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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 9 — Apr. 26, 2010
  • pp: 8948–8962
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Synergy of adaptive thresholds and multiple transmitters in free-space optical communication

James A. Louthain and Jason D. Schmidt  »View Author Affiliations


Optics Express, Vol. 18, Issue 9, pp. 8948-8962 (2010)
http://dx.doi.org/10.1364/OE.18.008948


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Abstract

Laser propagation through extended turbulence causes severe beam spread and scintillation. Airborne laser communication systems require special considerations in size, complexity, power, and weight. Rather than using bulky, costly, adaptive optics systems, we reduce the variability of the received signal by integrating a two-transmitter system with an adaptive threshold receiver to average out the deleterious effects of turbulence. In contrast to adaptive optics approaches, systems employing multiple transmitters and adaptive thresholds exhibit performance improvements that are unaffected by turbulence strength. Simulations of this system with on-off-keying (OOK) showed that reducing the scintillation variations with multiple transmitters improves the performance of low-frequency adaptive threshold estimators by 1-3 dB. The combination of multiple transmitters and adaptive thresholding provided at least a 10 dB gain over implementing only transmitter pointing and receiver tilt correction for all three high-Rytov number scenarios. The scenario with a spherical-wave Rytov number = 0.20 enjoyed a 13 dB reduction in the required SNR for BER’s between 10−5 to 10−3, consistent with the code gain metric. All five scenarios between 0.06 and 0.20 Rytov number improved to within 3 dB of the SNR of the lowest Rytov number scenario.

© 2010 OSA

1. Introduction

Laser communications offer tremendous advantages over radio frequency (RF) in bandwidth and security due to the ultra-high frequencies and point-to-point nature of laser propagation. In addition, optical transmitters and receivers are much smaller and lighter than their RF counterparts and operate at much lower power levels. Current airborne sensors are collecting data at an ever-increasing rate. With the advent of hyperspectral imaging systems, this trend will continue as two-dimensional data are replaced by three-dimensional data cubes at finer resolutions. RF communication systems cannot keep up with this trend. As a promising alternative, free-space optical communication (FSOC) systems can keep up as they are capable of transmitting at multi-gigabit per second rates [1

1. Staff Writers, “Northrop Grumman Awarded DARPA Contract To Design Hybrid Optical/RF Communications Network,” Spacedaily.com (2008). Dated 5 May 2008, URL http://www.spacedaily.com/reports/Northrop Grumman Awarded DARPA Contract To Design Hybrid Optical RF Communications Network 999.html.

].

2. Turbulence conditions

The spatial statistics of the turbulence effects also determine how far apart the transmitters must be to get good averaging. Good averaging occurs when the turbulence effects of two or more paths are relatively uncorrelated [8

8. J. A. Louthain, and J. D. Schmidt, “Anisoplanatism in airborne laser communication,” Opt. Express 16(14), 10,769–10,785 (2008). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-16-14-10769.

]. The farther the two transmitters are separated, the less correlated the effects become (i.e. anisoplanatic). This is important when multiple transmitters are used to average out the turbulence effects. Next, the anisoplanatic phase and amplitude effects are considered.

2.1. Anisoplanatic effects

As for the amplitude effects, this independence or uncorrelated angle occurs at much smaller separations. The correlation width ρcw is often used to determine how large receivers need to be to provide some degree of aperture averaging of the scintillation effects. The correlation width is defined as the 1/e 2 point of the normalized irradiance covariance function [12

12. L. C. Andrews, and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE Optical Engineering Press Bellingham, WA, 2005).

]. Since ρcw for weak turbulence varies between 1 to 3 Fresnel zones (L/k)1 / 2 depending on beam size [12

12. L. C. Andrews, and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE Optical Engineering Press Bellingham, WA, 2005).

], in this work we refer to the constant ρc = (L/k)1 / 2. In recent work, the principle of reciprocity was used to illustrate that transmitter separations of ρcw could provide adequate scintillation averaging in the receiver [8

8. J. A. Louthain, and J. D. Schmidt, “Anisoplanatism in airborne laser communication,” Opt. Express 16(14), 10,769–10,785 (2008). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-16-14-10769.

,10

10. J. A. Louthain, and J. D. Schmidt, “Anisoplanatic Approach to Airborne Laser Communication,” Meeting of the Military Sensing Symposia (MSS) Specialty Group on Active E-O Systems I(AD02), 1–20 (2007).

]. Due to angle-of-arrival considerations, the increase in off-axis irradiance variance, and negatively correlated amplitude effects near ρcw, very wide separations are not necessarily the optimal configuration [7

7. P. Polynkin, A. Peleg, L. Klein, T. Rhoadarmer, and J. Moloney, “Optimized multiemitter beams for free-space optical communications through turbulent atmosphere,” Opt. Lett. 32(8), 885–887 (2007). [CrossRef] [PubMed]

,8

8. J. A. Louthain, and J. D. Schmidt, “Anisoplanatism in airborne laser communication,” Opt. Express 16(14), 10,769–10,785 (2008). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-16-14-10769.

,10

10. J. A. Louthain, and J. D. Schmidt, “Anisoplanatic Approach to Airborne Laser Communication,” Meeting of the Military Sensing Symposia (MSS) Specialty Group on Active E-O Systems I(AD02), 1–20 (2007).

,12

12. L. C. Andrews, and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE Optical Engineering Press Bellingham, WA, 2005).

,13

13. J. A. Anguita, M. A. Neifeld, and B. V. Vasic, “Spatial correlation and irradiance statistics in a multiple-beam terrestrial free-space optical communication link,” Appl. Opt. 46(26), 6561–6571 (2007). [CrossRef] [PubMed]

]. Previously, we determined an angular separation of 2θ χ c = 2(Lk)-1/2, or a separation of 2ρc at the transmitters corresponding to about 30 cm for the 100 km air-to-air path was adequate [8

8. J. A. Louthain, and J. D. Schmidt, “Anisoplanatism in airborne laser communication,” Opt. Express 16(14), 10,769–10,785 (2008). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-16-14-10769.

].

3. Temporal considerations

Thus far, only spatial statistics have been used to describe the effects of atmospheric turbulence. In this section, the temporal statistics are considered to determine BER improvement afforded by multiple transmitters and adaptive thresholding. Taylor’s frozen flow hypothesis states that the turbulence structure is essentially frozen as it moves across the propagation path for short time intervals [14

14. M. C. Roggemann, and B. M. Welsh, Imaging Through Turbulence (CRC Press, 1996).

]. This idea was used to scroll the random phase screens across the propagation grid at different points along the path to generate a time series of the turbulence in the simulations performed in Section 4.

3.1. Frequency of the turbulence effects

3.2. Threshold determination

For a binary-symbol system like the one used here, once the signal is received a decision must be made whether a ‘1’ or a ‘0’ was sent based on a threshold. The transmitter modulates the intensity with on-off keying (OOK), where the laser turns on to transmit a ‘1’ and turns off to transmit a ‘0’. The transmission of a ‘1’ or ‘0’ is denoted by the event H1 or H0, respectively. The likelihood ratio test (LRT) determines the optimal decision threshold based upon the probability density function (PDF) of the measured current level im of the transmission of a ‘1’ p(im|H 1) and transmission of a ‘0’ p(im|H 0). Using the LRT and the assumption that P(H 0) = P(H 1) (equally likely signaling) leads to the following two relations [15

15. H. L. VanTrees, Detection, estimation, and modulation theory (Wiley, 2002).

]: if
p(im|H1)>p(im|H0)
(2)
the algorithm picks H 1 and if
p(im|H1)p(im|H0)
(3)
the algorithm picks H 0. The optimum detection criteria can best be described graphically as the intersection of the PDF of the measurement of the transmission of a ‘1’ and the PDF of the measurement of a ‘0’ transmission. The turbulence conditions vary significantly over time, and thus the receiver performance could benefit from a threshold that varies with the optical signal level [16

16. H. Burris, A. Reed, N. Namazi, W. Scharpf, M. Vicheck, M. Stell, and M. Suite, “Adaptive thresholding for free-space optical communication receivers with multiplicative noise,” in Proc. IEEE Aerospace Conference, vol. 3, pp. 1473–1480 (2002).

,17

17. P. N. Crabtree, Dissertation:Performance-Metric Driven Atmospheric Compensation for Robust Free-Space Laser Communication (Air Force Institute of Technology, Wright-Patterson AFB, OH, 2006).

].

3.2.1. Fixed Threshold

​ ​ ​ ​ ​ ​              P(H0)p0(iT)=P(H1)0p1(im|s)p(s)ds1σelecexp(iT22σelec2)=0p(s)σ1(s)exp{[iTim(s)]22σ12(s)}ds.
(5)

The threshold current iT (in μA) can be solved for numerically whether the PDF of the turbulence-induced power fluctuations p(s) is analytic, measured, or calculated from the histogram of the simulated received power before the measurement noise is applied. Since we want to compare the adaptive threshold approaches to the best possible fixed threshold performance, we used the PDF estimate p(s) of the simulated received power. The noise associated with measuring a ‘0’ is primarily due to thermal noise (a.k.a. Johnson noise). The probability of an error Pe is the probability of a missed detection Pmd plus the probability of a false alarm Pfa so that
Pe=P(H1)Pmd+P(H0)Pfa=Pmd2+Pfa2,
(6)
where

Pmd=120 erfc(im(s)iT2σ1(s))p(s)ds,
(7)
Pfa=12erfc(iT2σelec).
(8)

In Eqs. (7) and (8), erfc(x) is the complementary error function.

3.2.2. Adaptive optimal threshold

For temporally varying turbulence, an ideal optimal adaptive threshold results in the lowest probability of error for each instant in time [15

15. H. L. VanTrees, Detection, estimation, and modulation theory (Wiley, 2002).

,16

16. H. Burris, A. Reed, N. Namazi, W. Scharpf, M. Vicheck, M. Stell, and M. Suite, “Adaptive thresholding for free-space optical communication receivers with multiplicative noise,” in Proc. IEEE Aerospace Conference, vol. 3, pp. 1473–1480 (2002).

]. Since the threshold is determined for each current level, the PDF of the received signal level p(s) is not required for this calculation. Only the estimates of the means (μ 1 and μ 0) and the standard deviations (σ 1 and σ 0) of the two conditions are required to set the threshold. Solving for the optimal adaptive threshold current assuming Gaussian distributions for p 1(im) and p 0(im) yields [17

17. P. N. Crabtree, Dissertation:Performance-Metric Driven Atmospheric Compensation for Robust Free-Space Laser Communication (Air Force Institute of Technology, Wright-Patterson AFB, OH, 2006).

,20

20. H. Burris, A. Reed, N. Namazi, M. Vilcheck, and M. Ferraro, “Use of Kalman filtering in data detection in optical communication systems with multiplicative noise,” in Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP ’01), vol. 4, pp. 2685–2688 (7–11 May 2001).

]

iT=μ0σ12μ1σ02σ12σ02+σ0σ1σ12σ02(μ1μ0)2+​ 2(σ12σ02)ln(σ1σ0).
(9)

The work here assumes μ 0 = 0 (i.e. zero dark current) and σ 0 = σelec, since σshot = σASE = 0 when a ‘0’ is sent. This ideal adaptive threshold system calculates the optimal adaptive threshold for each time slice with the corresponding raw received signal level s in the simulation and implements that threshold to determine whether it is a ‘1’ or a ‘0’. For the adaptive threshold case, the probability of a missed detection and the probability of false alarm now have a threshold that varies with the signal level along with all of the other signal-dependent terms. Accordingly, Pmd becomes
Pmd=120erfc(im(s)iT(s)2σ1(s))p(s)ds,
(10)
where the threshold now becomes a function of the received power s. The Pfa also becomes a function of s given by

Pfa=120erfc(iT(s)2σelec)p(s)ds.
(11)

σ12=σelec2+σshot2+σASE2.
(13)

The estimator bandwidth and the signal level drive these noise sources in Eq. (13), but since the estimator bandwidth need only be in the kHz range to keep up with the turbulence, the noise power is relatively low. Reducing bandwidth of the estimator further increases the latency of the estimator and degrades the performance of the estimator. If μ 1 in Eq. (9) is set to equal the estimated signal i^sand μ00, the equation becomes
i^T=i^sσelec2σelec2σ^12+σelecσ^1σ^12σelec2i^s2+​ 2(σ^12σelec2)ln(σ^1σelec),
(14)
where σ^1is the estimate of σ1 using i^s.

4. Results

4.1. Simulation set-up

The turbulence effects explored subsequently in simulated scenarios were generated using ten Fourier-series-based random phase screens with the correct statistics placed along the path [21

21. B. M. Welsh, “Fourier-series-based atmospheric phase screen generator for simulating anisoplanatic geometries and temporal evolution,” Proc. SPIE 3125, 327 (1997). [CrossRef]

,22

22. J. A. Louthain and B. M. Welsh, “Fourier-series-based phase and amplitude optical field screen generator for weak atmospheric turbulence,” Proc. SPIE 3381, 286–296 (1998). [CrossRef]

]. The layered analytic spherical-wave coherence diameter r 0 sph, spherical-wave Rytov number , and isoplanatic angle θ 0 matched within 1% of the full path continuous atmospheric turbulence parameters.

Computer simulations of airborne single-Tx and double-Tx FSOC systems were performed for the scenarios described in Table 1. The separation distance for all five scenarios for the double-Tx system was 2ρc = 31 cm. The simulations propagate either one or two collimated Gaussian beams depending upon the Tx configuration with a 1/e field radius of W 0 = 2.5 cm using a split-step Fresnel propagation to a 20 cm diameter receiver aperture. Great care was taken to adequately sample the Fresnel propagation between the screens to avoid aliasing in the beam as well as the quadratic phase term [23

23. S. Coy, “Choosing Mesh Spacings and Mesh Dimensions for Wave Optics Simulation,” Proc. SPIE 5894 (2005).

]. At the Rx, the light is coupled into a single-mode fiber to be amplified by an EDFA with a spontaneous emission factor of nsp = 4 and a gain of 30, factoring into the ASE noise σ2 ASE [18

18. S. B. Alexander, Optical Communication Receiver Design, SPIE Tutorial Texts in Optical Engineering, vol. TT22; IEE Telecommunications Series, vol. 37 (SPIE Press, Bellingham, WA, 1997).

]. The simulations modeled the fiber coupling by projecting the field onto the guided mode of a single-mode 4 μm-radius fiber. For this single mode fiber, the efficiency of the coupling was modeled by the LP01 mode field using the Bessel functions of the first and second kind. The mode field diameter of the fiber was 10.5 μm with an index of refraction of n1 = 1.45 and a V number of 2.405. See Refs [24

24. J. A. Louthain, Dissertation: Integrated approach to airborne laser communication, Air Force Institute of Technology, Wright-Patterson AFB, OH, December 2008.

]. and [25

25. J. A. Buck, Fundamentals of Optical Fibers, Wiley-Interscience, 2004.

] for a description of the calculation of the coupling of the fundamental guided mode.

Section 4.2 describes the resulting temporal fade statistics of the detected signal. Section 4.3 compares the PDF’s of the received signal for single and multiple transmitter systems. Finally, Section 4.4 plots the BER for all five scenarios and for different techniques used to improve their performance.

4.2. Bit error rate (BER) fade statistics

Scenarios 1 and 3 did not experience any fades for the double-Tx cases according to the definition given above so the fades are not plotted. However, these scenarios did experience bit errors, and their performance are shown in Section 4.4. For the other three scenarios, Figs. 4
Fig. 4 BER fade statistics for Scenario 2 (HLL). (a) & (c) The mean fade length for a fade above an error rate of 10−3. (b) & (d) The number of fades per second above an error rate of 10−3. Dashed line is double-Tx case and solid line is single-Tx case.
6
Fig. 6 BER fade statistics for Scenario 5 (HHL). (a) & (c) The mean fade length for a fade above an error rate of 10−3. (b) & (d) The number of fades per second above an error rate of 10−3. Dashed line is double-Tx case and solid line is single-Tx case.
show that the double-Tx cases, denoted with dashed line, have shorter and less frequent fades than the single-Tx cases denoted by solid line for all cases. This is due to the fact that the fade depths are reduced when the multiple Tx's “smooth out” the variation in the received power. The only difference between Figs. 4 and 6 for these two cases is the Greenwood frequency of the turbulence. For the low-frequency case in Fig. 4, the fade length is about 4.4 times as long, but there are fewer fades than in the high-fG case in Fig. 6. All three adaptive threshold systems performed much better than the fixed threshold system. The higher-fidelity estimator with fs = 64 fG performed almost as well as the ideal adaptive threshold system. The low-frequency adaptive threshold estimator performed worse than the high-frequency estimator in almost all cases. The two estimators did perform comparably for an SNR above 20 dB for the two transmitter scenario 4 (HHH) case. Since the scintillation indicated by = 0.1979 for this scenario (HHH) was higher than the other four scenarios, the improvement in the low-frequency case was most likely due to the reduction in scintillations when using two transmitters. The peaks in each of the fade rates for Figs. 46 can be graphically explained by varying the threshold for a particular signal like the one shown in Fig. 3. As the threshold successively drops, more and more fades are encountered until the fades get so long that they merge to make longer fades, thereby reducing the number of threshold crossings and number of fades. In each case, as the SNR decreases, the mean fade length increases.

Fig. 5 BER fade statistics for Scenario 4 (HHH). (a) & (c) The mean fade length for a fade above an error rate of 10−3. (b) & (d) The number of fades per second above an error rate of 10−3. Dashed line is double-Tx case and solid line is single-Tx case.

4.3. Probability density function (PDF) estimates of the received signal

4.4. Bit error rate (BER)

Next, the BER's of ideal and realistic adaptive thresholds are compared to the optimal fixed case. Recall this optimal fixed case takes into account the PDF of the received signal p(is) over the ensemble of the runs calculated [see Eq. (5)]. There were 10 independent realizations with 1000 time slices for each realization. The time increments were determined by τs = 1/(64fG) for each of the scenarios. Therefore, each independent realization covered a time frame of over 15 Greenwood time constants, resulting in well over 150 relatively independent realizations per scenario.

It is clear from Fig. 8
Fig. 8 BER for systems with an optimal fixed threshold, ideal adaptive threshold, fs = 64 fG estimator adaptive threshold, and fs = 16 fG estimator adaptive threshold for single Tx (solid lines) and double Tx (dashed lines). Subplots (a)-(d) were calculated for scenarios 1, 2 & 5, 3, and 4, respectively. The data rate was 1 GHz.
that the BER significantly decreases when two transmitters are used (3-10 dB depending upon the scenario). The ideal adaptive threshold systems improved performance by up to 5 dB for the high-Rytov cases in plots (c) and (d). This is substantial since this was compared to the optimal fixed threshold case for the particular scenario which used the actual PDF of the received signal to determine the optimal threshold. This a priori knowledge of the turbulence resulted in an optimistic BER for the fixed threshold. In most cases, the fixed threshold is not chosen in such an accurate manner. The double-Tx systems outperformed all other techniques even though improvements due to the adaptive threshold technique were up to 5 dB. As expected, the system with an ideal adaptive threshold and two transmitters performed the best.

The realistic estimators simulated in this study did, in fact, improve the performance in all cases. The performances of three different adaptive threshold systems are compared in Fig. 8; an ideal adaptive threshold, an adaptive threshold with an estimator operating at fs = 64 fG, and another system with an estimator operating at fs = 16 fG. For a single transmitter, the performance for the fs = 16 fG estimator was the poorest for the highest-Rytov case in scenario 4 (HHH). For this and all other cases, this lower-sampling-rate estimator performance greatly improved when two transmitters were implemented. The single-transmitter cases have more variability in the received irradiance and require a higher fidelity estimator to keep up with the turbulence. This trickle-down effect indicates multiple transmitters can enable the use of cheaper, lower-sampling-rate estimators.

Finally, the turbulence effects for each of the scenarios are compared using the BER performance to determine causality. The only difference between scenarios 2 (HLL) and 5 (HHL) is the speed of the turbulence and therefore, as expected, their BER's are identical. The three scenarios with high Rytov numbers (scenarios 2, 4, and 5) have the worst performance, but the improvement provided by multiple transmitters is much greater for these scenarios. The combination of multiple transmitters and adaptive thresholding provided at least a 10 dB gain over implementing none of them for all three high-Rytov number scenarios. Scenario 5 with a Rytov number 0.20 enjoyed a 13 dB overall improvement. Due to the improvements afforded by these multiple techniques, the high-Rytov cases of 0.20 were on par with Rytov numbers of 0.06 without these techniques. All five scenarios tested 0.06<<0.20 were within 3 dB of each other when all of the improvement techniques were implemented.

5. Conclusion

In all scenarios tested, the coherence diameter r 0 was greater than the diameter of the receiver D, therefore changes in the Rytov number had a much larger effect than r 0 changes. If D/r 0 > 1, the phase effects due to the turbulence would likely have had a larger effect on the BER.

Adaptive thresholding systems provide significant improvement over optimal fixed thresholds for both single-Tx and double-Tx systems, providing an additional 3-4 dB over both systems. As long as the estimator kept up with the turbulence, the realistic estimators performed well. As the scintillation effects were stronger for the single-Tx high-Rytov scenario (HHH), the lower-bandwidth estimator performance lagged behind the high-bandwidth estimator and the ideal adaptive threshold system. The performance degradation in the lower-bandwidth estimator cases was mitigated by using two transmitters to reduce the scintillation. Lower scintillation causes less variability in the signal, allowing the lower-bandwidth estimator to keep up with the turbulence.

The improvement due to implementing two transmitters can be scaled to a small degree for multiple transmitters. A limit to this improvement does exist, since separating beams much greater than 2ρc results in diminishing improvement [8

8. J. A. Louthain, and J. D. Schmidt, “Anisoplanatism in airborne laser communication,” Opt. Express 16(14), 10,769–10,785 (2008). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-16-14-10769.

,10

10. J. A. Louthain, and J. D. Schmidt, “Anisoplanatic Approach to Airborne Laser Communication,” Meeting of the Military Sensing Symposia (MSS) Specialty Group on Active E-O Systems I(AD02), 1–20 (2007).

]. A trade-study should be performed to determine the optimal number of transmitters. The impact of non-uniform turbulence profile (such as slant path) would also be an interesting extension on this research. If further error reduction is required, an interleaver/FEC receiver could be implemented. An interleaver spreads out the errors randomly in time so the FEC code can be used more effectively. The averaging effect of two transmitters not only reduced the BER, it also reduced the length of a fade. Shorter fade lengths require shorter interleavers, reducing data latency and making shorter interleavers more effective.

Acknowledgements

The views presented in this paper are those of the authors and do not necessarily represent the views of the Department of Defense or its components.

References and links

1.

Staff Writers, “Northrop Grumman Awarded DARPA Contract To Design Hybrid Optical/RF Communications Network,” Spacedaily.com (2008). Dated 5 May 2008, URL http://www.spacedaily.com/reports/Northrop Grumman Awarded DARPA Contract To Design Hybrid Optical RF Communications Network 999.html.

2.

R. K. Tyson, J. S. Tharp, and D. E. Canning, “Measurement of the bit-error rate of an adaptive optics, free-space laser communications system, part 2: multichannel configuration, aberration characterization, and closed-loop results,” Opt. Eng. 44(9), (2005).

3.

A. Belmonte, “Influence of atmospheric phase compensation on optical heterodyne power measurements,” Opt. Express 16(9), 6756–6767 (2008). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-16-9-6756

4.

R. K. Tyson, “Adaptive optics and ground-to-space laser communications,” Appl. Opt. 35(19), 3640 (1996). [CrossRef] [PubMed]

5.

S. M. Haas and J. H. Shapiro, “Capacity of Wireless Optical Communications,” IEEE J. Sel. Areas Comm. 21(8), 1346–1357 (2003). [CrossRef]

6.

E. J. Lee and V. W. S. Chan, “Part 1: Optical Communication Over the Clear Turbulent Atmospheric Channel Using Diversity,” IEEE J. Sel. Areas Comm. 22(9), 1896–1906 (2004). [CrossRef]

7.

P. Polynkin, A. Peleg, L. Klein, T. Rhoadarmer, and J. Moloney, “Optimized multiemitter beams for free-space optical communications through turbulent atmosphere,” Opt. Lett. 32(8), 885–887 (2007). [CrossRef] [PubMed]

8.

J. A. Louthain, and J. D. Schmidt, “Anisoplanatism in airborne laser communication,” Opt. Express 16(14), 10,769–10,785 (2008). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-16-14-10769.

9.

R. J. Sasiela, Electromagnetic wave propagation in turbulence. Evaluation and application of Mellin transforms, 2nd Ed. (SPIE Publications, 2007).

10.

J. A. Louthain, and J. D. Schmidt, “Anisoplanatic Approach to Airborne Laser Communication,” Meeting of the Military Sensing Symposia (MSS) Specialty Group on Active E-O Systems I(AD02), 1–20 (2007).

11.

D. L. Fried, “Anisoplanatism in adaptive optics,” J. Opt. Soc. Am. A 72(1), 52–61 (1982). [CrossRef]

12.

L. C. Andrews, and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE Optical Engineering Press Bellingham, WA, 2005).

13.

J. A. Anguita, M. A. Neifeld, and B. V. Vasic, “Spatial correlation and irradiance statistics in a multiple-beam terrestrial free-space optical communication link,” Appl. Opt. 46(26), 6561–6571 (2007). [CrossRef] [PubMed]

14.

M. C. Roggemann, and B. M. Welsh, Imaging Through Turbulence (CRC Press, 1996).

15.

H. L. VanTrees, Detection, estimation, and modulation theory (Wiley, 2002).

16.

H. Burris, A. Reed, N. Namazi, W. Scharpf, M. Vicheck, M. Stell, and M. Suite, “Adaptive thresholding for free-space optical communication receivers with multiplicative noise,” in Proc. IEEE Aerospace Conference, vol. 3, pp. 1473–1480 (2002).

17.

P. N. Crabtree, Dissertation:Performance-Metric Driven Atmospheric Compensation for Robust Free-Space Laser Communication (Air Force Institute of Technology, Wright-Patterson AFB, OH, 2006).

18.

S. B. Alexander, Optical Communication Receiver Design, SPIE Tutorial Texts in Optical Engineering, vol. TT22; IEE Telecommunications Series, vol. 37 (SPIE Press, Bellingham, WA, 1997).

19.

J. D. Schmidt, Dissertation: Free-Space Optical Communications Performance Enhancement by Use of a Single Adaptive Optics Correcting Element (University of Dayton, Dayton, OH, 2006).

20.

H. Burris, A. Reed, N. Namazi, M. Vilcheck, and M. Ferraro, “Use of Kalman filtering in data detection in optical communication systems with multiplicative noise,” in Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP ’01), vol. 4, pp. 2685–2688 (7–11 May 2001).

21.

B. M. Welsh, “Fourier-series-based atmospheric phase screen generator for simulating anisoplanatic geometries and temporal evolution,” Proc. SPIE 3125, 327 (1997). [CrossRef]

22.

J. A. Louthain and B. M. Welsh, “Fourier-series-based phase and amplitude optical field screen generator for weak atmospheric turbulence,” Proc. SPIE 3381, 286–296 (1998). [CrossRef]

23.

S. Coy, “Choosing Mesh Spacings and Mesh Dimensions for Wave Optics Simulation,” Proc. SPIE 5894 (2005).

24.

J. A. Louthain, Dissertation: Integrated approach to airborne laser communication, Air Force Institute of Technology, Wright-Patterson AFB, OH, December 2008.

25.

J. A. Buck, Fundamentals of Optical Fibers, Wiley-Interscience, 2004.

26.

J. A. Louthain and J. D. Schmidt, “Integrated approach to airborne laser communication,” Proc. SPIE 7108(14), (2008). [CrossRef]

27.

J. D. Schmidt, and J. A. Louthain, “Integrated approach to free-space optical communication,” in Proc. SPIE, Optics in Atmospheric Propagation and Adaptive Systems XI, vol. 7200 (SPIE Press, Bellingham, WA, 2009).

OCIS Codes
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(060.4510) Fiber optics and optical communications : Optical communications
(060.2605) Fiber optics and optical communications : Free-space optical communication
(070.7345) Fourier optics and signal processing : Wave propagation

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: February 18, 2010
Revised Manuscript: March 29, 2010
Manuscript Accepted: April 7, 2010
Published: April 14, 2010

Citation
James A. Louthain and Jason D. Schmidt, "Synergy of adaptive thresholds and multiple transmitters in free-space optical communication," Opt. Express 18, 8948-8962 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-9-8948


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References

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