Abstract

In this paper, we analytically investigate an optical signal detection scheme to mitigate the scintillation effect with the assistance of a co-propagating reference continuous wave (CW) light. Using the correlation coefficient between the intensities of the data light and the reference CW light, we mathematically derive their joint intensity distributions under two widely used atmospheric turbulence channel models, namely log-normal distributed channel model and Gamma-Gamma distributed channel model, respectively. We also carry out the Monte-Carlo (MC) simulation and show that theoretical results agree with simulation results well. Our analytical results reveal that when the correlation coefficient is 0.99, the power reductions to achieve BER of 10−3 are 12.3 dB and 20.4 dB under moderate and strong atmospheric turbulence conditions (i.e., Rytov variances of 1.0 and 4.0), respectively. In addition, the feasibility of the scheme applied to wavelength-division-multiplexed (WDM) free-space-optical (FSO) transmission systems is also investigated, where only a single reference CW light could be used to mitigate the scintillation effects on all WDM channels.

© 2012 OSA

1. Introduction

Free-space optical (FSO) communication is anticipated to play an important role in future telecommunication networks. It can bridge the gap where optical fiber communication cannot reach and wireless communication cannot provide enough bandwidth. The advantages of FSO communication include high capacity, high security, free spectrum license and easy to install and remove [1,2]. Since the sizes of molecules in atmosphere such as oxygen, carbon dioxide and water vapor are comparable to optical wavelength, the intensity of an optical wave will fluctuate when the optical wave propagates through the atmosphere. Such fluctuation is called scintillation, which can severely deteriorate the FSO transmission performance [35]. The multiplicative scintillation is detrimental to FSO communication systems [6], and how to mitigate the scintillation effect with reasonable cost becomes a hot research topic recently [45,79].

It has been experimentally demonstrated in [10] that two optical waves experience almost identical scintillation process, when they co-propagate through the same atmospheric turbulence channel simultaneously. However, only the correlation coefficient between two optical waves has been experimentally investigated and no analytical results have been obtained. In this paper, firstly we mathematically derive the joint intensity distributions of two co-propagating optical waves under two widely used atmospheric turbulence channel models, namely log-normal distributed channel model and Gamma-Gamma distributed channel model [11], respectively. Using these joint intensity distributions, we then theoretically analyze the bit error rate (BER) performance of FSO transmission system that is assisted with a reference CW light to mitigate the effect of scintillation under different atmospheric turbulence conditions as well as under different correlation coefficients between the intensities of the data light and the reference CW light. We also carry out the Monte-Carlo (MC) simulation and show that theoretical results agree with simulation results well. Our results reveal that the power reductions to achieve a bit error rate (BER) of 10−3 are 12.3 dB, 20.4 dB under moderate and strong atmospheric turbulence conditions (i.e., Rytov variances of 1.0 and 4.0), respectively, when the correlation coefficient is 0.99. The feasibility of mitigating the scintillation effects by only using a single reference channel for WDM-FSO systems over a wavelength range of 100 nm is examined and discussed. And the improvement of transmission distance is also investigated.

The rest of this paper is organized as follows. Section 2 presents the atmospheric turbulence channel models that follow log-normal and Gamma-Gamma distributions. The scheme of mitigating the effect of scintillation by a reference CW light and the derivation of joint intensity distributions of two co-propagating optical waves are presented in Section 3. In Section 4, the BER performances of the on-off-keying (OOK) FSO system assisted by a reference CW light are evaluated under moderate and strong atmospheric turbulence conditions, followed by the feasibility study of using only a single reference CW light to mitigate the effect of scintillations on all the channels of a WDM-FSO communication system and the improvement of transmission distance. The conclusions are given in Section 5.

2. Channel model of FSO communication system

2.1 Log-normal distribution

When an optical wave propagates through the atmospheric turbulence channel, its intensity fluctuates due to scintillation. Several atmospheric turbulence channel models have been proposed to describe scintillation [5,1112]. Among them, the log-normal (LN) distribution is widely used to investigate the scintillation under weak and moderate atmospheric turbulence conditions [11,13]. Let IS be the normalized light intensity. In the LN distributed channel model, the probability density function (PDF) of IS is expressed by [1416]

fLN(IS)=12πσR2ISexp{[ln(ISI0)+12σR2]2/(2σR2)},
where σR2 is the Rytov variance, which is a general parameter representing the strength of atmospheric turbulence and I0 is the received intensity without turbulence, which is assumed to be unity in this work [16]. The Rytov variance is given by [11,1516]
σR2=1.23Cn2k7/6L11/6,
where L is the transmission distance; k is the wave number, i.e., k=2π/λ, where λ is the wavelength of optical wave; Cn2stands for refractive-index structure constant, varying from 10−17 m-2/3 to 10−13 m-2/3. Different values of the Rytov variance represent different atmospheric turbulence conditions. The weak, moderate and strong intensity fluctuations are associated withσR2<1, σR21and σR2>1, respectively [11].

2.2 Gamma-Gamma distribution

As reported in [1516], the log-normal distribution is not valid when σR2>1.2. Instead, Gamma-Gamma (GG) distribution is commonly used to represent the strong turbulence condition [5] where σR2>1. With the GG distributed channel model, the probability density function (PDF) of IS is expressed by [11,17]

fGG(IS)=2(αβ)α+β2Γ(α)Γ(β)ISα+β22Kαβ(2αβIS),
where Kn(·) is the modified Bessel function of the second kind of the order n, Г(·) is Gamma function. The parameters α and β are defined by Rytov varianceσR2,which are given by

α={exp[0.49σR2/(1+1.11σR12/5)7/6]1}1,
β={exp[0.51σR2/(1+0.69σR12/5)5/6]1}1.

3. OOK FSO communication system with a reference CW light

3.1 System model

It has been demonstrated in [10] that a reference CW light that records scintillation can be employed to mitigate intensity fluctuation on a data light under the same atmospheric turbulence channel. For the sake of clarity, in the rest of the paper, ‘data light’ and ‘data signal’ refer to the data before and after photo-detection, respectively. Figure 1 shows the schematic of an OOK FSO communication system with a reference CW light to mitigate the scintillation effect. An optical wave at wavelength λS is modulated with an on-off keying (OOK) signal through a Mach-Zehnder modulator (MZM). The data modulated optical wave is combined with a reference CW light at wavelength λR by a wavelength multiplexer (MUX), and then fed to a transmit aperture. The two combined optical waves pass through a fiber pig-tailed collimator in the transmit aperture [4], and then co-propagate through the same atmospheric turbulence channel simultaneously. After being collected by a receive aperture with a high speed and precise tracking mechanism [18], another fiber pig-tailed collimator couples the received signals to a wavelength de-multiplexer (De-MUX), which separates the data light from the reference CW light. After being detected by separate photo-detectors, both the data and reference signals are fed into a high-speed electrical signal processing circuit where the fluctuated data signal is divided by the fluctuated reference signal. Since the scintillations recorded on both optical waves (λS and λR) are highly correlated, the effect of scintillation on the data light at λS can be mitigated by the scintillation on the reference CW light at λR. Note that the MUX, De-MUX, transmit aperture and receive aperture are assumed to be ideal in our study (i.e., these devices do not contribute any noise to the detected signals), since our study is focused on the suppression of adverse effect of scintillation.

 

Fig. 1 Schematic of an OOK FSO communication system with a reference CW light to mitigate the scintillation effect.

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Let IS and IR be the normalized light intensities of the data light and the reference CW light, respectively. Both IS and IR follow the LN distribution for weak and moderate turbulence conditions in Eq. (1) and the GG distribution for strong turbulence conditions in Eq. (3). Let IP be the normalized amplitude of the data signal at the output of division circuit, which can be expressed as IP = IS/IR. The PDF of IP can be calculated by [19]

f(IP)=0IRf(IS,IR)dIR=0IRf(IRIP,IR)dIR,
where f(IS, IR) is the joint pdf of IS and IR. The derivations of f(IS, IR) are presented in Section 3.2 for joint LN distribution and in Section 3.3 for joint GG distribution.

3.2 Joint log-normal distribution

A LN distribution can be transformed from a normal distribution by using the Jacobian determinant [20]. Let us consider two normal distributed random variables x and y. We use μ1 andσ12to denote the expected value and the variance of x, respectively, and use μ2 andσ22to denote the expected value and the variance of y, respectively. The PDF of x is given by [21]

fx(x)=12πσ1exp((xμ1)22σ12).

The joint PDF of x and y can be described as

fxy(x,y)=12πσ1σ21ρN2exp(12(1ρN2)((xμ1)2σ122ρN(xμ1)(yμ2)σ1σ2+(yμ2)2σ22)).

The correlation coefficient ρN between the two normal random variables x and y is defined as [19]

ρN=cov(x,y)D(x)D(y)=E(xy)E(x)E(y)D(x)D(y),
where cov(·,·) is the covariance of two random variables; E(·) and D(·) denote the expected value and variance of a random variable, respectively.

We also consider a pair of log-normal distributed random variables u and v, whose relationships with x and y are described as follows [19]:

u=exp(x),
v=exp(y).

Let J1 be the Jacobian determinant for transforming (x, y) to (u, v), which is given by

J1=|xuxvyuyv|=|1u001v|=1uv.

Hence, the joint PDF of two log-normal distributed random variables u and v is given by

fuv(u,v)=J1fxy(x,y)=1uvfxy(x,y)=12πσ1σ21ρN2uvexp(12(1ρN2)((ln(u)μ1)2σ122ρN(ln(u)μ1)(ln(v)μ2)σ1σ2+(ln(v)μ2)2σ22)).

Similarly, we define ρLN as the correlation coefficient between the two log-normal distributed random variables u and v, which is given by [19]

ρLN=cov(u,v)D(u)D(v)=E(uv)E(u)E(v)D(u)D(v).
cov(u, v), D(u) and D(v) in Eq. (11) are given below:

cov(u,v)=E(uv)E(u)E(v)=exp(μ1+μ2)exp(σ12+σ222)(exp(ρNσ1σ2)1),
D(u)=E(u2)(E(u))2=exp(2μ1+σ12)(exp(σ12)1),
D(v)=E(v2)(E(v))2=exp(2μ2+σ22)(exp(σ22)1).

E(v) and D(v) are of the same expressions as that of E(u) and D(u), but with parameters μ2 and σ22. Substituting Eqs. (14a)(14c) into Eq. (13), we can obtain the expression of ρN in Eq. (12) in terms of ρLN as follows:

ρN=ln(ρLN(exp(σ12)1)(exp(σ22)1)+1)σ1σ2.

Replacing u and v with IS and IR, respectively, and substituting them into Eq. (13), we can obtain the correlation coefficient ρLN between the intensities of data light and reference CW light after collecting them by receiver aperture in Fig. 1. Substituting ρLN into Eq. (15), and then Eq. (15) into Eq. (12), we can get the f(IS, IR) that follows joint log-normal distribution. Substituting Eq. (12) into Eq. (6), the PDF of normalized amplitude IP after signal processing by the division circuit is obtained.

3.3 Joint Gamma-Gamma distribution

Due to the complexity of mathematics, to the best of our knowledge, there is no report on the joint PDF of GG distribution. We here generate the joint GG distribution numerically. Let us consider two random variables w and z that follow GG distribution and recall the two LN distributed random variables u and v in last subsection and their joint PDF is given in Eq. (12). The Jacobian determinant J2 is applied to transform (u, v) to (w, z),

J2=|uwuzvwvz|=|uw00vz|=dudwdvdz.

Thus, the joint PDF of the two GG distributed random variables w and z is

fwz(w,z)=J2fuv(u,v)=dudwdvdzfuv(u,v).
du/dwanddv/dz in Eq. (17) are the Jacobian determinants to transform u to w and v to z, respectively, which are described as follows:

J3=dudw=fGG(w)fLN(u),
J4=dvdz=fGG(z)fLN(v).

By solving the ordinary differential function (ODE) in Eq. (18), the mappings h(·) from random variable w to u and z to v are obtained:

u=hw(w).
v=hz(z).

Substituting Eqs. (18) and (19) into Eq. (17), the joint Gamma-Gamma distribution can be calculated numerically, as given in Eq. (20),

fwz(w,z)=fGG(w)fGG(z)fLN(u)fLN(v)fuv(u,v)=fGG(w)fGG(z)fLN[hw(w)]fLN[hz(z)]fuv[hw(w),hz(z)].

Note that in statistics, the correlation coefficient between two random variables w and z is described by [21]

ρGG=cov(w,z)D(w)D(z)=n(wz)(w)(z)[n(w2)(w)2][n(z2)(z)2],
where n is the length of both w and z. Applying the transformation from Gamma-Gamma distribution to log-normal distribution in Eq. (19) and from log-normal distribution to normal distribution in Eqs. (10), the correlation coefficient ρN in Eq. (12) is obtained. Substituting Eq. (12) into Eq. (18) and replacing w and z in Eq. (20) with IS and IR, respectively, we can obtain f(IS, IR) that follows joint Gamma-Gamma distribution. Substituting Eq. (20) into Eq. (6), the PDF of normalized amplitude IP after signal processing by the division circuit is obtained.

4. BER performance of OOK FSO communication systems

In this section, the BER performance improvement of OOK FSO communication systems by a reference CW light is numerically analyzed. We consider that an OOK optical signal of 10.7 Gbit/s with forward error correction (FEC) code [22] and a reference CW light are transmitted simultaneously through the same atmospheric turbulence channel and they are of different wavelengths but with the same transmitted power, as shown in Fig. 1. For the sake of simplicity, we assume that the wavelength of the reference CW light is fixed at 1550 nm, while the wavelength of the data light can be varied. In all the BER calculations, the receiver’s effective noise bandwidth is half of the bit rate [23].

We assume that the channel state information (CSI) is not available at the receiver. The bit error rate of an OOK signal is given by [24,25]

Pe=P(0)P(error|0)+P(1)P(error|1),
where P(0) and P(1) are the probabilities of data ‘0’ and ‘1’ transmitted (here P(0)=P(1)=0.5); P(error|0) and P(error|1) are the conditional error probabilities of data ‘0’ and ‘1’. Since scintillation is a multiplicative effect, it mainly affects data ‘1’. So the conditional error probabilities can be calculated as [2526]
P(error|0)=Ith12πσn2exp(r22σn2)dr=Q(Ithσn),
P(error|1)=Ith12πσn2exp((rI)22σn2)f(I)drdI=Q(IIthσn)f(I)dI,
where the responsivity of photo-detector is assumed to be unity. Q(·) is Q-function; r is the detected electrical signal; I represents the normalized intensity IS or normalized amplitude IP; f(I) is the PDF of IS or IP; σn2is the additive Gaussian white noise (AWGN) [23]. The decision threshold Ith is determined by the likelihood function Λat the unity value [25,27] such that the BER is minimized, as shown in Eq. (25),

Λ=12πσn2exp((IthI)22σn2)f(I)dI/(12πσn2exp(Ith22σn2))=exp((IthI)2+α22σn2)f(I)dI=1.

Substituting Ith into Eqs. (23)(24), and then Eqs. (23)(24) into Eq. (22), the BER performance of OOK signal becomes

Pe=12(Q(Ithσn)+Q(IIthσn)f(I)dI).

Replacing f(I) in Eq. (24) with f(IS) in Eq. (1) for log-normal distribution or in Eq. (3) for Gamma-Gamma distribution and with f(IP) in Eq. (6), we can obtain the BERs before and after the signal processing by the division circuit, respectively.

4.1 Moderate atmospheric turbulence condition

According to Eq. (2), the relationship between the Rytov varianceσR_S2of the data light IS and the Rytov varianceσR_R2of the reference CW light IR is described by

σR_R2=σR_S2(λS/λR)7/6.

Under the moderate atmospheric turbulence condition, the Rytov varianceσR_S2 of data light IS is assumed to be 1.0. According to Eq. (27), when the wavelength of IS is 1555 nm the Rytov varianceσR_R2of the reference CW light IR is 1.004, which is almost the same asσR_S2. The LN channel model described in Eq. (1) is still valid [16] for both the data light and the reference CW light. Hence, the joint log-normal distribution in Eq. (12) is applied. According to Eq. (15), when the correlation coefficients ρLN between the two LN distributed intensities IS and IR are 0.85 and 0.99, the values of ρN are 0.901 and 0.994, respectively. Substituting ρN into Eq. (12), and then Eq. (12) into Eq. (6), we can obtain the PDF of the normalized amplitude IP of the data signal at the output of the division circuit.

Figures 2(a) and (b) show the PDFs of the normalized intensity IS (amplitude IP) of the data light (signal) under moderate atmospheric turbulence condition with Rytov variance of 1.0 before and after the signal processing by the division circuit, respectively. After the signal processing, the PDF curve becomes much more concentrated at 1 than that before signal processing, indicating that the effect of scintillation is mitigated significantly by the division circuit.

 

Fig. 2 PDFs of the normalized intensity (amplitude) of the data light (signal) under moderate atmospheric turbulence condition with Rytov variance of 1.0: (a) before and (b) after the signal processing by the division circuit.

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For the case of moderate atmospheric turbulence condition, the transmitted optical power of the signal is set to be 0 dBm. The BER performance of the reference CW light assisted detection scheme is depicted in Fig. 3 , where analytical and MC simulation results match very well. We see that without the assistance of the reference CW light, the required power to achieve BER of 10−3 is −12.6 dBm; with the reference CW light the required powers are reduced to −21.6 dBm when the correlation coefficients ρLN between the two LN distributed intensities IS and IR is 0.85 and further reduced to −24.9 dBm when the correlation coefficients ρLN is 0.99. That is, the power reductions of 9.0 dB and 12.3 dB are achieved, respectively. Therefore, the reference CW light assisted detection scheme shown in Fig. 1 is more effective when the scintillations on two optical waves are highly correlated. Note that BER of 10−3 is usually used as the bench mark for communication systems, since error-free transmission can be achieved by applying FEC code [28].

 

Fig. 3 BER improvement of OOK FSO system by a reference CW light under moderate atmospheric turbulence condition with Rytov variance of 1.0: (a) correlation coefficient is 0.85 and (b) correlation coefficient is 0.99.

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4.2 Strong atmospheric turbulence condition

We assume that under the strong atmospheric turbulence condition, the Rytov varianceσR_S2of data light IS is 4.0, and the corresponding values of parameters α and β in Eq. (4) and Eq. (5) are 4.341 and 1.309, respectively. According to Eq. (27), the Rytov varianceσR_R2of reference CW light IR is 4.015, and the corresponding α and β are 4.344 and 1.307, respectively. Hence, the joint Gamma-Gamma distribution in Eq. (20) is applied. Based on the algorithm in subsection 3.3, when the correlation coefficients ρGG in Eq. (21) are 0.85 and 0.99, the values of ρN in Eq. (12) are 0.888 and 0.993, respectively.

Figure 4 depicts the PDFs and histograms of the normalized intensity IS (amplitude IP) of the data light (signal) under strong atmospheric turbulence condition with Rytov variance of 4.0 before and after the signal processing by the division circuit, respectively. We see that the higher the correlation coefficient is, the more the PDF curve concentrates at 1 after the signal processing by the division circuit. The histograms and the PDFs of the signal match with each other well, which indicates that the numerical results are reasonable.

 

Fig. 4 PDFs and histograms of the normalized intensity (amplitude) of the data light (signal) under strong atmospheric turbulence condition with Rytov variance of 4.0: (a) before signal processing, (b) after signal processing with correlation coefficient is 0.85 and (c) after signal processing with correlation coefficient is 0.99.

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The improvements of BER performance are shown in Fig. 5 . Since GG distribution with 4.0-Rytov variance represents the strong atmospheric turbulence condition, we set the transmitted optical power of the signal to be 5 dBm in this subsection to investigate the BER performance more thoroughly with a larger received power range. For the joint GG distribution, we cannot get the analytical closed form expression. Instead we use the numerical approach to study the performance improvement under GG distribution. As shown in Fig. 5, when the BER is larger than 10−3, the analytical and MC simulation results match very well. However, when the BER is smaller than 10−3, the analytical and MC simulation results do not match very well. This may be attributed to the fact that the mapping from GG distributed random number to LN distributed random number in Eq. (19) and the decision threshold in Eq. (25) were not precisely obtained during the numerical calculation and the MC simulation. Nevertheless, the trends of both the results are consistent. Before signal processing the required optical power to achieve BER of 10−3 is −4.2 dBm; after signal processing the required optical power is reduced to −19.7 dBm when the correlation coefficient is 0.85 and to −24.6 dBm when the correlation coefficient is 0.99. Hence, the power reductions for achieving BER of 10−3 by the reference CW light are 15.5 dB and 20.4 dB, respectively. Compared with the results in Fig. 3, we observe that the stronger the atmospheric turbulence is, the more effectively the reference CW light assisted detection scheme performs.

 

Fig. 5 BER improvement of OOK FSO system by a reference CW light under strong atmospheric turbulence condition with Rytov variance of 4.0: (a) correlation coefficient is 0.85 and (b) correlation coefficient is 0.99.

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4.3 WDM-FSO communication system

The system schematic shown in Fig. 1 could be applied to WDM-FSO transmission systems. In this subsection, we focus on the moderate atmospheric turbulence condition with data light’s Rytov variance of 1.0. According to Eq. (27), when the wavelength of the data light varies from 1500 nm to 1600 nm, the Rytov varianceσR_R2of reference CW light varies from 0.963 to 1.038 correspondingly, which makes the LN distribution in Eq. (1) is still valid [16]. According to Eq. (15), when the correlation coefficients ρLN between the intensities of data light IS and reference CW light IR are 0.85 and 0.99, the values of ρN in Eq. (12) are almost constant at 0.994 and 0.900, respectively.

Figure 6 shows the power reductions for achieving BER of 10−3 of a data signal under the moderate turbulence condition with Rytov variance of 1.0, where the signal wavelength is changed from 1500 nm to 1600 nm and the wavelength of the reference CW light remains unchanged at 1550 nm. When the correlation coefficient is 0.85, the power reduction also varies slightly from 8.9 dB to 9.0 dB; when the correlation coefficient between IS and IR is 0.99, the power reduction varies slightly from 12.3 dB to 12.4 dB. These results show that the power reduction is almost independent of the signal wavelength under the same correlation coefficient. Therefore we can conclude that only a single reference CW light is required to substantially mitigate the scintillation effects on all the channels of a WDM-FSO communication system within a wide wavelength range of 100 nm, indicating that the reference CW light assisted detection scheme is very cost-effective when it is applied to WDM-FSO systems. Note that WDM-FSO system should also be feasible under strong atmospheric turbulence conditions by applying one reference CW light.

 

Fig. 6 Power reductions for achieving BER of 10−3 in WDM-FSO system under moderate atmospheric turbulence condition (i.e., Rytov variance of 1.0).

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4.4 Improvement of transmission distance

In previous discussions, we investigate the power reduction to achieve BER of 10−3 by the reference CW light. Such comparison is based on the assumption that the Rytov variance of the signal remains the same for the two cases-with and without employing the reference CW light. Hence, without the consideration of beam divergence, the received optical power is related to the transmission distance [2930], i.e.,

PR(L)=PT(0)exp(AL),
where PR(L)is the received optical power, PT(0) is the transmitted optical power, A is the channel attenuation coefficient (km−1) and L is the transmission distance.

We assume that the attenuation coefficient A is 1.2 km−1. For the LN distribution, according to subsection 4.1, substituting the transmitted optical power, received optical power at BER of 10−3 and attenuation coefficient into Eq. (28), we can obtain the transmission distance. The obtained transmission distance is 2.42 km for the case without applying the reference CW light. With the assistance of the reference CW light the transmission distances are extended to 4.14 km when correlation coefficient is 0.85, and 4.78 km when correlation coefficient is 0.99, respectively. So the corresponding improvements of transmission distance are 1.72 km and 2.36 km, respectively. For the GG distribution, the improvements of transmission distance are 1.36 km when correlation coefficient is 0.85 and 2.30 km when correlation coefficient is 0.99, respectively.

5. Conclusion

We have analytically studied a reference CW light assisted optical detection scheme to mitigate the effect of scintillation in FSO transmission. Using the correlation coefficient between the intensities of the data light and the reference CW light, we have mathematically derived the joint intensity distributions of two co-propagating optical waves under log-normal distributed channel model and Gamma-Gamma distributed channel model, respectively. Using these joint intensity distributions, we have theoretically analyzed the BER performance of FSO transmission system that is assisted with a reference CW light to mitigate the effect of scintillation under different atmospheric turbulence conditions as well as under different correlation coefficients between the intensities of the data light and the reference CW light. We have also carried out the Monte-Carlo simulation and shown that theoretical results agree with simulation results well. The effectiveness of this scheme is strongly associated with both the strength of scintillation and the correlation coefficient between the intensities of data light and reference CW light. Our studies have showed that when the correlation coefficient is 0.99, the power reductions to achieve BER of 10−3 are 12.3 dB and 20.4 dB under moderate and strong scintillations (i.e., Rytov variances of 1.0 and 4.0), respectively. The power reductions for the data signal with a wavelength in the range of 1500 nm to 1600 nm are almost identical under a certain correlation coefficient, which demonstrates the feasibility of using a single reference CW light to mitigate the scintillation effects on all the channels of a WDM-FSO transmission system. The transmission distances are improved by 1.72 km and 2.36 km under the moderate atmospheric turbulence condition when the correlation coefficients are 0.85 and 0.99, respectively.

Acknowledgments

The authors would like to thank the support of A*STAR SERC PSF 092 101 0054, and the help of Dr. Bingxing Xia in SPMS, NTU.

References and links

1. A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels,” Opt. Express 19(14), 13480–13496 (2011). [CrossRef]   [PubMed]  

2. X. Liu, “Free-space optics optimization models for building sway and atmospheric interference using variable wavelength,” IEEE Trans. Commun. 57(2), 492–498 (2009). [CrossRef]  

3. N. Letzepis, I. Holland, and W. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wirel. Comm. 7(5), 1744–1753 (2008). [CrossRef]  

4. N. Cvijetc, D. Qian, J. Yu, Y.-K. Huang, and T. Wang, “Polarization-multiplexed optical wireless transmission with coherent detection,” J. Lightwave Technol. 28(8), 1218–1227 (2010). [CrossRef]  

5. N. Letzepis and A. G. i Fabregas, “Outage probability of the Gaussian MIMO free-space optical channel with PPM,” IEEE Trans. Commun. 57(12), 3682–3690 (2009). [CrossRef]  

6. A. Jurado-Navas, A. Garcia-Zambrana, and A. Puerta-Notario, “Efficient channel model for free space optical communications,” in IEEE Mediterranean Electrotechnical Conference, 2006. MELECON 2006 (IEEE, 2006), pp. 631–634.

7. I. B. Djordjevic, B. Vasic, and M. A. Neifeld, “Multilevel coding in free-space optical MIMO transmission with Q-ary PPM over the atmospheric turbulence channel,” IEEE Photon. Technol. Lett. 18(14), 1491–1493 (2006). [CrossRef]  

8. X. Zhao, Y. Yao, Y. Sun, and C. Liu, “Circle polarization shift keying with directed detection for free-space optical communication,” J. Opt. Commun. Netw. 1(4), 307–312 (2009). [CrossRef]  

9. W. Gappmair and M. Flohberger, “Error performance of coded FSO links in turbulent atmosphere modeled by Gamma-Gamma distribution,” IEEE Trans. Wirel. Comm. 8(5), 2209–2213 (2009). [CrossRef]  

10. K. J. Grant, K. A. Corbett, B. A. Clare, J. E. Davies, B. D. Nener, and A. Boettcher-Hunt, “Dual wavelength free space optical communications,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper CTuG3.

11. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

12. T. Wang and J. W. Strohbehn, “Perturbed log-normal distribution of irradiance fluctuations,” J. Opt. Soc. Am. 64(7), 994–999 (1974). [CrossRef]  

13. H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009). [CrossRef]  

14. C. H. Kwok, R. V. Penty, and I. H. White, “Link reliability improvement for optical wireless communication systems with temporal-domain diversity reception,” IEEE Photon. Technol. Lett. 20(9), 700–702 (2008). [CrossRef]  

15. W. O. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron. 2(1), 16–23 (2008). [CrossRef]  

16. G. R. Osche, Optical Detection Theory for Laser Applications (Wiley, 2002).

17. M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulence media,” Opt. Eng. 40(8), 1554–1562 (2001). [CrossRef]  

18. T. D. Pham, A. Bekkali, K. Kazaura, K. Wakamori, and M. Matsumoto, “A universal platform for ubiquitous wireless communications using radio over FSO system,” J. Lightwave Technol. 28(16), 2258–2267 (2010). [CrossRef]  

19. A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 2002).

20. C. H. Edwards and D. E. Penny, Multivariable Calculus with Matrices (Prentice Hall, 2002).

21. J. L. Devore, Probability Statistics for Engineering and the Sciences (Brooks/Cole, 2008).

22. F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010). [CrossRef]  

23. G. P. Agrawal, Fiber-Optic Communication Systems (Wiley Inter-Science, 2002).

24. J. G. Proakis, Digital Communications (McGraw-Hill, 2008).

25. D. K. Borah and D. G. Voelz, “Pointing error effects on free-space optical communication links in the presence of atmospheric turbulence,” J. Lightwave Technol. 27(18), 3965–3973 (2009). [CrossRef]  

26. J. Li, J. Q. Liu, and D. P. Taylor, “Optical communications using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007). [CrossRef]  

27. X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002). [CrossRef]  

28. N. Cvijetic, D. Qian, and T. Wang, “10Gb/s free-space optical transmission using OFDM,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OThD2.

29. S. S. Muhammad, B. Flecker, E. Leitgeb, and M. Gebhart, “Characterization of fog attenuation in terrestrial free space optical links,” Opt. Eng. 46(6), 066001 (2007). [CrossRef]  

30. A. Abushagur, F. M. Abbou, M. Abdullah, and N. Misran, “Performance analysis of a free-space terrestrial optical system in the presence of absorption, scattering, and pointing error,” Opt. Eng. 50(7), 075007 (2011). [CrossRef]  

References

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  1. A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels,” Opt. Express 19(14), 13480–13496 (2011).
    [Crossref] [PubMed]
  2. X. Liu, “Free-space optics optimization models for building sway and atmospheric interference using variable wavelength,” IEEE Trans. Commun. 57(2), 492–498 (2009).
    [Crossref]
  3. N. Letzepis, I. Holland, and W. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wirel. Comm. 7(5), 1744–1753 (2008).
    [Crossref]
  4. N. Cvijetc, D. Qian, J. Yu, Y.-K. Huang, and T. Wang, “Polarization-multiplexed optical wireless transmission with coherent detection,” J. Lightwave Technol. 28(8), 1218–1227 (2010).
    [Crossref]
  5. N. Letzepis and A. G. i Fabregas, “Outage probability of the Gaussian MIMO free-space optical channel with PPM,” IEEE Trans. Commun. 57(12), 3682–3690 (2009).
    [Crossref]
  6. A. Jurado-Navas, A. Garcia-Zambrana, and A. Puerta-Notario, “Efficient channel model for free space optical communications,” in IEEE Mediterranean Electrotechnical Conference, 2006. MELECON 2006 (IEEE, 2006), pp. 631–634.
  7. I. B. Djordjevic, B. Vasic, and M. A. Neifeld, “Multilevel coding in free-space optical MIMO transmission with Q-ary PPM over the atmospheric turbulence channel,” IEEE Photon. Technol. Lett. 18(14), 1491–1493 (2006).
    [Crossref]
  8. X. Zhao, Y. Yao, Y. Sun, and C. Liu, “Circle polarization shift keying with directed detection for free-space optical communication,” J. Opt. Commun. Netw. 1(4), 307–312 (2009).
    [Crossref]
  9. W. Gappmair and M. Flohberger, “Error performance of coded FSO links in turbulent atmosphere modeled by Gamma-Gamma distribution,” IEEE Trans. Wirel. Comm. 8(5), 2209–2213 (2009).
    [Crossref]
  10. K. J. Grant, K. A. Corbett, B. A. Clare, J. E. Davies, B. D. Nener, and A. Boettcher-Hunt, “Dual wavelength free space optical communications,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper CTuG3.
  11. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).
  12. T. Wang and J. W. Strohbehn, “Perturbed log-normal distribution of irradiance fluctuations,” J. Opt. Soc. Am. 64(7), 994–999 (1974).
    [Crossref]
  13. H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
    [Crossref]
  14. C. H. Kwok, R. V. Penty, and I. H. White, “Link reliability improvement for optical wireless communication systems with temporal-domain diversity reception,” IEEE Photon. Technol. Lett. 20(9), 700–702 (2008).
    [Crossref]
  15. W. O. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron. 2(1), 16–23 (2008).
    [Crossref]
  16. G. R. Osche, Optical Detection Theory for Laser Applications (Wiley, 2002).
  17. M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulence media,” Opt. Eng. 40(8), 1554–1562 (2001).
    [Crossref]
  18. T. D. Pham, A. Bekkali, K. Kazaura, K. Wakamori, and M. Matsumoto, “A universal platform for ubiquitous wireless communications using radio over FSO system,” J. Lightwave Technol. 28(16), 2258–2267 (2010).
    [Crossref]
  19. A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 2002).
  20. C. H. Edwards and D. E. Penny, Multivariable Calculus with Matrices (Prentice Hall, 2002).
  21. J. L. Devore, Probability Statistics for Engineering and the Sciences (Brooks/Cole, 2008).
  22. F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
    [Crossref]
  23. G. P. Agrawal, Fiber-Optic Communication Systems (Wiley Inter-Science, 2002).
  24. J. G. Proakis, Digital Communications (McGraw-Hill, 2008).
  25. D. K. Borah and D. G. Voelz, “Pointing error effects on free-space optical communication links in the presence of atmospheric turbulence,” J. Lightwave Technol. 27(18), 3965–3973 (2009).
    [Crossref]
  26. J. Li, J. Q. Liu, and D. P. Taylor, “Optical communications using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
    [Crossref]
  27. X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
    [Crossref]
  28. N. Cvijetic, D. Qian, and T. Wang, “10Gb/s free-space optical transmission using OFDM,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OThD2.
  29. S. S. Muhammad, B. Flecker, E. Leitgeb, and M. Gebhart, “Characterization of fog attenuation in terrestrial free space optical links,” Opt. Eng. 46(6), 066001 (2007).
    [Crossref]
  30. A. Abushagur, F. M. Abbou, M. Abdullah, and N. Misran, “Performance analysis of a free-space terrestrial optical system in the presence of absorption, scattering, and pointing error,” Opt. Eng. 50(7), 075007 (2011).
    [Crossref]

2011 (2)

A. Abushagur, F. M. Abbou, M. Abdullah, and N. Misran, “Performance analysis of a free-space terrestrial optical system in the presence of absorption, scattering, and pointing error,” Opt. Eng. 50(7), 075007 (2011).
[Crossref]

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels,” Opt. Express 19(14), 13480–13496 (2011).
[Crossref] [PubMed]

2010 (3)

2009 (6)

W. Gappmair and M. Flohberger, “Error performance of coded FSO links in turbulent atmosphere modeled by Gamma-Gamma distribution,” IEEE Trans. Wirel. Comm. 8(5), 2209–2213 (2009).
[Crossref]

X. Zhao, Y. Yao, Y. Sun, and C. Liu, “Circle polarization shift keying with directed detection for free-space optical communication,” J. Opt. Commun. Netw. 1(4), 307–312 (2009).
[Crossref]

D. K. Borah and D. G. Voelz, “Pointing error effects on free-space optical communication links in the presence of atmospheric turbulence,” J. Lightwave Technol. 27(18), 3965–3973 (2009).
[Crossref]

X. Liu, “Free-space optics optimization models for building sway and atmospheric interference using variable wavelength,” IEEE Trans. Commun. 57(2), 492–498 (2009).
[Crossref]

N. Letzepis and A. G. i Fabregas, “Outage probability of the Gaussian MIMO free-space optical channel with PPM,” IEEE Trans. Commun. 57(12), 3682–3690 (2009).
[Crossref]

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
[Crossref]

2008 (3)

C. H. Kwok, R. V. Penty, and I. H. White, “Link reliability improvement for optical wireless communication systems with temporal-domain diversity reception,” IEEE Photon. Technol. Lett. 20(9), 700–702 (2008).
[Crossref]

W. O. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron. 2(1), 16–23 (2008).
[Crossref]

N. Letzepis, I. Holland, and W. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wirel. Comm. 7(5), 1744–1753 (2008).
[Crossref]

2007 (2)

S. S. Muhammad, B. Flecker, E. Leitgeb, and M. Gebhart, “Characterization of fog attenuation in terrestrial free space optical links,” Opt. Eng. 46(6), 066001 (2007).
[Crossref]

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communications using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[Crossref]

2006 (1)

I. B. Djordjevic, B. Vasic, and M. A. Neifeld, “Multilevel coding in free-space optical MIMO transmission with Q-ary PPM over the atmospheric turbulence channel,” IEEE Photon. Technol. Lett. 18(14), 1491–1493 (2006).
[Crossref]

2002 (1)

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[Crossref]

2001 (1)

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulence media,” Opt. Eng. 40(8), 1554–1562 (2001).
[Crossref]

1974 (1)

Abbou, F. M.

A. Abushagur, F. M. Abbou, M. Abdullah, and N. Misran, “Performance analysis of a free-space terrestrial optical system in the presence of absorption, scattering, and pointing error,” Opt. Eng. 50(7), 075007 (2011).
[Crossref]

Abdullah, M.

A. Abushagur, F. M. Abbou, M. Abdullah, and N. Misran, “Performance analysis of a free-space terrestrial optical system in the presence of absorption, scattering, and pointing error,” Opt. Eng. 50(7), 075007 (2011).
[Crossref]

Abushagur, A.

A. Abushagur, F. M. Abbou, M. Abdullah, and N. Misran, “Performance analysis of a free-space terrestrial optical system in the presence of absorption, scattering, and pointing error,” Opt. Eng. 50(7), 075007 (2011).
[Crossref]

Al-Habash, M. A.

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulence media,” Opt. Eng. 40(8), 1554–1562 (2001).
[Crossref]

Allen, J.

W. O. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron. 2(1), 16–23 (2008).
[Crossref]

Andrews, L. C.

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulence media,” Opt. Eng. 40(8), 1554–1562 (2001).
[Crossref]

Bekkali, A.

Borah, D. K.

Castillo-Vázquez, B.

Castillo-Vázquez, C.

Chang, F.

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[Crossref]

Cowley, W.

N. Letzepis, I. Holland, and W. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wirel. Comm. 7(5), 1744–1753 (2008).
[Crossref]

Cvijetc, N.

Djordjevic, I. B.

I. B. Djordjevic, B. Vasic, and M. A. Neifeld, “Multilevel coding in free-space optical MIMO transmission with Q-ary PPM over the atmospheric turbulence channel,” IEEE Photon. Technol. Lett. 18(14), 1491–1493 (2006).
[Crossref]

Flecker, B.

S. S. Muhammad, B. Flecker, E. Leitgeb, and M. Gebhart, “Characterization of fog attenuation in terrestrial free space optical links,” Opt. Eng. 46(6), 066001 (2007).
[Crossref]

Flohberger, M.

W. Gappmair and M. Flohberger, “Error performance of coded FSO links in turbulent atmosphere modeled by Gamma-Gamma distribution,” IEEE Trans. Wirel. Comm. 8(5), 2209–2213 (2009).
[Crossref]

Gao, S.

W. O. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron. 2(1), 16–23 (2008).
[Crossref]

Gappmair, W.

W. Gappmair and M. Flohberger, “Error performance of coded FSO links in turbulent atmosphere modeled by Gamma-Gamma distribution,” IEEE Trans. Wirel. Comm. 8(5), 2209–2213 (2009).
[Crossref]

García-Zambrana, A.

Gebhart, M.

S. S. Muhammad, B. Flecker, E. Leitgeb, and M. Gebhart, “Characterization of fog attenuation in terrestrial free space optical links,” Opt. Eng. 46(6), 066001 (2007).
[Crossref]

Ghassemlooy, Z.

W. O. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron. 2(1), 16–23 (2008).
[Crossref]

Holland, I.

N. Letzepis, I. Holland, and W. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wirel. Comm. 7(5), 1744–1753 (2008).
[Crossref]

Huang, Y.-K.

i Fabregas, A. G.

N. Letzepis and A. G. i Fabregas, “Outage probability of the Gaussian MIMO free-space optical channel with PPM,” IEEE Trans. Commun. 57(12), 3682–3690 (2009).
[Crossref]

Kahn, J. M.

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[Crossref]

Kazaura, K.

Kwok, C. H.

C. H. Kwok, R. V. Penty, and I. H. White, “Link reliability improvement for optical wireless communication systems with temporal-domain diversity reception,” IEEE Photon. Technol. Lett. 20(9), 700–702 (2008).
[Crossref]

Leitgeb, E.

W. O. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron. 2(1), 16–23 (2008).
[Crossref]

S. S. Muhammad, B. Flecker, E. Leitgeb, and M. Gebhart, “Characterization of fog attenuation in terrestrial free space optical links,” Opt. Eng. 46(6), 066001 (2007).
[Crossref]

Letzepis, N.

N. Letzepis and A. G. i Fabregas, “Outage probability of the Gaussian MIMO free-space optical channel with PPM,” IEEE Trans. Commun. 57(12), 3682–3690 (2009).
[Crossref]

N. Letzepis, I. Holland, and W. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wirel. Comm. 7(5), 1744–1753 (2008).
[Crossref]

Li, J.

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communications using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[Crossref]

Liu, C.

Liu, J. Q.

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communications using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[Crossref]

Liu, X.

X. Liu, “Free-space optics optimization models for building sway and atmospheric interference using variable wavelength,” IEEE Trans. Commun. 57(2), 492–498 (2009).
[Crossref]

Matsumoto, M.

Misran, N.

A. Abushagur, F. M. Abbou, M. Abdullah, and N. Misran, “Performance analysis of a free-space terrestrial optical system in the presence of absorption, scattering, and pointing error,” Opt. Eng. 50(7), 075007 (2011).
[Crossref]

Mizuochi, T.

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[Crossref]

Muhammad, S. S.

S. S. Muhammad, B. Flecker, E. Leitgeb, and M. Gebhart, “Characterization of fog attenuation in terrestrial free space optical links,” Opt. Eng. 46(6), 066001 (2007).
[Crossref]

Neifeld, M. A.

I. B. Djordjevic, B. Vasic, and M. A. Neifeld, “Multilevel coding in free-space optical MIMO transmission with Q-ary PPM over the atmospheric turbulence channel,” IEEE Photon. Technol. Lett. 18(14), 1491–1493 (2006).
[Crossref]

Nistazakis, H. E.

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
[Crossref]

Onohara, K.

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[Crossref]

Penty, R. V.

C. H. Kwok, R. V. Penty, and I. H. White, “Link reliability improvement for optical wireless communication systems with temporal-domain diversity reception,” IEEE Photon. Technol. Lett. 20(9), 700–702 (2008).
[Crossref]

Pham, T. D.

Phillips, R. L.

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulence media,” Opt. Eng. 40(8), 1554–1562 (2001).
[Crossref]

Popoola, W. O.

W. O. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron. 2(1), 16–23 (2008).
[Crossref]

Qian, D.

Strohbehn, J. W.

Sun, Y.

Taylor, D. P.

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communications using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[Crossref]

Tombras, G. S.

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
[Crossref]

Tsiftsis, T. A.

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
[Crossref]

Vasic, B.

I. B. Djordjevic, B. Vasic, and M. A. Neifeld, “Multilevel coding in free-space optical MIMO transmission with Q-ary PPM over the atmospheric turbulence channel,” IEEE Photon. Technol. Lett. 18(14), 1491–1493 (2006).
[Crossref]

Voelz, D. G.

Wakamori, K.

Wang, T.

White, I. H.

C. H. Kwok, R. V. Penty, and I. H. White, “Link reliability improvement for optical wireless communication systems with temporal-domain diversity reception,” IEEE Photon. Technol. Lett. 20(9), 700–702 (2008).
[Crossref]

Yao, Y.

Yu, J.

Zhao, X.

Zhu, X.

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[Crossref]

IEEE Commun. Mag. (1)

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[Crossref]

IEEE Photon. Technol. Lett. (2)

I. B. Djordjevic, B. Vasic, and M. A. Neifeld, “Multilevel coding in free-space optical MIMO transmission with Q-ary PPM over the atmospheric turbulence channel,” IEEE Photon. Technol. Lett. 18(14), 1491–1493 (2006).
[Crossref]

C. H. Kwok, R. V. Penty, and I. H. White, “Link reliability improvement for optical wireless communication systems with temporal-domain diversity reception,” IEEE Photon. Technol. Lett. 20(9), 700–702 (2008).
[Crossref]

IEEE Trans. Commun. (4)

X. Liu, “Free-space optics optimization models for building sway and atmospheric interference using variable wavelength,” IEEE Trans. Commun. 57(2), 492–498 (2009).
[Crossref]

N. Letzepis and A. G. i Fabregas, “Outage probability of the Gaussian MIMO free-space optical channel with PPM,” IEEE Trans. Commun. 57(12), 3682–3690 (2009).
[Crossref]

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communications using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[Crossref]

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[Crossref]

IEEE Trans. Wirel. Comm. (2)

N. Letzepis, I. Holland, and W. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wirel. Comm. 7(5), 1744–1753 (2008).
[Crossref]

W. Gappmair and M. Flohberger, “Error performance of coded FSO links in turbulent atmosphere modeled by Gamma-Gamma distribution,” IEEE Trans. Wirel. Comm. 8(5), 2209–2213 (2009).
[Crossref]

IET Commun. (1)

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
[Crossref]

IET Optoelectron. (1)

W. O. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron. 2(1), 16–23 (2008).
[Crossref]

J. Lightwave Technol. (3)

J. Opt. Commun. Netw. (1)

J. Opt. Soc. Am. (1)

Opt. Eng. (3)

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulence media,” Opt. Eng. 40(8), 1554–1562 (2001).
[Crossref]

S. S. Muhammad, B. Flecker, E. Leitgeb, and M. Gebhart, “Characterization of fog attenuation in terrestrial free space optical links,” Opt. Eng. 46(6), 066001 (2007).
[Crossref]

A. Abushagur, F. M. Abbou, M. Abdullah, and N. Misran, “Performance analysis of a free-space terrestrial optical system in the presence of absorption, scattering, and pointing error,” Opt. Eng. 50(7), 075007 (2011).
[Crossref]

Opt. Express (1)

Other (10)

G. R. Osche, Optical Detection Theory for Laser Applications (Wiley, 2002).

A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 2002).

C. H. Edwards and D. E. Penny, Multivariable Calculus with Matrices (Prentice Hall, 2002).

J. L. Devore, Probability Statistics for Engineering and the Sciences (Brooks/Cole, 2008).

K. J. Grant, K. A. Corbett, B. A. Clare, J. E. Davies, B. D. Nener, and A. Boettcher-Hunt, “Dual wavelength free space optical communications,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper CTuG3.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

A. Jurado-Navas, A. Garcia-Zambrana, and A. Puerta-Notario, “Efficient channel model for free space optical communications,” in IEEE Mediterranean Electrotechnical Conference, 2006. MELECON 2006 (IEEE, 2006), pp. 631–634.

N. Cvijetic, D. Qian, and T. Wang, “10Gb/s free-space optical transmission using OFDM,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OThD2.

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley Inter-Science, 2002).

J. G. Proakis, Digital Communications (McGraw-Hill, 2008).

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Figures (6)

Fig. 1
Fig. 1

Schematic of an OOK FSO communication system with a reference CW light to mitigate the scintillation effect.

Fig. 2
Fig. 2

PDFs of the normalized intensity (amplitude) of the data light (signal) under moderate atmospheric turbulence condition with Rytov variance of 1.0: (a) before and (b) after the signal processing by the division circuit.

Fig. 3
Fig. 3

BER improvement of OOK FSO system by a reference CW light under moderate atmospheric turbulence condition with Rytov variance of 1.0: (a) correlation coefficient is 0.85 and (b) correlation coefficient is 0.99.

Fig. 4
Fig. 4

PDFs and histograms of the normalized intensity (amplitude) of the data light (signal) under strong atmospheric turbulence condition with Rytov variance of 4.0: (a) before signal processing, (b) after signal processing with correlation coefficient is 0.85 and (c) after signal processing with correlation coefficient is 0.99.

Fig. 5
Fig. 5

BER improvement of OOK FSO system by a reference CW light under strong atmospheric turbulence condition with Rytov variance of 4.0: (a) correlation coefficient is 0.85 and (b) correlation coefficient is 0.99.

Fig. 6
Fig. 6

Power reductions for achieving BER of 10−3 in WDM-FSO system under moderate atmospheric turbulence condition (i.e., Rytov variance of 1.0).

Equations (33)

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f LN ( I S )= 1 2π σ R 2 I S exp{ [ ln( I S I 0 )+ 1 2 σ R 2 ] 2 / ( 2 σ R 2 ) },
σ R 2 =1.23 C n 2 k 7/6 L 11/6 ,
f GG ( I S )= 2 (αβ) α+β 2 Γ(α)Γ(β) I S α+β2 2 K αβ (2 αβ I S ),
α= { exp[ 0.49 σ R 2 / ( 1+1.11 σ R 12/5 ) 7/6 ]1 } 1 ,
β= { exp[ 0.51 σ R 2 / ( 1+0.69 σ R 12/5 ) 5/6 ]1 } 1 .
f( I P )= 0 I R f( I S , I R ) d I R = 0 I R f( I R I P , I R ) d I R ,
f x ( x )= 1 2π σ 1 exp( ( x μ 1 ) 2 2 σ 1 2 ).
f xy ( x,y )= 1 2π σ 1 σ 2 1 ρ N 2 exp( 1 2( 1 ρ N 2 ) ( ( x μ 1 ) 2 σ 1 2 2 ρ N ( x μ 1 )( y μ 2 ) σ 1 σ 2 + ( y μ 2 ) 2 σ 2 2 ) ).
ρ N = cov( x,y ) D( x )D( y ) = E( xy )E( x )E( y ) D( x )D( y ) ,
u=exp( x ),
v=exp( y ).
J 1 =| x u x v y u y v |=| 1 u 0 0 1 v |= 1 uv .
f uv ( u,v )= J 1 f xy ( x,y )= 1 uv f xy ( x,y )= 1 2π σ 1 σ 2 1 ρ N 2 uv exp( 1 2( 1 ρ N 2 ) ( ( ln( u ) μ 1 ) 2 σ 1 2 2 ρ N ( ln( u ) μ 1 )( ln( v ) μ 2 ) σ 1 σ 2 + ( ln( v ) μ 2 ) 2 σ 2 2 ) ).
ρ LN = cov( u,v ) D( u )D( v ) = E( uv )E( u )E( v ) D( u )D( v ) .
cov( u,v )=E( uv )E( u )E( v ) =exp( μ 1 + μ 2 )exp( σ 1 2 + σ 2 2 2 )( exp( ρ N σ 1 σ 2 )1 ),
D( u )=E( u 2 ) ( E( u ) ) 2 =exp( 2 μ 1 + σ 1 2 )( exp( σ 1 2 )1 ),
D( v )=E( v 2 ) ( E( v ) ) 2 =exp( 2 μ 2 + σ 2 2 )( exp( σ 2 2 )1 ).
ρ N = ln( ρ LN ( exp( σ 1 2 )1 )( exp( σ 2 2 )1 ) +1 ) σ 1 σ 2 .
J 2 =| u w u z v w v z |=| u w 0 0 v z |= du dw dv dz .
f wz ( w,z )= J 2 f uv ( u,v )= du dw dv dz f uv ( u,v ).
J 3 = du dw = f GG (w) f LN (u) ,
J 4 = dv dz = f GG (z) f LN (v) .
u= h w ( w ).
v= h z ( z ).
f wz ( w,z )= f GG (w) f GG (z) f LN (u) f LN (v) f uv ( u,v ) = f GG (w) f GG (z) f LN [ h w ( w ) ] f LN [ h z ( z ) ] f uv [ h w ( w ), h z ( z ) ].
ρ GG = cov( w,z ) D( w )D( z ) = n( wz )( w )( z ) [ n( w 2 ) ( w ) 2 ][ n( z 2 ) ( z ) 2 ] ,
P e =P( 0 )P( error|0 )+P( 1 )P( error|1 ),
P( error|0 )= I th 1 2π σ n 2 exp( r 2 2 σ n 2 )dr =Q( I th σ n ),
P( error|1 )= I th 1 2π σ n 2 exp( ( rI ) 2 2 σ n 2 )f( I )drdI = Q( I I th σ n )f( I )dI ,
Λ= 1 2π σ n 2 exp( ( I th I ) 2 2 σ n 2 )f( I )dI / ( 1 2π σ n 2 exp( I th 2 2 σ n 2 ) ) = exp( ( I th I ) 2 + α 2 2 σ n 2 )f( I )dI =1.
P e = 1 2 ( Q( I th σ n )+ Q( I I th σ n )f( I )dI ).
σ R_R 2 = σ R_S 2 ( λ S / λ R ) 7/6 .
P R ( L )= P T ( 0 )exp( AL ),

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