Performance of 1‐D and 2‐D OCDMA systems in presence of atmospheric turbulence and various weather conditions
2017; Institution of Engineering and Technology; Volume: 11; Issue: 9 Linguagem: Inglês
10.1049/iet-com.2016.1008
ISSN1751-8636
AutoresAjay Pratap Yadav, Subrat Kar, Virander Kumar Jain,
Tópico(s)Optical Wireless Communication Technologies
ResumoIET CommunicationsVolume 11, Issue 9 p. 1416-1422 Research ArticleFree Access Performance of 1-D and 2-D OCDMA systems in presence of atmospheric turbulence and various weather conditions Ajay Yadav, Corresponding Author Ajay Yadav ajay.yadav@dbst.iitd.ac.in Bharti School of Telecommunication Technology and Management, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016 IndiaSearch for more papers by this authorSubrat Kar, Subrat Kar Department of Electrical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016 IndiaSearch for more papers by this authorVirander Kumar Jain, Virander Kumar Jain Department of Electrical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016 IndiaSearch for more papers by this author Ajay Yadav, Corresponding Author Ajay Yadav ajay.yadav@dbst.iitd.ac.in Bharti School of Telecommunication Technology and Management, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016 IndiaSearch for more papers by this authorSubrat Kar, Subrat Kar Department of Electrical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016 IndiaSearch for more papers by this authorVirander Kumar Jain, Virander Kumar Jain Department of Electrical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016 IndiaSearch for more papers by this author First published: 26 June 2017 https://doi.org/10.1049/iet-com.2016.1008Citations: 7AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In this study, the authors compare the performance of one-dimensional (1D) and two-dimensional (2D) optical code division multiple access (OCDMA) systems in presence of turbulence and various weather conditions. Lognormal fading model is used for analysis of weak turbulence and gamma–gamma model for moderate and strong turbulence. It is observed that presence of moderate and strong turbulence may lead to a complete link failure in 2D OCDMA system depending upon the number of users and turbulence level. The various weather conditions considered are very clear air, light fog and thick fog. The results show that the performance degradation due to thick fog is more than the light fog and very clear air in all turbulence regimes. 1 Introduction In free space optical (FSO) communication, light propagation through atmosphere is used for transmission of information. FSO removes last mile bottleneck between end users and optical network [1]. Nowadays, end users require high data rate for video conferencing, Internet Protocol television, online video games, etc. Radio frequency communication alone will be insufficient to deliver the high data rate [2]. Thus, FSO can reduce the burden on cellular networks by removing this bottleneck. In addition, for simultaneous transmission of data by multiple users through the same channel, optical code division multiple access (OCDMA) can be used due to its inherent security and scalability [3]. OCDMA is a multiple access data transmission technology which supports multiple users for simultaneous transmission of data in the same time slot and same frequency band using coding. In atmospheric OCDMA system, each user is assigned a codeword from the optical code set as the address of the intended receiver. An (n, w, , ) optical orthogonal code (OOC) is a family of {0,1} one-dimensional (1D) codewords of length n, Hamming weight w, with peak sidelobe (out of phase) autocorrelation and peak cross-correlation values and , respectively [4]. The number of users supported by 1D codes are less in comparison with two-dimensional (2D) codes for a given code length. To overcome this limitation of 1D codes, 2D codes are used. The 2D codes not only increase the number of users, make easier network control and management, lower processing time and reduce the complexity and cost of hardware. A 2D (, w, , ) wavelength-hopping/time-spreading optical code is a set of binary {0,1} matrices [5]. The advantages of atmospheric 2D OCDMA system are low cost of deployment, low operating cost, license free spectrum, simple layout modification, higher mobility and tolerance to disaster [6]. The challenges faced by atmospheric OCDMA communication systems are multiple user interference (MUI), beam divergence, attenuation by the atmosphere, fading of signal due to turbulence and background noise. In 2D OCDMA system, when data is sent from the transmitter, address matrix (i.e. codeword matrix) of the intended receiver is also transmitted with the data. The receiver accepts multiple matrices along with the desired matrix. The codeword matrices from the users other than the desired user (interfering users) give rise to MUI at the intended receiver which degrades system performance. In addition, beam divergence due to the diffraction of the optical beam around the aperture at the end of telescope in the transmitter leads to the power reduction at the receiver. Power reduction is also caused by the absorption and scattering in the atmosphere. The weather conditions which attenuate the optical beam in atmospheric OCDMA are fog, rain, snow, and dust particles [7]. Moreover, the fading of the optical signal takes place due to atmospheric turbulence. From Kolmogorov theory of turbulence, random subflows of velocity field in the atmosphere are called eddies [8]. Eddy formation takes place when hot air mixes with cold air. Atmospheric turbulence is due to random motion of the eddies [8]. Eddy size varies from few millimetres to a few metres. The atmospheric turbulence can be characterised in terms of refractive index structure constant which vary from to for weak to strong turbulence, respectively [9]. An optical beam propagating through turbulent atmosphere experiences three effects: scintillation, beam wandering and beam spreading. With the main effect being turbulence induced scintillation which is the temporal and spatial fluctuations of the beam and causes the amplitude of the received signal to change (up to 30 dB). It takes place when the eddy size is nearly equal to the beam diameter [7]. As turbulence is a random process, different fading models are used to analyse its effect. Lognormal model is suitable for weak turbulence because the distribution tail deviates from the experimental data for moderate and strong turbulence [10]. Gamma–gamma model is suited for moderate and strong turbulence regimes [11, 12]. Background noise due to natural light sources such as Sun, Moon and other celestial bodies also deteriorate the performance of atmospheric OCDMA system [7]. Jazayerifar et al. [13] have evaluated the performance of atmospheric 1D OCDMA system in presence of MUI, atmospheric turbulence, ambient light, shot noise and thermal noise. In this study, on–off keying (OOK)- and pulse position modulation-CDMA through single, multiple and compound channel with various receiver structures using lognormal fading model are considered. Islam et al. [14] evaluated the performance of the 1D OCDMA system in different weather conditions (fog, rain, and snow) without considering turbulence as a random process, i.e. without any fading model. Researchers have also examined the performance with lognormal and gamma–gamma models using time diversity [15, 16] in presence of atmospheric turbulence only. We have evaluated the performance of 2D atmospheric OCDMA systems in presence of MUI, atmospheric turbulence and various weather conditions for the first time by using photon count approach and combining the optical signal in the coupler before transmitting through atmosphere. In addition, we have compared the performance with 1D atmospheric OCDMA system. In the evaluation shot noise, thermal noise, dark current noises (due to surface leakage and bulk dark-currents) and background noise are also considered. One-coincidence frequency hopping code/OOC (OCFHC/OOC) is the 2D optical code in the 2D OCDMA system. An (, w, , ) OCFHC/OOC codeword consists of matrix where is the number of wavelengths [17]. The different weather conditions which have been considered are very clear air, light fog, and thick fog. The attenuation due to rain lies between clear air and light fog while due to snow between clear air and moderate fog, respectively [18]. Lognormal and gamma–gamma fading models are used for theoretical analysis of atmospheric turbulence. The results show that 1D and 2D atmospheric OCDMA systems perform worst in thick fog condition as compared with light fog (and best in very clear air). The performance can be improved further by increasing receiver aperture, diversity techniques, and adaptive optics [19, 20] The rest of the paper is organised as follows. In Section 2, system description and channel model by considering atmospheric turbulence and various weather conditions is described. In Section 3, probability of error is evaluated for three cases: (i) MUI alone, (ii) MUI and turbulence, and (iii) MUI, turbulence and various weather conditions. In Section 4, numerical results are presented and conclusions of study are drawn in Section 5. 2 System description and channel modelling The block diagram of atmospheric OCDMA system with N number of users is shown in Fig. 1. It consists of encoder, N:1 coupler and transmit optics (including the lens for collimated optical beam) at the transmitter side. In 1D OCDMA system, the message bits from the user are OOK modulated and encoded with the codeword of the intended user by using fibre-optic delay lines or other encoder. The encoder output is combined using N:1 coupler and transmitted via transmit optics. At the receiver optics, optical signal is distributed by the N:1 coupler. The decoder retrieves the intended information which is further converted to message bits by photodetector, sampling circuit and threshold detector. For 2D OCDMA system, the encoder and decoder consist of wavelength-division multiplexer, fibre optic delay lines and wavelength-division demultiplexer. The rest of the architecture is identical to the 1D OCDMA system. When '1' bit is transmitted then the encoded codeword '1001' for 1D and 2D code, respectively, is shown in the inset but for '0' bit codeword is not transmitted. Figure 1Open in figure viewerPowerPoint Atmospheric OCDMA system 2.1 Turbulence model Atmospheric turbulence is characterised by various models such as lognormal, K, I−K, negative exponential, gamma–gamma, etc. [13]. If x is the factor by which the signal at the receiver gets multiplied due to random atmospheric fading X. The probability density function (pdf) in lognormal model is given by [10] (1) where is the log intensity variance. For weak turbulence, the variance of X, is equal to which is also equal to (Rytov variance), i.e. . The pdf in gamma–gamma model is [11] (2) where is the gamma function, the modified Bessel function of the second kind of order n and and are the effective number of small and large-scale eddies, respectively. We have assumed plane wave model for analysis because the link distance (L) lies in the far field in our work. The parameters and are given as [9] (3) (4) where , is the wave number and the wavelength of operation. The pdf of the gamma–gamma model is dependent on the parameters and which are dependent on and L. However and values of the gamma–gamma model are very large for weak turbulence when L = 250 m. Hence, we have used lognormal model for weak turbulence [10] and gamma–gamma model for moderate and strong turbulence [11]. 2.2 Modelling of FSO channel In FSO communication, if is the transmitted power then the received power will be where a is the attenuation. a depends upon beam divergence and various weather conditions such as fog, haze, clear and, air is given by [13] (5) where A is the area of optical receiver, the angle of divergence (radian) and the attenuation coefficient (km−1), respectively. Here and are the attenuation factors due to beam divergence and weather conditions, respectively. Several models exist in the literature for calculation of attenuation coefficient. We have used Kim model because it is wavelength independent (for V < 0.5 km) and valid for distance less than 1 km (fog conditions). The attenuation coefficient due to Kim model is [18] (6) where V is the visibility at reference wavelength and depends upon the particle size distribution defined as [18] (7) The visibility for different weather conditions at 1550 nm is given in Table 1 [21]. Table 1. Visibility (in km) for different weather conditions Weather condition Visibility, km very clear air 50 clear air/drizzle 20 haze/light rain 6 light fog/heavy rain 2 thick fog 0.2 3 Probability of error analysis We analyse the performance of the proposed system using 1D OOC and 2D OCFHC/OOC codes. In the analysis, avalanche photodiode (APD) is taken to be chip synchronous and slot asynchronous. The analysis is carried out in presence of (i) MUI alone, (ii) MUI and turbulence, and (iii) MUI, turbulence and various weather conditions. These are discussed as follows. 3.1 Probability of error in presence of MUI The received power, with attenuation due to beam divergence can be expressed as (8) Here N represents splitting factor of the coupler at the receiver. When the power is incident on the photodetector, the average number of photons absorbed per chip time are (9) where the APD quantum efficiency, h the Planck's constant and f the optical frequency. The total photon absorption rate when bits '1' and '0' are transmitted is (10) In the above equation, is the average photon absorption rate due to background light, the APD bulk leakage current, e the electron charge and the extinction coefficient of the laser. The photodetector output arises due to electron-hole pairs from the desired user as well as the interfering users. When each user is assigned a codeword in atmospheric 1D OCDMA, the probability of interference, between two codewords is [4] (11) For the 2D OCFHC/OOC code, the probability of interference, between two codewords is [17] (12) In 1D OCDMA system, MUI at the intended receiver is given by cross-correlation function. For OOC, each interfering user can interfere at most one chip pulse position of the desired user during correlation time. If i denote the number of interferences caused by the interfering users, then the pdf of i is (13) Similarly, the pdf of i with N number of active users for the 2D OCFHC/OOC is (14) When data bit '1' is transmitted, the conditional pdf of the photodetector Gaussian output considering the effect of MUI is (15) where the mean and variance of are defined as (16) and (17) Here G is the average APD gain, the APD surface leakage current and the excess noise factor given by [16] (18) In the above equation, is the APD effective ionisation ratio, and the variance of thermal noise which is given as [16] (19) where is the Boltzmann constant, the receiver noise temperature and the receiver load resistor. Similarly, when data bit '0' is transmitted then conditional pdf of photodetector output considering the effect of MUI is (20) where mean and variance of are (21) and (22) Therefore, the probabilities of error and for the 1D and 2D OCDMA systems, respectively, in presence of MUI with OOK modulation scheme are (23) and (24) where is defined as (25) Here Th is threshold value. Substituting (13) and (14) in (23) and (24), respectively, we have (26) and (27) These expressions are used for the numerical evaluation of probability of errors. The results are shown in Figs. 2 and 3. Figure 2Open in figure viewerPowerPoint Probability of error versus threshold in presence of MUI for 1D OCDMA systems and 2D OCDMA systems Figure 3Open in figure viewerPowerPoint Probabilities of error versus transmitted laser power in presence of MUI for 1D and 2D OCDMA systems 3.2 Probability of error in presence of MUI and turbulence In this case, power received at the photodetector in presence of turbulence is . Hence, the average photon absorption rate is (28) Moreover, the total photon absorption rate when bits '1' and '0' are transmitted is given by (29) When data bit '1' is transmitted, the conditional pdf of the photodetector Gaussian output in presence of MUI and turbulence is (30) where the mean and variance of are defined as (31) and (32) Similarly, when data bit '0' is transmitted, the conditional pdf of photodetector output in presence of MUI and turbulence is (33) where mean and variance of are (34) and (35) Therefore, and in presence of MUI and turbulence will be (36) and (37) where is defined as (38) Hence, the average probabilities of error and in presence of MUI and turbulence are (39) and (40) where have lognormal distribution in weak turbulence (1) and gamma–gamma distribution in moderate and strong turbulence (2). Numerical results computed from the above equations are shown in Fig. 4. Figure 4Open in figure viewerPowerPoint Probabilities of error versus transmitted laser power in presence of MUI and under all turbulence regime's fading models for 1D and 2D OCDMA systems 3.3 Probability of error in presence of MUI, turbulence, and weather conditions The weather conditions further attenuate the optical signal due to absorption and scattering. In that case, the attenuated power in presence of MUI, turbulence and various weather conditions at the photodetector input will be , i.e. the received power will be multiplied by the additional attenuation coefficient which can be determined following Kim model [20] as mentioned earlier. As a result, the average photon absorption rate is (41) The error probability again can be evaluated from (39) and (40) by taking received power to be instead of . 4 Results and discussion In this section, we present numerical results on the performance analysis of 1D and 2D OCDMA systems. The various parameters which we have used for the analysis are given in Table 2. For comparison, w, n and are same for both OCDMA systems. The values of for weak, moderate and strong turbulence are , and , respectively [9]. We have used lognormal model for weak turbulence and gamma–gamma model for moderate and strong turbulence. Moreover, dense fog and strong turbulence do not occur simultaneously. The maximum safe power transmitted from a class 3B laser used for commercial terrestrial communication is 27 dBm (considering eye and skin safety) [18]. It is the upper limit on the power transmitted, . Table 2. Atmospheric OCDMA link parameters Symbol Quantity Value laser wavelength 1550 nm APD quantum efficiency 0.7 G APD gain 10 APD ionisation ratio 0.45 APD surface leakage current 10 nA APD bulk leakage current 0.1 nA background light photon arrival rate photons/s extinction ratio 100 receiver load resistor 1030 receiver noise temperature 300 K D aperture diameter 7.8 mm L propagation length 250 m w code weight 3 n code length 97 chip rate 4 Gchips/s The probabilities of error and with threshold Th for 1D and 2D OCDMA systems is shown in Fig. 2. For 1D OCDMA system, optimum Th values are 72,600 and 187,300 photo-electrons per baseband bit when is equal to 15 and 20 dBm, respectively. From Fig. 2, we observe that when increases from 15 to 20 dBm then optimum Th also increases due to increase in the number of photons falling on the photo-detector. Moreover, decreases stepwise for but not for because the effect of noise powers such as thermal noise, shot noise, background noise is negligible at high value of , and the main performance degradation effect is MUI due to interfering users. Similarly, decreases with increase in Th and . In addition, the number of steps in and for are equal to weight of the code (here w = 3 for both codes). The optimum Th values are 66,100 and 184,500 photo-electrons per baseband bit for 2D OCDMA system when is equal to 15 and 20 dBm, respectively. After the optimum threshold, and advance to 0.5 because Th becomes too high and there is no error for '0' bit transmission. As a result, the probability of error is only for '1' bit transmission which is 0.5. Fig. 3 shows and increase with increase in N due to MUI. Moreover, is less than for the same and N because MUI is less for the 2D OCDMA system due to different wavelengths used in OCFHC/OOC. Usage of different wavelengths provide wavelength diversity in OCFHC/OOC and decrease the probability of interference. To see the effect of atmospheric turbulence and various weather conditions on the error performance, we have used N = 8 for further evaluation. Fig. 4 shows the error probabilities in presence of MUI and under all turbulence regimes. The performance is worse in strong turbulence regime (gamma–gamma fading model) and significantly better in weak turbulence regime (lognormal fading model). is lower than the in the respective turbulence regimes. In the low turbulence regime, when but for moderate and strong turbulence it is >. is > in all turbulence regimes. In Fig. 5, and are shown in presence of very clear air, light fog, and thick fog in the weak turbulence regime. In this turbulence regime, when and 19.5 dBm in very clear air and light fog, respectively. is less than the in presence of very clear air and light fog. This shows that 2D optical code also perform better than 1D optical code in the weak turbulence regime in presence of very clear air and light fog. For the error probability of the order of , the optimum number of users in presence of very clear air and light fog are 14 and 9, respectively. Similarly, Figs. 6 and 7 show that the effect of thick fog is dominant in all turbulence regimes. For moderate and strong turbulence, is > in various weather conditions. The results show that due to thick fog performance degradation is more than the light fog and very clear air in all turbulence regimes. Figure 5Open in figure viewerPowerPoint Probabilities of error versus transmitted laser power in presence of weak turbulence and various weather conditions for 1D and 2D OCDMA systems Figure 6Open in figure viewerPowerPoint Probabilities of error versus transmitted laser power in presence of moderate turbulence and various weather conditions for 1D and 2D OCDMA systems Figure 7Open in figure viewerPowerPoint Probabilities of error versus transmitted laser power in presence of strong turbulence and various weather conditions for 1D and 2D OCDMA systems The error probability is reasonably higher in the analysis because we have considered eight user OCDMA system without considering the effect of aperture averaging and diversity techniques, i.e. performance enhancement techniques. We are working to improve the performance so that the error probability is of the order of or less. 5 Conclusion We have analysed the performance of 1D and 2D OCDMA systems in presence of atmospheric turbulence and various weather conditions. Lognormal model is used for weak turbulence and gamma–gamma model for moderate and strong turbulence. The results show that due to thick fog performance degradation is more than the light fog and very clear air. For 1D OCDMA system, performance is worse in all turbulence regimes irrespective of weather condition. It has been shown that 2D OCDMA system designed for eight users considering only MUI with may not work satisfactorily when atmospheric turbulence and/or different weather conditions are present. It is observed that all the eight users have in presence of very clear air, light fog in the weak turbulence regime with 2D OCDMA system, but not when the turbulence level is moderate and strong. 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