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Abstract
During sub-optimal weather, a free-space optical (FSO) link range degrades depending on attenuation (atmospheric extinction) and turbulence effects. The ability to predict the system level performance can be exceedingly challenging as the atmospheric variability in a maritime link can be large and difficult to model. Link budget estimation for FSO systems often takes a nominal view of atmospheric conditions; here, we use statistical atmospheric predictions specific to a geographic area of interest to enable performance trades to be evaluated through link budget analysis. We compare these models to field-collected data to show the utility of the statistical atmospheric analysis in predicting FSO link performance for specific parts of the world. We have performed shore-to-ship FSO communications field tests at 10 Gb/s with links reaching out to a horizon limit over 40 km away in times of moderate extinction to clear weather. We provide further analysis by describing the expected performance of the link using statistical probabilities via cumulative distribution functions of both extinction and turbulence. The atmospheric variability can be determined for nearly any region of interest through the implementation of numerical weather prediction data to calculate the atmospheric performance drivers. These conditions are specifically evaluated for the 2017 Trident Warrior field test off the coast of San Diego, California, USA.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Free space optical (FSO) communications enable ad-hoc networks for regions in which optical fiber or other high speed data links are difficult to deploy. In addition, these highly directional links inherently allow spectrum reuse and are minimally impacted by crosstalk from nearby optical links. Significant effort has gone into the development and optimization of the size, weight, and power (SWaP) of these systems in order to enable communications in a variety of applications [1]. The lack of regulatory restrictions and high bandwidth potential have made optical communications particularly appealing for satellite-to-satellite links, which do not have to contend with the challenges presented by earth’s atmosphere [2].
Terrestrial links are exceptionally difficult as they must contend with large variability in atmospheric conditions that can degrade data rates and link reliability. In order to better understand FSO performance and link availability, we have taken a statistical approach to the atmospheric effects that drive the performance of an FSO communications link. To inform our link budget models, we have built statistics on atmospheric extinction and turbulence through the use of numerical weather prediction datasets, such as the Modern Era Retrospective ReAnalysis-2 (MERRA-2) [3], and The European Centre for Medium Range Weather Forecasting ReAnalysis-5 (ERA-5) [4]. Using each of these models, we are able to construct regionally specific, statistically relevant inputs of both extinction and turbulence that enable detailed analyses of link performance.
In this paper, we will present shore-to-ship field test results on a Johns Hopkins University Applied Physics Lab (JHU/APL) built prototype FSO system. We present a novel approach to predicting the performance of terrestrial FSO links by leveraging global numerical weather prediction data to inform the variability of the atmospheric performance drivers: extinction and turbulence. Leveraging the large re-analysis datasets, we can construct our statistics for anywhere on the globe, enabling both spatial analyses (specific locations, regional) and temporal analyses (monthly, seasonal). This atmospheric variability is analyzed via cumulative distribution functions to describe probabilities of occurrence, enabling systems design trades to be performed prior to deployment and supporting post test performance evaluation. Finally, we present the analysis of our previously collected field data alongside the communications link budget model to show how this type of atmospheric analysis can be used to successfully project system availability in specific regions of the world.
2. Trident Warrior field test
We demonstrated our FSO communication capability during the Trident Warrior test event in June, 2017 [5]. Over the course of the two-week test campaign, the FSO system was evaluated in a maritime environment in both Ship-to-Shore and Ship-to-Ship configurations, with identical systems at each node and link distances ranging from 2-43 km (horizon limited). There were three primary scenarios of interest during the test. The first scenario was a ship-to-shore configuration with a constant link distance, where a link was formed at 5, 10, or 15 km and maintained over several hours by driving the ship along a constant-range arc. The second scenario was a ship-to-ship configuration with constant link distance, where we evaluated the performance of the link when both nodes were at sea. The limited link ranges due to line of sight made this scenario less stressing for the system than anticipated, as wave blockages of the beam occurred between 9 and 12 km. The third scenario, from which data is presented in this paper, was to close the link at close range (2-5km), and then drive the ship out away from the shore to determine the system’s maximum range. Figure 1 shows a map of the Ship-to-Shore test configuration when the ship was at the maximum distance of 43 km before the beam was blocked by the horizon. Data collected from this scenario across several test runs provides us with the ability to analyze our performance vs range by comparing field collected data to expected results from our link budget model.
Fig. 1. Trident Warrior field test ship to shore configuration. (a) Plan view of link at maximum horizon-limited range. (b) Shore station, perspective view. The shore location was $\approx$110 meters above sea level (ASL), the ship’s receiver was $\approx$ 3 meters above the water. Credit Google Earth.
The FSO system used at each node is a standalone, bidirectional, point-to-point FSO link consisting of an optical terminal housed in a stabilized maritime gimbal, an optical modem, an inertial navigational system, a system controller, and networking hardware (e.g., voice over internet protocol (VoIP) Phone, high definition (HD) camera, network testers) to emulate a user’s 10 Gb Ethernet network. The FSO link was closed using a nested coarse and fine tracking loop and maintained while the ship was on-the-move using gimbal and fast steering mirror (FSM) control. The architecture of the optical terminal is shown in Fig. 2.
Fig. 2. FSO receiver architecture. The system includes a fast steering mirror for tip-tilt correction to improve power in fiber. The power in fiber is measured at the output of the single mode fiber (SMF).
The optical payload is designed to operate in a bidirectional configuration. On the receive path, light is collected and focused via a lens telescope assembly. The incoming beam is directed using an FSM, which is then split with 90% of the light directed to a fiber collimator and 10% directed to a quadrant detector that is coupled with a free space spectral filter. The quadrant detector is used for beam sensing as the incoming beam position shifts and beam structure breaks down. A system controller collects the voltages outputs from the quadrant detector based on beam position and determines the offset between the ideal beam position and the current beam position [6]. This offset is then converted to a corresponding error signal to send to the FSM to direct the light to the ideal position that would maximize coupling into the receive fiber. The fiber collimator couples to a single mode fiber (SMF) circulator which supports the monostatic terminal design by enabling transmission on one wavelength simultaneously with signal reception on another. On the receive path of the circulator, a 1% tap coupler is used to monitor and record the Power-in-Fiber (PIF). While there are several key metrics that can be evaluated to determine the performance of an FSO link, including error rate, data rate, link availability, PIF, and strehl ratio, in this paper we choose to focus on comparing the modeled and measured PIF.
Because we employ forward error correction coding on our link, packet/frame error rate is not a useful metric due to the steep curve as power falls. The knee in this curve of error rate vs. received power lies at our receiver sensitivity of -44 dBm. When the incoming PIF is above the receiver sensitivity, the data on the channel will be error-free. Channel fades below -44 dBm can be overcome through the use of layer 2 packet retransmission. The total amount of data that can be sent error-free across the link at a given time is determined by the link availability, which we define as the percentage of time the PIF is above the receiver sensitivity. For example, if the link availability is 50%, the received PIF is above -44dBm 50% of the time, and the 10 Gb/s link should be able to support half of its capacity, or 5 Gb/s of error-free data transport through the use of retransmission. When choosing a metric for performance evaluation, specifically in the context of atmospheric variation, PIF stands out as the ideal candidate as it is tied to both the error rate through the receiver sensitivity and the data rate through the link availability.
Testing was performed in the marine atmospheric boundary layer. This is a complex region where the air-ocean interface directly influences atmospheric dynamics [7]. This region can experience large changes due to the exchange of heat and water, giving rise to large variability in both turbulence and extinction. In addition to contending with the marine layer, the team tested through a variety of conditions ranging from heavy fog to clear weather. Figure 3 shows photos taken on two different days approximately 6 km from the shore during the test campaign; one during nominally clear weather with good (16+ km) visibility conditions; and another showing moderate fog, during which time the local weather station was reporting 6.2 km visibility conditions. Analysis of the received power during these two different test conditions revealed that during the moderate fog, the link was subjected to approximately 1.7 dB/km of additional atmospheric loss as compared to the good visibility day. For a 10 km link, the additional 17 dB of required power during moderate fog was able to be overcome by system link margin; however, for a longer distance link this additional atmospheric loss would quickly become untenable.
Fig. 3. Photos taken from behind the optical terminals at a distance of 6 km from the shore. (a) A clearer day with visibility >16 km on June 13th. (b) A high extinction day with local visibility reported at 6.2 km on June 16th.
By pairing statistical analysis of the region-specific weather trends with our link budget calculations, we can know a priori the expected performance bounds. In the next section, we discuss the datasets and methods used for this analysis.
3. Atmospheric statistics and FSO performance drivers
Accurately modeling the atmospheric conditions in which an FSO system operates is extremely important to predicting link performance and reliability. The two major performance drivers are atmospheric extinction and atmospheric turbulence. Extinction along the path reduces the received power, and turbulence may cause pointing errors, laser beam spreading, and beam breakup that can result in deep fades, creating a loss of data. Both extinction and turbulence vary as a function of altitude, region and season. Thus, choosing singular values for either metric only tells a small part of the performance story. Turbulence induces large power fluctuations (we saw >20 dB in our testing on sub-millisecond scales). The additional penalties imparted by extinction make reliability a concern for communication system designers, who must balance these challenges against SWaP constraints. To address these concerns, we have taken a statistical approach to atmospheric propagation by looking at the variability in both extinction and turbulence. Using cumulative distributions to build statistics, we define a good atmospheric day as the 10%, an average day as the 50%, and a bad day as the 90% points in the cumulative distribution function (CDF). Using these values for both extinction and turbulence as inputs to our link budget, we can guide design trades in terms of expected operational reliability in a specific region of interest. For example, a system designer could choose to design to the 90% statistics and expect their system to meet performance requirements 9 out of 10 days in operation in that part of the world. This approach can be performed for any region of the world, but here we focus on atmospheric analysis specific to the coastal maritime region in San Diego, CA.
3.1 Extinction
Atmospheric extinction is the loss of energy due to scattering and absorption. Extinction in the lower atmosphere for $\lambda$ = 1.55 $\mu$m is generally driven by aerosol scattering. The aerosol loading can be highly variable and depend on wind (lofting maritime aerosols) as well as localized anthroprogenic sources. In order to accurately model the aerosol extinction for our maritime environment, we have chosen to use atmospheric aerosol datasets coupled with Mie scattering [8]. MERRA-2 is the Modern-ERA Retrospective Analysis for Research and Applications V2 (MERRA-2 [3]). MERRA-2 is a global atmospheric re-analysis model that contains information pertaining to atmospheric aerosol number density and type on a 0.5$^{\circ }\times$0.635$^{\circ }$ (latitude $\times$ longitude) spatial grid with 3-hour temporal resolution [3,9]. The MERRA-2 data was used to inform the aerosol type (index of refraction) and size distribution for a Mie scattering calculation of extinction. Calculations were performed for $\lambda$ = 1.55 $\mu$m using a year of data (2920 points, every 3 hours) for the region surrounding San Diego and the Trident Warrior field test. The cumulative distribution for the surface layer (~1 m ASL) of extinction for this region is shown below in Fig. 4(a). The cumulative distribution of the surface level extinction is used to inform a simplistic altitude dependence model of extinction, enabling line of sight geometries taking into account the curvature of earth as well as non-horizontal geometries.
Fig. 4. (a) Cumulative distribution of the modeled surface level extinction. Statistics are aggregating from a year of MERRA-2 data seeding a MIE scattering calculation ($\lambda$ = 1.55$\mu$m) for the region surrounding San Diego and the Trident Warrior field test. (b) The modeled altitude dependent extinction profiles used for statistical evaluation in the link budget calculation.
The 10%, 50%, and 90% percentile altitude profiles are shown in Fig. 4(b). The extinction coefficient is commonly used in atmospheric transmittance calculations for laser wavelengths and has units of $km^{-1}$. FSO losses are often discussed in terms of dB/km, and a simple conversion can be applied to convert from $km^{-1}$ to dB/km
We can also use the Kim-Kruse [10,11] model to approximate the visibility and extinction wavelength dependent relationship. The model constructs a visibility dependent power law scaling for the wavelength dependence of the extinction coefficient. Here, we define visibility as the range at which 2% transmittance occurs for $\lambda$ = 550 nm, the Koschmeider definition [12].
The Kim-Kruse model then enables wavelength scaling of the extinction coefficient by constructing a power law dependence:
whereApplying this model to the extinction coefficients retrieved from the MERRA-2 analysis facilitate estimations of the equivalent visibility. Shown below in Table 1 are the calculated extinction coefficients from the MERRA-2 and MIE scattering calculation and the conversion to visibility with Eq. (4). This model is useful in helping the observer relate visible conditions as seen by the human eye or other sensors to the expected performance for an FSO system.
Table 1. Kim-Kruse extinction and visibility relationship
3.2 Turbulence
Atmospheric turbulence causes image blur, laser beam pointing errors and beam breakup which can result in deep fades. Atmospheric turbulence is characterized by the index of refraction structure constant $C_{n}^{2}$ ($m^{-2/3}$), and in general has a strong altitude dependence that is driven by atmospheric temperature and humidity fluctuations, wind speed, and surface roughness. At optical wavelengths, humidity contributions are very small and generally ignored. Statistics for surface level atmospheric turbulence have been developed using the ERA-5 numerical weather prediction data-set as inputs to the Naval Atmospheric Vertical Surface Layer Model (NAVSLaM) [13,14]. ERA-5 includes surface level and altitude dependent measures of key atmospheric inputs (surface pressure, surface temperature, sea-surface temperature, humidity and windspeed) needed for the modeling of $C_{n}^{2}$ at the surface. A year of data (8760 hourly datasets) from ERA-5 are used to seed the model for the San Diego coastal region. The data is aggregated by taking a cumulative distribution across time of the surface level (1 m ASL) $C_{n}^{2}$ value. The cumulative distribution of the turbulence is shown below in Fig. 5(a). Here, we show that the 10th percentile $C_{n}^{2} \approx 7\times 10^{-16}$, 50th percentile $C_{n}^{2} \approx 10^{-14}$ and 90th percentile $C_{n}^{2} \approx 2\times 10^{-13}$. Others have taken a similar approach when evaluating turbulence by comparing their data to turbulence statistics and scaling the H-V 5/7 model to measured data, for example in the Korean peninsula [15,16]. Through our use of numerical weather prediction to drive turbulence models such as NAVSLaM, we can extend this analysis by constructing statistics for anywhere on the globe, enabling location specific evaluations, regional analysis, and even temporal analysis such as seasonal variation.
Fig. 5. (a) The aggregate cumulative distribution of the modeled surface level turbulence (1 m altitude) as calculated using NAVSLaM with hourly ERA-5 inputs for the San Diego coastal region. (b) Modeled altitude dependent profiles of turbulence using H-V 5/7 (dash-stars) and HAP (solid squares).
We use the surface level statistics from our numerical weather prediction and NAVSLaM calculated $C_{n}^{2}$ results to seed standard altitude dependent profiles. We chose to use both the Hufnagel-Valley (H-V 5/7) model [17] as well as the Hufnagel, Andrews and Phillips (HAP) model [18] as shown in Fig. 5(b). Note there is a significant difference in the rate at which the turbulence decreases with altitude within the surface layer when comparing the HAP model to the H-V 5/7 model. This difference is most noticeable for the average 50th (green), and bad 90th (yellow) percentile days.
3.3 Altitude dependence
The Trident Warrior FSO field test had the transmit aperture at approximately 110 m above sea level and the receiver was 3 m above sea level. During the field test data collection, the ship performed radially outbound transects starting as close as 2 km slant range from the shore and proceeding outbound until the link was lost at the horizon range limitation of $\approx$ 43 km. At each range, the resultant line of sight geometry changes slightly with the elevation angle from the shore side terminal slowly increasing. To accurately model the FSO link, we use altitude profiles for both extinction and turbulence. As noted above, the extinction vertical profile was built using a simplified pressure scaling applied to the surface level value. We calculate our atmospheric transmittance loss by leveraging the altitude dependent profile of the extinction along our specific line of sight throughout the duration of the test. We note that the altitude dependence of the extinction value is relatively constant within the surface layer; however, we include this dependence in order to further generalize the model as this extinction value will rapidly decrease with increasing altitude.
where $\alpha (r')$ is the range dependent extinction as defined in Fig. 4(b) at each range (r′) along the slant path from the shore-side transmitter at 110 m ASL to the ship-side receiver at 3 m ASL.The turbulence profile was constructed using the H-V 5/7 model as well as the HAP model. Given our transmit and receive aperture altitudes, we will see large differences in turbulence effects depending on the vertical structure of the turbulence in the surface level during the time of test, particularly for the longest ranges. In order to capture these differences, we evaluate our link budget model statistics using both the H-V 5/7 model as well as the HAP model. During the experimental data collects our line of sight starts at 110 m above the water and ends just 3 meters above the water’s surface. When comparing the H-V 5/7 model and HAP model we can see a large difference in the altitude dependence of the turbulence value. The H-V 5/7 model has a relatively weak altitude dependence when compared to the HAP model. This difference is important especially for larger $C_{n}^{2}$ turbulence values wherein we see significant degradation to our link budget. The HAP model for larger $C_{n}^{2}$ turbulence values sees an altitude dependent decrease of $\approx$ $alt^{-1}$, while the H-V 5/7 model in the same region is nearly constant. This difference in turbulence as seen in our FSO link can result in as much as an additional 10 dB of loss. The difference in modeled turbulence along the line of sight is shown below in Fig. 6 for 3 paths during our Maritime field test. Note that for each range calculated in our link analysis we have a new line of sight. In our case the shore-side terminal is held in a static position while the shipside terminal moves radially out bound from the shore. Because of the differences between these models, particularly in poor weather conditions, we present our link model results throughout the paper using both the H-V 5/7 and the HAP model for turbulence.
Fig. 6. Shown on the left (a) is the line of sight above sea level relative to the link range for a curved earth path. Note that for the 43 km link from 110 m altitude to 3 m we just barely skirt above the waters surface, longer ranges result in occlusion. The right panel (b) shows the 50% modeled turbulence value along the same line of sight for the HAP and H-V 5/7 vertical turbulence structure. Note the longest ranges show higher turbulence values as those ranges correspond to the ship-side terminal at 3 m ASL. Additionally the HAP model as expected shows a strong surface level altitude dependence relative to the H-V 5/7 model.
To further clarify this difference between models, we calculate the atmospheric seeing $r_{0}$ parameter for spherical waves referenced to the receiver optics Fig. 7 for our line of sight geometry, 110 m ASL shore transmitter to 3 m ASL ship receiver, over the full field test range using the assumed turbulence structure of both the H-V 5/7 and HAP models.
where k = 2$\pi /\lambda$ is the wavenumber, z is the altitude and L is the path-length.Fig. 7. The modeled atmospheric seeing (Fried, $r_{0}$) parameter for the 10th (purple), 50th (green), and 90th (yellow) percentile atmospheres assuming the altitude dependent structure of the HAP model (solid squares) and the H-V 5/7 model (dashed-stars), calculated from Eq. (3.3). In addition, the receive aperture size is plotted (red-diamonds) to show the relative impact of the turbulence. The H-V 5/7 model has a very weak surface level altitude dependence and results in significantly reduced atmospheric seeing.
4. Link budget estimation and field test data analysis
The FSO communications system performance was evaluated using a link budget model leveraging the previously mentioned statistics built from the numerical weather prediction data. The statistical data, along with the FSO system parameters, are used in all of our link budget calculations, and field test data is shown as measured PIF. The link model specifically includes the system details (power, aperture, beam divergence, Tx and Rx losses) as well as atmospheric variability including turbulence and extinction. The FSO system parameters and link budget summary for a 20 km path are shown below in Table 2.
Table 2. FSO specifications for link budget analysis - 20 km path.
Turbulence was implemented within the link budget analysis via a Strehl ratio scaling term [19]. This receive Strehl is determined by:
where d is the aperture of system (1" or 25.4 mm), $r_{0}$ is the Fried parameter determined by Eq. (4) and M is a scaling factor correction to account for the implementation of adaptive optics (AO). The AO scale factor M is equal to 1 without AO and 0.28 with tip/tilt, and <0.1 with higher order mode correction [15]. Note when the aperture (d) is equal to atmospheric seeing (Fried) parameter, the Strehl ratio is 43.5% without AO and 74.4% with tip/tilt correction. The FSO terminals include fast steering mirrors that implement a real-time tip-tilt correction and thus for our modeling we utilize M = 0.28.Using the transmitter and receiver specifications as described above in Table 2, we can determine the receive Power-in-Fiber (PIF) as a function of range and atmospheric conditions. As the ship heads away from land, the height of the slant path, or optical path (line-of-sight) varies as a function of range and terminal distance. At each specified range we calculate the specific altitude above sea-level of the line of sight and use the altitude to determine path dependent turbulence and extinction values. The range dependent atmospheric quantities are then used in our link analysis to calculate the receive PIF.
To compute receive power in fiber (PIF):
$T_{atm}$ is the atmospheric transmittance along the line of sight from Eq. (3.3),
$SR_{RP}$ is the receive plane Strehl calculated from Eq. (4), per the Field Guide [19],
$SR_{DP}$ is the pupil plane Strehl calculated from Eq. (4), per the Field Guide [19],
$\gamma _{tx \& rx}$ are the transmit and receive fiber insertion loss efficiencies,
$r_{rx}$ is the receive aperture radius,
$r_{spot}$ is the 1/e beam radius as a function of range = $\frac {190 \mu rad \times Range}{2}$.
To understand the performance of our FSO system we performed a statistical evaluation of the receive PIF, to account for the variability in the atmospheric conditions. Utilizing the statistical variation of the extinction and turbulence shown in Figs. 4 and 5 we perform link analyses for each profile. The resultant PIF is shown in Fig. 8. Each pair of color curves (purple, green and yellow) represent the 10th, 50th, and 90th percentile atmospheres. For each set of color curves, we use the same extinction profile and vary the turbulence structure using the HAP model for the solid squares and the H-V 5/7 model for the dashed stars. In addition, the color curves can be thought of as the percentage of time one would expect to achieve the associated PIF for a given range. We would only expect to meet or exceed the purple PIF 10% of the time given atmospheric variability but would expect to meet or exceed the yellow curve 90% of the time.
Fig. 8. The modeled Power-In-Fiber (PIF) for the 10th (purple), 50th (green), and 90th (yellow) percentile atmospheres. The matching color lines (e.g., purple-pair) utilize the same extinction profiles as defined in Fig. 4; however, for each matching color pair there are 2 independent turbulence profiles that have been modeled including the HAP model (solid squares) and the H-V 5/7 model (dashed-stars) (see Fig. 5). The difference in turbulence vertical structure is specifically addressed as it is very difficult to accurately model and important to show the resultant PIF variability. The open blue circles are the measured PIF from the outbound boat during the trident warrior field test on June 13. Note the discrete increase at 24 km is due to an increase in output power (2 Watts $\rightarrow$ 3 Watts) during the test. This power increase is responsible for the step in the receive PIF. The open orange circles are the measured PIF for June 16 during the low visibility event, the step increase at 13 km is from an alignment optimization. The black squares at -44 dBm is the system performance requirement and the noise floor is -51 dBm.
4.1 Field test comparison
A direct comparison of our link budget analysis to the measured PIF from the field test was performed for two separate outbound trips. Show in Fig. 8 is the measured PIF received by the ship as a function of range on June 13th (clear day) and June 16th (low-visibility day, see Fig. 3), overlaid on our modeled PIF plots using both the HV 5/7 (squares) and HAP (stars) models for turbulence, with plots for the 10th (purple), 50th (green), and 90th (yellow) percentile atmospheres. The measured PIF was collected at a 10 kHz sampling rate and is displayed utilizing a moving time average as open blue circles (June 13th) and open orange circles (June 16th).
On June 13th, the data collection started with ship greater than 15 km off the coast. Once the link was established the ship proceeded radially outbound until link was lost (PIF < -44 dBm), On clear days this loss occurs at the line-of-sight (horizon) limitation of $\approx$ 43 km. Comparing the resultant measured PIF on June 13th to our model, we find that it is likely represented by $\approx$70th percentile day atmospheric conditions. Note the upward kink at 23 km is a result of increasing the output power from 2W (33 dBm) to 3W (35 dBm), and as such we also increased the power in our link model at 23 km and beyond.
On June 16th, the data collection started at a much shorter range of 7 km, visibility was quite poor, and the boat again proceeded outbound until the link was lost around 18 km. The visibility was reported by a local weather station to be 6.2 km. Using Eq. (4) we determine the extinction at $\lambda$ = 1550 nm to be 0.16 $km^{-1}$ which is approximately a 90% day when referencing Fig. 4. The reduced visibility made tracking more difficult and as seen in Fig. 8 (open orange circles) we see a step up in the received power at 13 km resulting from an optimization in alignment. Note for our link budget modeling calculations we have not implemented any pointing error considerations.
Notably, there is a distinct difference in the slope of the PIF as a function of range when comparing the two outbound transects. The clear day combined atmospheric loss (turbulence and extinction) is 0.66 dB/km and on the lower visibility day we see a combined atmospheric loss of 2.36 dB/km. In each case with either increased output power (blue circles at 23 km) or improved alignment (orange circles at 13 km) we can achieve a slightly larger maximum link range but the slope of the loss remains consistent. Even increasing the power by 2 dB, we see that on our clear day we only expect to get an additional 3 km range (2/0.66) and on our low visibility day we expect less than 1 km range extension (2/2.3). The large variation in the slope of the PIF vs range projection given changes in the atmosphere, even for a specific region of the world, highlights the value of this type of analysis. In selecting benign conditions for our link budget model, it would be difficult to determine, based solely on the collected power in fiber data if the system performance is as expected. Depending on the level of optimism, this type of modeling could lead systems to significantly under perform in real-world conditions as compared to expectations. Comparing our observations about visibility conditions in the field and visibility as reported by a local weather station during the test, the PIF models which take atmospheric statistics into account help better understand the data taken from the same notional test scenario on two different days. In addition to allowing system designers useful information in terms of selecting an appropriate design point based on availability requirements, this type of modeling could also be used in situ to help operators understand the capabilities and limitations of their system based on local weather station information for a given day.
By evaluating the variability and impact on the FSO system, we can determine the long-term ability of the FSO system to close a link. This approach to region-specific performance modeling based on atmospheric statistics can be used in the design phase of a new FSO system enabling trades on aperture, power and FSO requirements in order to achieve a pre-determined quality of service based on a specific region of interest for eventual system operation.
5. Conclusions
A statistical approach to FSO link budget evaluation has been performed by comparing the receive PIF and FSO performance against cumulative distributions of the major atmospheric performance drivers, extinction and turbulence. Cumulative distributions of both extinction and turbulence were constructed utilizing global numerical weather prediction (NWP) for the San Diego coastal area. The data output from the NWP was used with models for determining extinction and turbulence at the surface layer. The resultant surface level values were coupled with altitude dependent profiles to inform our specific line of sight geometry. We found that the variation in both extinction and turbulence can result in markedly different estimates of receive PIF as a function of range. It is important to note that by designing an FSO communications link to the average ($\approx 50{\% }$) atmospheric conditions one should only expect link closure $\approx$50th of the time; much more useful would be to design to the 90th or worse conditions. Using our statistical approach to FSO link budget models we have estimated the variability in atmospheric conditions and resultant power in fiber for the Trident Warrior field test. Comparisons to the Trident Warrior field test data for both a low visibility day and a relatively clear day show that our model bounds the performance of our deployed FSO system. Thus, it is recommended that a larger statistical view be applied to link analyses particularly for surface level links where large variability in both turbulence and extinction are more likely.
Disclosures
The authors declare no conflicts of interest.
Data availability
The data associated with this paper are openly available at [3,20].
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