Performance of sub-carrier modulated Free-Space Optical ...

342 Int. J. Autonomous and Adaptive Communications Systems, Vol. 1, No. 3, 2008 

Performance of sub-carrier modulated Free-Space 

Optical communication link in negative exponential 

atmospheric turbulence environment 

W.O. Popoola and Z. Ghassemlooy* 

Optical Communications Research Group, NCR Lab, 

Northumbria University, 

Newcastle upon Tyne NE1 8ST, UK 

E-mail: wasiu.popoola@unn.ac.uk 

E-mail: fary.ghassemlooy@unn.ac.uk 

*Corresponding author 

V. Ahmadi 

Department of Electrical Engineering, 

Tarbiat Modares University, 

PO Box 14115 143, 

1463919111 Tehran, Iran. 

E-mail: v_ahmadi@modares.ac.ir 

Abstract: Free-Space Optical (FSO) communication is reputed for its ability to 

proffer solution to the access network bottle-neck but when used over long 

range communication links, it suffers from scintillation caused by the 

atmospheric turbulence. The scintillation is modelled using the negative 

exponential distribution. Hereby, we present the outage probability and the bit 

error probability equations of digital sub-carrier intensity modulated FSO 

system in atmospheric turbulence. 

Keywords: Free-Space Optical communication; FSO communication; outage 

probability; Phase Shift Keying; PSK; spatial diversity; sub-carrier modulation; 

turbulence. 

Reference to this paper should be made as follows: Popoola, W.O., 

Ghassemlooy, Z. and Ahmadi, V. (2008) ‘Performance of sub-carrier 

modulated Free-Space Optical communication link in negative exponential 

atmospheric turbulence environment’, Int. J. Autonomous and Adaptive 

Communications Systems, Vol. 1, No. 3, pp.342–355. 

Biographical notes: W.O. Popoola had his ND in Electrical Engineering from 

The Federal Polytechnic, Ilaro, Nigeria and later graduated with First Class 

(BSc honours) in Electronic and Electrical Engineering from the Obafemi 

Awolowo University, Ile-Ife, Nigeria. In 2006, he finished his MSc in 

Optoelectronic and Communication Systems with Distinction from the 

Northumbria University at Newcastle upon. Currently, Popoola is working on 

his PhD at the same University. His research interests include: optical 

communications, digital communication and signal processing. His research is 

partly sponsored by the British government under the ORSAS award; he also 

holds a research studentship from the Northumbria University. 

Copyright © 2008 Inderscience Enterprises Ltd.

Performance of sub-carrier modulated FSO communication link 343 

Z. Ghassemlooy received his BSc in Electrical and Electronics Engineering 

from the Manchester Metropolitan University in 1981; an MSc and a PhD from 

the University of Manchester Institute of Science and Technology in 1984 and 

1987, respectively. From 1987 to 1988, he worked as a Post-Doctoral Research 

Fellow on optical sensors at the City University, London. He joined the 

Sheffield Hallam University as a Lecturer in 1988 and became a Professor in 

1997. In 2004, he moved to the Northumbria University as an Associate Dean 

for research in the School of Computing, Engineering and Information 

Sciences. His research interests include: photonics networks, modulation 

techniques, high-speed optical systems, optical wireless communications and 

optical fibre sensors. He is a Chartered Engineer, a Fellow of IET and a Senior 

Member of IEEE. 

V. Ahmadi received his BSc in Electrical Engineering from the Sharif 

University of Technology, Tehran, Iran in 1985, and his MSc from the Tarbiat 

Modares University, Tehran, Iran in 1989, and his PhD from the Kyoto 

University, Kyoto, Japan in 1994 in Electronic Engineering–Optoelectronics. 

He joined the Tarbiat Modares University as an Assistant Professor in 1994 and 

became a Professor in 2006. He was the Head of the Semiconductor 

Department of Laser Research Centre, Tehran, Iran from 1994 to 2006. He 

became the Research Vice President of the Iran National Scientific Research 

Centre (1996–1997). His research interests include: quantum photonics devices, 

optical modulator and amplifiers, high-speed optical sources and detectors, 

optical microresonator active and passive devices, optical wireless 

communications and all optical switches. 

1 Introduction 

FSO communication systems as an alternative means of providing high bandwidth over a 

short to medium range links has seen a growing increase in research and development 

activities over the past few years. Increasing commercial deployment of the FSO could be 

said to be partly responsible for this surge in research activities (Willebrand and Ghuman, 

2002; Wilson et al., 2005). FSO is used in a number of applications including the cellular 

communication backhaul, optical fibre communications back-up links, exhibition halls 

and disaster recovery among other emerging applications (Willebrand and Ghuman, 

2002; Uysal, Li and Yu, 2006). However, of major concern in FSO systems is the 

dependence of its channel – the atmosphere – on the unpredictable weather conditions. 

Effects of fog, rain, atmospheric gases and aerosols result in beam attenuation due to 

photon absorption and scattering (Gagliardi and Karp, 1995). 

In dense fog conditions, laser radiations suffer prohibitive amount of attenuation 

limiting the FSO range to < 500 m in such conditions (Isaac, Kim and Korevaar, 2001). 

However, in clear atmosphere with low extinction coefficients, a longer range is easily 

achievable. In clear weather conditions, a primary factor that impairs the performance of 

a FSO link is the random changes in atmospheric temperature. The temperature 

fluctuations depend on the speed of wind and the height above the ground of the 

traversing laser radiation (Osche, 2002).The resulting eddies/cells of varying sizes (from 

~0.1 to ~10 m) act like refractive prisms of varying index of refraction (Killinger, 2002). 

Consequently, a laser radiation traversing a turbulence atmosphere experiences random 

variation (fading) in its irradiance and phase. A familiar effect of turbulence is the

344 W.O. Popoola Z. Ghassemlooy and V. Ahmadi 

twinkling of stars caused by random fluctuations of stars’ irradiance. The shimmer of the 

horizon on a hot day is another effect, this time caused by random changes in the optical 

phase of the light beam resulting in the reduced image resolution (Killinger, 2002). 

Techniques reported in literature to mitigate fading effect include forward error control 

(Simon and Vilnrotter, 2005; Uysal, Li and Yu, 2006) spatial and temporal diversity (Zhu 

and Kahn, 2002; Lee and Chan, 2004; Navidpour, Uysal and Jing, 2004) aperture 

averaging and adaptive optics (Elon Grave and Drenker, 2002; Kedar and Arnon, 2004; 

Razavi and Shapiro, 2005). 

The most reported modulation technique used for FSO is the On–Off Keying (OOK), 

but recently sub-carrier modulation has been attracting increased interest. The idea of 

sub-carrier modulation is borrowed from the widely used multiple carrier radio 

communication (e.g. OFDM systems). In optical fibre communication networks, this subcarrier 

modulation techniques has been commercially adopted in transmitting cable 

television signals and has also been used in conjunction with wavelength division 

multiplexing (Agrawal, 2002). For the seamless integration of FSO systems into today 

and future networks, which already comprise of sub-carrier modulated (or multiple 

carrier) signals, the study of sub-carrier modulated FSO is thus imperative. Other reasons 

for carrying out research in Sub-carrier Intensity Modulated (SIM) FSO systems include: 

1 It leverages on the already developed and evolved Radio Frequency (RF) 

communication components such as stable oscillators and narrow filters (Rongqing 

et al., 2002). 

2 It avoids the need for adaptive threshold required by optimum performing OOK 

modulated FSO (Popoola, Ghassemlooy and Leitgeb, 2007b). 

3 Can be used to increase capacity by accommodating data from different users on 

different sub-carriers. 

The performance of SIM in certain atmospheric turbulence conditions have been reported 

in the literature. For example, Huang et al. (1993) and Popoola, Ghassemlooy and 

Leitgeb (2007a) reported SIM in log normal modelled weak atmospheric turbulence. 

Others include the performance of SIM in weak to strong turbulence (Popoola, 

Ghassemlooy and Leitgeb, 2007b) employing the gamma–gamma turbulence model 

proposed by Andrews, Phillips and Hopen (2001). The negative exponential turbulence 

model is widely accepted and experimentally verified to be suitable in the limit of strong 

turbulence, (i.e. during saturation regime and beyond). The performance of the OOK and 

pulse position modulated FSO links have both been investigated in the limit of strong 

turbulence using the negative exponential model (Wilson et al., 2005; Garcia-Zambrana, 

2007) but not the SIM. Therefore, we present in this article SIM FSO with the spatial 

diversity in negative exponential turbulence. The spatial diversity scheme is 

advantageous in combating temporary link blockage by birds and misalignment when 

combined with a wide laser beamwidth, thereby eliminating the need for active tracking. 

It is also much easier to provide independent aperture averaging with the multiple 

separate aperture system, than in a single aperture where the aperture size has to be far 

greater than the irradiance spatial coherence distance (Lee and Chan, 2004). The article is 

arranged as follows: FSO system is briefly described in Section 2, sub-carrier modulation 

in Section 3 while performance metrics and conclusion are given in Sections 4 and 5, 

respectively.


2 FSO system description 

FSO like most communication systems has the following three functional elements. 

2.1 The transmitter 

This functional element has the primary function of converting the source information 

into optical radiation which is then propagated through the atmosphere to the receiver. 

The essential components of the transmitter are: the modulator in this case Phase Shift 

Keying (PSK) modulator; the driver circuit for the optical source, which also helps 

stabilise the optical radiation against temperature fluctuations and component ageing; the 

optical source with direct intensity modulation, where the radiation intensity/irradiance is 

proportional to the modulating signal (Gagliardi and Karp, 1995) the transmitter 

telescope which collects, collimates and directs the optical radiation towards the receiver 

telescope via the atmospheric channel. 

2.2 Atmospheric channel 

The optical radiation traversing the atmosphere suffers mainly from absorption, scattering 

and atmospheric turbulence. These effects are caused by the constituents of the 

atmosphere (aerosols, gases, smoke, etc.) and the weather effects (fog, haze, temperature 

fluctuations, etc.). The atmospheric channel might be the terrestrial distance traversed by 

the optical radiation as is the case in this work or the distance between a ground station 

and a satellite. The most deleterious of all is the thick fog. This can cause attenuation 

>200 dB km –1 (Bloom et al., 2003) thereby placing a fundamental limit on the achievable 

link range (1 km, the atmospheric 

turbulence becomes the prevailing source of FSO performance degradation and is the 

effect considered in this work. 

Solar radiation absorbed by the earth surface causes air around the earth surface to be 

warmer than those above them. This sheet of warmer air becomes less dense and rises to 

mix turbulently with the surrounding cooler air causing the air temperature to fluctuate 

randomly (Pratt, 1969). These temperature fluctuations are a function of altitude, 

atmospheric pressure and wind speed (Zhu and Kahn, 2002). This inhomogeneities 

caused by turbulence can be viewed as discrete cells of different temperature acting like 

refractive prisms of different indices of refraction. Then, they refract/scatter (depending 

on the relative size of the optical radiation) an optical radiation traversing the medium 

resulting in random irradiance and phase variations. Detailed study of atmospheric 

turbulence can be found in (Pratt, 1969; Goodman, 1985; Andrews, Phillips and Hopen, 

2001; Osche, 2002; Zhu and Kahn, 2002). In this work, the negative exponential model is 

considered with irradiation Probability Density Function (PDF) given by (1). 

2.2.1 Negative exponential model 

In the limit of strong irradiance fluctuations, (i.e. in the saturation regime and beyond) 

where link length spans several kilometres, the number of independent scatterings 

becomes large (Karp et al., 1988). The amplitude fluctuation of the field traversing the


turbulent medium in this situation is generally believed and experimentally verified to 

obey the Rayleigh distribution implying negative exponential statistics for the irradiance 

(Karp et al., 1988). That is: 

1 I 

 

pI ( ) exp , I0 

I I 

o 

o (1) 

where I o = E[I] is the mean irradiance. An important parameter for describing the strength 

of turbulence is the log intensity variance 

2 1 

. The Scintillation Index (S.I.) given by 

2 2 

SI .. { EI [ ]/( EI [])} 1 is another important parameter for describing turbulence 

strength. In fact, it is the log intensity variance normalised by the square of the mean 

irradiance. S.I. is sometimes referred to as ‘amount of turbulence induced fading’. For the 

turbulence model under consideration S.I.1. It should be noted that other turbulence 

models such as the log-normal-Rician distribution and the I–K which are both valid from 

weak to strong turbulence regime; the K-model – valid only for the strong regime and the 

gamma–gamma turbulence models which is reported to cover all regimes from weak to 

the saturation all reduce to the negative exponential in the limit of strong turbulence 

(Karp et al., 1988). 

2.3 Receiver 

This encompasses: 

1 The receiver telescope which essentially collects and focuses the incoming optical 

radiation on to the photodetector. (A large receiver telescope aperture is 

advantageous as it collects verse uncorrelated radiations and focuses their average on 

the photodetector. This is referred to as aperture averaging but a wide aperture also 

means more background radiation (noise)). 

2 An optical band-pass filter to reduce the background radiations. 

3 A photodetector. 

4 An amplifier. 

5 A decision circuit. 

Since, the atmospheric effects that significantly degrade FSO performance are known to 

be wavelength independent (Isaac, Kim and Korevaar, 2001). Therefore, FSO uses the 

same wavelength as optical fibre communications to leverage on the availability and 

maturity of devices at such wavelengths (785, 850 and 1,550 nm). In Manor and Arnon 

(2003), it is reported that improved availability can be achieved at 10 µm wavelength but 

at the very high cost of devices.


Figure 1 

FSO employing BPSK modulated SIM block diagram (a) transmitter and (b) receiver 

TIP-Trans-Impedance Amplifier; TT-Transmit Telescope and RT-Receive Telescope. 

3 Sub-carrier modulation 

In optical SIM, an RF signal (sub-carrier) pre-modulated with the source data is used to 

modulate the intensity of an optical carrier. SIM is considered because it does not need 

adaptive threshold to perform optimally (Popoola, Ghassemlooy and Leitgeb, 2007b), it 

is resilient to the irradiance fluctuation and can be easily demodulated coherently by 

using well evolved low phase noise RF oscillator (Rongqing et al., 2002). Figure 1 shows 

the block diagram of SIM FSO system. Prior to modulating the laser irradiance, the subcarrier 

signal is pre-modulated with the source data d(t) using PSK. The sub-carrier signal 

m(t) is DC-level shifted to ensure that the bias current is always equal to or greater than 

the threshold current. Direct detection is employed at the receiver and the instantaneous 

photocurrent of the PIN photodetector is modelled as: 

i r () t RI (1 

m ()) t n () t 

(2) 

where I = I peak /2, Ipeak is the peak received irradiance, is the modulation index and R is 

the photodetector responsivity. Over a symbol duration, the sub-carrier signal is given by


m(t) = Ag(t) cos( c t + ), where g(t) represents the rectangular pulse shaping function, c 

and A are the sub-carrier signal frequency and amplitude, respectively, and n(t)~N(0, 2 ) is 

the additive white Gaussian noise. is chosen to keep the optical transmitter within its 

dynamic range; in order to avoid clipping/over-modulation the condition m(t) 1 must 

be met at all times. An estimate of the absolute phase of the RF sub-carrier signal is then 

extracted from the photocurrent for subsequent coherent demodulation in order to recover 

the source data estimate dt ˆ( ). In some cases, the phase extraction might be very 

demanding; in such situations Differential PSK (DPSK) should be adopted. It is also 

possible to increase the system capacity by modulating different source data onto 

different RF sub-carrier frequencies. The composite RF signal can then be used to 

modulate the irradiance of the optical source resulting in multiple SIM. Though, 

increased capacity is achieved but at a cost of increased transmitted optical power and 

inter-modulation distortion. The analysis and performance of multiple SIM is outside the 

scope of this article. 

4 Performance metric 

Performance metrics are used to characterise, model and predict the behaviour of a 

system. In atmospheric turbulence, the popular performance metrics for FSO are: the 

outage probability which is a measure of the probability that the instantaneous Bit Error 

Rate (BER) is greater that a pre-determined threshold level, and the generic BER metric 

which models the fraction of bits received incorrectly in a digital communication system. 

In the following sections, we present and discuss the BER of BPSK modulated SIM FSO 

with and without spatial diversity. 

4.1 Bit error rate 

For an M-PSK modulated SIM optical communication link with atmospheric turbulence, 

where the Channel State Information (CSI) is unknown by the receiver, the BER is 

obtained by averaging the BER of the M-ary PSK modulated RF sub-carrier signal over 

the atmospheric turbulence statistics. For a Binary PSK (BPSK) modulated sub-carrier, 

this unconditional BER is given by: 

P Q( ) p( I)dI I 0 

e 

 

 

0 

(3) 

where p(I) is the PDF of the received irradiance given by (1) for a negative exponential 

2 2 

distributed turbulence, Qx ( ) 0.5erfc( x/ 2) and =(RAI) /2 is the electrical Signalto-Noise 

Ratio (SNRe) per bit at the input of the coherent demodulator. For DPSK based 

SIM, the BER expression is as given in (Popoola, Ghassemlooy and Leitgeb, 2007a). By 

substituting (1) into (3) and changing the order of integration, we easily obtain the 

following expression for the BER: 

/2 

2 

1 I I 

Pe 

exp 

dI 

d 

I 

 

 

4 K( ) 

I 

(4) 

 

 

0 0


where K() = 2 sin 2 /R 2 A 2 . 

Invoking the relation (3.322.2) given in Gradshteyn and Ryzhik (1994) and assuming 

that E[I] = I o = 1, the unconditional BER reduces to: 

/2 

1 

Pe 

K( )exp( K( ))erfc K( ))d . 

 

(5) 

0 

This expression above has no closed form and can thus be evaluated using numerical 

integration. However, an upper bound can be obtained for it by making = /2, this 

maximises the integrand resulting in the expression below: 

Pe K exp( K) Q( 2 K) 

(6) 

where K = 2 / R 2 A 2 . 

4.1.1 Equal gain combining spatial diversity 

In order to mitigate scintillation effect and temporary blocking caused by birds we 

consider the use of receiver array. The use of photodetector array also makes it easier to 

achieve aperture averaging compared to using a single photodetector of the same area as 

the combined array of photodetectors. The output of each photodetector in the array is 

scaled by a unity weighting factor, (i.e. in Figure 2). The outputs are co-phased and then 

combined; this approach is referred to as the Equal Gain Combining (EGC) in the 

literature. 

Figure 2 

Spatial diversity receiver with N-photodetectors 

The spatial diversity is premised on the spacing of the photodetectors being greater than 

the optical radiation transverse coherence distance. This is to guarantee uncorrelated 

received irradiance so that the N-photodetectors do not all experience deep irradiance 

fades at the same time. To facilitate a fair comparison between single-transmitter–single-


receiver-system and spatial diversity system, each pupil area in the N-photodetector 

system is assumed to be A D /N, where A D is the detector area under single transmitter– 

single receiver link. Therefore, it follows that the background radiation noise ni 

i 

1 

on 

each link with detector diversity is also reduced by a factor N from that with no spatial 

diversity resulting in n N 

2 

i N (0, / ) 

i 1 

i N . By assuming identical PIN diode detectors on 

 

each link, the combiner output photocurrent with suppressed DC component is given by: 

 

N R 

 

iT 

I (1 Ag()cos( 

1 

i t ct )) n() 

t 

i 

 

N 

 

 

 

where = [0, ]. The SNRe at the output of the EGC combiner conditioned on the 

received signal intensity can be derived as: 

RA 

2 N 

2 

I 

2 

i 1 

i 

N 

 

 

EGC 

2 

. 

 

N 

 

 

Assuming Z I 

i1 

i 

where the negative exponential distributed random variable I i is 

the irradiance received by the ith photodetector. For independent and identically 

distributed irradiance, the PDF of Z given by (9) and plotted in Figure 3 is quite straight 

forward; it is obtained by taking the inverse Fourier transform of the N-fold product of 

the characteristic function of I, with I o normalised to unity. 

N 

Z 

1 exp( Z) 

pZ ( ) 

, Z0. 

( N) 

Without CSI, the unconditional BER is thus given by: 

N 

(7) 

(8) 

(9) 

P Q( ) p( Z)dZ 

e 

 

 

0 

EGC 

/2 

1 

N 1 2 

Z exp( K1( ) Z Z)dZd 

( N) 

 

0 0 

(10) 

where K() = R 2 A 2 / 4 2 N 2 sin 2 (). The expression has no known closed form. 

Employing equation (3.462) in (Gradshteyn and Ryzhik, 1994) and the approached used 

in Section 4.1, an upper bound is obtained as: 

N 

/2 

(2 K1) 

e 1 

P exp(1/ 8 K ) D 

N (1/ 2 K) 

(11) 

2 

where D n is the parabolic cylinder function (Gradshteyn and Ryzhik, 1994). 

4.2 Outage probability, P o 

The outage probability is another metric for characterising the performance of digital 

communication systems in fading channels. This metric measures the probability that the


BER of the systems is greater than a pre-defined threshold value. This is akin to 

evaluating the probability that the instantaneous SNR e is lower than a threshold * . SNR e 

Unlike the average BER which does not necessarily reflect the effect of fading at every 

instant, the outage probability reflects this as it compares the instantaneous SNR e with a 

threshold value. It should be stressed that the irradiance fading experienced in FSO is 

turbulence induced unlike the multipath induced fading that characterises RF wireless 

communication. 

* 

e e 

P p(BER>BER*) p(SNR SNR ). 

(12) 

Figure 3 

The PDF of sum of negative exponential varying irradiance 

* 

Assume SNR e 

to be the SNR e in the absence of irradiance fluctuation and by introducing 

a variable m as the additional power needed to achieve outage probability P o , the 

following expression is obtained: 

Io 

/ m 

 

 

0 

P pI ( I / m) pI ( )d I. 

From (5) and (13), the power margin m can thus be obtained as: 

(13) 

1 

[ 1n(1 )] . 

(14) 

m P 

With EGC spatial diversity, the outage probability P o = p ( EGC < *), is obtained by 

introducing a parameter m EGC defined as the amount of additional irradiance needed on 

each branch of the N-photodetector array to achieve an outage probability P o ; this results 

in the following: 

 

 

mEGC 

N 

P p 

I 

1 

i I p( Z IN / mEGC 

). 

N 

 

i 

 

 

 

(15)


This expression denotes the cumulative distribution function of Z at the specified point; 

combining with (9), the outage probability is derived as: 

o 

N/ 

mEGC 

 

P p( Z)dZ 

0 

N/ 

mEGC 

 

N 1 

Z exp( Z) / ( N)d Z. 

0 

(16) 

Equation (16) can be expressed as in implicit function in terms of the incomplete gamma 

function (a, x) (Gradshteyn and Ryzhik, 1994) or as a series, that is: 

P 

( N, N / mEGC 

)/ ( N) 

k Nk 

1 ( 1) ( N / mEGC 

) 

( N) k 0 

k!( N k) 

(17) 

a1 

where ( ax , )= exp( tt ) d t. 

x 

 

0 

4.3 Results and discussion 

A plot of the exact BER obtained via numerical integration of (5) and the upper bound 

given by (6) against the normalised SNR = (E[I]R) 2 / 2 for a number photodetectors used 

are presented in Figure 4. The upper bound is not very tight as seen from the figure. It 

lags behind the exact BER curve by about 4 dB mainly due to the approximation carried 

out in arriving at the upper bound expression. From the figure, it is evident that an 

unmitigated scintillation results in SNR > 55 dB to attain an unconditional BER that is 

less than 10 –3 . The figure also reveals that the gain improvement in the SNR when using 

more than one photodetector particularly at low values of BER. 

Figure 4 

BER against the SNR of BPSK SIM FSO in negative exponential atmospheric 

turbulence


Figure 5 

The outage probability against the power margin, m (dBm) for 1, 2 and 4 photodetectors 

using EGC diversity 

Figure 6 Diversity gain against number of independent photodetectors at BER and P o of 10 –6 

Figure 5 shows the extra power margin required to achieve a certain outage probability P o 

with and without spatial diversity. The gain of employing diversity is quite apparent from 

the figure just as in the case under the BER performance metric. For instance at P o of 

10 6 , a diversity gain of nearly 30 dB is predicted and this increases to about 43 dB with 

four photodetectors. This significant gain is down to the fact that with multiple 

photodetectors, more independent irradiances are received. In the case of a single 

photodetector with an aperture size same as that of N-photodetectors combined, the 

increased noise level from background sources tends to cancel out any potential gain 

from aperture averaging that large aperture area proffers. 

To further elucidate the gain of employing spatial diversity for FSO in atmospheric 

turbulence, we show in Figure 6 the predicted diversity gain (ratio of SNR or m with one


photodetector to that of N-photodetectors at the specified BER or P o ) as a function of the 

number of photodetector N. As the number of photodetectors increases, the diversity gain 

plateaus. 

It should be noted that both P o and BER are different by definition; but they both 

resulted in the similar inferences as seen in Figure 6. However, it should be motioned that 

using an array of photodetectors adds to the cost and design complexity. 

5 Conclusions 

In this article, we presented the performance of SIM FSO in negative exponential 

atmospheric turbulence. The outage probability and BER expressions have been 

presented as well as an expression for the BER upper bound. We equally derived 

expressions for the stated metrics with photodetector array as way of ameliorating 

scintillation effect. The gain in power from the adoption of photodetector array has also 

been presented. A diversity gain of ~50 dB is predicted at BER of 10 –6 with just two 

independent PIN photodetectors in fully developed speckle. And as more photodetectors 

are added, the diversity gain value tends toward an asymptotic value. Although, P o and 

BER are different metrics by definition but they resulted in similar inferences. 

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