Communications and Network, 2013, 5, 200-203
http://dx.doi.org/10.4236/cn.2013.53B2038 Published Online September 2013 (http://www.sci r p.org/journal/cn)
Performan ce Comparison of P IN an d APD based FS O
Satellite Systems for various Pulse Modulation Schemes in
Atmospheric Turbulence
Pooja Gopal1, V. K. Jain2, Subrat Kar2
1Bharti Schoo l of Telecom Tech. and Mgmt., IIT Delhi, New Delhi, India
2Electri cal Engin eering Dept., IIT Delhi, New Delhi, India
Received June, 2013
ABSTRACT
In this paper, the performance of various Pulse Position Modulation (PPM) schemes has been analysed for PIN and
APD receivers in the presence of atmospheric turbulence. It is observed that the performance of the APD receiver is
always better than that of the PIN receiver as expected. Among the various modulation schemes, the performance of
Differential Amplitude PPM (DAPPM) scheme with more number of amplitude levels is better than that of the other
schemes for the same single level peak amplitude. Further, the optimum gain of APD receiver does not change substan-
tially for different modulatio n schemes and turbulent conditio ns.
Keywords: Free Space Optics; Pulse Modulation; Ground-to-satellite Communic a tions
1. Introduction
Terrestrial Free Space Optical (FSO) systems such as
optical fibre backup links, cellular communication back-
haul li n ks, multi -ca mpus links, etc. have been performing
well right fro m their emergence. Inter-satellite FSO lin ks
have already been established, while the FSO link be-
tween a ground station and an orbiting satellite is being
extensively reported [1,2].
The major advantages offered by this technology over
the conventional Radio Frequency (RF) satellite systems
are the following: (i) the size and weight of the payload
are critical parameters in any satellite system. These pa-
rameters in FSO systems are one third less than that of
corresponding RF systems [3], (ii) the beam divergence
angle i n RF systems is large, which results in large foot-
prints. This li mits the number of satellites usi ng the same
spectrum and also poses a threat to the security of such
systems. In contrast to this, the extremely small beam
widths and divergence angles of lasers offer links which
are basically immune to interference and offer high secu-
rity, and (iii) there are as yet no restrictions on the band-
widt h used in F SO syst ems. F urther , they o ffer ve ry hig h
data rates which are virtually unconstrained by the carrier
frequencies.
Pulse Position Modulation (PPM) is very popular in
long distance optical communication systems because of
its high power efficiency. Also, due to its high Peak to
Average Po wer Ratio (P APR), it is resilient to the effects
of noise. The bandwidth requirement which increases
with the order of the PPM, is directly proportional to the
power efficiency i.e., higher order PPM schemes are
more power efficient and resilient to noise. Ground-to-
satellite optical communications have to undergo the ill
effec ts o f a t mos phe r ic t urbul e nc e, the a mo unt o f which is
proportional to the strength of turbulence. The pulse
broadening limits the rate at which data can be sent
through the turbulent channel. Hence, PPM may not be
an ideal choice of modulation scheme in all atmospheric
conditions because of its high bandwidth requirement.
Several variants of PPM scheme have been in use, which
offer a trade-off between the power efficiency and band-
width efficiency. In this paper, the comparison of the Bit
Error Rate (BER) performance of the various PPM
schemes is analysed.
This paper is organized as follows. In Section 2, a
brief description of the PPM schemes is given. The Sec-
tion 3 contains the system model used for subsequent
analysis. The methodology for system performance
evaluation and the numerical results in graphical form
are presented in Section 4. The conclusions of the study
are gi ven in Sectio n 5.
2. Modulation Schemes
In Differential Pulse Position Modulation (DPPM), all
the empty slots follo wing the pulse in P PM ar e removed.

P. GOPAL ET AL.
201
This reduces the average symbol length implying im-
proved bandwidth efficiency. Also, there is an inherent
symbol synchronization capability as every symbol ends
with a pulse. Like PPM and unlike On-Off Keying
(OOK), DPPM does not require an adaptive threshold at
the receiver.
Differential Amplitude Pulse Position Modulation
(DAPPM) is a combination of DPPM and Pulse Ampli-
tude Modulation (PAM). The average number of empty
slots following a pulse in DPPM can be reduced by in-
creasing the number of amplitude levels A. This in turn
increases the bandwidth efficiency. But, it adds the re-
quirement of having an adaptive threshold, due to the
presence of multi-amplitudes. A well designed DAPPM
system would require less bandwidth in comparison to
OOK, PPM and DPP M systems [2]. It has inherent sym-
bol synchronization cap a bility like DPPM.
3. System Model
The three most reported models for irradiance fluctua-
tions in a turbulent channel are: log-normal, gamma-
gamma a nd ne ga ti ve exp o ne nt ia l. T heir respective ra nge s
of validity are in the weak, weak-to-str ong a nd sa tura tio n
regimes. In the region of weak fluctuations, t he statistics
of the irradiance fluctuations have been experimentally
found to obey the log-normal distribution [4]. The prob-
ability density function of log-normal distribution is
given by
( )( )
( )
2
0
2
2
ln[ ]
11
exp, 0
2
2I
I
I IEI
pI I
I σ
πσ

−

=−≥



(1)
and the scintillation index
2
I
σ
is given by the expres-
sion
2
22
[]
1
[]
I
EI
EI
σ = −
(2)
where I is the received field intensity in presence of tur-
bulence and
0
I
the received field intensity without the
effect of turbulence,
2
I
σ
the log-intensity variance and
[]EI
the mean of log-intens ity variance. For the case of
strong turbulence, the probability density function is
given by the negative exp onential distribution
( )
{ }
00
1exp I
pI II = −
(3)
The Avalanche Photo Diode (APD) is generally used
in long distance optical communications because of the
low received power levels. An APD performs better than
a PIN diode receiver, when the received power levels are
low. A high avalanche gain requires a high reverse bias
voltage. The higher gain doesn’t imply a better signal to
noise ratio (SNR) si nce the performance degrades beyond
a certain gain as the effect of noise becomes dominant.
Hence the optimum gain of APD for the particular sys-
tem has to be used. A comparative study of APD receiver
vis-à -vis P IN receiver is made in the following sectio n.
4. Methodology for System Performance
Evaluation
The number of photons received at the detector,
s
N
would be a log-normal distributed random variable (in
the case of weak turbulence) or a negative exponentially
distributed random variable (in the case of strong turbu-
lence). The conditional Bit Error Rate (
BER
) is then
given by
/
()
1
22s
bi QN
P erfc

=


(4)
where
()
s
QN is the Q-parameter. The unconditional
BER
is then given by
( )
0
b ss
i
BERPp NdN
∞
=
∫
(5)
where
()
s
pN
is the probab ility density functio n of
s
N
.
Since, s
N
is proportional to the received irradiance I,
( )
s
pN
can be determined from eqn. (1) or (3) depend-
ing on the level of turbulence. After simpl ification using
the Gauss-Hermite approximation [6], the corresponding
BER
expressions are obtained. The
BER
expressions
for the different modulation schemes are derived by tak-
ing into consideration the respective bandwidth and
power requirements. The Symbol Error Rate (
SER
) ex-
pressions are obtained from the respective
BER
ex-
pressions.
The
SER
expressions for PIN and APD receivers when
different modulation schemes are used are obtained from
eqs. (1)-(5). The modulation schemes considered are
64-PPM, 64-DPPM, 64-DAPPM (A=2, L=32; A=4, L=16
and A=8, L=8). The numerical results computed from
these expressions are shown in Figures 1-4 . Figures
1(a)-(b) and Figure 2(a) give the graphs of
SER
vs.
s
N
(in dB) for the PIN receiver for
2
sc
σ
= 0 (no turbu-
lence), 0.5 (low turbulence) and 1 (high turbulence), re-
spectively. The corresponding graphs for the APD re-
ceiver are given in Figures 2(b), Fiugres 3(a) and (b) ,
respectively.
We observe from Figure 1(a) that the performance of
DPPM is better than that of PPM. Further, the perform-
ance of DAPPM is better than that of DPPM and PPM.
The performance of DAPPM becomes still better if the
number of levels is increased from 2 to 8. This trend re-
mains the same irrespective of the turbulence level. In
case of APD receiver, the comparative performance of
different modula tion sc hemes is similar to that of the P IN
case. But, the required
SNR
to obtain a particular
SER
is muc h les s than that of the PIN receiver.
In Fig ures 4(a) and (b), the variations of
SER
vs.
APD gain are given for low turbulence and high turbu-

P. GOPAL ET AL.
202
lence cases, respectively. It is observed that there is not
much d iffere nce in t he opt imum gai n for d ifferent modu-
lation schemes. The optimum gain for different turbu-
lence conditions is almost same. But, we see that the
degradation in performance with increase in gain, beyond
the optimum ga in is more in the c ase of high turbulence.
(a) (b)
Figure 1 . (a) SER vs. Ns in PIN rece iver f or diffe rent modulat io n sche mes wi thout tur bulenc e; (b) S ER vs. Ns in PIN receiver
for different modul ation schemes in low turbulenc e.
(a) (b)
Figure 2 . (a) S ER vs. Ns in P IN recei ver for dif fere nt mod ulati on s che mes i n high t urb ule nce; (b) SER vs. Ns in APD recei ver
for different modulation schemes without turbulence.
(a) (b)
Figure 3 . (a) S ER vs. Ns in APD recei ver for dif fe rent mod ulat i on sc he mes i n low t urbul enc e; (b) S ER vs. Ns in APD receiver
for differe nt modulation sc hemes in high turbul ence.

P. GOPAL ET AL.
203
(a) (b)
Figure 4 . (a) SER vs. g i n APD receiver for diffe rent modulati on sch emes in low turbule nce; (b) SER vs. g in AP D receiver for
diff ere nt mod ul ation schemes in high t urbulence.
Table 1. Parameter values in numerical computation.
Parameter Value
Bit rate (1/T) 1 Gbps
Receiver temperatu r e ( T0) 300 K
Average APD gain (g) 150
Load r esistance (RL) 100 Ω
APD noise fi gure 6.756
Ionization factor 0.02
Order of PPM (M) 64
The numerical values of the parameters used in the
computatio n are given in Ta b le 1.
5. Conclusions
The performance of APD receiver is much better than
that of corresponding PIN receiver. This is because of the
gain factor and also the low received power levels.
Hence for satellite communications which involve long
distances implying less received power, APD receivers
are more suitable. Also, there is no substantial change in
the optimum gain for different modulation schemes and
atmospheric conditions. The disadvantage is the re-
quirement of high bias voltages for more gains, which
will add to the payload.
The better performance of the DAPPM scheme as
compared to PPM and DPPM schemes can be attributed
to the fact that more number of levels reduce the effec-
tive s ymb ol le ng th, whic h i n t ur n r ed uc e s t he b it dur at io n
and hence inter symbol interference is ca used due to tur-
bulence. This also explains why DAPPM schemes with
more number of levels perform better.
The degradation of performance with increase in gain
beyond an optimum value is due to the fact that the noise
is amplified along with the signal and beyond a certain
point, the effect of amplified noise is more than that of
the signal. Similarly, the degradation is more in the case
of strong turbulence because, turbulence causes random
variation of received signal which is amplified similar to
the noise .
We can conclude that because of the time varying na-
ture of the atmospheric channel, the performance of the
link depends on the turbulence conditions. Hence by
adaptively changing the modulation, a more robust sys-
tem performance can be expected.
REFERENCES
[1] H. Kaushal, V. K. Jain and S. Kar, “Performance Im-
provement with Coding of Free Sp ace Optical Ground to
Satellite Link in Atmospheric Turbulence Environment ,”
AIP Con ference Proceedings, Kerala, 2011.
[2] P. Gopal, V. K. Jain and S. Kar, “Performance Analysis
of Ground to Satellite FSO System with DAPPM Scheme
in Weak Atmospheric Turbulence,” International Con-
ference on Fibre Optics and Photonics, Chennai, India,
WPo. 43, December 2012.
[3] L. C. Andrews and R. L. Phillips, Laser Beam Propaga-
tion Through Random Media, 2nd Edition, SPIE Press,
Wa s hing t on, 2005
[4] R. L. Phillips and L. C. Andrews, “Universal Statistical
Model for Irradiance Fluctuations in a Turbulent Me-
dium,” Journal of Optical Society of America, Vol. 72,
No. 7, 1982, pp. 864-870. doi:10.1364/JOSA.72.000864
[5] G. P. Agrawal: Fiber Optic Communication Systems,
Wiley, India, 2002. doi:10.1002/0471221147
[6] K. Kiasaleh, “Performance of APD-based, PPM Free
Space Optical Communication Systems in Atmospheric
Turbulence,” IEEE Transactions on Communications,
Vol. 53, No. 9, 2005, pp. 1455-1461.
doi:10.1109/TCOMM.2005.855009