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This PDF file contains the front matter associated with SPIE
Proceedings Volume 7814, including the Title Page, Copyright
information, Table of Contents, and the Conference Committee listing.
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A 10 Gbps aperture agnostic data buffer has been developed to mitigate packet loss over highly scintillated FSO links
operating in a hybrid FSO/RF network. The buffer incorporates a custom IP packet inspection and scheduling processor.
Packet buffering and transmission scheduling is determined from link availability and a QoS parameter in the IP header
based upon RFC 2474 (Differentiated Services). Buffer metric parameters are monitored and could be provided to the
network management system. Integration of the novel buffer into the FSO link along with improved network routers
allows operation under strong scintillation conditions at fade margins as low as 8 dB. We present the salient performance
characteristics of a buffered FSO modem with VOA-emulated atmospheric fading statistics. Application test cases,
including a TCP/IP MPEG-4 video stream, have been emulated both to determine the effects of packet loss, latency and
intra-packet jitter introduced by buffering and to optimize traffic flow settings.
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We present results of the acquisition and pointing system from successful aircraft-to-ground optical communication
demonstrations performed at JPL and nearby at the Table Mountain Facility. Pointing acquisition was accomplished by
first using a GPS/INS system to point the aircraft transceiver's beam at the ground station which was equipped with a
wide-field camera for acquisition, then locking the ground station pointing to the aircraft's beam. Finally, the aircraft
transceiver pointing was locked to the return beam from the ground. Before we began the design and construction of the
pointing control system we obtained flight data of typical pointing disturbances on the target aircraft. We then used
these data in simulations of the acquisition process and of closed-loop operation. These simulations were used to make
design decisions. Excellent pointing performance was achieved in spite of the large disturbances on the aircraft by
using a direct-drive brushless DC motor gimbal which provided both passive disturbance isolation and high pointing
control loop bandwidth.
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Fundamental characteristics of non-directed line-of-sight links for indoor wireless optical communication systems have
been widely discussed. In this paper, we present experimental visible light channel characterization results, including
impulse response and path loss, and further predict the fundamental communication system performance trade-offs
among transmitted optical power, range, data rate and bit-error rate. These results provide guidelines to system design.
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Directional wireless networks using FSO and RF transmissions provide wireless backbone support for mobile
communications in dynamic environments. The heterogeneous and dynamic nature of such networks challenges their
robustness and requires self-organization mechanisms to assure end-to-end broadband connectivity. We developed a
framework based on the definition of a potential energy function to characterize robustness in communication networks
and the study of first and second order variations of the potential energy to provide prediction and control strategies for
network performance optimization. In this paper, we present non-convex molecular potentials such as the Morse
Potential, used to describe the potential energy of bonds within molecules, for the characterization of communication
links in the presence of physical constraints such as the power available at the network nodes. The inclusion of the
Morse Potential translates into adaptive control strategies where forces on network nodes drive the release, retention or
reconfiguration of communication links for network performance optimization. Simulation results show the effectiveness
of our self-organized control mechanism, where the physical topology reorganizes to maximize the number of source to
destination communicating pairs. Molecular Normal Mode Analysis (NMA) techniques for assessing network
performance degradation in dynamic networks are also presented. Preliminary results show correlation between peaks in
the eigenvalues of the Hessian of the network potential and network degradation.
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Olivier Bouchet, Pascal Porcon, Joachim W. Walewski, Stefan Nerreter, Klaus-Dieter Langer, Luz Fernández, Jelena Vucic, Thomas Kamalakis, Georgia Ntogari, et al.
During the European collaborative project
OMEGA, two optical-wireless prototypes have been
developed. The first prototype operates in the near-infrared
spectral region and features Giga Ethernet connectivity, a
simple transceiver architecture due to the use of on-off
keying, a multi-sector transceiver, and an ultra-fast switch
for sector-to-sector hand over. This full-duplex system,
composed by one base station and one module, transmits
data on three meters.
The second prototype is a visible-light-communications
system based on DMT signal processing and an adapted
MAC sublayer. Data rates around to 100 Mb/s at the
physical layer are achieved. This broadcast system,
composed also by one base station and one module, transmits
data up to two meters.
In this paper we present the adapted optical wireless
media-access-control sublayer protocol for visible-light
communications. This protocol accommodates link
adaptation from 128 Mb/s to 1024 Mb/s with multi-sector
coverage, and half-duplex or full-duplex transmission.
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Indoor Optical Wireless and Non-Line-of-Sight FSO Communication
We report some latest experimental results on non-line-of-sight (NLOS) ultraviolet (UV) scattering communication
channel characteristics. Those results include both channel path losses and impulse responses, critical for UV
communication system design. Path losses were measured using a UV light-emitting-diodes (LEDs) based test-bed,
while impulse responses by a UV laser based test-bed. The effects of transmitter and receiver pointing angles, separation
distance and transmit beam angle are demonstrated.
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High-speed optical wireless systems are challenging to implement, due to limitations in available components, and
implementation of the necessary high speed electronics. In this paper we report on the development of a gigabit/s class
infrared indoor optical wireless system that uses commercially available components. System challenges and design
choices are discussed together with details of demonstrator construction. Results from the implementation of a
demonstration system are also detailed, together with a discussion of how this might scale in the future.
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The performance of non-line-of-sight (NLOS) ultraviolet (UV) communication receiver has been analyzed under an
assumption of no inter-symbol interference (ISI) in the literature. However, ISI may become detrimental when the data
rate increases in a multiple scattering UV channel. We consider relatively high data rate and develop a performance
model with the ISI effect due to channel delay spread. Both analytical derivation and newly reported experimental
results on impulse response and path loss are introduced and incorporated. The results reveal the close connection
between bit error rate (BER) performance and data rate in different transmit/receive geometry, and the power penalty
compared with that of an ISI-free system.
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The 'internet of things' will require very low power wireless communications, preferably using sensors that scavenge
power from their environment. Free space optics allows communications over long ranges, with simple transceivers at
each end, offering the possibility of low energy consumption. In addition there can be sufficient energy in the
communications beam to power simple terminals. In this paper we report experimental results from an architecture that
achieves this. A base station that tracks sensors in its coverage area and communicates with them using low divergence
optical beams is presented. Sensor nodes use modulated retro-reflectors to communicate with the base station, and the
nodes are powered by the illuminating beam. The paper presents design and implementation details, as well as future
directions for this work.
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In terrestrial free-space laser communication, aside from pointing issues, the major problem that have to be dealt
with is the turbulent atmosphere that produces irradiance fluctuations in the received signal, greatly reducing
the link performance. Aperture averaging is the standard method used to mitigate these irradiance fluctuations
consisting in increasing the area of the detector, or effectively increasing it by using a collecting lens with a
diameter as large as possible. Prediction of the aperture averaging factor for Gaussian beam with currently
available theory is compared with data collected experimentally and simulations based in the beam propagation
method, where the atmospheric turbulence is represented by linearly spaced random phase screens. Experiments
were carried out using a collecting lens with two simultaneous detectors, one of them with a small aperture to
emulate an effective point detector, while the other one was mounted with interchangeable diaphragms, hence
measurements for different aperture diameters could be made. The testbed for the experiments consists of a
nearly horizontal path of 1.2 km with the transmitter and receiver on either side of the optical link. The analysis
of the experimental data is used to characterize the aperture averaging factor when different values of laser
divergence are selected.
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Signal encryption and recovery using chaotic optical waves has been a subject of active research in the past 10 years. Since an acousto-optic Bragg cell with zeroth- and first-order feedback exhibits chaotic behavior past the threshold for
bistability, such a system was recently examined for possible chaotic encryption using a low-amplitude sinusoidal signal
applied via the bias input of the sound cell driver 1, 2. Subsequent recovery of the message signal was carried out via a
heterodyne strategy employing a locally generated chaotic carrier, with threshold parameters matched to the transmitting
Bragg cell. The simulation results, though encouraging, were limited to relatively low chaos frequencies and sinusoidal
message signals only. In this paper, we extend the previous work by (i) increasing the chaos frequency using appropriate
parameter control; (ii) carefully examining the system sensitivity to three system parameters, viz., feedback delay,
feedback gain, and dc bias level; (iii) examine signal recoverability relative to shifts in the three parameters mentioned
above relative to the transmitter; and (iv) determining the robustness of such a system relative to the primary transmitter
parameters. Additionally, we consider also the effect of the additive bandpass noise (obtained from white Gaussian noise
in the simulator) on signal recovery in such a system from a performance standpoint. It is also conjectured that signal
recovery can be effected by passing the modulated light through a second sound cell in a matched chaotic regime. This
aspect is also under investigation.
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Free space optical (FSO) sensor networks using direct line of light (LOS) laser links can provide spatially efficient and
physically secure connectivity. The data rates can range from bits/s to hundreds of Mb/s with the complete optical
transceiver system consuming power in the tens of mW. These features are advantageous for low-power communication
networks over short distances in environments where LOS is available, and where radio frequency connectivity must be
avoided because of interference or security problems. The range of links in FSO networks is limited by power
requirements and angular coverage. In order for FSO directional networks to provide viable short-range connectivity, the
networks must provide signal coverage over a wide field of view and operate with efficient media access protocols to
minimize random access times for the independent transmitting nodes within the network. In this paper, the system
design of a FSO sensor network is presented. The system includes a network of small, low power (mW), integrated
systems, or "motes," that transmit data optically to a central "cluster head," which controls the network traffic of all the
motes and can relay data to another cluster head in a series of multi-hops to achieve data communication over longer
distances. To provide wide field of view signal coverage, each cluster head is equipped with multiple vertical cavity
surface emitting lasers oriented in different directions and controlled to diverge at 10°. To implement the proper media
access controls, a properly designed master-slave network connecting multiple motes to a cluster head was developed
and implemented. The network can handle multiple access from all motes within each cluster head's field of view, as
well as set up a directional network backbone between multiple cluster heads, so that signals collected from a mote can
be relayed through other cluster heads, until the signal is delivered to its destination. This paper presents the network
architecture and optical communication system hardware of our FSO sensor network, and some experimental
performance results of our multiple access protocol attempting to resolve channel contention between 10 motes and a
cluster head.
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Optical Turbulence Characterization and Beam Propagation I
In a laboratory experiment we propagate a continuous-wave, expanded laser beam over a surface with evenly
distributed heat and record the received distorted optical signal. Temperature is continuously measured in two
fixed points to determine turbulence strength. Through a number of trials covering a wide range of turbulence
conditions we demonstrate that the temporal correlation of the received signal fluctuations has a strong dependence
on the turbulence strength at the link path. Power spectra of the received signals show a clear increase
in both slope and maximum frequency as the temperature gradient increases. Measurements suggest that scintillation
also correlates with temporal correlation at weak turbulence conditions and such correlation decays in
stronger conditions.
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We use the results of the theory of wave propagation in turbulence to analyze the effects of the atmospheric turbulence
on the Free-Space Optical Communication systems under weak and strong scintillation conditions. We found that for the
traditional fiber coupling arrangement statistics of the Power-in-Fiber (PIF) is sensitive to the phase fluctuation at the
collecting aperture, rather than amplitude fluctuation (scintillation). Larger receiving aperture produces stronger PIF
fluctuation. Similar to the scintillation of the sharp focused beams second-order scattering dominates PIF fluctuation for
the weak and strong scintillation conditions. This should have serious effect on the probability distribution of the PIF.
A new coupling arrangement is suggested that alleviates the destructive effect of the phase fluctuation, and allows the
use of large receiving apertures. The trade-off is the decreased coupling efficiency. For our new coupling scheme the PIF
fluctuation is determined by the power flux fluctuation through the collecting aperture. This allows taking advantage of
the scintillation averaging effect to suppress the fading. We review the results of the rigorous Markov-approximation-based
theory of the scintillation averaging that is valid both for a weak and strong scintillation conditions. This technique
reveals several distinct regimes of the power flux fluctuation including the situation where fluctuation is relatively small,
but is not described by the perturbation (Rytov's) theory. We also show how the energy conservation principle inherent
to the wave propagation in the clear air turbulence provides an accelerated rate of the scintillation averaging compare to
the typical averaging estimates.
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A portable differential image motion sensor (DIMS) has been developed and field demonstrated to measure the
atmospheric coherence diameter, or Fried parameter, r0, both at daytime and at night. The hardware design was
developed using system requirements and performance analysis. A graphical user interface (GUI) and software were
developed to automatically measure r0 from collected imagery data. The DIMS system uses a short wave infrared
(SWIR) camera, IR telescope with custom environmental enclosure, a rack-mount computer accessed remotely through a
laptop, and an equatorial mount and tripod for accurate pointing at a selected star. The system is two-man portable. The
sensor continuously measures r0 from star imagery during clear weather at any time of day or night, with an update rate
of 10 minutes. A continuously nutating optical wedge moves the star image in a circle allowing automatic background
subtraction. Data output is provided at the SWIR 1.6 μm wavelength and scaled to 0.55 μm and pointing at zenith. Valid
r0 measurements range is from 1 cm to 20 cm (in the visible waveband). The r0 measurements over time were performed
at daytime at sea level in San Diego. The largest values of r0 were observed near and after the sunset. This approach
provides a straight-forward path to sea-based seeing measurements with an addition of a stabilized platform.
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Irradiance data were collected over a 1km horizontal terrestrial path using several different sized receiving apertures.
The data were collected under moderate-to-strong turbulence conditions. The receiver system consisted of a 154mm
(6") refracting telescope outfitted with several removable apertures. The path was instrumented with three 3-axis
anemometers and three scintillometers, two of which were capable of measuring the inner scale of turbulence in addition
to Cn2. Histograms were formed with the data and compared to the Log-Normal and Gamma-Gamma PDF models. As
expected, neither PDF model was applicable under all conditions of aperture averaging. Hypotheses are made as to why
the models were unable to completely capture the effects of aperture averaging on received irradiance data.
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Optical Turbulence Characterization and Beam Propagation II
We present some preliminary results from our recent free-space optical communications field test experiments in
the foggy littoral environment along the coast of Point Loma, San Diego, conducted between October 2009 and
June 2010. Our custom-built 850nm lasercomm system uses on-off keyed non-return-to-zero intensity-modulation
and direct-detection to transmit pseudo-random bit sequences (PN-11 codes) at 250 Mbps over a 300m horizontal
atmospheric path. We investigate improvements offered by using the latest Advanced Navy Aerosol Model to
calculate the aerosol size-distribution function, a fundamental input to the radiative transfer code which we use
to generate an estimate of the channel frequency response/impulse-response function. The estimated channel
response function is used to design an equalization filter to correct signal distortion due to multiple-scattering
effects and additive noise. We compare the performance of the Advanced Navy Aerosol Model against the
more simplistic log-normal, Gaussian, and Mooradian Pt. Loma distributions. In this conference proceeding
manuscript we are presenting only preliminary findings of our work in progress. Additional analysis, verification,
and study is required before any final results can be posited from these preliminary findings.
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The AFIT Center for Directed Energy's High Energy Laser End-to-End Operational Simulation (HELEEOS) model
allows for the calculation of the irradiance from within a high energy laser beam that is scattered by molecules and
particulates in the atmosphere to an off-axis observation point, while incorporating the spreading effects of the
turbulence and thermal blooming. Field experiments conducted at Wright-Patterson AFB, Ohio in summer 2009
allowed for validation measurements for the HELEEOS off-axis algorithm to be collected. Turbulence strength
measurements were made at a wavelength of 1.55 μm using a state of the art bistatic turbulence profiler for both
horizontal and vertical paths. Pressure, wind speed, wind direction, relative humidity and aerosol loading data were
collected simultaneously with the Cn2 measurements. As part of the experiment, the profiler's beams were imaged offaxis
with a calibrated camera array and the received irradiance of the off-axis scattering was quantified.
Characterization of the aerosol distribution along the laser path and the path to the observer is accomplished by
determining the visibility and climatological aerosols for southwestern Ohio. Comparisons between predicted and
measured off-axis irradiance are made.
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Atmospheric turbulence can cause severe blurring and scintillation in images. These distortions result in less
detailed images. Using only image enhancement techniques can improve the quality of the images to some extend,
but usually not enough to see all details. Turbulence correction techniques, such as post-processing techniques
using a deconvolution, are developed and show good results. A more profound understanding of atmospheric
turbulence, and especially the impact of turbulence on the image quality, might help to improve the quality of
these images even further.
To this end, we present a simple method of estimating the shape and size of the point spread function. The
method is tested using images from an ongoing trial in South-Africa.
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Laser beam propagation in maritime environment is particularly challenging, not only for scattering and absorption due
to high humidity, but also for a different behavior of atmospheric turbulence with respect to terrestrial propagation.
Recently, a new power spectrum for the fluctuations of the refractive index in the Earth's atmosphere has been
introduced to describe maritime atmospheric turbulence. This maritime power spectral model shows a characteristic
bump, similar to Hill's bump, that appears when the product between the wavenumber and the inner scale is around
unity, κ • l0 ~1. In this paper, under weak turbulence conditions, we use the mentioned maritime power spectrum to
analyze long term beam spread, beam wander and Strehl ratio of a Gaussian beam wave propagating through maritime
atmospheric turbulence.
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We have developed an approach to multiple-access lasercom that adopts the commercial paradigm of sharing the most
expensive terminal resources among all users. Space-time division multiple access (STDMA), analogous to an optical
space-time switch, hops the transmit beam and receive direction among multiple users and exchanges data while the
beam dwells on a user. A key enabler of STDMA is electronic beam steering using liquid crystal optical phased arrays,
which provides fast, precise, and agile beam re-pointing. We have built the first optical STDMA terminal, combining
beam hopping between remote terminals with coherent combining of both transmit and receive apertures, which is an
effective means for increasing antenna gain in systems for which large aperture components are impractical. Coherent
beam combining provided the expected increase in antenna gain, and the terminal was found to re-point the beam among
users quickly and precisely enough to suffer only minor throughput degradation. Communications test were performed
using 10 Gb/s Ethernet for a single-aperture configuration. Performance is presented as a function of angle scan speed
and STDMA dwell time per remote terminal. The results suggest that STDMA is a viable technology for supporting
multiple-access space-based laser communication.
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Free space optical technologies are currently only very marginally used in aviation, particularly for communication
purposes. Most applications occur in a military environment, with civilian aviation remaining oblivious to its advantages.
One of these is high-bandwidth communication between the various actors available in an aeronautical network.
Considerable research is underway in order to resolve a multitude of issues like reliable reception and transmission of the
optical signal and the construction of high performance, small and lightweight terminals for the optical transceiver. The
slow Pointing, Acquisition and Tracking of the latter represents a significant issue, which detracts from their usability in
such an environment. Since an aircraft may carry only a limited number of such terminals on board, the delay of a
terminal in reacquiring a target (which is in the order of several seconds) constitutes a significant hurdle in achieving
satisfactory connectivity. This paper proposes an optimization technique, in which packet are reordered dynamically
before transmission in the sender node in order to minimize terminal movement and thus avoid the time-consuming PAT
process. Several parameters are considered such as QoS of the packets, minimization of the number of movements of the
terminal and of the distance it must traverse when it reacquires a target. The algorithm was tested by integrating it into a
custom built, discrete event SystemC simulator. The results verify that incorporating into such a system yields tangible
benefits in terms of the practical throughput achieved by the system through the minimization of idle time, while
moving.
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In this paper we describe a free-space optics (FSO) based mobile sensor network that is not subject to RF interference
common to wireless sensor networks. FSO-based mobile sensor networks can potentially be used in applications where
security of communication, including freedom from susceptibility to jamming, is important. The design of nodes
containing multiple transceivers each composed of an LED and an angle-diversity array of identical photo detectors is
discussed in this paper. Depending on the number of photodetectors in the array and the angular field of view of each
photo detector we may obtain an increase in the signal to noise ratio of the overall optical communication system.
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In this paper, we propose a Free-Space Optical (FSO) system model based on multiple subcarrier modulation
(MSM) using M-ary Phase Shift Keying (M-ary PSK) scheme over Intensity Modulation Direct Detection optical
link. We investigate the impact of aperture averaging on our model across weak-to-strong turbulence regimes
taking into consideration the intermodulation distortion term due to the laser diode non-linearity. By using
a modified model for aperture averaging technique, we also show that there is a design tradeo¤ between the
receiver lens aperture and the required average Carrier-to-Noise and Distortion Ratio to achieve a given average
bit error rate, ensuring substantial scintillation fade reduction.
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We present an overview of an air-to-ground laser communications demonstration performed at MIT Lincoln
Laboratory. Error-free communication at 2.5 Gb/s was demonstrated along a 25-km slant path between a 1-in
transmit aperture on an aircraft at 12 kft altitude and ground terminal with 4 separate 1-cm receivers. Power
fluctuations from turbulence-induced scintillation are mitigated in the spatial domain by use of the multiple
ground receivers and in the time domain by the use of forward error correction and interleaving. The optical
terminals are monitored by multiple high-rate sensors which allow us to quantify total system performance.
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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.
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Satellite laser communication involves communications between GEO satellites and LEO satellites. The optical
link can be built by the accurate pointing and tracking, which often employs the combination effect of coarse
pointing assembly and fine pointing assembly. In order to achieve this goal with ratable wedged-plate lenses, the
mathematic model of transfer function of control loop is obtained by analyzing the total control loop for such
complex axis. One can also get the optimized programs between coarse and fine pointing assembly.
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The design and fabrication of an optical 2×4 90° hybrid based on birefringent crystals for coherent receiver in free-space
optical communication system are presented. For the quadrature receiver two pairs of 180° phase shifted outputs are
obtained and one pair has a phase difference of 90° with respect to the other. The 90° hybrid comprises two pairs of
stacked birefringent plates, a phase retardation plate and an analyser birefringent plate. The testing results measured by
heterodyne method verify that the 2×4 optical 90° hybrid can work correctly and effectively. The phase compensation
and further optimization schemes are also proposed.
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The time-delay self-homodyne interferometric detection used in 2×4 90° optical hybrid for free-space optical
communication is presented. An asymmetric Mach-Zehnder interferometer splits the received signal into two paths and
recombines these two signals after a optical path difference. A balanced receiver follows the interferometer as a
multiplier. The modulation contrast in the interferometer depends on the interference of identical wave-fronts, not on the
quality of the wave-front itself. So it does not require wave-front compensation techniques, a local oscillator laser nor
does it need frequency locking. The scheme can eliminate the effect of wave-front deformation on coherent detection in
free-space optical communication effectively.
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The paper deals with the results of a propagation study on a fixed hybrid Free Space Optical (FSO) and Radio
Frequency (RF) system operating in 850 nm / 58 GHz bands. Propagation models for the availability assessment of both
FSO and RF links were examined against a comprehensive database of meteorological attenuation events. The
influences of individual hydrometeors were analyzed and the availability performances of the simulated FSO/MMW
hybrid link were evaluated. The study pointed out that visibility and rainfall measurements can be only used for the raw
assessment of availability performance due to the concurrent occurrence of different attenuation effect.
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The quadratic residue codes are a class of the error correcting codes with interesting mathematics. Among them, the (31,
16, 7) quadratic residue code is the code with reducible generator polynomial and three-error-correcting capacity. The
algebraic decoding algorithm for the (32, 16, 8) quadratic residue code is developed by Reed et al. (1990). In this paper,
a simplified decoding algorithm is proposed. The algorithm uses bit-error probability estimates, which is first developed
by Reed MIT Lincoln Laboratory Report (1959), to cancel the third error and then uses the algebraic decoding algorithm
mentioned above to correct the remaining two errors. Simulation results show that this modified decoding algorithm
slightly reduces the decoding complexity for correcting the third error while maintaining the same BER performance in
additive white Gaussian noise (AWGN). Also, the flowchart of the above decoding algorithm is illustrated with Fig. 1.
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