Copyright © 2009 Arun K. Majumdar1 Free-Space Laser Communications: Fundamentals, System Design, Analysis and Applications Lecture Series:1 Brno University

Copyright © 2009 Arun K. Majumdar 1

Free-Space Laser Communications: Fundamentals, System Design, Analysis

and Applications

Lecture Series:1

Brno University of Technology, Brno, Czech Republic

December 1-6, 2009

Dr. Arun K. [email protected]

105 W. Mojave Rose Ave.Ridgecrest, California 93555,

USA


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


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


Course Outline

• Received Power

• Link Margin

• Data Rate

• Reliability


Course Outline

5. Basic Free-Space Laser Communications System

- Wavelength Selection- Free-Space Lasercom Subsystems


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


Course Outline

7. Mitigating Turbulence Effects

• Multiple Transmitters

• Adaptive Optics

8. Animation Show

9. Summary: Improvement of Lasercom Performance

REFERENCES


Objectives

At the end of the course participants will be able to:• Understand basic operational principles of free-

space 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)


WHAT IS THE BIG PICTURE OF FREE-SPACE LASER COMMUNICATIONS?

• Air-to-Air

• Air-to-Ground

• Ground-to-Air

• Ground-to-Ground


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 !


Optical and RF comparison

Antenna Gain

Comparison for

Optical and RF


Major sub-systems for laser communications systems and Link

Analysis

– Laser Transmitter

– Transmitter Optics

– Beam Propagation

– Optical Receiver

– Receiver Optics

– Acquisition, Pointing and Tracking


Modulation Method

• Figure. Selected Modulation Formats


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


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.


Optical ReceiversReceiver 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 / (σ2

T + σ2s+ σ2

sig-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 –I0) / σ021/2}]

Where I1 and I0 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 I0) / (σ1+ σ0)

Thus, BER = (1/2) erfc(Q/21/2), where Q = (I1- I0) / (σ1+ σ0)

17Copyright © 2009 Arun K. Majumdar

Free-Space Laser Communication:the Atmospheric Channel

Transceiver A Transceiver B

Laser power reduction due to atmospheric channel effects

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


Various atmospheric effects relevant to free-space laser communications


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.


The Atmospheric Channel: Scattering

No smokeBER 10-8

Weak smokeBER 10-4

Heavy smokeBER 10-3

CommunicationTransmitter (155Mb/s)

Transmitter

z

0o

dzexpI

I(z) Transmittance (scattering + absorption):

• caused when wavelength collides with scattering particle

• no loss of energy, only directional redistribution

• physical size of particle determines type of scattering:

particle Rayleigh scattering (symmetric)

particle Mie scattering (forward direction)

particle extreme forward scattering

Aerosols & droplets

Atoms & molecules


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 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

Visibility in Km 0.05 0.2 0.5 1 2 4 10 23 Atten.dB/Km @800 nm

345 88 33 16 7.5 3.1 1.05 0.5

Atten,dB/Km@1550 nm

345 87 34 10.5 4.5 2.1 0.4 0.2


Atmospheric Turbulence Effects on Propagation

Fluctuations of the refractive index are locally homogeneous and isotropic: oonn LrlrCnrnrD

,)0()()( 3/222


December 15, 2002 December 16, 2002 December 17, 2002

February 8, 2003 February 12, 2003 February 13, 2003

Turbulence-Induced Refractive Index Fluctuations


Atmospheric Models

• Hufnagel-Valley (HV) model:

where is the rms wind speed. Typical value of the parameter, A=1.7x10-14 m-2/3.

• Modified Hufnagel-Valley (MHV) model:

100exp

1500exp107.2

1000exp)10(

2700594.0)( 16105

22 h

Ahh

hhCn

100exp1090.1

1500exp1002.3

1000exp1016.8)( 151710542 hhh

hhCn


• SLC-Day model:

Cn2 = 0 0 m < h < 19 m

= 4.008 x 10^13h^-1.054 19 m < h < 230 m

= 1.300 x 10^-15 230 m < h < 850 m

= 6.352 x 10^-7h^-2.966 850 m < h < 7000m

= 6.209 x 10^-16h^-0.6229 7000 m <h < 20,000 m


CLEAR1 Model

3034.10 h

}]/)[(5.0exp{)(log 22210 FEhDChBhACn

where A= -17.0577, B= -0.0449, C= -0.0005 D= 0.6181, E= 15.5617, F= 3.4666


Propagation of a Gaussian Laser Beam in Free Space

Receiver beam size:

Transmitter focusing parameter:

Normalized diffractive distance:

Receiver radius of curvature:

2

22

z)ˆ1(ˆ

)zˆ(z)z(

rr

rR

o

o zz)(ˆ

R

-Rr

dz

zz 2/z 2

od kw

2

122 )zˆ()z( rww

o


Goal: Maximization of Intensity on Receiver

-2 -1 0 1 2

Beam Profile on Target (m)

Ave

rage

Pow

er D

ensi

ty

turbulence

free space

0 1000 2000 3000 4000 5000

Propagation Distance (m)

Ave

rage

Pea

k Po

wer

Den

sity

strongturbulence

weakturbulence

Focused Beam


N o r m a l i z e d v a r i a n c e o f i r r a d i a n c e ( I ) f l u c t u a t i o n s :

2

222

I

III

F o r w e a k s c i n t i l l a t i o n r e g i m e , t h e i r r a d i a n c e v a r i a n c e i s p r o p o r t i o n a l t o t h e R y t o v v a r i a n c e f o r a p l a n e w a v e ,

6/116/722

1 23.1 LkC n

T h e t h r e e - d i m e n s i o n a l p o w e r s p e c t r u m o f r e f r a c t i v e i n d e x f l u c t u a t i o n s i s t h e o r i g i n a l K o l m o g o r o v s p e c t r u m :

,033.0)( 3/112 nn C

1 / L 0 < < < < 1 / l 0

w h e r e = 2 / t u r b u l e n c e s i z e


w h e r e k i s t h e w a v e n u m b e r . T h e m o d i f i e d v o n K a r m a n s p e c t r u m i s : ( t a k i n g i n t o a c c o u n t o f i n n e r a n d o u t e r s c a l e s )

0,)(

)/exp(033.0)(

6/1120

2

222

m

nn C

m l 0 = 5 . 9 2 a n d

0 = 1 / L 0 F i g u r e s h o w s t h e p o w e r s p e c t r u m o f r e f r a c t i v e i n d e x f l u c t u a t i o n s f o r v a r i o u s t u r b u l e n c e m o d e l s :

F o r W e a k t u r b u l e n c e r e g i m e : F o r p l a n e w a v e : 6/116/722

12 23.1)( LkCL nI ,


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 Aperture-Averaged Log-Irradiance = (1.0)(.75) =0.75

25% reduction in scintillation

)Aσσ( 2I

2I

Fluctuations in intensity are “averaged” over receiving aperture of diameter D:

2/1

211

0

2

22

o

22

o

2

o

2

o

22

x1xxcos(z)w

φρ

zw

ρ2

ρ

x-Dexpdxx

π

16A

Aperture Averaging Model*:

*Ricklin and Davidson, JOSA A 20(5), 856, 2003.


Behavior of the Aperture Averaging Factor A

0.00 0.02 0.04 0.06 0.08 0.10

Lens Diameter (m)

0.0

0.2

0.4

0.6

0.8

1.0

Aper

ture

Ave

ragi

ng F

acto

r ACn2 = 10e-14Cn2 = 5x10e-14

L = 2000 m = 0.785

0.00 0.05 0.10 0.15 0.20

Lens Diameter (m)

0.0

0.2

0.4

0.6

0.8

1.0

Aper

ture

Ave

ragi

ng F

acto

r A

Cn2 = 10e-14Cn2 = 5x10e-14

L = 2000 m = 1.55

• 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


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


0 5 10 15 20 25 30 35 40 45 50 55 60 65

radial distance from beam center (cm)

0

2

4

6

8

10

Log-

inte

nsity

Var

ianc

e

Divergent Beam

= 0.785 mz = 2000 mwo = 2.5 cm

Cn2 = 1x10-14 m-2/3

s = 20

s = 50

s = 1000

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

radial distance from center of receiver aperture (cm)

0.025

0.030

0.035

0.040

0.045

0.050

Ape

rture

-ave

rage

d Lo

g-in

tens

ity V

aria

nce

Divergent Beam

= 0.785 mz = 2000 mwo = 2.5 cm

Cn2 = 1x10-14 m-2/3

D = 10 cm

s = 20

s = 50

s = 1000

Aperture-Averaged Log-Intensity Variance

log-intensity variance showingoff-axis fluctuations (point receiver)

log-intensity variance averagedover 10 cm diameter aperture

=

)A( 2Zln

2Zln



Optical Communication Link• Figure 1 illustrates the major subsystems in a complete free-space

laser communications system.

Transmitter Channel Receiver Data

Source Laser

Modulator Internal External

Bit Rate

Coding

Amplifier

Free-Space Absorption Scattering Turbulence Background radiance

Detection Direct Detection Optical Preamplified Heterodyne

Demodulation Incoherent/Coherent Optical/Electrical

Detector p-i-n PD

APD

Data

Decoding

Bit-Error Rate (BER)


Basic Free-Space Laser Communications System


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)


Free-Space Laser Communications Link Analysis

Consider a transmitter antenna with gain GT transmitting a total power PT Watts for a communication range, L.


Free-Space Laser Communication Link Equation, Link Margin and Data Rate

• Received PowerLink 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)


• 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/θT

2L2)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.


• Ref. Scott Bloom, Eric Korevaar, John Schuster and Hienz Willebrand, “Understanding the performance of free-spaceoptics,” JON (OSA), Vol.2, No.6, 178-200 ((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).


Table 1. Link Analysis Example of a Satellite-to-Ground Laser Communication SystemParameter Value/Factor

dB

Wavelength () Range (L) Data Rate Receiver Diameter (D) Transmitter Divergence Angle (T) Transmitter Antenna Gain (GT = 16/ (T)2) Transmitter Optical Loss Space Loss ( S = (/4L)2 ) Receiver Antenna Gain ( GR = (D/)2 ) Receiver Optical Loss SYSTEM LOSS Atmospheric Turbulence Margin Clear Air Transmission Loss TOTAL LINK LOSS LINK MARGIN DESIGN LOSS Required Received Signal at 3 Gbps Required Laser Power at 3 Gbps = Required received signal – Design Loss

0.635 micrometer 4.83 x 105 meter 3 Gbps 1.4 meter 2.07 x 10-4 radians 3.73 x 108 0.1 1.09 x 10-26 47.974 x 1012 0.1 9.36 x 10-8 Watt 4.14 Watt (= 10 6.17/10 )

+85.72 -10.0 -259.61 +136.81 -10.0 -57.08 -11.30 -2.08 -70.46 -6.00 -76.46 -70.29 (=10 log10 9.36x10-8) -70.29+76.46 = 6.17


Example 2. Link Budget for 10 Gbps Laser Communication between Satellite and Ground Station

Parameter/Item Downlink(satellite -to- ground)

Uplink(ground-to-satellite)

WavelengthLaser PowerTransmitting Antenna (efficiency= 50%)Antenna GainRangeFree-Space LossReceiving Antenna (efficiency=50%)Antenna GainAtmospheric 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 PowerSensitivityREQUIRED POWERMARGIN

1.55 micrometer1 Watt20 cm

109.15 dB38,000 km-289.77 dB100 cm

123.13 dB–10.1 dB

-37.59 dBm70 photons/bit40.47 dBm2.9 dB

1.55 micrometer1 Watt100 cm

123.13 dB38,000 km-289.77 dB20 cm

109.15 dB-9.6 dB

-34.09 dB70 photons/bit40.47 dBm4.6 dB


EXAMPLE 3. Very Short Range through Low Visibility Atmospheric Laser Communication Link

Parameter/ItemFactor

Atmospheric LossWavelengthRangeData RatePeak Laser Power

Transmit ApertureTransmit Divergence (at 1/e2 point)Receiver Aperture

Receiver SensitivityPeak Laser Transmit PowerExtinction ratio degradationPointing LossGeometric Range LossAtmospheric LossAtmospheric Scintillation Fade

Receive Optics AttenuationBandpass Filter Loss

RECEIVED PEAK POWER AT DETECTOR

REQUIRED PEAK POWER AT DETECTOR

LINK MARGIN AT RANGE

-200 dB/Km785 nm200 meter1250 Mbit/s1.mW

5 cm 0.5 mradian7.5 cm

800 nWatt-14.44 dBW-0.2 dB-1 dB -2.50 dB-40 dB-1 dB

-1.4 dB-0.7 dB

-61.24 dB

-60.97 dB

-0.27 dB


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:

• •• • where A is the limiting attenuation coefficient value, which is given by• A = [LM(D)/D].1000, D being the range.

A

av AdApT

0

)()(%100


One of the possible ways to determine the distribution of p(A) is based on long-time monitoring of of a received signal level of a real measuring link. Another way consists in utilizing data that was collected in the past. Visibility V[km] is the quantity to be monitored and it serves to determine the attenuation coefficient. Statistical distribution functions F(A< ) can be created, which represents statistical link models. The values of the above integral can be determined from these functions for given limiting attenuation coefficients. An example of statistical link model is shown in the following figure.

Note that for two limiting attenuation coefficient values A= 21 dB/km, and A= 8 dB/km, the corresponding link availabilities are Tav = 93% and Tav = 91% .


P R O B A B I L I T Y D E N S I T Y F U N C T I O N S O F I R R A D I A N C E F L U C T U A T I O N S S c i n t i l l a t i o n c a n l e a d t o p o w e r l o s s e s a t t h e r e c e i v e r : e v e n t u a l l y c a n c a u s e f a d i n g o f t h e r e c e i v e d s i g n a l b e l o w a p r e s c r i b e d t h r e s h o l d v a l u e . T h e r e f o r e w e n e e d t o k n o w t h e f o r m o f t h e P D F t o e v a l u a t e l a s e r c o m s y s t e m p e r f o r m a n c e . S o m e o f t h e P D F s : L o g n o r m a l d i s t r i b u t i o n :

,),(2

),(2

1

),(ln

exp2),(

1)(

2

2

2

Lr

LrLrI

I

LrIIp

I

I

I

I > 0 ( n o n n e g a t i v e

i r r a d i a n c e )

K D i s t r i b u t i o n : ),2()()(

2)( 1

2/)1( IKIIp

I > 0

L o g n o r m a l - R i c i a n D i s t r i b u t i o n : z

rerIp

2

)1()(

022

22

0 ,2

)2

1(ln)1(

exp)1(

2z

dzz

z

Ir

z

rIrI

z

z

I > 0

G a m m a - G a m m a D i s t r i b u t i o n : dxxpxIpIp xy )()()(0

= ,2)()(

)(2 12/)(

2/)(

IKI

I > 0


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



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.


C A S E : N O T U R B U L E N C E

O u t p u t c u r r e n t f r o m t h e d e t e c t o r : NS iii

Si ( t h e s i g n a l c u r r e n t ) i s g i v e n b y

h

ePi S

S

h

PeeBii S

SN

B22 2

2

B = b a n d w i d t h

2Ni = 2

N

N

STURBNO

iSNR

.

= Bh

P S

2

I f w e t a k e i n t o a c c o u n t o f t h e b a c k g r o u n d n o i s e , P B , w e c a n w r i t e a m o r e g e n e r a l e x p r e s s i o n f o r S N R a s f o l l o w s :

)(2

.

BS

STURBNO

PPBh

PSNR


C A S E : W I T H T U R B U L E N C E N o t e t h a t Si i s f l u c t u a t i n g a n d i s a r a n d o m v a r i a b l e . T h e m e a n s i g n a l c u r r e n t i s

h

Pei S

S

w h e r e 2SP =

22SS PP

.20

.

)( TURBNOIS

S

TURBNO

SN

STURB

SNRDP

P

SNRiSNR

w h e r e )(2 DI = A )0(2I ,

A b e i n g t h e a p e r t u r e a v e r a g i n g c o e f f i c i e n t

h

PBeP

h

e

iii

SS

NSSSN

22

2

2222

2


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/(hB) - Poisson probability, p(n)= e- n / n ! where = P/(hB) - P[01] = p(0) = e- - BER = p(1) P[01] +p(0) P[10] = ½ e- P/(hB) - 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 )


A n e r r o r o c c u r s i f I < I D f o r a “ 1 ” b i t , o r i f I > I D f o r a “ 0 ” b i t . W e c a n c a l c u l a t e t h e B E R a s f o l l o w s : B E R = p ( 1 ) P [ 0 1 ] + p ( 0 ) P [ 1 0 ] P r o b a b i l i t y o f P r o b . o f d e t e c t i n g a “ 0 ” t r a n s m i t t i n g a “ 1 ” g i v e n t h a t a “ 1 ” w a s s e n t ( u s u a l l y = 1 / 2 ) A s s u m i n g a G a u s s i a n P D F s w i t h v a r i a n c e

0 , 1 w e f i n d ,

B E R =

D

D

I

I

dIIppdIIpp )()0()()1( 01

= )2

()2

((4

1

0

0

1

1

II

erfcII

erfc DD

a s s u m e p ( 0 ) = p ( 1 ) = 1 / 2 I n t h e a b o v e e q u a t i o n e r f c d e n o t e s t h e c o m p l i m e n t a r y e r r o r f u n c t i o n :

x

dyyespxerfc )(2

)( 2

W e c a n a l s o f i n d t h e o p t i m a l d e c i s i o n t h r e s h o l d t h a t m i n i m i z e d t h e B E R f r o m : d ( B E R ) / d I D = 0 , a n d i s g i v e n b y : p 1 ( I D ) = p 0 ( I D )


i . e . , w h e r e t h e p d f f o r “ 1 ” s i n t e r s e c t t h e p d f f o r “ 0 ” s . T h i s i s a t r a n s c e n d e n t a l e q u a t i o n f o r I D t h a t h a s t o b e s o l v e d n u m e r i c a l l y . B y c h o o s i n g I D s o t h a t P [ 1 0 ] = P [ 0 1 ] , g i v e s a v e r y g o o d a p p r o x i m a t e v a l u e f o i r t h e o p t i m u m d e c i s i o n l e v e l a s

10

0110

II

I D

Q - V a l u e a n d R e c e i v e r S e n s i t i v i t y I t i s t h e n u s e f u l t o d e f i n e t h e Q - v a l u e a s a m e a s u r e

10

01

II

Q a n d t h e B E R i s t h e n r e l a t e d t o t h e Q a s

2

)2/exp(

22

1 2

Q

QQerfcBER

Q i s t h e o p t i c a l S N R . T h e r e f o r e w e c a n a l s o w r i t e ,

22

1 SNRerfcBER

O n c e I 0 , I 1 , 0 a n d 1 a r e f o u n d , t h e B E R c a n b e f o u n d f r o m t h e Q .



M o d u l a t i o n u s e d i n a d i g i t a l c o m m u n i c a t i o n s y s t e m i s “ b i n a r y t r a n s m i s s i o n ” b y a s e q u e n c e o f b i t s d e n o t e d b y t h e s y m b o l s “ 1 ” a n d “ 0 ” . T h e p e r f o r m a n c e m e a s u r e i n d i g i t a l c o m m u n i c a t i o n s i s p r o v i d e d b y “ p r o b a b i l i t y o f e r r o r ” , t h e b i t e r r o r - r a t e ( B E R ) . T h e m o s t b a s i c f o r m o f p u l s e d m o d u l a t i o n i n b i n a r y d i r e c t d e t e c t i o n r e c e i v e r i s o n - o f f k e y i n g ( O O K ) . T h e o b j e c t i s t o d e t e r m i n e t h e p r e s e n c e o f s i g n a l i n a n o i s y e n v i r o n m e n t . I f a “ 0 ” i s m i s t a k e n b y “ 1 ” , t h e p r o b a b i l i t y i s d e n o t e d b y P r ( 1 0 ) , w h i l e a “ 1 ” m a y b e m i s t a k e n b y a “ 0 ” w i t h p r o b a b i l i t y P r ( 0 1 ) . T h e o v e r a l l p r o b a b i l i t y o f e r r o r P r ( E ) i s :

P r ( E ) = p 0 P r ( 1 0 ) + p 1 P r ( 0 1 ) , p 0 i s t h e t r a n s m i s s i o n p r o b a b i l i t y o f a b i n a r y “ 0 ” , p 1 i s t h e t r a n s m i s s i o n p r o b a b i l i t y o f a b i n a r y “ 1 ” . F o r O O K t r a n s m i s s i o n , a s s u m i n g G a u s s i a n d i s t r i b u t i o n f o r n o i s e a l o n e a n d s i g n a l p l u s n o i s e ,

P r ( 1 0 ) =

N

T

i

i

N

ierfcdie

T

N

22

1

2

1 22 2/

P r ( 0 1 ) =

N

TS iierfc

22

1

N O T U R B U L E N C E : B E R N O T U R B . = P r ( E ) =

222

1

22

1 .TURBNO

N

SSNR

erfci

erfc

W I T H T U R B U L E N C E : B E R T U R B . = P r ( E ) = dsi

SNRerfcsp

S

SI

0 22)(

2

1


-50.0 -45.5 -41.0 -36.5 -32.0 -27.5 -23.0 -18.5 -14.0

Receiver Power (dBm)

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Bit

Err

or R

ate

L = 1000 m

D = 4 cm, Cn2 = 10e-14D = 8 cm, Cn2 = 10e-14D = 4 cm, Cn2 = 5x10e-14D = 8 cm, Cn2 = 5x10e-14

no turbulence

-50.0 -45.5 -41.0 -36.5 -32.0 -27.5 -23.0 -18.5 -14.0

Receiver Power (dBm)

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Bit

Err

or R

ate

L = 2000 m

D = 4 cm, Cn2 = 10e-14D = 8 cm, Cn2 = 10e-14D = 4 cm, Cn2 = 5x10e-14D = 8 cm, Cn2 = 5x10e-14

no turbulence

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

What to do? Adaptive Optics


-65 -60 -55 -50 -45 -40 -35 -30 -25

Popt (dBm)

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Bit

Err

or R

ate

= 0.785 m

z = 2000 m

wo = 2.5 cm

D = 10 cm

Collimated Beam

coherent beampartially coherent beam

free

space

Cn2 = 1x10-15 m-2/3

Cn2 = 1.2x10-14 m-2/3

Partial Coherence: Poor Man’s Adaptive Optics

Weak turbulence:

PCB reduces BER by 3 orders of magnitude

Moderate turbulence:

PCB reduces BER by only 1 order of magnitude


The figure shows a plot of BER as a function of SNR for different signal fluctuations, defined by 6/116/722

0 50.0 LkCn (for weak fluctuation, 2

0=0.1, and for moderate to strong fluctuations, 2

0=4).

•*Laser Beam Scintillation with Applications, L.C. Andrews, R.L. Phillips, and C.Y. Hopen (SPIE Press, Bellingham, 2001).


P R O B A B I L I T Y O F F A D E T h e p r o b a b i l i t y t h a t t h e o u t p u t c u r r e n t o f t h e d e t e c t o r w i l l d r o p b e l o w a p r e s c r i b e d t h r e s h o l d i T i s d e f i n e d b y

0 0

)()()(Ti

INSTr didsspsipiiP Ti

I diip0

)(

F a d e t h r e s h o l d p a r a m e t e r :

TT I

LIF

),0(log10 10 d B

C a s e 1 . T e r r e s t r i a l L a s e r C o m m u n i c a t i o n L i n k T h e f i g u r e s h o w s p r o b a b i l i t y o f f a d e a s a f u n c t i o n o f t h r e s h o l d l e v e l , D = 0 d e f i n e s a p o i n t r e c e i v e r . T h e F o l l o w i n g f i g u r e s s h o w t h e p r o b a b i l i t y o f f a d e f o r v a r i o u s p a t h l e n g t h s , C n

2 = 1 0 - 1 3 m - 2 / 3 , w a v e l e n g t h , = 1 . 5 5 m . •Laser Beam Scintillation with Applications, L.C. Andrews, R.L. Phillips, and C.Y. Hopen (SPIE Press, Bellingham, 2001).


Case 2. Uplink Slant Path Laser Communication Link Note that the atmospheric model for Cn

2 is to be taken from Hufnagel-Valley (H-V) model, described earlier. This model shows the variation of Cn

2 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.


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).


Mitigating Turbulence Effects

Multiple Transmitters Approach

(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

Input data output

data

Sources / modulators

Expander/collimator

Collecting lens

opfilter

elect.filter

noisy detector

D

z

d

1

2

3

4

encoder(OOK) decoderInput

data output data

Sources / modulators

Expander/collimator

Collecting lens

opfilter

elect.filter

noisy detector

D

z

d

1

2

3

4

encoder(OOK)encoder(OOK) decoderdecoder



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).


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).

Documents

Copyright © 2009 Arun K. Majumdar1 Free-Space Laser Communications: Fundamentals, System Design, Analysis and Applications Lecture Series:1 Brno University