International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013
Performance Analysis of 6×6 Mimo
Free Space Optical Links with Misalignment
1
2
Siva Prasad Siddu.P (M.Tech),
Ms. H. D. Praveena, M.Tech, Assistant professor
1
Department of Electronics and Communication, Sri
2
Department of Electronics and Communication,Sri
Vidhyanikethan Engineering College, TIRUPATI – 517102, A.P.
Vidhyanikethan Engineering College, TIRUPATI – 517102, A.P.
INDIA.
INDIA.
Abstract- A statistical channel model for 6×6 multiple input and
atmospheric turbulence and misalignment. The atmospheric
multiple output is developed with Free space Optical
turbulence gives the scintillation by fading the signal
Communication channel which is effected by misalignment
intensity. And these scintillations is controlled by the
parameters
between
transmitters
and
receivers.
This
misalignment impairs the Optical channel link performance.
For performance measure the outage probability is derived for
6×6 by using the Equal gain combining technique at receiver,
refractive index parameters. And the transmitters and
receivers are aligned for point to point communication. And
due to the winds, thermal effects in transmitters etc., the
when the optical link is affected by misalignment (pointing)
misalignment will occur. And its time varying, pointing
fading with atmospheric fading. At a given SNR the outage
errors will occur and it effects the FSO link channel
probability is reduced by increasing the number of transmitters
performance.
and receivers.
The pointing error fading analyzed by using the intensity
Keywords: Free Space Optical communications, 6×6 multiple
modulated laser with PAM. And the atmospheric fading is
inputs and multiple output (MIMO), outage capacity, pointing
analyzed using the Galton distribution.
effect, Galton distribution, and atmospheric turbulence.
I .INTRODUCTION
II. CHANNEL MODEL
In wireless communications a line-of- sight technology is
establishes a communication link between transmitters and
receivers by transmitting a laser beam through the
atmosphere [1]. The main application for optical wireless
communication is Free-space optical (FSO) communications
To analyze the 6×6 system first we consider the below
conditions for M×N system. Fig. 1 presents a diagram of a
MIMO FSO system with M transmitters (lasers) and N
receivers (apertures). The received N×1 vector is given by
in which a point-to point communication link is established
over a range of 1 − 5 km with a data rate on the order of 1 –
10 Gbps.
Y = HT x + z
(1)
In FSO communication, the performance is gained by
overcoming the fading. This fading occurs mainly because of
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013
where H is an M×N channel matrix where the entry Hmn ≥ 0
represents the channel gain from transmitter m to receiver n
with m = 1,2,….M and n = 1,2…..N. The vector x = [x1……
xM]T is the transmitted set of symbols and z = [z1, ….,. zM]T is
a noise vector of White Gaussian distribution. Because of the
nonnegative transmitted signal the (xmn ≥ 0), is limited to P
where (E{xm } ≤ P).
Fig: 1 the beam footprint path at the receiver point of view.
Where Z is the Gaussian noise with variance 2 , and the
signal to noise ratio is
SNR = P/
(3)
And the channel gain is
N
N
H   H mn
(4)
n 1 m 1
And here Hmn is effect of misalignment and atmospheric
(a)
fading. So the channel gain from transmitter m and receiver n
is
by using the equal gain combining technique the output
a
p
H mn  H mn
H mn
signal with repeated transmission signal is
(5)
Here Hamn is atmospheric fading and Hpmn is pointing error
fading between transmitter m and receiver n. Here Hamn is
Y=HX+Z
(2)
atmospheric fading and Hpmn is pointing error fading between
transmitter m and receiver n. Atmospheric-induced strong
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013
turbulence fading in outdoor FSO systems can be modeled as
If there is no misalignment then Qm = Pm and if Y‫ ׀‬is zero then
a multiplicative random process which follows the Galton
the misalignment is unidirectional.
distribution.
In week turbulence regime the atmospheric
From fig.1 the displacement Rmn is distance between Qm and
fading is modeled as [2]
Pm are
a
H mn =
Here
(6)
is a Gaussian random variable. Assume that all
=  Qm – P m 2
as independent and identically distributed random variables
For the radial displacement of Rmn in the receiver plane
between the center of the transmitter beam m and the center
=
of the aperture n [3] the loss due to the misalignment is
2
p
H mn
 A 0 e  2 R mn
‫׀‬
‫׀‬
+2
‫׀‬
‫׀‬
(P m – P n ) +  Pm – P m 2
/w2
The channel gain between transmitter m and receiver n is
(8)
Here A0 is equivalent receiver area and w is equivalent beam
waist at receiver [4]. The Rmn will depend on the two cases,
‫׀‬
‫׀‬
i.e. misalignment in X or misalignment in X and Y
a
p
H mn  H mn
H mn
 A0e X mn
‫׀‬
2
2 Rmn
/ w2
(9)
III STATISTICAL CHANNEL MODEL
Misalignment fading depends on the geometric arrangement
The total channel gain from equation (4) is
of transmitter lasers and receiver apertures. First by
considering M = N, we align the transmitter laser to the
N
N
H  A0 e T  e X mn U mn
corresponding receiver aperture. Let p denote the coordinate
n1 m1
vector of all receiver apertures. And also let p n p denote
(10)
the coordinate vector of the nth receiver and Qm denote the
mth transmitter coordinate vector. At receiver point the
coordinate vector of pn random displacement X‫׀‬
in x-
A common assumption is the misalignment in X‫ ׀‬and Y‫ ׀‬are
jointly Gaussian. Since Xmn also Gaussian
direction And Y‫ ׀‬in y- direction is
 X '
Qm     Pm
Y '
N
N
e   e X mn U mn
G
n1 m 1
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(11)
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013
Where G is a Gaussian random variable rate R0 is defined as
with mean  G and variance
. by substituting
(11) in (10),
Outage capacity with misalignment
the channel gain is
R0 is transmission rate, If the probability of transmitter rate
=
=
(12)
exceeds the instantaneous mutual information of the channel
capacity is called outage, and the probability of this outage is
outage probability and at a given
Where V= G-T with probability density functions is [5]
(
(v) =
|
( | )
(t)dt
)=
( <
)
And here the channel capacity is corrupted by atmospheric
and misalignment fading then the outage probability is [4,
IV PROBABILITY OF OUTAGE
III-B],
For analysis the slow fading channel is considered which is
the coherence time is larger than the symbol duration. And
(
also PAM modulated FSO communication system is
considered for amplitude non negativity and average
constraints.
)=
( )
log
<
---- (15)
Here we are considering the misalignment fading in two
The upper bounded capacity of FSO channel is [5]
scenarios, which is depends on the X‫ ׀‬and Y‫ ׀‬random
displacement in two dimensional or unidirectional (Y ‫ =׀‬0).
( )=
(
) ≤ log
+2
(16)
(13)
∞
=
The lower bound capacity of FSO channel is expressed by
1
2πσ
(
(µ
σ
e
))
.
considering an arbitrary input distribution in the mutual
information, and the capacity is
Where
(
)≥ ( ; |
= ℎ)
=
( )≜
σ
2
2−
And
(
) ≈ log
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013
=
σ −µ
+∑
+
erfc
--- (19)
√
V SIMULATIONS RESULTS
Substituting s = v+ B2 the outage probability we can derive in
we consider a 6×6 MIMO system and wavelength
closed form expression as [5]
nm, beam waist
= 1550
= −10
= 2 cm, and radius of curvature
m at the transmitter. The beam propagates a distance
σ
+
⎡
1⎢
( ) = ⎢
2
⎢+
⎣
√2σ
+
−
√2
√2σ
⎤
⎥
⎥
⎥
⎦
km through a turbulent medium characterized by
receiver has a circular aperture of radius
set to
rate
In unidirectional scenario X ~ (0, σ ) and
‫׀‬2
′ = 0. And the
2
probability density functions of T= 2X / w is modeled as
. Each
= 5 cm. The
= 20 cm and results in independent
0
2
as shown.
= 0.1 m2 is considered and
= 1 bits/channel is considered. The effect of weak or
strong weather conditions the parameter
‫׀‬
=1
spacing between transmitters (as well as between receivers) is
The misalignment variance of
--- (17)
2
2
varies and also
variance. Here we consider the variance as 0.3.
Here in Fig: 2 we are considering 4×4 and 6×6 MIMO
system
symmetric misalignment
and
compared
their
performance with their outage and SNR values. In this Fig 3
( )=
(18)
√
shows that the SNR versus outage probability has compared.
The outage probability is
( )=
( )
,
∞
=
|
( | )
(t)dtdv
This equation is approximated [] as
(
) ≈ 1−
1
2
−
√2σ
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013
Fig:2 The 4×4 and 6×6 MIMO system of SNR and outage probability with
symmetric misalignment.
A statistical model for 6×6 MIMO FSO channels which is
impaired by atmospheric and misalignment fading is
developed. This model is utilized to study the outage
probability of FSO channels at high signal-to-noise ratio.
Closed-form expressions for the outage probability are
derived with different misalignment fading scenarios. In the
presence of atmospheric and misalignment fading, the
diversity gain depends only on the misalignment parameters
and is independent of both the number of transceivers and
atmospheric fading parameters. In this case increasing the
number of transmitters and receivers decreases the outage
probability for a given SNR
REFERENCES
Fig 3 The 4×4 and 6×6 MIMO system of SNR and outage probability with
unidirectional misalignment.
And here the outage probability of
6×6 and 4×4
both have less outage, but if we see the SNR
values, the 6×6 system have less SNR comparing
with 4×4. So the performance of the 6×6 gives the
less outage, and high intensity input. And in Fig:3
we are considered 4×4 and 6×6 MIMO system with
unidirectional misalignment. Here the performance of the
unidirectional
gives
the
better
than
the
symmetric
[1] J.M.Khan and J.R.Barry, “wireless infrared communications,”
Proc.IEEE, vol.85.pp.265-298, Feb, 1997.
[2] X.Zhu and J.H.Khan, “Free space optical communication through
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[3] L.Andrews and R.Phillips, Laser Beam Propagation Through Random
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[4] A.A.Farid and S.Hranilovic, “Outage capacity optimization for free space
optical links with pointing errors,” IEEE J. Light wave Technol., vol25,pp.
1702-1710, July 2007.
[5] A.A.Farid,and Steve Hranilovic, “Diversity Gain and Outage Probability
for MIMO Free Space Optical Links with Misalignment, vol.,60, NO.2,Feb
2012.
[6] S.M.Navidpour, M.Uysal, and M,Kavehrad, “BER performance of freespace optical transmission with spatial diversity,” IEEE Trans, wireless
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[7] A.A.Farid,and Steve Hranilovic, “Outage capacity for MISO Intensitymodulated
FSO
Links
with
Misalignment”,
J.OPT.Commun.NETW/Vol.3,N).10,OCT-2011.
misalignment.
If we compare the SNR values of 6×6 and 4×4, By
increasing the Signal to Noise ratio the transmission power
also will increase. So for the 6×6 system the SNR is reduced
so the transmission power also we average by increasing the
transmitters and receivers.
VI .CONCLUSIONS
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