IOSR Joural of Electroics ad Commuicatio Egieerig (IOSR-JECE) e-issn: 78-834,p- ISSN: 78-8735.Volume 9, Issue 3, Ver. III (May - Ju. 014), PP 01-08 Free Space Optical Wireless Commuicatios uder Turbulece Chael Effect Mazi Ali A. Ali Departmet of Physics / College of Sciece / AL-Mustasiriyah Uiv., Iraq-Baghdad. Abstract: This article is focused o the turbulece atteuatio ad their effect o optical beam i free space. Aalysis has bee doe for compariso the atmospheric turbulece effect betwee two classical methods, Rytov approximatio ad Adrews's method. The SNR was calculated for ot weak turbulece employig Tailor series at differet stregth of scitillatio. These calculatios ru for commuicatios of wavelegths 850m ad 1550m. The distace betwee the trasmitter ad receiver o horizotal lik set to value rage (0-000) m. Keywords: Rytov variace, Atmospheric turbulece, Rytov approximatio, Adrews's method. Sigal to oise ratio. I. Itroductio I wireless optical commuicatio liks, atmospheric turbulece causes fluctuatios i both the itesity ad the phase of the received light sigal, impairig lik performace [1, ]. Turbulet fluctuatios i the wid velocities i the upper atmosphere mix layers of differig temperatures, desities ad water vapor cotet causes chage i refractive idex [1, ]. Thus the idex of refractio of each level of the atmosphere fluctuates. The fluctuatios origiate from the eergy coversio of solar eergy. The solar power heats the atmosphere irregular, differet cells i the atmosphere exhibit differet temperatures ad i the atmosphere appear turbuleces. This reflects as variatios i the idex of refractio of the atmosphere that create fluctuatios i the amplitude of the received optical sigal with a frequecy spectrum betwee 0.01 ad 00 Hz. This is due to the fact that light trasmissio i a medium occurs accordig to the priciple that light travelig from oe poit to aother follows the shortest optical path (Fermat s priciple), ad this depeds ot oly o the geometrical distace, but also o the optical characteristics of the medium, from which oe of the most importat oes is the idex of refractio. The idex of refractio value i the atmosphere depeds o temperature, pressure, ad humidity of air ad o the wavelegth used for the trasmissio [3]. II. Atmospheric Turbulece Model There are several models which describe atmospheric turbulece atteuatio. There are the Rytov approximatio ad the Adrews s method. The Rytov method widely used to calculate the effect of the atmosphere turbulece. It gives quite good agreemet with the experimetal data [4]. The Adrews s method takes ito accout the size of receiver optical les D REC.Not log ago it was published other method. It is called Method of Available Power [5]. 1. Adrews s Method This method is derived o the basis of a detailed mathematical aalysis of the turbulece i atmospheric trasmissio media preseted by Larry C. Adrews [6]. The resultat expressio for the theoretical mea variaceof optical itesity is give as: 0.49 0 7 / 5 1 / 5 1 0.18d 0.56 0 exp I D REC 1 (1) 5 / 6 1 / 5 0.51 0 1_ 0.69 0 1 / 5 1 0.9 0.6. d d 0 I relatio (1), two parameters are used. The first parameter d, which cotais iformatio about the wavelegth of optical source, distace betwee the trasmitter ad receiver L, ad receivig optical les diameter D REC. 1 Page
d. D REC () 4L While the secod parameter is 0 give by the relatio 7 / 6 11/ 6 0 0.5C. k L (3) Where C, is the refractive idex structure parameter, k is the wave umber. This method takes ito accout the size of receivig optical les D REC. Aperture averagig is the most valuable asset of Adrews s method. Due to this fact we expect the lowest resultat turbulece atteuatio whe Adrews s method is applied. I this case the turbulece atteuatio i db is give by the relatio [7]: Adrews 10.log 1 I DREC (4). The Rytov Approximatio Model The Rytov approximatio starts from the premise that a air mass behaves as a fluid. O the basis of Rytov s aalysis [6], the relatioship betwee refractive idex structure parameter C, which characterizes the volume of atmospheric turbulece ad relative variace of optical itesity, was set by Rytov as 7 / 6 11/ 6 I, rel K. C. k L (5) Where K is the costat 1.3 for the plae wave ad 0.5 for the spherical wave, this model sets scitillatio variace which is expressed by relatio 7 / 6 11 6 3.17C. k. L l (6) The turbulece atteuatio is related to scitillatio ad it is equal to ad thus the relatio for turbulece atteuatio α Rytov ca be writte as [8] 7 / 6 11/ 6 Rytov. 3.17. C. k. L (7) This method is ot cocer with the effect of aperture averagig. III. Turbulece Effect Ad SNR Relatio For a practical FSO system (plae wave) with weak ad symmetrical atmosphere turbulece the log irradiace variace is give by [9]: 7 / 6 11/ 6 0.31C k L (8) Therefore, the oise source is the atmosphere turbulece l( 1 ) (9) A ( r) / A0 ( r) Where χ represet the fluctuatios of the log of the amplitude of the field, A (r) is the amplitude of oise, A 0 (r) is the amplitude of laser beam the atmosphere without turbulece. The SNR i terms of mea sigal ad oise sigal itesity I 0 ad <I >, respectively is give by[10]: I,rel I 1 0 A0 ( r) SNR (10) I A ( r) Page
For weak turbulece mode, ε, is very small thus eq. (9) is give as [11]: l(1 ) (11) With this approximatio SNR is writte as SNR 1 7 / 6 11/ 6 1 (0.31C k L ) (1) Without the above approximatio eq. (11) is writte as l( 1 ) ( e 1) (13) 14 /3 For weak turbulece ( C 10 m ), the SNR is give by eq. (1), whe the turbulece is ot weak 14 /3 ( 10 m ), C the relatioship betwee the SNR ad χ is much more complicated. But by usig the Tailor series for fuctio [11]: f ( ) ( e 1) ad with some simplificatio, eq. (10) ca be writte be approximated to 1 1 SNR (14) 3... Whe 1 ad represets the stregth of scitillatio (for worst case ) IV. Results ad discussios The calculatio of turbulece atteuatio carried out by matlab to show the effect of turbulece o free space optical commuicatios. Atmospheric widows with wavelegths of 850m ad 1550m are used i the computatios. Refractive idex structure parameters C were set to 10-15 m -/3, 10-14 m -/3, 10-13 m -/3, 10-1 m -/3. The first calculatio (fig.1) proceeded comparig betwee the plae ad spherical waves for the refractive idex structure parameter 10-15 m -/3. Accordig to the results obtai the rytov approximatio give differet resultat atteuatio for plae ad spherical waves uder wavelegths study 850m, 1550m. The secod calculatio applied the refractive idex structure parameter 10-14 m -/3, which meas a higher Rytov variace. It is evidet that the Rytov variace icreasig with icreases the atmospheric turbulece. 3 Page
Whe we calculate with C = 10-13 m -/3, 10-1 m -/3 (higher atmospheric turbulece), the tred of turbulece atteuatio is take the same behavior. We obtai characteristics as show i fig. (3, 4). More over rytov approximatio give differet results for plae ad spherical waves for wavelegths uder study. 4 Page
The turbulece atteuatio calculated depeded o Rytov approximatio ad Adrews's method. The calculatio proceeded with the followig parameters: λ= 805m, 1550m, D REC =10cm, L= (0-000) m. The compariso of Rytov approximatio ad Adrews's method has show i fig. (5). We performed the same calculatios also for C = 10-14 m -/3. There is almost differece i the characteristics determied whe the turbulece i icreasig as show i fig. (6) Also the aalogous calculatios whe the turbulece is strog C = 10-13 m -/3, C = 10-1 m -/3 as show i fig. (7, 8). It is evidet that the results from Adrews's method has o differece for 850m, 1550m, o the other had the results the turbulece has almost differece for the Rytov approximatio ad Adrews's method, this differece icreased with icreasig turbulece atteuatio 5 Page
Whe the turbulece is ot weak ( C = 10-14 m -/3, C = 10-13 m -/3, C = 10-1 m -/3 ), the SNR calculated by usig Tailor series for differet values of α (the stregth of turbulece). The SNR proceeded for 850m as show i fig. (9), we observe that a mior differece betwee the curves of the SNR which has oe type of turbulece such as C = 10-14 m -/3 The same calculatios ru for wavelegth 1550m fig. (10). There is almost o differece i the behavior of the curves ad the SNR for may values of α. 6 Page
V. Coclusio The effect of atmospheric turbulece o refractive idex variatio has bee aalyzed. The spherical waves has less Rytov variace the plae waves, especially the wavelegth 1550m which was less Rytov variace the 850m at differet atmospheric turbulece applied. O the other had the turbulece atteuatio calculated usig Adrews's method ad Rytov approximatio. I the case of calculatig turbulece atteuatio by Adrews's method we foud that there is o differece betwee the atteuatios of these wavelegths. Also calculated SNR whe the turbulece is ot weak, we employed the stregth of turbulece α i this study. The wavelegth 1550 m has the best SNR compared with the wavelegth 850 m at the same stregth of turbulece α ad refractive idex structure parameter C. Refereces [1]. A. Prokeš, Modelig of Atmospheric Turbulece Effect o Terrestrial WOC Lik, Radio Egieerig, vol. 18, o. 1, 008. []. A. C. Motlagh, V. Ahmadi, Z. Ghassemlooy, K. Abedi, The Effect of Atmospheric Turbulece o the performace of the Free Space Optical Commuicatios, Iteratioal Symposium o Commuicatio Systems, Networks ad Digital Sigal Processig, 6 th, CNSDSP, 008. [3]. R. I. Roberto, S. M. IDRUS, ad S. Zira, Optical wireless commuicatios: IR for wireless coectivity, New York: CRC Press, 007. [4]. P. Liu,K. Kazaura, K, Wakamori, M. Matsumoto, Studies o C ad its effects o free space optical commuicatio system,8th Asia-Pacific Symposium o Iformatio ad Telecommuicatio Techologies, APSITT, 010. 7 Page
[5]. L. Dordova, O. Wilfert, Calculatio ad Compariso of Turbulece Atteuatio by Differet Methods, Radio Egieerig, vol. 19, o. 1, 010. [6]. L. C. Adrews, Field Guide to Atmospheric Optics, Washigto: SPIE Press, 004. [7]. L. C. Adrews, Laser Beam Scitillatio with Applicatios, SPIE Optical Egieerig Press, Belligham, Washigto, 001. [8]. M. AL-Naboulsi, H, Sizum, F. De, Fore, Propagatio of Optical ad Ifrared Waves i the Atmosphere, i the proceedigs of the XXVIIIth URSI Geeral Assembly i New Delhi, 005, New Delhi (Idia): URSI. [9]. X. M. Zhu, M. Kha, Free-Space Optical Commuicatio through Atmospheric Turbulece Chaels, IEEE Trasactios o Commuicatios, vol.50, o. 8,00. [10]. H. E. Nistazakis,T. A. Tsiftsis, G. S. Tombras, Performace aalysis of free-space optical commuicatio systems over atmospheric turbulece chaels, IET Commuicatio, vol. 3, Issue 8, pp. 140 1409, 009. [11]. X. Guoliag, Z. Xupig, W. Juwei, F. Xiaoyog, Ifluece of atmospheric turbulece o FSO lik performace, Proc. SPIE, Optical Trasmissio, switchig, ad Subsystems, vol. 581, 004. 8 Page