Capacity and BER Analysis of FSO Link in Adverse Weather Conditions over K-Distribution

Volume 119 No. 1 18, 139-147 ISSN: 1311-88 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu Capacity and BER Analysis of FSO Link in Adverse Weather Conditions over K-Distribution Rahul Kaushik 1, Balkrishna Shukla, Vishal Saxena Department of Electronics and Communication Engineering Jaypee Institute of Information Technology, Noida, INDIA-137 E-mail: 1 rahul.kaushik@jiit.ac.in Abstract In a free-space optical (FSO) link, the propagating optical signal is deteriorated by turbulence induced fading in the atmosphere and attenuation due to adverse weather conditions. The performance of the link is also degraded due to pointing error resulting from the misalignment of laser at the transmitter and photodetector at the receiver. In this paper, closed form analytical expressions to evaluate average capacity and BER in turbulence alongwith pointing error and path loss due to adverse weather are given. The turbulence in the atmosphere is assumed to be modelled by k-distribution. This analysis reveals that performance of a FSO link is degraded in adverse weather conditions and the most severe degradation in the performance is observed in foggy conditions. Keywords: Turbulence, k-distribution, free space optics, pointing error, bit-error rate, capacity, path los. 1. Introduction FSO communication is the transmission of optical signal via free space. FSO communication systems have the advantage of licence-free operation with ultra-high bandwidth in contrast to radio frequency (RF) communication. However, FSO systems are highly sensitive to degrading effect of turbulence in the atmosphere and pointing error [1]. Variation in the refractive index in the channel causes turbulence induced fading or scintillation resulting in irradiance fluctuation of the received signal. Dynamic winds loads and buildings sway due to weak earthquakes causes misalignment of transmitter and receiver leads to pointing error. [1,]. Over the years, different statistical models have been given for varying strength of atmospheric turbulence. k -distribution is considered a suitable model for strong turbulence regime due to good agreement between experimental and theoretical data []. Usyal and Li calculated pair-wise error probability (PEP) and BER of coded FSO system considering k distribution for atmospheric turbulence induced fading [3]. Kiasaleh evaluated the BER performance for an FSO link with heterodyne detection considering k-distributed turbulence induced fading channel [4]. Outage probability for a multi-hop FSO link over k distribution was analyzed by Karagiannidis et al. [5]. The synergy of pointing error and turbulence on performance of terrestrial FSO link has been investigated by Arnon considering the detector of negligible aperture size with reference to beamwidth [6,7]. Average channel capacity for an FSO link with pointing error over k - turbulence fading channels has been evaluated by Pandey [8]. Cao et al. investigated the BER of an FSO link over k distributed turbulence channel alongwith pointing error [9]. However, the BER and channel capacity performance of FSO communication in k- distributed turbulence ISSN: XXXX-XXXX IJXX Copyright c XXXX SERSC 139

induced fading in existence of pointing error together with atmospheric weather attenuation has not been found in these studies. The remainder of this paper is as follows: The system and channel model is discussed in section. Section 3 presents the probability density function (PDF) of channel under consideration. The Average BER analysis of FSO system is discussed in section 4. Section 5 describes the average capacity of FSO channel. Numerical results are presented and discussed in section 6. Section 7 concludes the paper.. System and Channel Model An intensity modulated direct detection (IM/DD) FSO link employing on-off keying (OOK) modulation is taken for this study. Input data is modulated onto the intensity of a laser beam. The transmitted optical signal passes through an atmospheric channel. Assuming that channel is ergodic, memoryless, stationary with independent and identical statistics, the received electrical signal y at the photodetector can be expressed as [1, 11,1]: y = R x + n (1) where R is the photodetector responsivity and x is the transmitted binary signal i.e. x, P t where P t is the average power of transmitted optical signal. n is the signal independent Gaussian noise with zero mean and variance σ n. represents the fluctuations in the intensity of optical signal caused by channel conditions which can be modelled as [13]: = a p l () here, a is the random fading due to atmospheric turbulence, p is the pointing error caused by the misalignment between transmitter and receiver and l is the attenuation/path loss due to weather which is deterministic and can be evaluated by various mathematical models..1. Fading due to atmospheric turbulence The k- distribution is a model for atmospheric turbulence induced fading strong regime and its probability density function (PDF) is [, 8, 9]: ϸ a θθ+1 a = θ 1 Γ θ a k θ 1 θ a ; a > (3) where θ being the parameter for turbulence induced fading which depends on the effective discrete scatterers. Γ θ is the gamma function and k θ 1 is the modified Bessel function of second kind... Attenuation due to adverse weather Attenuation due to adverse weather also degrades the performance of the link. It occurs due to physical phenomena such as scattering and absorption by the water droplet and other particles such as fog, aerosols etc. The attenuation in the atmosphere can be calculated using Beer- Lambert Law as [14,15]: l = exp β. L (4) where β is the attenuation coefficient and L being the transmission distance. The value of β in different climates can be calculated as discussed below. 14

A. Fog / Haze attenuation The value of attenuation in fog/haze can be determined using visibility range in the atmosphere with the simple empirical formula given as [14,15]: β fog km 1 = 3.91 V(km ) λ(nm ) 55 q (5) with V being the visibility range in Km and λ is the operating wavelength in nm. The parameter q represents the distribution of particle size. B. Rain attenuation As recommended by ITU- R, the attenuation in rain depends on rainfall rate and can be calculated as [14,15]: β rain db/km = 1.76R.67 (6) where R (mm/r) is the rainfall rate. The attenuation in different weather conditions are calculated using Eq. (5) and Eq, (6) for a wavelength of 155 nm in [14, 15, Table 1]..3. Pointing Error For an optical beam with Gaussian profile and photodetector with circular aperture of radius r, the PDF of attenuation caused by pointing error is given as [13]: ϸ p p = ξ A p ξ 1 ; p A (7) here, the ratio of equivalent radius of beam at the detector to the displacement due to pointing error is given by, ξ = w eq σ s with w eq being the corresponding beam width which is related to beam waist, w z as w eq = w z π erf V V exp V and A = erf V is the received power at r =. erf ( ) is the error function and V = πr w z. 3. PDF of the FSO Channel The overall PDF of FSO channel, ϸ, can be obtained by using the PDFs of atmospheric turbulence induced fading [Eq. (3)] and pointing error [Eq. (7)] as [8,13]: ϸ = ϸ a a ϸ a a d a (8) Where ϸ a a represents the conditional probability, conditioned over atmospheric turbulence a and can be expressed as: ϸ a a = 1 l a ϸ p = ξ l ξ a A a l l a ξ 1 Substituting Eq. (9) and (7) into (8), the PDF of FSO channel can be written as (9) 3 141

ϸ = ξ ξ 1 θ +1 θ ξ ξ l A Γ θ θ +1 a 1 ξ k θ 1 A a θ a (1) Using Meijer-G function, modified Bessel s functions can be written as [8, 16,19]: k a μ = 1 G,, μ 4, a, a (11) Substituting this in Eq.(1) and by using [8, Eq. (8)], the integral form in Eq. (1) can be written as : ϸ = θξ A Γ θ G3, 1,3 θ A l ξ 1 + ξ, θ 1, It is worth noting that Eq. (1) represents a closed form of PDF of FSO channel. (1) 4. BER Analysis of FSO System The BER of an IM/ DD FSO link employing OOK modulation conditioned on channel state is given as [9], P b e = Q P t σ n (13) The above equation gives the conditional BER of the FSO link, where Q(. ) represents Gaussian Q- function. The average bit-error P b e of an FSO system can be determined by statistical averaging of conditional BER over the density function of FSO channel as [1]: P b e = P b e ϸ d (14) The Gaussian Q- function can be written in terms complimentary error function as erfc x = Q x. Further, using Meijer-G function, we can write [8, 17]: erfc μ = 1 π G, 1, μ,, 1 1 (15) Substituting Eq. (1) and using Eq. (13) and Eq. (15), Eq. (14) can be rewritten as: P b e = θξ Г θ 1 π G 3, 1,3 θ A l ξ 1 + ξ, θ 1, G, 1, P t σ n,, 1 1 By using Eq. [19, Eq. (1)] and [16, Eq. (9.31),we can obtain a closed form analytical expression of Eq. (16) as: d (16) P b e = ξ θ 3 π 3 θ G 5 6 3 16P t A l σ n θ ξ, 1 θ, θ,, 1, 1, 1, ξ (17) The above expression given in Eq. (18) represents the closed form expression to 4 14

evaluate the BER of an FSO link over k distributed atmospheric turbulent channel subjected to both pointing error and attenuation due to weather conditions. 5. Average Capacity of FSO Link The average capacity of the FSO link (in bits/sec.) is given as [1,11]: C = W log 1 + γ ϸ d = W ln ln 1 + γ ϸ d (18) where γ represents the instantaneous electrical signal to noise ratio (SNR) at receiver. W is the bandwidth of the channel in Hz. The instantaneous SNR γ varies randomly due to channel conditions. Assuming that detector is ideal with responsivity, R = 1, the instantaneous SNR for an FSO system employing OOK modulation is given as [8,13] : γ = P t (19) σ n Substituting Eq. (1) and Eq. (19) in Eq. (18), average capacity of the link can be obtained as : C = W θξ ln Γ θ ln 1 + P t σ n. G 3, 1,3 θ A l ξ 1 + ξ, θ 1, d () Using Meijer-G function, ln 1 + γ can be written as [19, Eq. (11)]: ln 1 + γ = G 1,, γ 1, 1 1, (1) Substituting this in Eq. (), the average channel capacity given can be rewritten as: C = W αξ ln A Γ θ G 1,, P t 1, 1 σ n,. G 3, 1,3 θ A l ξ 1 + ξ, θ 1, d () By using Eq. [19, Eq. (1)], the average capacity of the FSO link (in bits/sec) can be obtained as: C = W.θ ξ π ln θ G 1, 8 8, 4 3P t A l σ n θ 1, 1, 1 ξ, ξ 1 θ, ξ 1,,1 ξ θ,, 1/ (3) Therefore, the average capacity per unit bandwidth for an FSO system can be obtained as: <C> W (in bits/ sec/hz) = θ γ π ln θ G 1, 8 8, 4 3P t A l 1, 1, 1 ξ θ σ n 1,, ξ, 1 θ ξ,1 ξ θ,, 1/ (4) The above Eq. (4) gives a closed form analytical expression to evaluate of average capacity of the FSO link in adverse weather conditions and pointing error over k distributed turbulence. 5 143

Average BER International Journal of Pure and Applied Mathematics 6. Numerical Results In this section, the performance of the FSO link in the k distributed turbulence is evaluated in existence of pointing error and adverse weather conditions. The average BER of the FSO link evaluated using proposed closed form expression given in Eq. (17). Further, the average capacity is calculated using proposed Eq. (4). An FSO link operating at λ=155 nm with normalized jitter σ s r =.1 and turbulence fading parameter θ = is considered. Standard deviation of AWGN is assumed to be σ n = 1 7 A Hz. The performance of the link is evaluated in four weather conditions i.e. clear air, haze, rain and fog. Fig. 1 shows the variation average BER against transmitted optical power for different atmospheric conditions. It can be seen that in optimum BER performance is achieved in clear air due to minimum atmospheric attenuation. However, BER degrades when weather condition deteriorates from clear air to fog. 1 1-1 clear air Haze Rain Fog 1-1 -3 1-4 1-5 -1-5 5 1 15 5 Transmitted power/dbm Fig.1. BER Vs transmitted optical power for different atmospheric condition Fig. depicts the variation of average capacity against transmitted optical power for different atmospheric conditions. It is seen that increase in atmospheric attenuation leads to reduction in average capacity. It is also observed that the performance of FSO link in terms of both BER and average capacity improves with increasing transmitted power in all weather conditions. The performance in presence of rain is found to be better in comparison to foggy conditions. 6 144

Average capacity( (bits/sec)/hz) International Journal of Pure and Applied Mathematics 3 5 clear air Haze Rain Fog 15 1 5-1 -5 5 1 15 5 Transmitted power/dbm Fig.. Average Capacity for various atmospheric Condition 7. Conclusion: The analytical expressions for the evaluation of BER and channel capacity of a free space optical link affected with pointing error, attenuation due to adverse weather and turbulence induced fading modeled by k-distribution are given. It has been observed that the performance of the link is degraded in adverse weather conditions. The maximum degradation in the performance is produced by fog, irrespective of pointing error and strength of turbulence induced fading. The analysis presented in this paper will be helpful for the system designers in estimating the achievable performance of a FSO communication system affected by different atmospheric losses. References [1] D. Kedar and S. Arnon, Urban optical wireless communication networks: the main challenges and possible solutions, IEEE Commun. Mag., vol. 4, no. 5, (4), pp. S S7. [] L. Andrews, R. L. Philips, and C. Y. Hopen, Laser Beam Scintillation with Applications, SPIE Press, Bellingham, Washington, USA (1). [3] M. Usyal and J. T. Lee, "BER performance of coded Free space optical link over strong turbulence channel," Proceedings of IEEE Vehicular Technological conference (VTC), (4) pp. 168-17. [4] K. Kiasaleh, Performance of coherent DPSK free Space optical communication system in K- distributed Turbulence," IEEE Trans. Commun., vol. 4, no. 4, (6), pp 64-67. 7 145

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