Transcript Fundamentals of Free-Space Laser Communicatios

Free-Space Laser Communications:
Fundamentals, System Design, Analysis and
Applications
Dr. Arun K. Majumdar
[email protected]
105 W. Mojave Rose Ave.
Ridgecrest, California 93555,
USA
Lecture Series:1
Brno University of Technology, Brno,
Czech Republic
December 1-6, 2009
Copyright © 2009 Arun K. Majumdar
1
Course Outline
1.
•
•
•
•
Introduction
Definition of free-space laser communications
Why optical communications? Optical / RF comparison
Basic block diagram
Applications overview
2.
Major sub-systems for laser communications systems
and Link Analysis
Laser Transmitter
Modulation methods
Transmitting optics
•
•
•
Copyright © 2009 Arun K. Majumdar
2
Course Outline
•
•
Optical Receiver
– Photo-detectors
– Pre-amplifier
– Optics, Fiber Optics
Acquisition, Pointing, and Tracking
3.
•
•
•
Optical Signal Detection
Direct Detection: Detection statistics
SNR Bit-Error-Rate (BER) probability
Coherent Detection
4.
•
•
•
•
•
Atmospheric Channel Effects
Attenuation
Beam Wonder
Turbulence (Scintillation/ Fading)
Turbid (rain, fog, snow)
Cloud-free line of sight
Copyright © 2009 Arun K. Majumdar
3
Course Outline
•
•
•
•
Received Power
Link Margin
Data Rate
Reliability
Copyright © 2009 Arun K. Majumdar
4
Course Outline
5. Basic Free-Space Laser Communications System
- Wavelength Selection
- Free-Space Lasercom Subsystems
Copyright © 2009 Arun K. Majumdar
5
Course Outline
6.
•
•
•
•
Free-Space Laser Communications Systems
Performance
Metrics for evaluating the performance
SNR and BER in presence of atmospheric turbulence
Probability of Fade
Examples
– Terrestrial (Horizontal Link)
– Uplink
– Downlink
Copyright © 2009 Arun K. Majumdar
6
Course Outline
7.
•
•
Mitigating Turbulence Effects
Multiple Transmitters
Adaptive Optics
8.
Animation Show
9.
Summary: Improvement of Lasercom Performance
REFERENCES
Copyright © 2009 Arun K. Majumdar
7
Objectives
At the end of the course participants will be able to:
• Understand basic operational principles of freespace laser communications
• Describe lasercom systems using fundamental
design concepts
• Describe atmospheric propagation effects on
lasercom performance
• Quantitatively evaluate degradation in system
performance as a function of various atmospheric
parameters
• Perform link budget analysis and calculate Bit
Error Rate (BER)
Copyright © 2009 Arun K. Majumdar
8
WHAT IS THE BIG PICTURE OF FREE-SPACE LASER
COMMUNICATIONS?
•
Air-to-Air
• Air-to-Ground
• Ground-to-Air
• Ground-to-Ground
Copyright © 2009 Arun K. Majumdar
9
Why Optical Communications?
• The main reason is the potential increase in
information and power that can be
transmitted
• Note: For a circular lens antenna of
diameter d, transmitting an electromagnetic
wave of wavelength λ, the antenna
transmitter gain:
• Gain, Ga=16/ӨT2
• ӨT = transmitting divergent angle ≈ λ/d, so
that Ga = 16 d 2/ λ2
Example: 6 in lens antenna at 6x10^14 Hz has
122 dB Gain, compared to an improvement
over an RF antenna of 210 ft (~ 64 m)
generating gain of 60 dB !
Copyright © 2009 Arun K. Majumdar
10
Optical and RF comparison
Antenna Gain
Comparison for
Optical and RF
Copyright © 2009 Arun K. Majumdar
11
Major sub-systems for laser
communications systems and Link
Analysis
– Laser Transmitter
– Transmitter Optics
– Beam Propagation
– Optical Receiver
– Receiver Optics
– Acquisition, Pointing and Tracking
Copyright © 2009 Arun K. Majumdar
12
Modulation Method
•
Figure. Selected Modulation Formats
Copyright © 2009 Arun K. Majumdar
13
Optical Receivers
The purpose of the receiver is:
(i) To convert the optical signal to electrical
(ii) Recover data
DIRECT DETECTION
Figure. Typical direct detection digital optical receiver
Copyright © 2009 Arun K. Majumdar
14
Coherent Detection
For detecting weak signal, coherent detection scheme is
applied where the signal is mixed with a single-frequency
strong local oscillator signal. The mixing process converts
the weak signal to an intermediate frequency (IF) in the RF
for improved detection and processing.
Copyright © 2009 Arun K. Majumdar
15
Optical Receivers
Receiver performance
The Signal-to-Noise-Ratio for an optical receiver containing a
p-i-n diode preceded by an EDFA of the receiver can be
calculated as:
SNR =Ip2 / (σ2T + σ2s+ σ2sig-sp+ σ2sp-sp)
The Bit-Error-Rate (BER), is the probability of incorrect bit
identification by the decision circuit of the receiver. With
equal occurrence probabilities of logical “1” s and “0”s ,
and Gaussian noise, the BER is given by:
BER = (1/4)· [erfc{(I1 –ID) / σ121/2} + erfc{(ID –I ) / σ021/2}]
Where I1 and I are the average signal currents at the input of
the decision circuit for a “1” and “0”, respectively.
σ1 and σ0 are the rms noise currents for a “1” and “0”. ID is
the threshold current value of the decision circuit. An
adequate choice of ID is: ID = (σ0 I1 + σ1 I ) / (σ1+ σ0)
Thus, BER = (1/2) erfc(Q/21/2), where Q = (I1- I ) / (σ1+ σ0)
0
0
0
0
Copyright © 2009 Arun K. Majumdar
16
Free-Space Laser Communication:
the Atmospheric Channel
Transceiver A
Laser power
reduction due
to atmospheric
channel effects
Transceiver B
Potential atmospheric effects:





Physical obstructions – birds, bugs, tree limbs, other
Absorption – primarily due to water vapor and carbon dioxide
Scattering – dust particles, water droplets (fog, rain, snow)
Building sway – wind, differential heating/cooling, ground motion
Scintillation – atmospheric turbulence
Copyright © 2009 Arun K. Majumdar
17
Various atmospheric effects relevant to freespace laser communications
Copyright © 2009 Arun K. Majumdar
18
The Atmospheric Channel: Absorption
•
•
Absorption depends on water vapor and
carbon dioxide content of the atmospheric
channel, which in turn depends on
humidity and altitude
Transmission “windows” occur at visible
wavelengths and in the ranges 1.5-1.8 m,
3-4 m, and 8-14 m.
Copyright © 2009 Arun K. Majumdar
19
The Atmospheric Channel:
Scattering
•
•
•
caused when wavelength collides with scattering particle
no loss of energy, only directional redistribution
Atoms & molecules
physical size of particle determines type of scattering:
particle   
particle   
Rayleigh scattering (symmetric)
Mie scattering (forward direction)
particle   
extreme forward scattering
Aerosols & droplets
 z

I(z)
 exp   dz 
Transmittance (scattering + absorption): 
Io
 0

No smoke
BER 10-8
Communication
Transmitter (155Mb/s)
Weak smoke
BER 10-4
Transmitter
Copyright
© 2009 Arun K. Majumdar
Heavy smoke
BER 10-3
20
The result for the scatter attenuation depends on the visibility, V in Km and
the wavelength  given in m. Visibility V is that distance within which the
naked eye can still recognize larger buildings. If mist or fog is in the
atmosphere, visibility decreases. From the above equation we can generate
the following Table:
Weather
Fog
Visibility in Km
Atten.dB/Km @800
nm
Atten,dB/Km@1550
nm
0.05
345
345
Medium Fog
Extreme rain up to
180 mm/h, hail
storm
Haze
Rain with 100
medium rain light to
mm/h, medium
to 45 mm/h, medium
snow fall, light fog light snow rain
fall, mist
Clear
0.2
88
0.5
33
1
16
2
7.5
4
3.1
10 23
1.05 0.5
87
34
10.5
4.5
2.1
0.4
Copyright © 2009 Arun K. Majumdar
21
0.2
Hum
idity
grad
ient
Tem
pera
ture
grad
ient
Atmospheric Turbulence Effects on Propagation
Fluctuations of the refractive index are locally homogeneous and
isotropic: Dn (r)   n(r)  n(0) 2  Cn2 r 2 / 3 , lo  r  Lo


Copyright © 2009 Arun K. Majumdar
22
Turbulence-Induced
Refractive Index Fluctuations
December 15, 2002
December 16, 2002
December 17, 2002
February 8, 2003
February 12, 2003
February 13, 2003
Copyright © 2009 Arun K. Majumdar
23
Atmospheric Models
•
Hufnagel-Valley (HV) model:
h 
h 
 


 h 
2
16
Cn (h)  0.00594  (105 h)10 exp 
  2.7  10 exp 
  A exp 

27
1000
1500
100
 






2
where  is the rms wind speed. Typical value of the
parameter, A=1.7x10-14 m-2/3.
•
Modified Hufnagel-Valley (MHV) model:
 h 
 h 
 h 
2
17
15
Cn (h)  8.16  1054 h10 exp 

3
.
02

10
exp


1
.
90

10
exp





1000
1500
100






Copyright © 2009 Arun K. Majumdar
24
•
SLC-Day model:
Cn2 = 0
0 m < h < 19 m
= 4.008 x 10^13h^-1.054
= 1.300 x 10^-15
= 6.352 x 10^-7h^-2.966
= 6.209 x 10^-16h^-0.6229
19 m < h < 230 m
230 m < h < 850 m
850 m < h < 7000m
7000 m <h < 20,000 m
Copyright © 2009 Arun K. Majumdar
25
CLEAR1 Model
10 .34  h  30
log10 (Cn )  A  Bh  Ch 2  D exp{0.5[(h  E) / F ]2 }
2
where A= -17.0577, B= -0.0449, C= -0.0005
D= 0.6181,
E= 15.5617, F= 3.4666
Copyright © 2009 Arun K. Majumdar
26
Propagation of a Gaussian Laser Beam in Free Space
Receiver beam size:
w(z)  w (rˆ 2 
o
1
zˆ 2 ) 2
Receiver radius of curvature:
R( z) 
z (rˆ 2  zˆ 2 )
rˆ(1  rˆ)  zˆ 2
Transmitter focusing parameter:
R -z
rˆ(z)  o
Ro
Normalized diffractive distance:
z
zˆ d  kwo2 / 2
zˆ 
zˆ d
Copyright © 2009 Arun K. Majumdar
27
Goal: Maximization of Intensity on Receiver
Focused Beam
Average Peak Power Density
Average Power Density
free space
turbulence
-2
-1
0
1
2
weak
turbulence
strong
turbulence
0
1000
Beam Profile on Target (m)
Copyright © 2009 Arun K. Majumdar
2000
3000
4000
5000
Propagation Distance (m)
28
Normalized variance of irradiance (I)
fluctuations:
I 
2
I2  I
I
2
2
For weak scintillation regime, the irradiance
variance is proportional to the Rytov
variance for a plane wave,
 1 2 1.23C n 2 k 7 / 6 L11 / 6
The three-dimensional power spectrum of
refractive index fluctuations is the original
Kolmogorov spectrum:
 n ( )  0.033C n 2 11 / 3 ,
1/L0<<  << 1/ l0
where  =2/turbulence size
Copyright © 2009 Arun K. Majumdar
29
where k is the wave number.
The modified von Karman spectrum is: (taking into account of inner
and outer scales)
 n ( )  0 . 033 C n 2
exp(  2 /  m )
,
2
( 2   0 ) 11 / 6
2
0    
ml0 = 5.92 and 0 = 1/L0
Figure shows the power spectrum of refractive index fluctuations for various turbulence
models:
For Weak turbulence regime: 2
 I ( L )   1 2  1.23C n 2 k 7 / 6 L11 / 6
For plane wave:
,
Copyright © 2009 Arun K. Majumdar
30
What is Lens Aperture Averaging?
Aperture-Averaging Factor A: describes the percent decrease in intensity
fluctuations due to having a receiver that is larger than a point.
Example: Log-Irradiance Variance = 1.0 A = 0.75 (σI  Aσ I )
Aperture-Averaged Log-Irradiance = (1.0)(.75) =0.75
2
2
25% reduction in scintillation
Fluctuations in intensity are “averaged” over receiving aperture of
diameter D:
Aperture Averaging Model*:
 -D2 x 2  ρ 2
16
2  o 
A   x dx exp
2
π
 w 2 zˆ 2
ρ
 o  o
0
1
  1
 cos x   x1  x 2 1/ 2 
o

2

 

w (z) 

2
ρ φ
2
Copyright © 2009 Arun K. Majumdar
*Ricklin and Davidson, JOSA A 20(5), 856, 2003.
31
Behavior of the Aperture Averaging Factor A
• Aperture averaging can significantly reduce intensity scintillations
• Scintillations increase with path length
• For smaller aperture sizes in stronger turbulence, scintillations can be
severe
• Doubling the receiver aperture size decreases scintillations by about a
factor of two
• Doubling the wavelength roughly doubles the aperture size required to
“average” scintillations
• Degree of beam divergence does not play a significant role
1.0
Cn2 = 10e-14
Cn2 = 5x10e-14
0.8
Aperture Averaging Factor A
Aperture Averaging Factor A
1.0
L = 2000 m
 = 1.55
0.6
0.4
Cn2 = 10e-14
Cn2 = 5x10e-14
0.6
L = 2000 m
 = 0.785 
0.4
0.2
0.2
0.0
0.00
0.8
0.05
0.10
Lens Diameter (m)
0.15
0.20
0.0
0.00
0.02
Copyright © 2009 Arun K. Majumdar
0.04
0.06
Lens Diameter (m)
0.08
0.10
32
Coherence-Induced “Artificial” Aperture Averaging
Aperture Averaging: Fluctuations in intensity
are “averaged” over the receiving aperture of
diameter D
“Artificial” Aperture Averaging: reduce the beam
coherence length rather than increase the receiving
lens diameter
Copyright © 2009 Arun K. Majumdar
33
Aperture-Averaged Log-Intensity Variance
Divergent Beam
Divergent Beam
0.050
s = 1
 = 0.785 m
z = 2000 m
wo = 2.5 cm
8
2
-14
Cn = 1x10
Aperture-averaged Log-intensity Variance
Log-intensity Variance
10
m
-2/3
6
s = 20
4
=
s = 50
2
s = 1000
 = 0.785 m
z = 2000 m
wo = 2.5 cm
0.045
Cn2 = 1x10-14 m-2/3
s = 1
D = 10 cm
0.040
s = 20
0.035
s = 50
0.030
s = 1000
0.025
0
0
5
10
15
20
25
30
35
40
45
50
55
60
65
radial distance from beam center (cm)
log-intensity variance showing
off-axis fluctuations (point
receiver)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
radial distance from center of receiver aperture (cm)
log-intensity variance averaged
over 10 cm diameter aperture
Copyright © 2009 Arun K. Majumdar
( ln2 Z  A ln2 Z )
34
5.0
Copyright © 2009 Arun K. Majumdar
35
Optical Communication Link
• Figure 1 illustrates the major subsystems in a complete free-space
laser communications system.
Data
Transmitter
Source
Laser
Modulator
Internal
External
Bit Rate
Coding
Amplifier
Channel
Receiver
Free-Space
Detection
Absorption
Scattering
Turbulence
Background
radiance
Direct Detection
Optical Preamplified
Heterodyne
Data
Demodulation
Incoherent/Coherent
Optical/Electrical
Detector
p-i-n PD
APD
Decoding
Copyright © 2009 Arun K. Majumdar
Bit-Error Rate (BER)
36
Basic Free-Space Laser Communications System
Copyright © 2009 Arun K. Majumdar
37
Wavelength selection criteria
Choice of the transmitting laser wavelength will depend upon:
- Atmospheric propagation characteristics
- Optical background noise
- Technologies developed for lasers, detectors, and spectral
filters
(wind velocity of 30 m/s, and a 45º zenith angle for propagation using
Hufnagel approximation were assumed)
Copyright © 2009 Arun K. Majumdar
38
Free-Space Laser Communications Link
Analysis
Consider a transmitter antenna with gain GT transmitting a
total power PT Watts for a communication range, L.
Copyright © 2009 Arun K. Majumdar
39
Free-Space Laser Communication Link Equation,
Link Margin and Data Rate
• Received Power
Link equation combines attenuation and geometrical aspects to calculate the received optical
power as a function of range, telescope aperture sizes and atmospheric transmissions.
The link equation can be used to generate power detection curves as a function of range.
Figure shows the calculated received power as a function of range for the case of a 10 Mbit/s
bandwidth, using a LED operating at 0.85- μm wavelength, 40 mW power, 13-cm receiver,
atmospheric transmission r3eceiver4 optical efficiency of 0.2, transmitter divergence angle of
1 degree =0.0175 radians, and NEP (noise equivalent power) of the Si detector of 300 nW for
daytime operation.
(Ref. Dennis Killinger, “Free space optics for laser communication
through air,” Optics & Photonics News, October 2002)
Light Haze: low attenuation (10-4/m or 0.2 dB/Km)
Clouds similar to modertae fog- Modertae attaenuation ( 10-2/m or 20
dB/Km)
Copyright © 2009 Arun K. Majumdar
40
•
Link Margin
Link margin describes how much margin a given system has at a given
range to compensate for scattering, absorption and turbulence losses.
The link margin is defined as: M = (Received Power Available)/
(Required Received Power)
Required Received power for a given data rate and receiver sensitivity
is:
Preq = Nb.r.(hc/λ) where Nb is the receiver sensitivity (Photons/Bit), r is the data
rate, h = Planck’s constant, c = velocity of light
The Margin, M is then given by:
M = PT/[r.(hc/λ) ].(dR2/θT2L2)τatm τ TτR.(1/ Nb)
•
Data Rate
The data rate is given by: r = (PT τatm τ TτR..A)[π(θT/2)2L2.Ep. Nb.]
where Ep is the laser photon energy=hc/ λ.
Example: For a 10 cm telescope, diffraction limited divergence = 14
μrad, transmitter peak power =200 mW, transmitter efficiency =o.5,
receiver efficiency = 0.5, and using an avalanche photo-detector with
sensitivity of 60 photons/bit for 10-8 BER , the Figure shows the data rate
as a function of range, L.
Copyright © 2009 Arun K. Majumdar
41
•
Ref. Scott Bloom, Eric Korevaar, John
Schuster and Hienz Willebrand,
“Understanding the performance of freespaceoptics,” JON (OSA), Vol.2, No.6, 178200 ((2003).
•
Ref. E. Korevaar, S. Bloom, K. Slatnick, V.
Chan, I.Chen, M.Rivers, C. Foster, K. Choi and
C.S. Liu, “Status of SDIO/IS&T Lasercom
Testbed Program,” SPIE. Vol.1866 (1993).
Copyright © 2009 Arun K. Majumdar
42
Table 1. Link Analysis Example of a Satellite-to-Ground Laser Communication System
Parameter
Value/Factor
Wavelength ()
Range (L)
Data Rate
Receiver Diameter (D)
Transmitter Divergence
Angle (T)
Transmitter Antenna
Gain (GT = 16/ (T)2)
Transmitter Optical Loss
0.635 micrometer
4.83 x 105 meter
3 Gbps
1.4 meter
2.07 x 10-4 radians
dB
3.73 x 108
+85.72
0.1
-10.0
Space Loss ( S = (/4L)2 )
Receiver Antenna
Gain ( GR = (D/)2 )
1.09 x 10-26
-259.61
47.974 x 1012
+136.81
Receiver Optical Loss
0.1
-10.0
SYSTEM LOSS
-57.08
Atmospheric Turbulence
Margin
Clear Air Transmission
Loss
-11.30
TOTAL LINK LOSS
LINK MARGIN
DESIGN LOSS
-70.46
-6.00
-76.46
Required Received Signal
at 3 Gbps
Required Laser Power at 3
Gbps = Required received
signal – Design Loss
-2.08
9.36 x 10-8 Watt
-70.29 (=10 log10 9.36x10-8)
4.14 Watt (= 10 6.17/10 )
-70.29+76.46 = 6.17
Copyright © 2009 Arun K. Majumdar
43
Example 2. Link Budget for 10 Gbps Laser Communication between
Satellite and Ground Station
Parameter/Item
Downlink
(satellite -to- ground)
Uplink
(ground-to-satellite)
Wavelength
Laser Power
Transmitting Antenna (efficiency=
50%)
Antenna Gain
Range
Free-Space Loss
Receiving Antenna
(efficiency=50%)
Antenna Gain
Atmospheric Loss ,
etc.(Absorption loss: 3.0 dB, Strehl
ratio due to the atmospheric
turbulence: 0.27 dB, coupling loss
for wavefront sensing:0.5 db)
Receiving Power
Sensitivity
REQUIRED POWER
MARGIN
1.55 micrometer
1 Watt
20 cm
1.55 micrometer
1 Watt
100 cm
109.15 dB
38,000 km
-289.77 dB
100 cm
123.13 dB
–10.1 dB
123.13 dB
38,000 km
-289.77 dB
20 cm
109.15 dB
-9.6 dB
-37.59 dBm
70 photons/bit
40.47 dBm
2.9 dB
-34.09 dB
70 photons/bit
40.47 dBm
4.6 dB
Copyright © 2009 Arun K. Majumdar
44
EXAMPLE 3. Very Short Range through Low Visibility Atmospheric Laser Communication Link
Factor
Parameter/Item
Atmospheric Loss
Wavelength
Range
Data Rate
Peak Laser Power
-200 dB/Km
785 nm
200 meter
1250 Mbit/s
1.mW
Transmit Aperture
Transmit Divergence (at 1/e2 point)
Receiver Aperture
5 cm
0.5 mradian
7.5 cm
Receiver Sensitivity
Peak Laser Transmit Power
Extinction ratio degradation
Pointing Loss
Geometric Range Loss
Atmospheric Loss
Atmospheric Scintillation Fade
800 nWatt
-14.44 dBW
-0.2 dB
-1 dB
-2.50 dB
-40 dB
-1 dB
Receive Optics Attenuation
Bandpass Filter Loss
-1.4 dB
-0.7 dB
RECEIVED PEAK POWER AT DETECTOR
-61.24 dB
REQUIRED PEAK POWER AT DETECTOR
-60.97 dB
LINK MARGIN AT RANGE
-0.27 dB
Copyright © 2009 Arun K. Majumdar
45
RELIABILITY OF LASER COMMUNICATION
LINKS
•
•
•
•
•
•
•
•
•
•
Consider the link power budget. It includes all average losses of optical power
P [dBm], which arise between the laser source and the receiving photo-detector.
Pt [dBm] = transmitter power, Prec [dBm] = received power, P0 [dBm]
= receiver sensitivity and Lp [dBm] = propagation loss. LM is an initial link
parameter that serves to express the reliability of the lasercom system.
LM = Pt - Lp - P0
The link availability is a percentage of time Tav[%], when the data transmission
bit error rate is less than its defined value. The link availability can be
expressed as by a probability that additional optical power losses LA [dB]
caused by atmospheric effects are less than link margin LM. The attenuation
of radiation in the atmosphere has a dominant share among all losses.
The link availability can be expressed by means of a probability density p(A)
of an attenuation coefficient A [dB/km] from the following equation:
A
Tav  100%   p(A)  d (A)
0
where A is the limiting attenuation coefficient value, which is given by
A = [LM(D)/D].1000, D being the range.
Copyright © 2009 Arun K. Majumdar
46
Copyright © 2009 Arun K. Majumdar
47
PROBABILITY DENSITY FUNCTIONS OF IRRADIANCE
FLUCTUATIONS
Scintillation can lead to power losses at the receiver: eventually can cause
fading of the received signal below a prescribed threshold value. Therefore
we need to know the form of the PDF to evaluate lasercom system
performance.
Some of the PDFs:
Lognormal distribution:



1
p( I ) 
exp
I I (r , L) 2



irradiance)
 

 1 2
I
   I (r , L)
ln
   I (r , L)   2

2
2 I (r , L)
p( I ) 
K Distribution:
Lognormal-Rician Distribution:
 (1  r ) rI
  I 0 2
z
0


2



,



I>0 (nonnegative
2
(I ) ( 1) / 2 K  1 (2 I ),
( )
p( I ) 
I>0
(1  r )e  r
2  z
1 2 2


 (1  r ) I (ln z  2  z )  dz

 exp  
 2
2
z
2 z


z


,
I>0

Gamma-Gamma Distribution:
p ( I )   p y ( I x ) p x ( x ) dx
0


2( ) (   ) / 2 (   ) / 2 1
I
K    2 I , I > 0
=
( )(  )
Copyright © 2009 Arun K. Majumdar
48
The Probability of Error, Bit Error Rate (BER)
pI(s) = probability distribution of
irradiance
Is= instantaneous signal current with
mean value
<Ps> = mean signal value
<SNR> is the mean SNR in presence
of turbulence
Copyright © 2009 Arun K. Majumdar
49
Copyright © 2009 Arun K. Majumdar
50
DIRECT DETECTION
Signal to be detected is always mixed with noise, such as background and
detector (shot) noise. The signal in presence of noise can be detected using
thresholding technique. The signal is present if the output of the receiver
exceeds that threshold value. If noise alone exceeds that threshold, it is
interpreted as signal, which is termed as “false alarms”. If the noise and the
signal together does not exceed the threshold (even if the signal is present)
we call this “Missed detection”. The following figure depicts this concept.
Copyright © 2009 Arun K. Majumdar
51
CASE: NO TURBULENCE
Output current from the detector:
iS
( the signal current) is given by
iS 
iN
2
i  iS  i N
ePS
h
2e 2 BPS
 2eBiS 
h
B=bandwidth
iN
SNR NO TURB . 
2
=
 N2
iS
N
=
PS
2 h B
If we take into account of the background noise, P B, we can write a more
general expression for SNR as follows:
SNRNO TURB . 
PS
 2hB 

( PS  PB )



Copyright © 2009 Arun K. Majumdar
52
CASE: WITH TURBULENCE
Note thatiS is fluctuating and is a random variable. The mean signal
current is
iS 
e PS
h
 SN 2  iS 2  iS
e

h
where
2
PS
2
PS
2
SNRTURB 
iS
 SN
 iN
2

2
2 e 2 B PS
= PS

h
2
 PS
2
SNRNO TURB .
PS 0
2
  I ( D) SNRNO TURB .
PS
where
 I 2 (D)
 I 2 ( 0)
=A
,
A being the aperture averaging coefficient
Copyright © 2009 Arun K. Majumdar
53
Bit Error-Rate (BER) Performance
Some Basics of BER
The bit-error-rate (BER) is the probability of incorrect bit
identification by the decision circuit.
A typical requirement for optical receivers is BER < 10 -9 (i.e., less
than one error in one billion bits). The receiver sensitivity is the
minimum average received optical power required to achieve BER
= 10-9
Let us calculate the BER for an “Ideal Receiver”- light signal
with power P and B is the bit rate.
- # Photons/sec = P/h.
- Ave # Photons/bit interval = P/(hB)
-
Poisson probability, p(n)= e- n / n ! where  = P/(hB)
P[01] = p(0) = e-
BER = p(1) P[01] +p(0) P[10] = ½ e- P/(hB)
For BER = 10-12, we need an average of 27 photons per bit
The figure shows the time fluctuating digital signal and probability
distribution centered at average signal levels I1 and I0 (point of decision:
time wise, t = td, and signal wise I = ID )
Copyright © 2009 Arun K. Majumdar
54
An error occurs if I<ID for a “1” bit, or if I>ID for a “0” bit.
We can calculate the BER as follows:
BER = p(1) P[01] +p(0) P[10]
Probability of
transmitting a “1”
(usually=1/2)
Prob. of detecting a “0”
given that a “1” was sent
Assuming a Gaussian PDFs with variance 0,1
we find,
ID


ID
BER = p(1)  p1 ( I )dI  p(0)  p 0 ( I )dI
I  I0
I  ID
1
(erfc ( 1
)  erfc ( D
)
= 4
1 2
0 2
assume p(0) = p(1) =1/2
In the above equation erfc denotes the complimentary error function:
erfc ( x ) 
2


 esp ( y
2
) dy
x
We can also find the optimal decision threshold that minimized the BER
from:
d(BER)/dID = 0 , and is given by: p 1(ID) = p0(ID)
Copyright © 2009 Arun K. Majumdar
55
i.e., where the pdf for “1”s intersect the pdf for “0”s. This is a
transcendental equation for ID that has to be solved numerically. By
choosing ID so that P[10] = P[01], gives a very good approximate value
foir the optimum decision level as
ID 
 0 I1   1 I 0
 0 1
Q-Value and Receiver Sensitivity
It is then useful to define the Q-value as a measure
Q
I1  I 0
 0 1
BER 
and the BER is then related to the Q as
1
Q
exp( Q 2 / 2)
erfc

2
2
Q 2
Q is the optical SNR. Therefore we can also write,
BER 
1
SNR
erfc
2
2
Once I0, I1, 0 and 1 are found, the BER can be found from the Q.
Copyright © 2009 Arun K. Majumdar
56
Copyright © 2009 Arun K. Majumdar
57
Modulation used in a digital communication system is “binary transmission” by a
sequence of bits denoted by the symbols “1” and “0”. The performance measure in
digital communications is provided by “probability of error”, the bit error-rate (BER).
The most basic form of pulsed modulation in binary direct detection receiver is on-off
keying (OOK). The object is to determine the presence of signal in a noisy environment.
If a “0” is mistaken by “1” , the probability is denoted by Pr(1 0), while a “1” may be
mistaken by a “0” with probability Pr(01). The overall probability of error Pr(E) is:
Pr(E) = p0 Pr(1 0) + p1 Pr(01) ,
p0 is the transmission probability of a binary “0”,
transmission probability of a binary “1”.
p 1 is the
For OOK transmission, assuming Gaussian distribution for noise alone and
signal plus noise,
Pr(1 0) =
1
2  N

e
 i 2 / 2 N 2
iT
 i S  iT
1

erfc
Pr(01)= 2
 2
N

di 
 i
1
erfc T
 2
2
N









NO TURBULENCE: BERNO TURB. = Pr(E) =
 i
1
erfc S
2
 2 N
 1
 SNRNO TURB . 
  erfc


 2
2 2



WITH TURBULENCE: BERTURB.

 SNR S
1
= Pr(E) =  p I ( s)erfc
20
 2 2 iS
Copyright © 2009 Arun K. Majumdar

ds


58
Effect of Atmospheric Turbulence on Bit Error Rate
• Atmospheric turbulence significantly impacts BER
• Even with aperture averaging, reduction in BER is several orders of
magnitude
• As atmospheric turbulence strength and path lengths increase, so does
the BER
L = 2000 m
L = 1000 m
0
10
100
D = 4 cm, Cn2 = 10e-14
D = 8 cm, Cn2 = 10e-14
D = 4 cm, Cn2 = 5x10e-14
D = 8 cm, Cn2 = 5x10e-14
10-1
10-1
10-2
Bit Error Rate
Bit Error Rate
10-2
10-3
no turbulence
10-4
10-5
D = 4 cm, Cn2 = 10e-14
D = 8 cm, Cn2 = 10e-14
D = 4 cm, Cn2 = 5x10e-14
D = 8 cm, Cn2 = 5x10e-14
10-3
no turbulence
10-4
10-5
10-6
10-6
10-7
10-7
10-8
10-8
-50.0
-45.5
-41.0
-36.5
-32.0
-27.5
-23.0
-18.5
-14.0
-50.0
-45.5
-36.5
-32.0
-27.5
-23.0
-18.5
Receiver Power (dBm)
Receiver Power (dBm)
Copyright © 2009 Arun K. Majumdar
What to do?
-41.0
Adaptive Optics
59
-14.0
Partial Coherence: Poor Man’s Adaptive Optics
Collimated Beam
coherent beam
partially coherent beam
10-1
Cn2 = 1.2x10-14 m-2/3
-2
Bit Error Rate
10
 = 0.785 m
z = 2000 m
wo = 2.5 cm
10-3
D = 10 cm
-4
10
free
space
10-5
10-6
10-7
Cn2 = 1x10-15 m-2/3
10-8
-65
-60
-55
-50
-45
-40
-35
-30
-25
Popt (dBm)
Weak turbulence:
PCB reduces BER by 3 orders of magnitude
Moderate turbulence:
PCB reduces BER by only 1 order of
magnitude
Copyright © 2009 Arun K. Majumdar
60
The figure shows a plot of BER as a function of SNR for
different signal fluctuations, defined by  0 2  0.50C n 2 k 7 / 6 L11 / 6
2
(for weak fluctuation,  0 =0.1, and for moderate to strong
2

fluctuations, 0 =4).
•*Laser Beam Scintillation with Applications, L.C. Andrews, R.L. Phillips, and C.Y.
Hopen (SPIE Press, Bellingham, 2001).
Copyright © 2009 Arun K. Majumdar
61
PROBABILITY OF FADE
The probability that the output current of the detector will drop
below a prescribed threshold iT is defined by
 iT
Pr (i  iT )    p S  N (i s ) p I ( s ) dids 
0 0
Fade threshold parameter:
iT
p
I
(i )di
0
 I (0, L)
FT  10 log10 
 IT




dB
Case 1. Terrestrial Laser Communication Link
The figure shows probability of fade as a function of threshold
level, D=0 defines a point receiver.
The Following figures show the probability of fade for various
path lengths ,
Cn2 = 10-13 m-2/3 , wavelength,  = 1.55 m.
•Laser Beam Scintillation
with Applications, L.C.
Andrews, R.L. Phillips,
and C.Y. Hopen (SPIE
Press, Bellingham,
2001).
Copyright © 2009 Arun K. Majumdar
62
Case 2. Uplink Slant Path Laser Communication
Link
Note that the atmospheric model for Cn2 is to be
taken from Hufnagel-Valley (H-V) model,
described earlier. This model shows the variation of
Cn2 as a function of height taking into account of the
zenith angle. The probability of fade for an uplink
spherical wave to a geo-stationary satellite under
various atmospheric conditions is shown in the
following figure.
Case 3. Downlink Slant Path Laser
Communication Link
The plane wave model can be used to calculate the
irradiance variance and then probability of fade.
The figure shows the probability of fade for a
downlink path from a satellite in geo-stationary
orbit.
Copyright © 2009 Arun K. Majumdar
63
Probability of Fade for Uplink and Downlink
•* Laser Beam Scintillation with Applications, L.C. Andrews, R.L. Phillips, and C.Y. Hopen (SPIE
Press, Bellingham, 2001).
Copyright © 2009 Arun K. Majumdar
64
Mitigating Turbulence Effects
Multiple Transmitters Approach
Input
data
encoder
(OOK)
decoder
Expander/
collimator
1
Sources /
modulators
elect.
filter
2
4
output
data
Collecting
lens D
d
3
z
noisy
op detector
filter
(Courtesy Jaime Anguita: Ref. Jai Anguita, Mark A. Neifeld and Bane Vasic, “Multi-Beam Space-Time
Coded Communication Systems for Optical Atmospheric Channels,” Proc. SPIE, Free-Space Laser
Communications VI, Vol. 6304, Paper # 50, 2006)
Aperture averaging and multiple beams is effective in reducing
scintillation, improving performance
Adaptive Optics approach can be incorporated to mitigate
turbulence effects for achieving free space laser communications
Copyright © 2009 Arun K. Majumdar
65
Copyright © 2009 Arun K. Majumdar
66
•
•
•
•
•
•
•
•
•
•
REFERENCES
1. Free-Space Laser Communications: Principles and Advances, A. K.
Majumdar and J. C. Ricklin, Eds. (Springer, 2008)
1a. A.K. Majumdar and J.C. Ricklin, “Effects of the atmospheric channel
on free-space laser communications”, Proc. of SPIE Vol. 5892, 2005.
2. J. C. Ricklin and F. M. Davidson, “Atmospheric optical communication
with a Gaussian Schell beam,” J. Opt. Soc. Am. A 20(5), 856-866 (2003).
3. J. C. Ricklin and F. M. Davidson, “Atmospheric turbulence effects on a
partially coherent Gaussian beam: implications for free-space laser
communication,” J. Opt. Soc. Am. A 19(9), 1794-1803 (2002).
4. W. B. Miller, J. C. Ricklin and L. C. Andrews, “Log-amplitude variance
and wave structure function: a new perspective for Gaussian beams,” J.
Opt. Soc. Am. A 10(4), 661-672 (1993).
5. L. C. Andrews, W. B. Miller and J. C. Ricklin, “Geometrical
representation of Gaussian beams propagating through complex optical
systems,” Appl. Opt. 32(30), 5918-5929 (1993).
6. Laser Beam Propagation Through Random Media, L. C. Andrews and
R. L. Phillips (SPIE Press, Bellingham, 1998).
7. Laser Beam Scintillation with Applications, L.C. Andrews, R.L. Phillips,
and C.Y. Hopen (SPIE Press, Bellingham, 2001).
8. Optical Communications, R.M. Gagliardi and S. Karp (R.E. Krieger
Publishing Company, 1988).
9. Optical Channels, S. Karp, R.M. Gagliardi, S.E. Moran and L. B.
Stotts ( Plenum Press, New York, 1988).
Copyright © 2009 Arun K. Majumdar
67
REFERENCES
• 10. I.I. Kim, H.Hakakha, P. Adhikari, E. Korevaar and A.K.
Majumdar, “Scintillation reduction using multiple transmitters”
in Free-Space Laser Communication Technologies IX, Proc.
SPIE, 2990,102-113 (1997).
• 11. A.K. Majumdar, “Optical communication between aircraft in
low-visibility atmosphere using diode lasers,” Appl. Opt. 24,
3659-3665 (1985).
• 12. A.K. Majumdar and W.C. Brown, “Atmospheric turbulence
effects on the performance of multi-gigabit downlink PPM laser
communications,” SPIE Vol.1218 Free-Space Laser
Communication Technologies II , 568-584 (1990).
Copyright © 2009 Arun K. Majumdar
68