hahroodut.ac.ir cintillation, imilar to the fading effect in F wirele communication []. So far fading mitigation technique uch a diverity technique have been extenively tudied in the literature. Spatial diverity involve the uage of multiple tranmitter and multiple receiver in FSO communication. With patial diverity a reducing the probability of beam blockage, ytem can cover longer ditance []. However, ometime the patial correlation among the aperture and ub-channel in a FSO link i not negligible and play a key role in determining link performance []. SIO (Single-Input ultiple-output and ISO (ultiple-input Single-Output FSO link have been propoed a another approach with le complexity than the IO (ultiple-input ultiple-output deign. The performance of a link with -Array baed receiver and a ingle tranmitter uing OOK (On-Off Keying modulation ha been invetigated in [3]. It i hown that in thee ytem there i a maller critical link range in comparion with a decreae in the S for higher value of [4]. Temporal diverity a another olution i tudied in [5], however it often impoe long delay and neceitate uing large memorie for toring long data frame. Over the year, a number of tatitical channel model have been propoed to decribe weak or trong atmopheric turbulent channel [5]. For weak turbulence regime, the probability denity function (PDF of the intenity fluctuation i modeled a log-normal ditribution, wherea for trong regime K-ditribution and negative exponential model [6] how an excellent agreement between theoretical and experimental data [7]. In a K-ditributed turbulence channel, the error performance with pointing error [8], outage probability and capacity [9] and DPSK modulation [] of FSO link are tudied. Thee paper reult ignify that a SISO link everely uffer from trong turbulence therefore jutifying the uage of mitigation technique uch a robut modulation (for example PP and patial diverity, which are our focu in thi paper. In our imulation we aume that laer ource that all are pointed toward an array of photodetector. We tudy the influence of both weak and trong atmopheric turbulence. The ret of thi paper i organized a follow: in ection II, we outline the theoretical analyi for turbulence etimation model and PP modulation i introduced. In ection III, ymbol error rate for a diverity baed ytem i decribed in Journal Homepage:

2 . ofidi et al. 37 different cae. Outage channel capacity i introduced in ection IV. umerical reult and comparion between ytem are aeed in ection V. Finally concluion are provided in ection VI. II. THEOY OF AALYSIS When an optical beam propagate through the atmophere, the beam i ditorted due to aborption, cattering and refractive index fluctuation (turbulence []. For a plane wave ytov uggeted a variance for the log intenity fluctuation in weak turbulence condition [] i decribed by: 7 σ.3c 6 L 6 n k ( where k π λ i the wave-number, L i the range and the C n i the refractive index tructure coefficient. In practice Equation ( only predict the correct variance provided σ <. 3 (weak turbulence. An attribute of an optical beam i intenity, which can be ued to tranmit information. Conidering that the atmophere turbulence mainly affect the light intenity (and OOK i o uceptible in thi cae, PP i commonly ued in FSO communication. An -Ary PP cheme tranmit Llog bit per ymbol, providing high power efficiency. Each ymbol conit of a pule of contant power occupying one lot, along with - empty lot. The poition of the pule correpond to the decimal value of the Llog data bit. Hence, the information i encoded by the poition of the pule within the ymbol. In thi cheme, the tolerance to the atmopheric turbulence improve, becaue different -Ary PP ymbol experience different atmopheric turbulence condition. Each laer power, meaured at the receiver after all link loe, i a contant P r watt. Thu, P r repreent the peak power, and the received optical energy per ymbol in the abence of fading i E P T P T joule, where the ignaling r r interval of T (ymbol duration i divided into lot and T i the lot time. Thi can be related to the energy per information bit by E Eb log. In abence of fading, due to the Poion point proce [], the effective count of photoelectron i: n ηpr T ηe photoelectron lot ( hf hf / where η i the quantum efficiency, h i the Planck contant and f i the optical wave frequency. III. SYBOL EO ATE AALYSIS We analyze the error performance in two cae: non-faded and faded channel auming the abence of background light. In the former, the one error reult if adapted lot in receiver ide regiter zero count and zero error i not probable becaue of firt aume (no background light. The Poion property expree the ymbol error probability a: η( P T hf E hf [ r / e / ] e / η (3 P In the latter, and preence of turbulence, we invetigate two condition: weak and trong atmopheric turbulence condition. A. Weak Turbulence In a weak regime the probability error in Equation (3 mut be averaged over the intenity fluctuation correponding to a received one. With deignation a a the received light intenity that follow a log-normal ditribution [3]: f A (ln a µ x ( a exp( (4 a σ ( πσ where µ x i mean and σ x i variance of received irradiance. With appropriate depoition of tranmitter and receiver, there are path gain that each of them experience independent fade, o conidering Equation (3 and averaging over the PDF of received intenity, the average ymbol error reult: a E hf P e f A a da ( / / ( η (5 B. Strong Turbulence The K-ditributed channel i claified a trong turbulence, which i characterized by a cintillation index (S.I. greater than that i calculated a [7]: β + SI (6 β Thi model i valid for propagation ditance more than m or everal kilometer. The PDF of the K-modeled ignal irradiance a, that can be conidered a a product of two independent model (exponential ditribution and gamma ditribution i given by [7]: ( β + / β ( β / a a K β ( βa (7 Γ( β f A ( where Γ(. i the gamma function, K ν (. i the modified Beel function of the econd kind of order ν, while the parameter β i related to the effective number of dicrete catterer in the atmopheric channel. A noted earlier, we are encountered with the ituation which the value of S.I. exceed. The SE (P over the K-ditributed channel can be obtained by averaging (3 over the irradiance fluctuation a: a P f A a e ( E hf ( / / da η (8 Thi time-conuming integral can be etimated by expreing K ν (. a eijer G-function[4]:

3 International Journal of Computer Science and Telecommunication [Volume 3, Iue 7, July ] 38 K G x 4 v, v ( x,, v (9-5 SISO,, 5, SISO,8,8 5, E (dbj b - Figure. SE v. bit energy in ISO ytem at weak turbulence -5 - SISO,, 5, SISO,8,8 5, E (dbj b Figure. SE v. bit energy in SIO ytem at weak turbulence which i a tandard built-in function that can be etimated intantly with the mot of the mathematical oftware package. Thi operator i a very general function which reduce to impler pecial function in many common cae. E P β G, 4 6η β, β,,.5 hf π Γ( β 4, IV. OUTAGE CAPACITY ( The outage capacity i an important metric for digital communication ytem in turbulent environment. Thi parameter meaure whether the probability of the capacity of the ytem i greater than a pre-defined threhold value SISO,, 5,,6 5, E (dbj b Figure 4. SE v. bit energy in ISO ytem at trong turbulence -5 - ISO, ISO,8 SIO, SIO, SISO,, 5,,6 5, E (dbj b Figure 3. SE v. bit energy in ISO and SIO ytem with 5 at weak turbulence E (dbj b Figure 5. SE v. bit energy in SIO ytem at trong turbulence

4 . ofidi et al ISO, ISO,6 SIO, SIO, E (dbj b Figure 6. SE v. bit energy in ISO and SIO ytem with 5 at trong turbulence Unlike the average SE which doe not reflect the channel fading degree intantaneouly, the outage capacity reflect thi a it compare the intantaneou expected capacity with a threhold value. Thi threhold i aumed to be.5log (half of the maximum capacity in a channel. Thi maximum achievable data rate, at which reliable tranmiion of information over the channel i poible, ha been derived in [5] for weak turbulence condition (by uing log-normal model and multiple receive/tranmit aperture. Thereby and uing K-ditribution model for trong turbulence circumtance the capacity i calculated and it i compared with aumed threhold: LinkOutage xηe hf >. 5log < log ( f A( a e dx ( Link Etablih m n Equivalently, in our analyze P out mean that the link i out of ervice and P out mean that the link i reetablihed. IV. ESULTS AD DISCUSSIO Following the analytical tudy preented in ection III, we plot the SE performance and outage channel capacity reult of a FSO link for variou number of tranmit/receive aperture. η, σ, and S.I. are aumed to be.5,.3 and.5, repectively. egarding Eq. and a a calibration point E -6 joule correpond to about 8 photon/ymbol received. Fig. illutrate the SE parameter for ISO link. The performance of a SISO link i alo included a a benchmark in,8. It how that SISO link have a ditinct difference in error rate from diverity-baed tranmitter, particularly in higher received energie. Alo a the Fig. clearly how, increaing the number of tranmit aperture lead to better performance which i the reult of reducing atmopheric variance by a factor of. oreover the performance i improved for higher value of, however a increae, for a fixed bit rate the peak power need to be increaed to maintain fixed energy per ymbol. Fig. illutrate the performance of a SIO link howing that in all atmopheric condition enhancement of the E b (or tranmitted power caue a decreae of the SE.A expreed for a ISO ytem, increaing the number of receive aperture and parameter caue to better efficiency, but in thi cheme the effect of adding diverity appear more intene for 5. Fig. 3 how the comparion between the two ytem mentioned above for the cae of 5. Although the overall behavior of thee cae i imilar to each other, ome major difference are oberved. It can be oberved that the performance of a SIO link i better than ISO type. For example, in E b 8 dbj an improvement about five order of magnitude ( -5 i achieved for. On the other hand, in a SIO ytem the required energy ( Eb for a fixed SE i lower than a ISO link. Furthermore SIO outperform ISO with increment of aperture number. Fig.4 how the error performance of ISO FSO link with,5 tranmit aperture employing,6-pp over a K- ditributed channel. P out P out ISO,3 SIO,3 ISO,5 SIO,5 SISO E (dbj Figure 7. P out v. ymbol energy in weak turbulence ISO,3 SIO,3 ISO,5 SIO,5 SISO E (dbj Figure 8. P out v. ymbol energy in trong turbulence

5 International Journal of Computer Science and Telecommunication [Volume 3, Iue 7, July ] 4 It i obviou that even for high value of received energy (for example [-4,-] dbj SE i not exceeding -5, which i not an acceptable rate for practical communication ytem, which i the rational reaon to ue patial diverity. It i hown that the SE i ignificantly improved a the number of aperture increae. oreover, with 5 aperture an improvement of about 9dBJ can be obtained at SE -6 in contrat to SISO link. The overall treat of Fig.5 how that the SIO link performance i imilar to ISO ytem with better error rate. It i noticeable that increaing the value affect the SE more than the increment. Fig.6 demontrate the comparion between SIO and ISO link in a fixed, we can ee the better performance of SIO link with an approximately contant difference repect to a ISO one. We how in Fig.7 outage channel capacity veru ymbol energy for SIO and ISO ytem with 3,5 or 3,5 and 8. It i hown that the SISO link require the highet received energy to etablih the connectivity between tranmitter and receiver. SIO link ha better performance than the ISO cheme for example in 5, and thi i about 8dBJ in E. It alo can be noted if one were chooing between multiple receiver or multiple tranmitter it would be more advantageou to have extra reource at receiver end (the difference between 3 and 5 i double of which in 3 and 5, where the increaed aperture ize can be exploited due to aperture averaging technique (auming the total power at tranmitter aperture i fixed in a defined number of tranmitter. In a imilar way and in trong turbulence outage probability of capacity i hown in Fig.8. At firt, a coniderable difference can be een between the energy required in both trong and weak turbulence in all cae (for example 8dBJ in SISO link between two atmopheric condition. Increaing the number of receiver in thi condition lead to a better performance in energy conuming too, but the energy required for SIO and ISO link to witch from P out to P out i maller than the weak turbulence. V. COCLUSIO In thi paper, we have invetigated the SE performance of FSO link over both the log-normal and K-ditributed fading channel uing -PP modulation. It i hown that a SISO link cannot deliver an acceptable SE particularly in trong atmopheric turbulence. Becaue of further complexity in implementation of IO link, we conclude that employing the SIO and ISO type i uperior. Comparion of SIO and ISO link how that the efficiency of adding diverity in error rate and outage capacity appear more in SIO, both in the weak and trong turbulence condition. EFEECES [] L.C. Andrew and. L. Phillip, Laer Beam Scintillation with Application, SPIE Pre,. [] K. 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