Comparisons of Cn 2 measurements and power-in-fiber
data from two long-path free-space optical communication
experiments
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Citation
Ronald R. Parenti, Steven Michael, Jeffrey M. Roth and Timothy
M. Yarnall, "Comparisons of Cn2 measurements and power-infiber data from two long-path free-space optical communication
experiments", Proc. SPIE 7814, 78140Z (2010);
doi:10.1117/12.864256 © 2010 SPIE
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http://dx.doi.org/10.1117/12.864256
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http://hdl.handle.net/1721.1/61641
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Detailed Terms
Comparisons of Cn2 Measurements and Power-in-Fiber Data from
Two Long-Path Free-Space Optical Communication Experiments
Ronald R. Parenti, Steven Michael, Jeffrey M. Roth, and Timothy M. Yarnall
Massachusetts Institute of Technology Lincoln Laboratory, Lexington, MA 02420-9108
ABSTRACT
Over a two-year period beginning in early 2008, MIT Lincoln Laboratory conducted two free-space optical
communication experiments designed to test the ability of spatial beam diversity, symbol encoding, and interleaving to
reduce the effects of turbulence-induced scintillation. The first of these exercises demonstrated a 2.7 Gb/s link over a
ground-level 5.4 km horizontal path. Signal detection was accomplished through the use of four spatially-separated 12
mm apertures that coupled the received light into pre-amplified single-mode fiber detectors. Similar equipment was
used in a second experiment performed in the fall of 2009, which demonstrated an error-free air-to-ground link at
propagation ranges up to 60 km. In both of these tests power levels at all fiber outputs were sampled at 1 msec intervals,
which enabled a high-rate characterization of the received signal fluctuations.
The database developed from these experiments encompasses a wide range of propagation geometries and turbulence
conditions. This information has subsequently been analyzed in an attempt to correlate estimates of the turbulence
profile with measurements of the scintillation index, characteristic fading time constant, scintillation patch size, and the
shape parameters of the statistical distributions of the received signals. Significant findings include observations of rapid
changes in the scintillation index driven by solar flux variations, consistent similarities in the values of the alpha and
beta shape parameters of the gamma-gamma distribution function, and strong evidence of channel reciprocity.
This work was sponsored by the Department of Defense, RRCO DDR&E, under Air Force Contract FA8721-05-C-0002.
Opinions, interpretations, conclusions and recommendations are those of the authors and are not necessarily endorsed by
the United States Government.
Keywords: free-space optical communications, laser communications, turbulence models, optical scintillation
1. INTRODUCTION
In a five-month rapid development effort that began in the spring of 2008, the Advanced Lasercom Systems and
Operations Group at MIT Lincoln Laboratory built and fielded two custom 2.7 gigabaud lasercom terminals at field sites
located in the western suburbs of Boston. The 1.55 µm transmitter was situated in a shed attached to a fire tower, while
the receiver was housed in the dome of the Laboratory's Firepond telescope facility in Westford, Massachusetts. The
topology of the 5.4 km, near-horizontal propagation path is shown in Figure 1.
Figure 1. Vertical profile of the propagation path for the Firepond communication link experiment. The total propagation
distance was 5.4 km.
Free-Space Laser Communications X, edited by Arun K. Majumdar, Christopher C. Davis,
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This initial field effort, which was known as the MASIVS test, was designed to transmit light from a single activelytracked aperture; at the opposite end of the communication link, signals from four independently-tracked and
temporally-synchronized receivers were summed to reduce the effects of scintillation. To stabilize the pointing of the
transmit beam, low-power laser beams were sent from each of the four receiver apertures back to the transmitter.
Temporal diversity was achieved using symbol interleaving combined with forward error correction coding (FEC),
which was capable of imposing interleaver spans as long as 2 seconds. Data were transmitted via standard terrestrial
network protocols, specifically, Ethernet over SONET. This field effort culminated in a series of data collects
throughout much of September 2008. These results verified the ability of the system to provide high-reliability, errorfree communications under widely varying turbulence conditions using small (12 mm diameter) transceiver optics and a
communications laser that supplied less than 50 mW of optical power1.
In the spring and summer of 2009, an airborne link demonstration referred to as the FOCAL (Free-Space Optical
Communications Airborne Link) experiment was assembled using essentially the same communication hardware
employed in the horizontal-path test. During this exercise, a 2.7 gigabaud link was established between a single 25 mm
transmitter in a Twin Otter aircraft and four 12 mm receivers situated in a small optical dome on the roof of Lincoln
Laboratory's main facility. Owing to line-of-sight limitations of the ground facility the flight profiles were restricted to
arcs that covered about 180°, as illustrated in Figure 2. Although this hardware was initially designed to achieve a
maximum range of 25 km with a 200 mW source, in the final set of flights of the 13-flight sequence reliable links were
maintained out to a range of 60 km by increasing the transmit power to 700 mW. This test successfully demonstrated
file transfers of frames containing random data fields as well as high definition video recorded by the MASIVS (MultiAperture Sparse-Imager Video System) sensor constructed by the Advanced Electro-Optical Systems Group at Lincoln
Laboratory.
During both of the experimental efforts just described, ancillary measurements of channel conditions were provided by
portable weather stations and a Scintec BLS900 scintillometer; in addition, a Goodrich infrared camera was used to
obtain 2-dimensional imagery of receiver-plane scintillation patterns. A description of the data generated by this
instrument suite is the primary subject of this article.
Figure 2. Example of a flight path used for the FOCAL air-to-ground communication experiment. A total of 13 flights
were performed, and the radii of the flight arcs ranged from 25 to 60 km.
2. TRANSCEIVER ARCHITECTURE OVERVIEW
The suppression of turbulence-induced scintillation is essential for achieving good performance in free-space links that
operate at optical wavelengths. The system constructed by Lincoln Laboratory incorporates two separate approaches to
mitigate the impact of scintillation. Spatial diversity is exploited through the use of multiple small-aperture receivers,
which are specifically designed to exhibit uncorrelated fluctuation statistics. In the limit of zero mutual correlation, the
variance of the sum of N receiver outputs will be reduced by a factor of 1/N. The likelihood of data loss is further
reduced through byte-level interleaving combined with forward error correction. A more detailed discussion of the
theoretical performance of this encoding and interleaving scheme has been published2.
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A schematic description of the transmit and receive optics used in the MASIVS and FOCAL experiments is shown in
Figure 3. The 1.55 µm downlink laser source propagates through a single-aperture transmitter, as indicated by the arrow
that projects from the beam-tracking module on the left side of Figure 3. Transmitter beam stabilization is maintained
using centroid information derived from four mutually-incoherent 1.55 µm tracking lasers propagated from the ground
terminal (signified by the arrows emanating from the trackers on the right side of Figure 3). The ground terminal
incorporates four receivers, each of which is independently pointed to ensure that the collected light is efficiently
coupled into pre-amplified single-mode fiber detectors. The electrical signals from these four detectors are incoherently
added, and the summation signal is subsequently sent to the symbol decoding hardware.
Figure 3. Downlink optical diagram showing the data-transmission beam (indicated by the arrows projecting from the left
side of this figure) and upward-propagating tracking beams (indicated by the arrows projecting from the right side of
this figure). Separate high-bandwidth trackers are used to stabilize the pointing direction of each of the laser sources
and correct angle-of-arrival errors at the detectors.
The data encoding and interleaving hardware constructed for these experiments is beyond the scope of this paper, but a
detailed description can be found elsewhere3. A key aspect of this architecture is that network-compatible interfaces
were incorporated in both transceiver nodes, which facilitated the transmission of Gigabit Ethernet (GbE) and SONET
(OC-12, OC-48) for the 2.5G rate families. Additionally, client interfaces of OC-192 and 10GE-WAN with interleaved
OTU2 on the free space interface for the 10G rate families can be supported by this hardware. These capabilities allow
terrestrial fiber-optic network traffic to be transparently transported over the free-space optical link. It should be
emphasized that this implementation of data interleaving does not reduce the overall data rate, but increased network
latency is an inherent side effect of temporal interleaving.
3. MEASUREMENTS OF CHANNEL BEHAVIOR
Previous comparisons of scintillometer and power-in-fiber output generated during the MASIVS horizontal-path
experiment indicate that the magnitude of the signal fluctuations under daytime conditions are consistent with those
predicted by the Hufnagel-Valley (HV5/7) model4. The anticipated diurnal cycles were seen during those measurements;
2
the daily channel patterns usually included brief periods of very low Cn readings during the morning and evening
transition periods. Rapid changes in the channel characteristics were also discovered during daytime operation on
partly-cloudy days, which were well correlated with the fluctuations in the solar radiance along the propagation path; the
2
time constants of these Cn fluctuations were typically of the order of a few minutes. The propagation path described
previously in Figure 1 was about 50 m above terrain that was covered primarily by natural vegetation.
During the FOCAL air-to-ground communication link tests, ground-level measurements of the scintillation strength were
made over a 1.6 km horizontal path between two building roof-tops on Hanscom field. The data illustrated in Figure 4
show a somewhat larger day/night variation than that seen in the prior year for the vegetation-covered terrain, but rapid
2
changes in the Cn conditions were again observed when the strength of the solar radiance varied. On average, the
turbulence strength was in good agreement with that predicted by the HV5/7 model.
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Figure 4. Scintillometer results from one week of channel measurements during the FOCAL experiment.
The two-dimensional scintillation imagery, which was collected at the focal plane of the receiver in both sets of
experiments, provided another useful characterization of channel behavior. As suggested in Figure 5, the spatial
structure of the far-field intensity pattern was found to be inversely related to the turbulence strength. Several published
2
theories predict that this correlation parameter will be independent of Cn for weak turbulence and approximately equal
to the Fresnel distance for a propagation path of length L
ρI ≈ λ L ,
(1)
whereas for strong turbulence the functional relationship is expected to be5
ρI ≈
Moderate Turbulence
0.4 λ L
( )
σ I2
35
.
(2)
Strong Turbulence
Figure 5. Scintillometer imagery collected during moderate and strong turbulence conditions over a 5.4 km propagation
path. The characteristic scale size of the intensity fluctuations is found to be a function of the turbulence strength, and
2
becomes smaller as Cn becomes large.
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Scintillation Reduction Factor
Equations (1) and (2) have a direct impact on the design of multiple small-aperture transceivers, since the chosen
aperture diameter must be smaller than the expected r0 value to avoid the need for high-order phase correction and have
an aperture spacing greater than ρI to ensure that the scintillation-induced signal fluctuations will be uncorrelated. The
relationship given in Equation (2) was qualitatively verified during the horizontal-path experiments, for which the
average receiver separation was about 15 cm. As indicated in Figure 6, the ratio between the signal variation measured
by a single receiver and the incoherent sum of four receivers has a strong dependence on the measured turbulence
2
strength, and the ratio approaches 4 as Cn value becomes large. While the full benefit of multiple receivers is not
realized under weak turbulence conditions, scintillation mitigation is less important in this regime since the absolute
magnitude of channel-induced fluctuations is much smaller.
2
Figure 6. Ratio of single-receiver signal fluctuations and the average of four incoherent signals as a function of Cn . These
results are consistent with a correlation distance that is inversely proportional to the strength of the turbulence along the
propagation channel. These data were derived from the MASIVS horizontal-path experiment.
4. ANALYSIS OF AIR-TO-GROUND POWER-IN-FIBER SIGNAL FLUCTUATIONS
The air-to-ground link geometry used in the series of tests performed in 2009 provided a good opportunity to compare
measurements of the scintillation index with predictions derived from several turbulence profile models. Estimates were
made using the spherical-wave expression for Rytov scintillation for propagation from the slant range L to the ground
L
σ R2
≈ 0.561 k
76
∫
0
Cn2 ( z ) z 5
6
z⎞
⎛
⎜⎝ 1 − ⎟⎠
L
56
dz .
(3)
The data shown in Figure 7 were taken from a single day during which the Twin Otter aircraft was flown at
approximately 12 kft at slant ranges from 20 km to 60 km. As indicated in this figure, the collected data were most
accurately predicted by calculations based on the HV5/7 daytime turbulence profile.
The mean signal power transmitted through the optical channel and the scintillation index provide a rough estimate of
the static and dynamic propagation losses due to the effects of atmospheric attenuation and turbulence, but it is well
known that the detailed structure of the low-signal tail of the signal distribution function has a strong impact on the
performance of free-space communications. In recent years the 2-parameter gamma-gamma function proposed by
Andrews and Phillips6 has been widely applied to this problem, and several experimental groups have reported good
success in applying this model. The Lincoln Laboratory link experiments performed in 2008 and 2009 also show good
agreement with the gamma-gamma model, but the analysis of these data consistently show that a 1-parameter variation
of this model that incorporates the constraint α=β yields adequate accuracy. This result is illustrated in Figure 8, which
compares the 1-parameter model with signal distributions derived from receiver data generated by both the ground-based
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and airborne receivers during a typical FOCAL communication test. An analysis of data from the MASIVS experiment
performed in the previous year produced similar conclusions2.
Figure 7. Comparison of measured power-in-fiber scintillation index with predictions derived using standard turbulence
profile models. Best agreement was usually obtained with the Hufnagel-Valley daytime model.
Receiver Power
- .- - r-r Model with a =
Four-Laser
Sum Output
x= 3.6
Receiver Power
- r'-rModeIwithu=
10
-45
-40
-55
-50
-40
-.45
45
-45
-40
-35
-30
-25
-20
Power-In-FIber (dBmW)
Powr-Th-FIbe.r dBmW)
Airborne Receiver
Ground Receiver
-15
-10
Figure 8. Results of optimal curve fitting to received-signal probability density data collected by the ground and airborne
receivers in the FOCAL system. Calculations of this type consistently found good fits to gamma-gamma functions
with the constraint α=β.
A possible explanation for the observed degeneracy of the distribution shape parameters is the incorporation of highprecision tracking in the transceivers at both ends of the communication link. This premise was tested analytically by
first assuming a degenerate form of the gamma-gamma distribution to represent the scintillation function
pscint ( I o ) =
2 α 2α
⎛ Io ⎞
⎜ ⎟
2
Γ (α ) μ ⎝ μ ⎠
α −1
(
K0 2 α
Io μ
)
,
(4)
and constructing a power-law function to describe the effect of Gaussian pointing errors applied to a two-dimensional
Gaussian beam7
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ptilt ( I I o ) =
n
Io
(I
Io )
n−1
.
(5)
The marginal distribution shown below was then computed numerically for a range of parametric values
pnet ( I ) =
∞
∫ ptilt ( I Io ) pscint ( Io ) d Io
.
(6)
0
The resulting functions were found to closely resemble the 2-parameter gamma-gamma model, and curve fits to the
gamma-gamma function yielded α and β parameters that were identical until the tracking errors become comparable to
the diffraction-limited angular resolution of the receiver. Once the tracking errors reach this threshold the values of the
two shape parameters rapidly diverge, with one growing much larger than the zero-jitter value. The results of this study,
which are briefly summarized in Figure 9, are consistent with measurements made during tests when the track
stabilization was intentionally disabled or suffered a mechanical malfunction.
Figure 9. Dependence of the gamma-gamma fit parameters on the severity of the receiver tracking error. The values of the
parameters are found to diverge when the tracking errors becomes comparable to the receiver's diffraction-limited
angular resolution.
5. CHANNEL RECIPROCITY
As discussed in Section 2 of this article and illustrated in Figure 3, the high-bandwidth data link demonstrated in these
tests was established between the single transmitter on the airborne transceiver and four ground-based receivers.
However, the four upward-propagating tracking beams generated by the ground node are incoherently collected by a
single receiver and the received power is sampled at 1 kHz by a single-mode fiber detector. In this manner,
simultaneous measurements of channel transmission were obtained, which enabled a variety of interesting crosscorrelation statistics to be computed. Of particular interest is the evidence of channel reciprocity. Point-to-point channel
reciprocity was rigorously proven by Shapiro8 in 1971 and subsequently addressed by Fried and Yura9, but to our
knowledge has never been validated outside of the laboratory. Time-correlated analysis of data from both the
horizontal-path experiments and air-to-ground experiments conducted by Lincoln Laboratory has uncovered strong
evidence of the reciprocity effect in an optical link that incorporates transmit and receive apertures of finite dimensions.
Figure 10 shows an example of a cross-correlation function developed from optical power time series collected
simultaneously by the two receiver nodes. The cross-correlation peak at zero time shift is seen to be very strong, and the
width of the peak is only slightly larger than one sampling time period. (The slight offset seen in this chart is due to a
misalignment of the two computer clocks.) The insert shows a short time sequence comparison for zero-time
displacement.
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o .6
0.5
I
0.4
O3
0.2
Time Series Comparison
0.1
-01
-10
5
0
5
10
Displacement (sec)
Figure 10. Cross-correlation function for the time-series outputs of receivers of the two nodes of the optical link. The peak
offset is due to a time misalignment of the two computers used in the data recording.
Figure 11 gives a more quantitative summary of the results derived in this mutual-correlation analysis. The most
significant number in this table is the correlation between the single receiver on the airborne platform (which
incoherently sums the four tracking beams) and the sum output of the four ground-based receivers. The numbers shown
are typical for the range of test conditions covered; correlation values in the range of 50 to 80% were routinely obtained.
The implication of this result is that it is possible for the transmitter to estimate the likelihood that a bit will be correctly
received before it is sent. This information can potentially be used in a variety of ways to improve link reliability and
reduce laser power requirements.
Figure 11. Representative correlation results for the horizontal-path and air-to-ground experiments. The correlation values
in the last column represent to the closest match between the bi-directional path geometries defined by the propagation
paths of the four tracking beams projected from the ground-based transceiver. The propagation ranges for these two
tests were 5.4 km and 40 km, respectively.
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6. CONCLUSIONS
In support of a comprehensive set of free-space communication link experiments conducted over a two-year period by
Lincoln Laboratory, a variety of data analysis activities were performed that have added to our understanding of the
optical channel. Measurements of the ground-level turbulence strength generally confirmed the predictions of the HV5/7
2
model, but rapid variations in the daytime Cn values were also observed and found to be well correlated with
fluctuations in solar illumination. Two-dimensional images of far-field scintillation patterns were recorded frequently
during these experiments, and subsequent analysis of these data demonstrated that the characteristic spatial correlation
radius is a function of both the Fresnel distance and the scintillation index. The validity of the gamma-gamma model
was also investigated, and it was found that the two shape parameters were usually equivalent for the propagation
geometries used in these measurements.
One of the more interesting observations made during these tests was the high correlation between the power-in-fiber
signal fluctuations seen by the two transceiver nodes. The practical utility of this effect is still undetermined, but the
potential exists for improved link reliability and more efficient use of source power.
REFERENCES
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Henion, S. R., "Architecture Overview and Data Summary of a 5.4 km Free-Space Laser Communications
Experiment," SPIE 7464, 746404 (2009).
[2] Michael, S., Parenti, R. R., Moores, J. D., Wilcox Jr., W. E., Yarnall, T. M., Volpicelli, A. M., and Taylor, J. A.,
"The Use of Statistical Channel Models, Full-Field Propagation Codes, and Field Data to Predict Link
Availability," SPIE 7464, 74640O (2009).
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Optical Communication Experiment," SPIE 7464, 746409 (2009).
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Fluctuations Observed During a 5-km Communication Link Experiment," SPIE 7324, 73240B (2009).
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[8] Shapiro, J. H., "Reciprocity of the Turbulent Atmosphere," J. Opt. Soc. Am. 61, 492 (1971).
[9] Fried, D. L. and Yura, H. T., “Telescope-Performance Reciprocity for Propagation in a Turbulent Medium,” J. Opt.
Soc. Am. 62, 600 (1972).
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