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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/[email protected] 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 16 Cn (h) 0.00594 (10 5 h)10 exp 2.7 10 exp A exp 27 1000 1500 100 2 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 1054 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 log 10 (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 ẑ 2 ) 2 Receiver radius of curvature: R( z) z (rˆ 2 ẑ 2 ) rˆ(1 rˆ) ẑ 2 Transmitter focusing parameter: R -z rˆ(z) o Ro Normalized diffractive distance: z ẑ d kwo2 / 2 ẑ ẑ 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 ẑ 2 ρ o o 0 1 1 cos x x1 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 -2/3 m 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 ( ln2 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 = (/4L)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: 2 , I>0 (nonnegative 2 (I ) ( 1) / 2 K 1 (2 I ), ( ) p( I ) Lognormal-Rician Distribution: I>0 (1 r )e r 1 2 2 (ln z z ) (1 r ) rI (1 r ) I dz 2 I 0 2 exp 2 2 z z 2 z 0 z 2 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 i iS i N Output current from the detector: iS ( the signal current) is given by iS iN 2 ePS h 2e 2 BPS 2eBiS h B=bandwidth iN SNRNO TURB. 2 = N 2 iS N = PS 2hB If we take into account of the background noise, PB, we can write a more general expression for SNR as follows: SNRNO TURB. PS 2hB ( PS PB ) Copyright © 2009 Arun K. Majumdar 52 CASE: WITH TURBULENCE Note that iS 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 2 PS 2 PS 2 SNRTURB SN 2 2 e 2 B PS h PS PS 2 = iS iN 2 SNR NO TURB. PS 0 2 I ( D ) SNRNO TURB. PS 2 2 where I ( D) =A I (0) , 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/(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 ) 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[01] +p(0) P[10] 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) p0 ( 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: p1(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[10] = P[01], 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(01). The overall probability of error Pr(E) is: Pr(E) = p0 Pr(1 0) + p1 Pr(01) , 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 di i 1 erfc T 2 2 N i S iT 1 Pr(01)= 2 erfc 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 2 2 i 20 S 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 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 10-2 Bit Error Rate Bit Error Rate 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 10-1 10-2 10-3 0 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 Bit Error Rate 10 Cn2 = 1.2x10-14 m-2/3 -2 = 0.785 m z = 2000 m wo = 2.5 cm 10-3 D = 10 cm 10-4 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 (for weak fluctuation, 0 2 =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 log 10 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