Performance Comparison of PIN and APD based FSO Satellite Systems for various Pulse Modulation Schemes in Atmospheric Turbulence

doi:10.4236/cn.2013.53B2038

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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

Email: [email protected]

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

( )( )

( )

ln[ ]

exp, 0

I IEI

pI I

πσ



−



=−≥







(1)

and the scintillation index

is given by the expres-

sion

[]

= −

(2)

where I is the received field intensity in presence of tur-

bulence and

the received field intensity without the

effect of turbulence,

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

( )

{ }

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,

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

()

22s

bi QN

P erfc







(4)

where

()

QN is the Q-parameter. The unconditional

BER

is then given by

( )

b ss

BERPp NdN

∞

∫

(5)

where

()

is the probab ility density functio n of

Since, s

is proportional to the received irradiance I,

( )

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.

(in dB) for the PIN receiver for

= 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

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provement with Coding of Free Sp ace Optical Ground to

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[2] P. Gopal, V. K. Jain and S. Kar, “Performance Analysis

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in Weak Atmospheric Turbulence,” International Con-

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[3] L. C. Andrews and R. L. Phillips, Laser Beam Propaga-

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