P. GOPAL ET AL.

Copyright © 2013 SciRes. CN

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

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

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

(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 (

) is then

given by

/

1

22s

bi QN

P erfc

=

(4)

where

s

QN is the Q-parameter. The unconditional

is then given by

(5)

where

s

is the probab ility density functio n of

.

Since, s

is proportional to the received irradiance I,

s

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

expressions are obtained. The

expressions

for the different modulation schemes are derived by tak-

ing into consideration the respective bandwidth and

power requirements. The Symbol Error Rate (

) ex-

pressions are obtained from the respective

ex-

pressions.

The

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

vs.

s

(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

to obtain a particular

is muc h les s than that of the PIN receiver.

In Fig ures 4(a) and (b), the variations of

vs.

APD gain are given for low turbulence and high turbu-