This article describes observations made during a recent series of single-mode lasercom experiments in which high-rate data transmission was demonstrated between a small aircraft and a ground station separated by distances up to 80 km. A significant result of the subsequent data analysis was the discovery of near-unity correlations between the signal fluctuations observed by power monitors at the two ends of the link. This evidence of reciprocity is presented, along with the description of a preliminary concept for utilizing this channel state information to improve link performance.
©2012 Optical Society of America
Theoretical descriptions of electromagnetic irradiance reciprocity were first published in the late 1800's , and rigorous proofs of optical-wavelength reciprocity between point transceivers embedded in a fading channel appeared in 1971 [2, 3]. Although a number of articles have speculated on the existence and utility of this phenomenon in an optical communications environment, experimental evidence of this effect from long-range field measurements has only recently been reported [4, 5].
Beginning in 2008, the Advanced Lasercom Systems Group at Lincoln Laboratory conducted a three-year experimental effort to evaluate the performance of free-space optical transceivers that utilize a novel set of techniques to mitigate turbulence-induced fading. An important outcome of these tests was the observation that the outputs of the single-mode receivers at the opposite ends of the link were strongly correlated. In the most recent of these experiments, correlation coefficients in excess of 99% were routinely measured. These correlation numbers are much higher than those reported in our first disclosure of this effect , but it will be shown that this enhancement is primarily the result of improvements to the symmetry of the link architecture.
The primary purpose of the communication link tests performed by Lincoln Laboratory between 2008 and 2010 was a demonstration of techniques to reduce the effects of turbulence-induced scintillation through the use of spatial diversity combined with forward error correction and byte interleaving. Detailed descriptions of the system configuration and its demonstrated performance have been reported in earlier publications [6–9], but a general description of the optical construction is essential to this discussion. The flight tests performed in 2009 and 2010 are referred to by the acronym FOCAL (Free-Space Optical Communications Airborne Link).
As shown in Fig. 1 , the system provides a unidirectional high-bandwidth link from the test aircraft to the ground. Spatial diversity to reduce scintillation is accomplished through the use of multiple ground-based receivers. Although there is no communication uplink, each of the four receivers also projects a single-mode laser beam upward that is used by the aircraft's tracking sensor to point the downlink laser. These four tracking beams have slightly different frequencies, and their total power at the aircraft is monitored by a single-mode fiber that combines the beams incoherently. The four ground-based receivers are also single-mode devices, and their outputs are incoherently summed after detection. All of the laser sources are single-mode transmitters, and each propagates through the same tracking path as its associated receiver. The trackers in the aircraft and ground-based transceivers have all been carefully designed to minimize beam jitter due to platform motion and atmospheric effects. A correction bandwidth in excess of 100 Hz was maintained in the aircraft by sampling the 2-dimensional tracking errors at a rate of 4.5 kHz. Tracking errors of the order of 0.3 λ/D were measured in the flight tests performed in 2009 , and in 2010 this number was reduced to 0.1 λ/D following the correction of a minor stiction problem.
The downlink architecture illustrated in Fig. 2 is representative of all link nodes, and illustrates the common-path characteristics of light propagation in both the fiber and free-space paths. The downlink laser transmitter and uplink tracking beams are merged in single-mode fiber at the circulator, and both are subject to closed-loop tilt correction using the same fast-steering mirror (FSM). Pointing errors made by the tilt corrector cause a loss in received optical power at both the ground station and the uplink monitor. It is noted that radio-frequency transceivers constructed in a similar manner have demonstrated strong signal-strength correlation properties [10, 11], and reports of enhanced backscatter in optical LIDAR systems having co-located transmitters and receivers is a related phenomenon [12, 13]. More recently, Shapiro and Puryear have shown that a link between two single-mode common-path transceivers will be reciprocal for any turbulence profile and for optical apertures of arbitrary dimensions .
2. Free-space optical experiments
The system described schematically in Fig. 1 was used in three separate field tests, the first of which was a 5.5 km horizontal-path experiment and the last two experiments were performed with the high-bandwidth transmitter mounted in a Twin Otter aircraft. Pictures of the aircraft and the downlink ground station are shown in Fig. 3 . The airplane was typically flown at an altitude of 12 kft in a semicircular pattern at ranges between 25 and 60 km around the ground station. Link functionality was demonstrated out to 80 km with the aircraft at 16 kft. Each of the four ground receivers had individually tracked 12 mm apertures, whereas the aircraft transmitter used a single 25 mm aperture. At maximum range the communication downlink functioned an output beam power of approximately 500 mW. As described in Ref , the link hardware incorporated real-time interleavers and encoders to reduce errors due to channel fading. Error correction was achieved using a Reed-Solomon 255/239 code. In the last set of link experiments conducted in 2010, 12 separate flights were performed at various times of the day. The average duration of these tests was about 3 hours, and data were collected continuously during those periods.
The common-path optical layout of the ground station shown on the right side of Fig. 1 was chosen primarily to simplify the terminal construction and demonstrate an ability to build a terminal having low size, weight, and power (SWAP) characteristics. Since it was a unidirectional downlink test the airborne terminal did not include a communications receiver, but a single-mode power-in-fiber monitor was included in order to obtain a high-rate measurement of the radiation received from the tracking beams. Using a design similar to that applied in the ground terminal, the light into the power monitor passed through the same beam-tracking path as the downlink laser beam. These design decisions resulted in a two-way path configuration that was well suited to measure signal reciprocity with high fidelity. The two sensor outputs that will be discussed in the next section refer to the incoherently-combined light collected by the aircraft's power monitor, and the sum of the four incoherent sensor data outputs in the ground station. All of the information collected were accurately time-stamped, and the sampling rates for the aircraft and ground power meters were 4 kHz and 1 kHz, respectively.
During the 12 flights performed between 10 November and 19 November 2010, link performance data were collected over a variety of ranges and at times ranging from 8 AM to midnight. The stability of the tracking systems were examined by subjecting the aircraft to pitch and yaw maneuvers, and the ability to rapidly reestablish the link after blockage was quantified by intentionally interrupting the beam. An average link reacquisition time of about 8 seconds was demonstrated in these tests. The severity of the ground-level turbulence was monitored throughout these tests using a commercial Scintec BLS900 scintillometer over a 1.6 km horizontal path positioned near the communication link ground station. Measurements made on a typical test day are shown in Fig. 4 .
The statistical characteristics of the power-in-fiber data gathered during the 2010 FOCAL flights were similar to those seen in the earlier horizontal-path and downlink experiments. Overall the data were well described by the gamma-gamma channel model , but as noted in prior descriptions of these experiments the derived values for the α and β shape parameters were consistently equivalent . This parametric degeneracy, which may be related to the elimination of beam wander through the use of high-bandwidth tracking systems, permits the use of a model for the power-in-fiber, I, that is completely specified by the distribution mean, μ, and the scintillation index,
An example of the application of this model to a typical receiver time series is illustrated in Fig. 5 , which compares the signal distribution derived from a single ground-based receiver (solid green curve) with the model defined in Eq. (1) (dashed black curve). The accuracy of this simplified statistical representation was found to be very high for single-receiver outputs having scintillation indexes in the range of . The effective scintillation index for the 4 receiver sum output seldom exceeded 0.5, however, due to the exploitation of channel diversity in the system architecture.
3. First observations of single-mode signal correlation
Our initial observations of strong reciprocal behavior were made as a result of a detailed analysis of data collected during the FOCAL experiments conducted in 2009, and was reported in the following year . At that time peak correlation values in the range of 80% were computed from measurements made during the first series of downlink tests. However, it was later determined that tracking laser powers detected at the aircraft were unbalanced due to a misalignment of one of the laser spectral filters. This condition had no impact on the performance of the communication link tests, but it did reduce the collective transmit/receive symmetry of the ground station terminal ensemble. A representative correlation summary derived from data collected in one of those tests is shown in Fig. 6 .
The results shown in Fig. 6 are completely consistent with a reciprocal bidirectional transmission geometry in which the transceiver output is derived from the incoherent sum of four detectors, only three of which transmit a beam in the opposite direction. For incoherent beam addition the time-dependent uplink and downlink signals for the transceiver structure shown in Fig. 1 can be written as follows
where M is the number of receivers included in the downlink signal summation and N<M is the number of active uplink beams; a and b are fixed geometric gain factors for the two propagation directions; and pi and q represent the uplink and downlink laser powers. Turbulence-induced signal fluctuations are described by the time-dependent channel transmission parameters and , which are normalized to have unity means. If the receivers are spatially separated such that the correlation coefficient factors and are zero for but = 1 for all values of i due to reciprocity, then the following result obtains
From the Schwarz inequality it follows that ρ is maximized when the uplink laser powers are identical, and ρ can only achieve unity when that condition is met and . Thus, with one tracking laser disabled the maximum correlation coefficient for the aircraft and ground receiver sum signals is 87%. Using the same set of simplifying assumptions, the correlation between the aircraft sum signal and the individual ground receivers is predicted to be 58%. These numbers are seen to be in good qualitative agreement with the results shown in Fig. 6. A subsequent reanalysis of the horizontal-path data collected in 2008 provided additional verification of strong correlation behavior, but since those tests were performed at short range usually only one or two of the four tracking beams were active.
4. Channel reciprocity results from the 2010 FOCAL test
The experimental evidence just presented is qualitatively consistent with the theoretical proof of point-source reciprocity that appeared in an article published by Shapiro in 1971 , but both of these studies leave unanswered the question of the limits of this effect when applied to a practical transceiver architecture. In order to exploit this phenomenon in the design of a real system, an engineer would need a detailed understanding of the dependence of correlation strength on factors such as aperture dimension, turbulence profile, and propagation distance. Many of these concerns have been addressed in the investigation conducted by Shapiro and Puryear , which demonstrates that common-path single-mode links are inherently reciprocal for apertures of arbitrary dimension and for propagation channels of arbitrary turbulence strength and profile; moreover, this statement also applies to systems incorporating phase-compensation devices such as trackers and adaptive optics. The key assumptions made in Ref . are that each terminal incorporates a common-path transmit/receive architecture, the propagation delay is small with respect to the atmospheric time constant (frozen turbulence), and the point-ahead angle is small with respect to the isoplanatic angle.
Although channel correlation studies were not the primary goal of the test series performed in 2010, steps were taken to minimize system design anomalies that might interfere with these measurements. As discussed in Section 1, signal fading due to platform motion was essentially eliminated through the use of high-bandwidth tracking devices at both ends of the communication link. Attention was also given to the power balance of the four ground-based tracking lasers and their throughput into the aircraft receiver's power monitor. In the data analysis performed following the experiment it was discovered that a small amount of transmitter power leaked through the circulator into the receiver power monitor in the aircraft. This additive signal resulted in a minor distortion of the fading statistics measured by the aircraft, which was quantified and removed prior to the data correlation calculations. These measures proved to be a key factor in the validation of the theoretical predictions of reciprocal channel behavior.
The degree of correlation between the downlink receiver output and the tracking laser power monitor in the Twin Otter aircraft is graphically demonstrated by the two-dimensional probability density function shown in Fig. 7(a) . Each of the associated marginal distributions is well described by the model given in Eq. (1), with their respective shape parameters being nearly identical. The correlation-coefficient function given in Fig. 7(b) provides a more quantitative measure of the correlation strength, as well as a measure of the correlation time. In general, the cross-correlation and autocorrelation time constants are approximately equal and have values of the order of 5 msec.
Time series correlations for 14 representative data segments collected between 12 and 19 November, 2010 are given in Fig. 8 . The figure on the left plots the linear correlation as a function of the average scintillation index measured by the four ground-based receivers. The chart on the right shows the same data plotted as a function of aircraft range. These results indicate consistent correlation coefficient values in the 97% and 99% range, and the median value for the sample ensemble is 98.4%. The two charts suggest that there is no parametric dependence on either scintillation index or the length of the link, which is in agreement with predictions for this single-mode transceiver configuration . It should be noted, that the photon time of flight for the longest propagation paths encountered in these tests was significantly smaller than the nominal atmospheric time constant and that the point-ahead angle was small compared to the estimated isoplanatic angle.
5. Strategies for exploiting channel reciprocity
In recent years designers of transceivers for free-space optical links have attempted to mitigate the receiver fluctuations imposed by atmospheric turbulence through the use of advanced beam control methodologies (adaptive optics and receiver diversity), exploitation of statistical knowledge of channel behavior (forward error correction and interleaving), signal level measurements at the receiver (soft decision decoding), and retransmission requests based on the detection of lost data segments. Channel reciprocity expands this toolset by enabling the transmitter to exploit real-time knowledge of the channel conditions as seen by the receiver. This allows the transmitter to adaptively adjust the data flow strategy to the actual conditions rather than a statistical estimate of the conditions. The advantage gained is critically dependent on the quality of this knowledge, but these tests have shown that for single-mode systems the channel state can be predicted with very high reliability.
There are a wide variety of constructs that might be considered to optimize performance according to some established metric. Adjustment of the transmitter power to compensate channel loss is one possibility, although the power amplifiers used for communications tend to be peak-power limited. Other possibilities include adjustments of the bit rate or code rate. A simpler approach, which is illustrated in Fig. 9 , gates the data flow when the effective transmission drops below the threshold for reliable detection. Each end of the link employs a first-in, first-out (FIFO) buffer, and the client input rate at the transmitter is adjusted to maintain the average buffer fill factor near 50%. The control logic for this system is very straightforward, and preliminary performance analyses indicate that its throughput will approach the theoretical channel capacity.
While the use of reciprocity is applicable to a wide range of free-space optical communication geometries, its benefits are perhaps most easily understood in the context of a minimal-cost unidirectional link that is incapable of sending frequent retransmission requests. A schematic representation of such a system is illustrated in Fig. 10 . A link design of this type capable of gigabit-class data rates can be readily be constructed using hardware that has already been demonstrated in prior programs .
Strong experimental evidence of channel reciprocity for single-mode optical transceivers has been presented, and these results are shown to be in complete agreement with recently-derived analytical descriptions of link behavior in a fluctuating channel. This phenomenon is restricted, however, to frozen turbulence conditions and common-path geometries, which places an upper limit on parameters such as the propagation distance and point-ahead angle. These requirements, however, are satisfied for a wide range of ground-to-ground and air-to-ground communication link geometries, thus for these situations a priori knowledge of the channel state can be used to design systems that achieve channel capacity with minimal latency.
This work is sponsored under Air Force Contract #FA8721-05-C-0002. Opinions, interpretations, conclusions and recommendations are those of the author and are not necessarily endorsed by the United States Government.
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