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Citation: Popoola, Wasiu Oyewole, Ghassemlooy, Zabih, Allen, Joe, Leitgeb, Erich and
Gao, Steven (2008) Free-space optical communication employing subcarrier modulation
and spatial diversity in atmospheric turbulence channel. IET Optoelectronics, 2 (1). pp.
16-23. ISSN 1751-8768
Published by: IET
URL: http://dx.doi.org/10.1049/iet-opt:20070030 <http://dx.doi.org/10.1049/iet-
opt:20070030>
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Free-space optical communication employing
subcarrier modulation and spatial diversity in
atmospheric turbulence channel
W.O. Popoola, Z. Ghassemlooy, J.I.H. Allen, E. Leitgeb and S. Gao
Abstract: An expression for the bit error rate of a multiple subcarrier intensity-modulated
atmospheric optical communication system employing spatial diversity is derived. Spatial diversity
is used to mitigate scintillation caused by atmospheric turbulence, which is assumed to obey log-
normal distribution. Optimal but complex maximum ratio, equal gain combining (EGC) and rela-
tively simple selection combining spatial diversity techniques in a clear atmosphere are considered.
Each subcarrier is modulated using binary phase shift keying. Laser irradiance is subsequently
modulated by a subcarrier signal, and a direct detection PIN receiver is employed (i.e. intensity
modulation/direction detection). At a subcarrier level, coherent demodulation is used to extract
the transmitted data/information. The performance of on–off-keying is also presented and com-
pared with the subcarrier intensity modulation under the same atmospheric conditions.
1 Introduction
Free-space optical (FSO) communications have been the
focus of growing research activities as an alternative – or
even the ultimate solution – to the access network bottle-
neck. The increasing research in FSO is spurred by its suc-
cessful commercial deployments [1]. The capacity of FSO
is comparable with that of an optical fibre-based system
but at relatively low cost; it requires less time to deploy,
is re-deployable (no sunk cost) and is more environmentally
friendly as it requires no digging of trenches or cutting of
roads and rights of way [2, 3]. FSO finds application in a
number of areas such as the cellular communication back
haul, optical fibre communication (in the form of redundant
links), exhibition halls and disaster recovery among other
emerging applications [4, 5]. Of primary concern in FSO,
however, is the dependence of the channel on weather
which, unfortunately, is not of fixed characteristics, unlike
optical fibre-based systems [2, 6]. Effects of fog, rain,
atmospheric gases and aerosols result in beam attenuation
because of photon absorption (extinguishing of photons)
and scattering (change in the direction of photons) [7, 8].
Strong wind and building sway also result in performance
degradation and the background radiations from both
natural and artificial sources add to the system noise level
[9]. There is also a safety requirement that limits the allow-
able laser power transmitted.
Furthermore, shape, direction and electromagnetic prop-
erties of a laser beam are affected by atmospheric turbu-
lence [7]. Turbulence is due to random changes in the
refractive index of the atmosphere, an effect that results
from a combination of randomly varying temperature,
wind speed and pressure. In a clear atmosphere, attenuation
coefficient is considered to be low and turbulence becomes
the main source of impairment in long-range (over 1 km)
FSO links [10]. The turbulence-induced fading (scintil-
lation) in the clear atmosphere can be circumvented
through aperture averaging, robust error control coding
and diversity techniques. For aperture averaging, the recei-
ver aperture needs to be far greater than the spatial coher-
ence distance
r
o
of the atmospheric turbulence. This
condition is not always achievable in FSO as the spatial
coherence distance is of the order of centimetres [10]. For
coding to be effective in FSO, it needs to be robust to
detect/correct burst errors as well as random errors. This
is mainly due to the temporal coherence time
t
0
of atmos-
pheric turbulence, which is much greater than the symbol
duration T. In this work receiver (spatial) diversity is con-
sidered as a means of circumventing scintillation. In
addition, binary phase shift keying (BPSK)-based subcarrier
intensity modulation (SIM) is employed to avoid the need
for adaptive threshold required by optimum on–off–
keying (OOK). Moreover, SIM has the capability to
increase the system capacity by modulating multiple
digital and/or analogue information sources onto different
electrical subcarriers, which are then used to modulate the
intensity of a continuous wave laser that serves as the
optical carrier. This, however, comes at the price of
increased signal-to-noise ratio (SNR) at a given level of
bit error rate (BER) performance. Hence, multiple SIM
can only be used when increased capacity is of paramount
importance over power requirement. This technique (also
termed multiple carriers in ratio frequency (RF)) has been
successful in RF communications, has been deployed in
many applications such as digital TV, local area networks
(LANs), asymmetric digital subscriber line (ADSL) and
4G communications and has already found its way into
the optical fibre communication systems [11, 12].
At the receiver end, direct detection using PIN photode-
tectors is adopted and the laser beam intensity fluctuation
in weak turbulence is modelled as a log-normal distribution.
# The Institution of Engineering and Technology 2008
doi:10.1049/iet-opt:20070030
Paper first received 10th April and in revised form 10th July 2007
W.O. Popoola, Z. Ghassemlooy, J.I.H. Allen and S. Gao are with Northumbria
Communication Research Lab (NCRLab), Northumbria University, Newcastle
upon Tyne, UK
E. Leitgeb is with Institute of Broadband Communications, Graz, TU, Austria
E-mail: wasiu.popoola@unn.ac.uk
IET Optoelectron., 2008, 2, (1), pp. 16– 23
16
The channel noise (shot, background radiation and thermal)
is modelled as an additive white Gaussian noise with the
background radiation being the dominant source [13]. The
link is assumed to be basically a line-of-sight with no multi-
path; hence inter-symbol interference (ISI) is not con-
sidered. The rest of the paper is arranged as follows:
a weak turbulence model is discussed in Section 2, OOK
is discussed in Section 3 for completeness and a comparison
with subcarrier modulation discussed in Section 4. Finally,
the spatial diversity and conclusions are presented in
Sections 5 and 6, respectively.
2 Log-normal turbulence model
Atmospheric turbulence results from random fluctuation of
the atmospheric refractive index n along the path of a wave
traversing the atmosphere. This refractive index fluctuation
is the direct product of random variations in atmospheric
temperature from point to point [7]. The random tempera-
ture changes are a function of altitude and wind speed.
The interaction between the laser beam and the turbulent
medium results in random amplitude and phase variations
(fading) of the information-bearing laser beam – an effect
referred to as scintillation [7]. This scintillation causes
impairment and performance degradation for long-range
(’1 km and above) atmospheric optical communication
link length [10]. The relationship between the temperature
of the atmosphere and its refractive index variation is
given by
n ¼ 1 þ 77:6(1 þ 7:52 10
3
l
2
)
P
T
10
6
(1)
where P is the atmospheric pressure in millibars, T the
temperature in kelvin and
l
the wavelength in micro
metres [14].
Turbulence is usually modelled based on a ‘frozen-in’
premise [14]. This premise assumes that turbulent eddies
are fixed and vary only with the wind speed in some way.
It goes on to imply that the temporal variation in statistical
properties of the turbulent atmosphere is caused by the
airmass movement [14]. The smallest eddy size l
0
is
called the turbulence inner scale, with a value of a few
millimetres, whereas the largest eddy size L
0
, termed
outer scale of turbulence, has its value running to several
metres [10].
The effect of turbulence of concern is the intensity fluctu-
ation of laser light traversing the atmosphere-scintillation.
The strength of wave amplitude fluctuation in a turbulent
medium is given by the variance of log amplitude X (also
called the Roytov parameter
s
X
2
) and the transverse coher-
ence length of turbulence
r
o
, which are given by (2) and (3),
respectively [14]
s
2
X
¼ 0:307C
2
n
K
7=6
L
11=6
(2)
r
0
’
ffiffiffiffiffiffi
l
L
p
(3)
These equations are valid for l
0
ffiffiffiffiffiffi
l
L
p
L
0
, where L is
the FSO link range, C
n
2
the refractive index structure con-
stant (which characterises the strength of refractive index
variation in the medium) and K ¼ 2
p
/
l
the wave number.
Considering that single scattering characterised weak tur-
bulence and assuming that the log intensity l of laser light
traversing the turbulent atmosphere to be normally distribu-
ted (i.e. l N(2
s
l
2
/2,
s
l
2
), the probability density function
(pdf) of light intensity I ¼ I
0
exp (l) is given by [14]
p
I
(I) ¼
1
ffiffiffiffiffiffi
2
p
p
s
l
1
I
exp
(ln(I=I
0
) þ
s
2
l
=2)
2
2
s
2
l
I 0
(4)
where I
0
is the received intensity without turbulence. Note
that in (4),
s
l
2
¼ 4
s
x
2
and we have assumed that
E[I] ¼ I
0
to obtain E[l] ¼ 2
s
l
2
/2 [15].
The normalised variance of the intensity
s
N
2
is derived as
follows
s
2
N
¼
E[I
2
] (E[I])
2
I
2
0
¼ exp (
s
2
l
) 1
(5)
The turbulence model discussed thus far is valid for the
weak turbulence with small values of
s
l
2
. For
s
l
2
1.2, sat-
uration sets in and the model no longer holds [14]. Further
details of turbulence can be found in [10, 14 – 16] and refer-
ences therein.
3 OOK modulation
In OOK, a digital data bit d(t) ¼ f0g is transmitted as an
absence of light pulse and d(t) ¼ f1g as a pulse of finite dur-
ation. OOK is well studied and is known for its simplicity
but requires an adaptive threshold to perform optimally in
a turbulent atmosphere [10].
3.1 Error probability (adaptive threshold) with
scintillation
Here, we assume that the receiver has no prior knowledge of
the instantaneous atmospheric scintillation, but is
acquainted with its statistics. Without loss of generality,
we normalise the receiver area to unity such that optical
power can henceforth be represented by the optical intensity
I.IfR represents the responsivity of the PIN photodetector,
the generated photocurrent is given by
i
r
(t) ¼ RI þ n(t) (6)
where n(t) N(0,
s
2
) is the additive noise.
The marginal probabilities below are obtained by aver-
aging the conditional pdf of i
r
(t) over the scintillation stat-
istics. Note that scintillation does not have any effect when
no pulse was transmitted
Pi
r
=0
¼
1
ffiffiffiffiffiffiffiffiffiffiffi
2p
s
2
p
exp
i
2
r
2
s
2
(7)
Pi
r
=0
¼
ð
1
0
Pi
r
=1, I
P
I
(I)dI
¼
ð
1
0
1
ffiffiffiffiffiffiffiffiffiffiffi
2
ps
2
p
exp
(i
r
RI)
2
2
s
2
1
ffiffiffiffiffiffiffiffiffiffiffi
2
ps
2
l
p
1
I
(8)
exp
(ln(I=I
0
) þ
s
2
l
=2)
2
2
s
l
2
dI
Using the optimal maximum a posteriori (MAP)
symbol-by-symbol detection with equiprobable OOK data
[17], d(t) is decoded as
^
d(t) ¼
arg max
d
P(i
r
=d(t)) and the
IET Optoelectron., Vol. 2, No. 1, February 2008 17
likehood function is given by
L ¼
ð
1
0
exp
((i
r
RI)
2
i
2
r
)
2
s
2
1
ffiffiffiffiffiffiffiffiffiffiffi
2p
s
2
l
p
1
I
exp
(ln(I=I
0
) þ
s
2
l
=2)
2
2
s
2
l
dI
(9)
The threshold level, ith is obtained from (9) with L ¼ 1.
The plot of ith for different levels of turbulence with R and
I
0
both normalised to unity is shown in Fig. 1.Thisfigure
clearly illustrates the dynamism in the OOK threshold
level. The receiver must therefore be able to select the
threshold point adaptively for the optimal performance.
Implementation of this is not trivial and we therefore con-
sider SIM as an alternative in the section that follows. The
threshold is, however, observed to approach a value of 0.5
as the scintillation level decreases.
The probability of bit error P
e
can be obtained from (10)
P
e
¼ P(0)
ð
1
i
th
Pi
r
=0
di
r
þ P(1)
ð
i
th
0
Pi
r
=1
di
r
(10)
4 Subcarrier modulation
In optical communication systems, SIM is achieved by
modulating a digital and/or analogue information source
onto an electrical subcarrier, which is in turn used to modu-
late the intensity of a continuous wave laser that serves as
the optical carrier [8, 11, 18]. Information from different
sources can also be pre-modulated on different subcarrier
signals at different but orthogonal frequencies in multiple
SIM (Fig. 2). Optical SIM inherently benefits from more
mature RF devices and advances in signal processing.
These factors make the implementation of SIM easier, com-
pared with the optimum OOK with adaptive threshold dis-
cussed in Section 3. Although the terrestrial FSO link
under consideration is assumed horizontal and the channel
non-dispersive, SIM is also advantageous in a multipath/
dispersive channel. With sufficient number of subcarriers
to attain a higher or same overall data rate as a single
carrier system, the overall symbol interval of SIM can be
made significantly larger than the multipath/dispersive
channel delay spread by transmitting at sufficiently low
data/symbol rate on each subcarrier [19]. This results in
arbitrarily small ISI and eliminates the need for an
equaliser.
In addition, subcarrier multiplexing or multiple SIM can
be achieved by modulating multiple digital and/or analogue
information sources onto different electrical subcarriers,
which are then used to modulate the intensity of a continu-
ous wave laser that serves as the optical carrier. Multiple
SIM obviously demands tight synchronisation at the recei-
ver side with a major drawback being its poor power effi-
ciency [11, 18, 20]. This results from the fact that the
multiple SIM electrical signal is a sum of modulated sinu-
soids (i.e. dealing with both negative and positive values)
and as the intensity of an optical carrier can never be nega-
tive, a DC bias b
o
is therefore added to this composite signal
before it is used to modulate the laser diode intensity. As the
number of subcarriers rises, the minimum value of the mul-
tiple SIM electrical signal decreases and the required DC
bias increases. This factor places a bound on the allowable
number of subcarriers for a given peak optical power.
However, different approaches have been proposed to alle-
viate the poor power efficiency, see [11, 18, 20] and refer-
ences therein. Multiple SIM power efficiency
improvement will therefore not be discussed here.
4.1 Subcarrier generation and detection
Fig. 2 depicts the block diagram of an FSO system employ-
ing subcarrier modulation scheme.
The instantaneous photocurrent i
r
(t) is expressed as [8]
i
r
(t) ¼ RI (1 þ
b
m(t)) þ n(t) (11)
where I ¼ I
peak
/2, I
peak
the peak received irradiance,
b
the
modulation index, m(t) the multiple subcarrier signals and
n(t) N(0,
s
2
) the additive noise. For M subcarriers,
Fig. 1 OOK threshold level against the log intensity standard
deviation for a range of turbulence levels
Fig. 2 Block diagram of FSO employing SIM
IET Optoelectron., Vol. 2, No. 1, February 200818
m(t) over one symbol duration is given by
m(t) ¼
X
M
j¼1
A
j
g(t) cos (w
cj
t þ
u
j
) (12)
g(t) ¼
10 t T
0 elsewhere
(13)
where g(t) is the rectangular pulse shape function, {w
cj
}
M
j¼1
the angular frequency and {A
j
}
M
j¼1
the peak amplitude of
each subcarrier. For a continuous wave laser transmitter to
operate within its dynamic range, j
b
m(t)j1. Throughout
this work, BPSK is assumed on each subcarrier. With
A
j
¼ A and
b
normalised to unity, the peak amplitude
A 1/M. The photocurrent for each subcarrier with filtered
out DC component and
u
j
¼ f0, pg is given by
i
r
(t) ¼ +IRAg(t) cos (w
c
t) þ n(t) (14)
The electrical SNR (SNR
e
),
g
, at the input of the subcar-
rier demodulator can be derived from (14) as
g
¼
(IRA)
2
2
s
2
(15)
For a fixed value of
b
, increasing M will result in reduced
SNR as A 1/M and subsequently higher BER. In the case
of coherent demodulator, the bandpass filter must have twice
the transmitted signal bandwidth as made evident by (14).
4.2 Error probability (no spatial diversity)
For a coherent BPSK demodulator, the probability of bit
error conditioned on the intensity fluctuation can be
derived as
P
ec
¼ Q
ffiffiffi
g
p
(16)
Averaging (16) over intensity fluctuation statistics results
in the following unconditional BER P
e
P
e
¼
ð
1
0
Q
ffiffiffi
g
p
1
ffiffiffi
2
p
p
s
2
l
1
I
exp
(ln(I=I
0
) þ
s
2
l
=2)
2
2
s
2
l
dI
(17)
A closed-form solution of (17) does not exist and could
result in truncating the upper limit using the numerical inte-
gration. The presence of the argument of the Q-function at
the lower limit of the integral poses analytical problems
[21]. By using an alternative representation of the
Q-function (18) together with the Gauss–Hermite quadra-
ture integration (19), these problems can be circumvented.
See [21] and [22] for further details of (18) and (19),
respectively
Q( y) ¼
1
p
ð
p
=2
0
exp
y
2
2 sin
2
u
d
u
(18)
ð
1
1
f (x) exp (x
2
)dx ffi
X
m
i¼1
w
i
f (x
i
) (19)
where {x
i
}
m
i¼1
and {w
i
}
m
i¼1
represent the zeros of the mth
order Hermite polynomial He
n
(x) and the corresponding
weight factors, respectively. The degree of accuracy of
(19) is determined by the value of m. Invoking a change
in variable y ¼ðln (I=I
0
) þ
s
2
l
=2Þ=
ffiffiffi
2
p
s
l
in (17) and com-
bining this with (18) and (19), we derive the unconditional
BER as
P
e
ffi
1
p
ð
p=2
0
1
ffiffiffiffi
p
p
X
m
i¼1
w
i
exp
K
2
exp
2(
ffiffiffi
2
p
s
l
x
i
s
2
l
=2)
2sin
2
u
0
@
1
A
d
u
ffi
1
ffiffiffiffi
p
p
X
m
i¼1
w
i
Q
Ke
(x
i
ffiffi
2
p
s
l
s
2
l
=2)
(20)
where K ¼RI
0
A=
ffiffiffi
2
p
s
. It should be noted that x
i
and w
i
terms in (20) are independent of
u
.
Fig. 3 shows the BER performance against the SNR
obtained using (20) and (17) for m ¼ 20. There is an excel-
lent agreement between the results, but the Gauss–Hermite
quadrature integration (20) is preferred for its compactness
and relative simplicity.
5 Subcarrier modulation with spatial diversity
We assume the receivers’ spatial separation, s .
r
o
, result-
ing in each detector receiving independent signals;
r
o
being
of the order of a few centimetres’ [14] makes this assump-
tion realistic. However, the use of detector diversity in ter-
restrial atmospheric optical communication comes with the
price of complex tracking and alignment – especially in the
presence of building sway and strong winds [9]. We also
assumed that the laser radiation to be diffraction-limited
and that the beamwidth at the receiver end is sufficiently
broad to cover the entire field of view of all the
N-detectors. The N-detector photocurrents {i
ri
(t)}
N
i¼1
(Fig. 4) are combined before being sent to the coherent
demodulator that separates the composite signal into its
constituent subcarriers and demodulates each subcarrier.
Spatial diversity combining techniques considered are the
maximum ratio combining (MRC), the equal gain combin-
ing (EGC) and the selection combining (SelC).
Scintillation, being a random phenomenon that changes
with time, makes the received signal intensity to also be
time variant with coherence time
t
0
of the order of millise-
conds [13]. However, within time duration t ,
t
0
, the
received signal intensity is presumably constant and time
invariant. With the symbol duration T
t
0
(T ¼ 1ns
when transmitting at a moderate 1 Gbps symbol rate) it
Fig. 3 BER against SNR; Numerical and Gauss–Hermite
approach solutions for m ¼ 20
IET Optoelectron., Vol. 2, No. 1, February 2008 19
