June 10, 2010 / Vol. 8, No. 6 / CHINESE OPTICS LETTERS 537
Analysis of average capacity for free-space optical links with
pointing errors over gamma-gamma turbulence channels
Chao Liu (444 ), Yong Yao ( ]]])
∗
, Yunxu Sun (RRR), and Xinhui Zhao (ëëë###)
Department of Electronic and Information Engineering, Shenzhen Graduate School,
Harbin Institute of Technology, Shenzhen 518055, China
∗
E-mail: yaoyong@hit.edu.cn
Received October 12, 2009
A novel closed-form expression for average capacity is derived for free-space optical (FSO) links over
Gamma-Gamma turbulence channels by considering the effect of misalignment (pointing errors). The
simulation results show that the average capacity of the FSO links can be analyzed with the effects of
atmospheric turbulence condition, beam width, detector size, jitter variable, and transmitted optical p ower.
Meanwhile, the results are further provided to verify the accuracy of our mathematical analysis. This work
is useful for the FSO designer.
OCIS co des: 010.1300, 010.1330, 060.4510.
doi: 10.3788/COL20100806.0537.
Free-space optical (FSO) communication systems have
several advantages over conventional radio frequency
(RF) communication systems, such as high bandwidth,
secure transmission, smaller size, and more freedom from
interferences
[1−3]
. However, long distance outdoor FSO
links are always affected by the atmospheric turbulence
and pointing errors. Atmospheric turbulence can cause
severe degradation in the received signals, known as fad-
ing or scintillation. Pointing errors due to building sway
is another concern in outdoor FSO links. Thermal expan-
sion, dynamic wind loads, and weak earthquakes result
in the sway of high-rise buildings, which causes vibra-
tions of the transmitted beam, so the effect of misalign-
ment (pointing errors) occurs between the transmitter
and receiver
[4]
.
Various statistical models have been proposed to de-
scribe atmospheric turbulence channels with respect to
the strength of turbulence
[1]
. It was found that for
moderate-to-strong turbulence conditions the Gamma-
Gamma (GG) distribution almost accurately predicts the
probability of fade, the expected number of fades per
second, and the mean fading time for the irradiance fluc-
tuations collected by finite-sized apertures that are sig-
nificantly smaller than the coherence radius
[5]
. Nistaza-
kis et al. used the GG turbulence model to evaluate
the average capacity of FSO links by considering the
different link length, operation wavelength, and strength
of turbulence
[6]
. The average capacity over generalized-
K fading channels has been analyzed and evaluated
[7]
.
In Ref. [8], the ergodic capacity of a FSO communica-
tion system under strong turbulence regime that follows
the K distribution was evaluated. However, the com-
bined effects of atmospheric turbulence and pointing er-
rors on average capacity were not considered. In Ref.
[9], the probability density function (PDF) in no closed-
form solution for the combined effects has been investi-
gated based on GG distribution and the outage capacity
has b een studied considering beam width, pointing er-
ror variance, and detector aperture size. The bit-error
rate (BER) performance of FSO links has been studied
in log-normal (LN) distribution and K distribution in tur-
bulence channels with pointing errors
[6,10]
. The analyses
of ergodic capacities were presented in LN distribution
and GG distribution without considering the effects of
beam width and detector aperture size
[11]
. Unlike these
earlier works, our theoretical model considers the average
capacity in closed-form solution for FSO links over GG
turbulence channels with the combined effects of atmo-
spheric turbulence and pointing errors. The closed-form
expression of average capacity is presented by consider-
ing the effects of atmospheric turbulence condition, beam
width, detector size, jitter variable, and transmitted op-
tical power.
In this letter, we consider a FSO communica-
tion system using intensity modulation/direct detec-
tion (IM/DD) with on-off keying (OOK). The laser
beams propagate along a horizontal path through GG
turbulence channel with additive white Gaussian noise
(AWGN) in the presence of pointing errors. The channel
is assumed to be memoryless, stationary, and ergodic,
with independent and identically distributed intensity
fast fading statistics. We also consider that the chan-
nel state information is available at both transmitter and
receiver. The statistical channel model is given by
y = hx + n, (1)
where y is the electrical signal at the receiver, h is nor-
malized channel fading coefficient considered to be con-
stant over a large number of transmitted bits, and n is
AWGN with variance σ
2
n
. Since the atmospheric turbu-
lence and pointing errors are random factors which cause
the channel fading, h can be expressed as
h = h
a
h
p
, (2)
where h
a
is the attenuation due to atmospheric turbu-
lence and h
p
is the attenuation due to pointing errors.
In the GG turbulence channel, the PDF of h
a
is given
by
[1]
f
h
a
(h
a
) =
2(αβ)
(α+β)/2
Γ(α)Γ(β)
(h
a
)
(α+β)
2
−1
K
α−β
³
2
p
αβh
a
´
, (3)
1671-7694/2010/060537-04
c
° 2010 Chinese Optics Letters
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