Effect of particulates on performance of optical communication in space and an adaptive method to minimize such effects. S. Arnon and N. S. Kopeika.
Effect of particulates on performance of optical communication in space and an adaptive method to minimize such effects S. Arnon and N. S. Kopeika
Decreased signal-to-noise ratio and maximum bit rate as well as increased in error probability in optical digital communication are caused by particulate light scatter in the atmosphere and in space. Two effects on propagation of laser pulses are described: spatial widening of the transmitted beam and attenuation of pulse radiant power. Based on these results a model for reliability of digital optical communication in a particulate-scattering environment is presented. Examples for practical communication systems are given. An adaptive method to improve and in some cases to make possible communication is suggested. Comparison and analysis of two models of communication systems for the particulate-scattering channel are presented: a transmitter with a high bit rate and a receiver with an avalanche photodiode and a transmitter with a variable bit rate and a new model for an adaptive circuit in the receiver. An improvement of more than 7 orders of magnitude in error probability under certain conditions is possible with the new adaptive system model.
1.
Introduction
Space optical communication is generally considered to be of great potential. At first glance it seems that this propagation medium is an ideal channel, but deeper study indicates some factors that cause this channel to be nonideal and problematic: the limits of transmitter powers in spacecraft and 1the3 large distances between receiver and transmitter, - background illumination, 4 vibrations, 5 and particulates that scatter and absorb the laser radiation. Sources of particulates are numerous and can be separated into two areas: free space6 and the atmosphere. 7 Sources of particulates in free space include interstellar clouds of particulates, 6 crumbled meteorites (meteorite belt), wakes of comets, gas and particulate exhaust from spacecraft engines, and explosions in space. Sources of particulates and aerosols in the atmosphere include water vapor, volcanic eruptions, whirlwind-like tornados and hurricanes that lift up particulates from the ground, pollution from industrial burning (e.g., the oil well fires in Kuwait), and The authors are with the Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel. Received 4 September 1992; revised manuscript
received 14
January 1994. 0003-6936/94/21493008$06.00/0. © 1994 Optical Society of America.
4930
APPLIED OPTICS / Vol. 33, No. 21 / 20 July 1994
burning up of meteorites in the atmosphere. The use of optical communication in space is generally described from the point of view of technological aspectsl 2 81 5 and only a brief treatment of the effects of the environment on the reliability of the communication is given. Leeb4 analyzes the effects of background power on the signal-to-noise ratio over the space data link. Monte Carlo simulation has been used in the study of particulate effects.16-2 An experiment and Monte Carlo simulations for fog and rain in lower levels of the atmosphere have also been described.2 2 -2 7 Characteristics of particulates in the atmosphere and space have been profiled in the literature. 6 7 28 32 Two scenarios of optical communication can be affected by particulates and aerosols (Fig. 1): communication between LEO's and airplanes and communication between two LEO's. In this paper we analyze the first scenario because this scenario is more practical. In this paper we describe simulation of optical communication systems with a scatter channel, a system approach and analysis of particulate effects on space communication systems, and a new model of an adaptive system suggested for the particulate environment. In the paper we consider the phase function of the particulates according to Mie formulas, multiple-scattering simulation, effects on light propagation by the particulate channel, and comparison and analysis of ordinary and adaptive communication systems for the scattering channel.
lates) for irregular particulates be appropriated for observation angles less than approximately 100°. It is assumed that these characteristics of the particulates are representative.
LEO 2
B. Propagation Model
Assume that light is propagating in a medium that contains vacuum and particulates with known density. The shape of the medium is cylindrical. The cylinder radius is 5 units. The cylinder height is 1 unit. The receiver is placed at the center of the base. The transmitter is placed at the center of the top. The light is monochromatic, with frequency f and photon energy hf. Photon emission is assumed to be 8(xy, z, t) from (0, 0, 0, 0) in a four-coordinate (x,y, z, t) system. Emitted photons (Fig. 2) move in space until collision with a particulate. The new direction of the photons, if they are not absorbed, if they do not escape, or if they are received, derives from three elements: the rotation angle 0, with
Fig. 1.
Two scenarios of satellite optical communication:
commu-
nication between low Earth-orbiting satellite (LEO) and airplane and communication between two LEO's.
It is hoped that this paper will lead to improved performance of optical communication and generate deeper awareness as to the effects of particulates on optical communication in atmosphere and space. 2.
Models
This paper is based on models of three aspects of communication over the scattering channel: the phase function model of single scatter, a model of light propagation over a particulate channel, and models of performance of optical digital communication. A.
Phase Function Model
The shape, size, and composition of particulates in the atmosphere and in free space vary and are known only partially. To treat the problem of scatter of photons at different angles, we must define the parameters of the particulate and then solve the wave equation. Mie formulas are solutions of the wave equation for homogeneous-scattering spheres. Mie formulas are used to describe scattering characteristics such as the scattering-angle distribution and the cross section of scatter and extinction of particulates for broad ranges of size, wavelength, and refractive index. The characteristics of the particulates (average size and index of refraction of the particulate) were estimated from the literature on the average sizes of particulates in the atmosphere and in space6 7 26 32 and from research on the indices of refraction of particulates in the atmosphere and in space,6 ,16,26,29-33 with the constraint that the accuracy of the Mie formulas (developed for spherical particu-
Fig. 2.
Simplified flow chart for propagation of photons in a
particulate channel. 20 July 1994 / Vol. 33, No. 21 / APPLIED OPTICS
4931
uniform distribution; the polar angle 0, with distribution from the Mie formula; and the distance r to7the9 next collision, with an exponential distribution.' -' The probability of a photon being absorbed or scattered depends on the relation between the extinction cross section and the absorption cross section. The mean free path between sucessive collisions is calculated from'82 0 the extinction cross section ae and the particulate density N as 1
I" =_ C
(1)
Photons escape if their position is outside the cylinder boundaries. To make the result below as general as possible, a scaling equation 8 is used to define
T
BER constant when the received power is fading. A fundamental model relating variances to the system bandwith is
a12= CB + C2 JB + C3B2,
(5)
go2= CB + C2 J0 B + C3B2,
(6)
where Jo, J, are signal radiant powers that contribute to the variance, B is bandwidth, and C,, C2 , C3, and R' are constants of the receiver. The means of the electronic signals are
(8)
1. Standard Model The transmitter is a laser with a constant high bit rate. The receiver includes an optical detector in direct detection mode and an electronics amplifier. In such systems the BER for an optimal threshold
Jo = 0,
SO = 0,
P(S,) = P(SO)= 2. The probability that a signal transmitted as S is falsely identified as So is (X
rD
1
Two models of optical communication systems are presented here: a standard model and an adaptive model. The standard system exhibits a bit error rate (BER) that is dependent on the mean and the variance of the probability density function (PDF) of the received signal. The adaptive model results in a constant BER despite fading of the received signal. The fading of the received signal is caused by absorption and spatial widening of radiation propagating in the scattering channel.
expi
(21T12)1/2
1 )2 2
dx
2x2
1
(9)
dx,
=Adexp-
where D = decision level and Q =ALl
- D .(10)
The probability that a signal transmitted as So is falsely identified as S, is
E =
o1
x )) fexp(-
=
1
f'exp(-
is3 4
) dx, (11)
BER =
2e
1- erf X
=-e2rx
Il
[o
e [-( rl + o)]
p[_(y2)]dy.
(3)
where
D
Q=-.
(12)
(4)
efx= o~
This analysis derives from an assumption of Gaussian approximation,3 4 ' 35 where RI is the mean of signal S, PDF, ,uois the mean of signal So PDF, crl2 is the variance of signal S, PDF, uro2is the variance of signal So PDF, and S, S2 are optical radiant powers. Adaptive Model Light propagating in a scattering channel is attenuated. The idea of the adaptive system is to vary the bandwidth of the communication system to keep the 4932
= R'So.
We assume that
C. Model of Optical Digital Communication Reliability
receiver
(7)
1o
(2)
where r is the optical thickness of the particulate channel and T is the physical thickness of the particulate channel.
Ai = R'Si,
APPLIED OPTICS / Vol. 33, No. 21 / 20 July 1994
From Eqs. (6), (8), and (9)
D = Q(CB + C3B2 )]1/2 .
(13)
From Eqs. (5), (7), and (10)
D = PI, - Q[(CB + C2 JB + C3B2 )]1/2.
(14)
From Eqs. (13) and (14) Q[(CB + C3B2)]1/2 =
[LI -
Q[(CB + C 2 JlB + C3B2 )]1/2 . (15)
Squaring Eq. (15) results in
our simulation were as follows: index of refraction of the particulate = 1.51 + j8.41 x 10-4, index of refraction of the medium = 1, wavelength of the radiation = 0.8 m, and particulate radius = 0.3 jim. These values were selected according to the assumptions in Subsection 2.A. The phase function (Fig. 3) displays strong forward scatter, with a reduction of
Q2(CjB + C3B2) = AL2 + Q2 (CIB + C2 JB + C3B2) -
2piQ[(CB+ C2 JB + C3B2 )]1/2 , (16)
or
scatter at larger angles. From the result of the
A2 +
Q2 C2 JB
= 2 1 ,Q[(CB+ C2 J1B + C3B2)]1/2. (17)
Squaring Eq. (17) leads to 1i 4 + (Q 2C 2 Jl)2 B 2 + 2Q 2C 2JB 2
= 4(pQ)
1,2
(CjB + C2 J1B + C3B 2). (18)
Equation (18) is a quadratic equation for the bandwidth B; i.e.,
B2[(Q2C2j)2 - 4(pQ)
2
C3 ]
2
- B[2Q C 2 J1p1 2 + 4(RjQ) 2 C,] + p14 = 0,
(19)
the solution of which is
_
B
[2Q 2C 2Jlg, 2[(Q2C2Jl)2
2
program it is found that the average cosine ((cos 0)) = 0.6533, the scatter efficiency = 2.33, and the extinction efficiency = 2.34; the extinction
efficiency is
related to relatively high absorption by particulates. The calculation of the distribution function (Fig. 4) is accomplished by integrating the density function from 00 to 1800. The distribution function becomes saturated (more than 90% of total distribution) at 800. This result is in agreement with McCartney.2 6 B. Light Propagation Code
The simulation considers propagation of the laser radiation in a multiscatter channel. We assume that 40,000 photons are transmitted. Photon advance is traced until the photons are absorbed, escape, or are received. The simulation uses a pseudorandom generator to create random propagation of the photons.
+ 4(p1Q)2 C1]_ {[2Q2 C2 JL~,2 + 4(p1Q)2C1]2- 4[(Q2 C2 Jl) 2 - 4( ,Q)2C3],4.} - 4(jiQ)2 C3 2[(QIC2jl)2 - 4(V1,Q)2C3 ]
Equation (20) relates system bandwidth and the received signal and noise as follows:
Ai2 (C2J1 + 2C,) -
(C2 Ji
(20)
From the result of the simulation, expressions for the received scattered and unscattered radiation are de-
+ 2C,)2 -
[c 2 Jl)2 -
10.5)
4pl2C3]
(21)
[(QC2 J,)2 - 4pl 2C 3] 3.
100.................
Computer Code
.......... . .. .... .... ..... . .................. ................ .................. . ................ ..................
The simulations were carried out with a UNIX workstation, VAXmainframe, and MATLAB software.
........... . ................
..........
.................
A. Phase Function Code
The program for Mie function calculation is based on an algorithm of Bohren and Huffman.3 3 The program calculates the normalized density function according to Mie formulas at intervals of 1 from 0 to 1800,with the values of the parallel and the perpendicular polarization terms averaged. The normalization factor is calculated according to the condition that the distribution functions have a maximum value of unity. The scatter and the extinction cross sections are calculated as part of the program. The data input to the program are the complex index of refraction of the particulate, the real index of refraction of the medium, the wavelength of the radiation, and the dimension of the particulate. The values in
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-= l
0
20
40
60
80
100
120
140
160
180
6 (degrees) Fig. 3. Density function according to Mie formulas for particulate index of refraction 1.51 + j18.41 x 10-4, medium index of refraction unity, radiation wavelength 0.8 ,um, and particulate radius 0.3 pLm. 20 July 1994 / Vol. 33, No. 21 / APPLIED OPTICS
4933
100
0.9
o.8~
~
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0.4k................. ..........
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0 C')
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w
0C1A
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10-1
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60
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100
120
140
160
Distribution
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5.... 2........ . 2...
. 1..5....
3.........5
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5.... 4......... 4...
... .
5........... 5...
6
Fig. 5.
Unscattered light as a function of optical thickness.
function according to Mie formulas.
rived. The expression for the unscattered light is (Fig. 5) (22)
Punscat= P 0 exp(-Tr).
The expression for the scattered light is (Fig. 6) PsCat=
1
180
0 (degrees) Fig. 4.
.. . . . . . . . . . . . . . .
I.-
29.6 P
DR ) 2
r exp(0.59T).
(23)
In Eqs. (22) and (23) it is assumed that 1 • Tr • 6 and Dr «
