View metadata, citation and similar papers at core.ac.ukIEEE ICC 2015 - Optical Networks and Systems Symposium brought to you by CORE provided by Institute of Transport Research:Publications Performance of FSO Links under Exponentiated Weibull Turbulence Fading with Misalignment Errors P. K. Sharma†,1, A. Bansal‡,2, P. Garg‡,3, T. A. Tsiftsis††,4 and R. Barrios†‡,5 †Department of EECE, ITM University, Gurgaon, India ‡ Division of ECE, Netaji Subhas Institute of Technology, New Delhi, India †† Dept. of Electrical Engineering, Technological Educational Institute of Central Greece, Lamia, Greece †‡ Institute of Communications and Navigation, German Aerospace Center (DLR), 82234 Wessling, Germany [email protected], [email protected], parul [email protected], [email protected], [email protected] Abstract—The exponentiated Weibull (EW) distribution has link in the receiver side. The placement of the collecting been recently proposed for the modelling of free-space optical aperture integrates the more light in the receiver plane and (FSO) links in the presence of finite sized receiver aperture. thus a greater portion of the incoming wavefront can be In this paper, the performance of FSO communication sys- tems over EW is studied. Specifically, the probability density concentrated into the photodetector of the point receiver. function (PDF) and cumulative distribution function (CDF) The characterization of the atmospheric turbulence induced of the instantaneous signal-to-noise ratio (SNR), over EW fading is an important step in the performance analysis of an turbulence fading, are studied. The derived statistics of the SNR FSO communication systems. The existing channel models is utilized to analyse the performance of an FSO communication such as log-normal and Gamma-Gamma can not be used in system over a generalized communication environment with turbulence induced fading, misalignment errors and path loss. all turbulence situations, and even sometimes they do not New expression for the outage probability is obtained, and exact provide a good fit for experimental and simulated data [2], expressions for the average bit error rate (BER) are derived [5]. Recently, Barrios et. al. in [6], [7] proposed a new dis- for various binary modulation schemes. Finally, the obtained tribution, known as exponentiated-Weibull (EW) distribution, analytical results are verified via Monte Carlo simulations. to model the atmospheric turbulence induced fluctuations in the irradiance received at the finite size aperture-averaged I. INTRODUCTION receiver. The EW distribution captures the effect of aperture- Free-space optical (FSO) communication has emerged averaging through its constituent parameters as these pa- recently as an efficient solution to match the larger bandwidth rameters depend on the scintillation index of the received and high data rates requirement of the upcoming wireless irradiance. communication systems. However, the major challenge in The performance of the FSO communication system over establishing a wireless link at optical frequencies is atmo- EW channels has been analysed in [8]-[12]. The approximate spheric turbulence experienced by the laser beam when it expressions for the bit error rate (BER) are derived in propagates through the medium [1]. The atmospheric turbu- [8]-[11]. In [8], [11], the BER is obtained using Gauss- lence causes various perturbations in the propagating beam Laguerre quadrature rule, while Gauss-Hermite quadrature like scintillation which represents the random fluctuations approximation is used in [9]. The average capacity of the in the beam irradiance, beam wander which stands for the optical wireless communication systems over EW distribution random movement of the instantaneous centre of the beam turbulence channels is derived in [12]. However, the analysis at receiving aperture, and beam spreading that indicates the in all these works utilized the probability density function spreading beyond the diffraction limit of the beam radius [2]. (PDF) of the fading channel, and none of them derived and The receivers in FSO systems generally have the point ge- utilized the PDF of the signal-to-noise ratio (SNR). The sta- ometry which further worsens their performance in presence tistical analysis through SNR based approach is less complex of the atmospheric turbulence. To improve the performance of and more general as can be extended to different modulation a communication system in atmospheric turbulence, several techniques directly. So in this paper we, first derive the techniques have been proposed in the literature [3]-[4]. The distribution of the instantaneous SNR, and apply the derived larger dimensions of the apertures in the receiver may help in statistics to analyze the outage and error performance of the collecting the higher irradiance flux, but it will place a hard- FSO communication systems. Specifically, expression for the ware constraint on the receiver structures. Aperture averaging outage probability using the cumulative distribution function is one of the most widely used alternative technique due to its (CDF) of the instantaneous SNR is obtained. Finally, the simplicity and lower cost. In aperture averaging, to mitigate expression for the average bit error rate (BER) is derived, the adverse effect of the atmospheric turbulence induced which is applicable for various binary modulation schemes fading, a collecting aperture is placed at the end of the FSO such as coherent binary frequency shift keying (BFSK), non- 978-1-4673-6432-4/15/$31.00 ©2015 IEEE 5110 IEEE ICC 2015 - Optical Networks and Systems Symposium coherent BFSK, coherent binary phase shift keying (BPSK), particles given by and differential BPSK. 1.6 for V > 50 km The rest of this paper is organized as follows: In section II 1.3 for 6 <V < 50 km the detailed description of channel model is given. The PDF ψ(V )= 0.16V +0.34 for 1 <V < 6 km (5) and CDF of the instantaneous SNR are derived in section III. V − 0.5 for 0.5 <V < 1 km Performance analysis metrics such as the outage probability 0 for V < 0.5 km . and average BER are presented in Section IV. Section V details the numerical results and conclusions are given in section VI. III. STATISTICS OF THE INSTANTANEOUS SNR In this section we derive the PDF and CDF of the II. CHANNEL MODEL instantaneous received SNR in the receiver. For a subcarrier intensity modulated communication, the SNR over channel 2 2 (Pt ζ) We consider the composite model for the channel between is given by , where R . The term h γ =γ ¯0|h| γ¯0 = N0 the source and the destination, represented by the channel co- Pt is the average transmitter power, R is the responsitivity efficient h. It is composed of atmospheric turbulence induced of the photodetector, N0 is the average noise power of the fading represented by the coefficient hI , the misalignment additive white Gaussian noise at the receiver, and ζ is the fading denoted as hm, and distance dependent path loss hℓ. modulation index [8, Eq. 3]. The average SNR can be given 2 Thus composite channel coefficient can be given as as γ¯ =γ ¯0E[|h| ], where E[·] is the expectation operator [16]. h = hI hmhℓ. (1) Lemma 1: The PDF of the instantaneous SNR γ can be given as The atmospheric turbulence induced fading is modelled ∞ 2 ρ − β under EW distribution. The PDF of the coefficient hI (hI > f (γ) = B Ψ(j)γ 2 1Γ τ,B (j)γ 2 , (6) ), is [6] γ 1 2 0 j=0 ∑ [ ] − j 2 β−1 β β α 1 ( 1) Γ(α) αρ αβ hI hI hI where Ψ(j) = − ρ2 , B1 = ρ2 , f h , 1− 2(hℓηA0√γ¯0) hI( I )= exp − 1 − exp − j!Γ(α j)(1+j) β η η η η 2 ( ) [ ( ) ]{ [ ( ) ]} ρ − 1+j (2) τ = 1 − , and B2(j) = β , Γ(·) is the gamma β (hℓηA0√γ¯0) where β > 0 and α> 0 are the shape parameters, and η > 0 function, and Γ(·, ·) is the upper incomplete gamma function is the scale parameter. The parameter α,β depends on the [17]. scintillation index of the irradiance [13, Eq. 20,21], and the Proof: In (1), the terms hI and hm are random variables (RVs) whose PDFs are given in (2) and (3), respectively, and parameter η depends on the mean value of the irradiance. The the term hℓ is deterministic. In order to obtain the PDF of shape parameter α not characterizes the fading conditions of h, first we derive the PDF of RV X = hI hm. The PDF of the link but also it along with parameter β captures the effect X can be written as, of aperture averaging. [13]. ∞ fX (x) = fhm (x|hI )fhI (hI )dhI . (7) Assuming a Gaussian spatial intensity profile for the beam x ∫ A0 waist, the misalignment fading hm is statistically charac- terized in [14]. For independent but identical Gaussian Using (2) and (3), (7) can be written as, ∞ β−1 β distributed horizontal sway and elevation, the radial displace- 2 2 2 ρ ρ −1 −ρ αβ hI hI fX (x)= 2 x hI exp − ment at the receiver follows a Rayleigh distribution. Now ρ A x η η η 0 ∫ A0 ( ) [ ( ) ] using these facts the PDF of hm is given, as in [12], as − β α 1 hI 2 × 1 − exp − dh . (8) ρ 2 I ρ 1 { [ η ]} fhm (hm)= 2 hm − , 0 ≤ hm ≤ A0 (3) ( ) A0 A1 where A0 is the fraction of the collected optical power To solve the integration| in (8), we{z expand the }A1 using ω the Newton’s generalized binomial theorem i.e. (1 + y)t = and ρ = 2σ , ω is the equivalent beam width at the s Γ(t+1)yj 2 ∞ receiver, and σs is the variance of pointing error displacement j=0 Γ(t j+1)j! . After some mathematical manipulations characterized by the horizontal sway and elevation.