Angle Of Arrival Fluctuations Research Articles

A new statistical fading model for loss factor induced by angle-of-arrival fluctuations in free space optical communication.

The impact of angle-of-arrival (AOA) fluctuations on the loss factor is investigated, and a new fading model is proposed to describe the associated attenuation. Distinct decay characteristics induced by AOA fluctuations are revealed, which depend on the ratio of detector size to beam width (M). The fading model can be divided into two sub-models based on the value of M0, where M0 is the value of M when the root-mean-square errors of the two sub-models are equal. In the case of M⩾M0, this fading model follows an inverse S-shaped pattern to describe the impact of AOA fluctuations. When M < M0, an exponential function to characterize the attenuation induced by AOA fluctuations. The numerical computation results indicate that the proposed fading model offers higher accuracy compared to traditional methods. Furthermore, the continuous analytical expressions for the probability density function (PDF) and cumulative density function (CDF) of the presented fading model caused by AOA are derived. Based on the proposed PDF and CDF models, the outage probability of inter-satellite laser link is analyzed.

Study of convective air turbulence based on the probability distribution function of angle of arrival fluctuations

This study investigates the probability density function (PDF) of angle of arrival (AoA) fluctuations of a laser beam propagating through convective air turbulence in two settings: indoor turbulence and atmospheric surface layer. The indoor turbulence is generated by an electric heater with a 50 cm × 100 cm surface area placed horizontally on the bottom. The atmospheric turbulence experiments are conducted over a level at 60 cm height from an asphalted area using a slightly divergent laser beam that propagates along 350 m. Image motion monitoring of four sub-apertures installed in front of the receiving telescope aperture is used to record the AoA fluctuations and their PDFs over the entrance pupil at the sub-aperture locations for both types of turbulence. The observations are made in two perpendicular directions to the propagation of the laser beam. The experimental PDFs of the AoA fluctuations are fitted with Gaussian, Lognormal, Weibull, and Gamma distribution functions. The results show that the Weibull and Gamma models are more consistent with the experimental data for the indoor convective air and atmospheric turbulence respectively. For the indoor convective turbulence, the full width at half maximum and the peak location of the measured PDFs increase with the heater temperature, as well as the goodness of fit, which saturates at high temperatures.

Analysis of Tip/Tilt Compensation of Beam Wandering for Space Laser Communication

Laser communication has been considered as a novel method for earth observation satellites with generation of high data volume. It offers faster data transmission speeds compared to conventional radio frequency (RF) communication due to the short wavelength and narrow beam divergence. However, laser beams are refracted due to atmospheric turbulence between the ground and the satellite. Refracted laser beams, upon reaching the receiver, result in angle-of-arrival (AoA) fluctuation, inducing image dancing and wavefront distortion. These phenomena hinder signal acquisition and lead to signal loss in the course of laser communication. So, precise alignment between the transmitter and receiver is essential to guarantee effective and reliable laser communication, which is achieved by pointing, acquisition, and tracking (PAT) system. In this study, we simulate the effectiveness of tip/tilt compensation for more efficient laser communication in the satellite-ground downlink. By compensating for low-order terms using tip/tilt mirror, we verify the alleviation of AoA fluctuations under both weak and strong atmospheric turbulence conditions. And the performance of tip/tilt correction is analyzed in terms of the AoA fluctuation and collected power on the detector.

Performance of HQAM/XQAM Laser Communication System in Anisotropic Non-Kolmogorov Ground–HAP–Satellite Uplink

Satellite laser communication can achieve high-speed, high-precision, and high-security broadband communication without being constrained by the electromagnetic spectrum, which has attracted attention. So, this paper proposes the use of a high-altitude platform (HAP) under anisotropic non-Kolmogorov turbulence to improve the communication performance of the system. Cross quadrature amplitude modulation (XQAM) and hexagon quadrature amplitude modulation (HQAM) are applied to the ground–HAP–satellite (G-H-S) laser communication system. Considering the combined effects of uplink light intensity scintillation, beam wander, and the angle of arrival fluctuation, the G-H-S system’s bit error rate (BER) closure expression is derived under the EW distribution. Simultaneously, the relationship between the G-H-S system’s signal-to-noise ratio (SNR) and BER under different anisotropic factor u values is simulated and compared with the traditional ground–satellite (G-S) system. The results show that the communication performance of the G-H-S system with HQAM modulation is better. In addition, the effects of the zenith angle, receiving aperture, transmitter beam radius, and beam divergence angle on the BER performance of the system are also studied. Finally, the correctness of the analysis results is verified via Monte Carlo simulation. This research will benefit the design and optimization of satellite laser communication systems.

Outage Probability and Average BER of UAV-Assisted Dual-Hop FSO Communication With Amplify-and-Forward Relaying

Unmanned aerial vehicles (UAVs) can be harnessed as relay nodes in free-space optical (FSO) communication systems to realize a flexible and cost-effective approach for delivering on-demand communication in next-generation wireless communications. However, fading channels can adversely affect the performance of UAV-assisted dual-hop FSO systems owing to various factors. This paper presents a unified system performance analysis of UAV-assisted dual-hop FSO/FSO systems with the amplify-and-forward relaying protocol and intensity modulation/direct detection technique. For general applicability, the influence of the attenuation loss, atmospheric turbulence, pointing error impairments, and angle-of-arrival (AOA) fluctuations on the FSO link between the source and the UAV is considered. Meanwhile, the FSO link between the UAV and the destination is modeled using Málaga distribution channels, which are affected by atmospheric turbulence. The tight closed-form expressions for the outage probability and the average bit error rate of the dual-hop system are derived, followed with the diversity order of the system in the high signal-to-noise ratio range. Furthermore, the impact of various system parameters and channel parameters correlated with the attenuation loss, atmospheric turbulence, pointing error impairments, and AOA fluctuations on the system performance is studied, and a detailed comparative investigation of the various modulation schemes is conducted. Finally, simulation results are presented to validate the analytical results.

Study on the Difference of Wavefront Distortion on Beams Caused by Wavelength Differences in Weak Turbulence Region

In dual-wavelength free-space optical communication systems, the wavefront distortion differences caused by the wavelength difference of the signal and beacon lights cannot be completely corrected. In this study, according to the method of geometric optics, the relationship between the wavefront phases of the signal and beacon lights is analyzed by establishing a mathematical model of the cross-correlation ratio of the arrival-angle fluctuation and phase relationship of different Gaussian-beam wavelengths under weak turbulence near the surface. The numerical results show that after Gaussian beams of different wavelengths propagate through the same atmospheric channel, the cross-correlation number of the arrival-angle fluctuation decreases with an increase in the wavelength difference, waist radius, and turbulence intensity, and increases with an increase in propagation distance. The beam-wavefront phase difference increases with an increasing wavelength difference. Finally, a wavefront distortion correction experiment of a dual-wavelength adaptive optical system verified the correctness of the wavefront phase-difference relationship between the signal light and beacon light established in this study.

Outage probability analysis of maritime FSO links

In this paper, the outage performance of the maritime free-space optical (FSO) communication system is analyzed, and a new maritime FSO link configuration is presented. The channel model for maritime FSO link includes the combined effect of turbulence, pointing error, angle-of-arrival (AOA) fluctuations, and attenuation. While the maritime turbulence channel is modeled by lognormal distribution, pointing error and AOA fluctuations are assumed to be Beckmann and Rayleigh distributed, respectively. The turbulence power spectrum is considered to present the Kolmogorov characteristics, and the Rytov variance of a propagating Gaussian beam in maritime environment is obtained. The probability density function (PDF), cumulative distribution function (CDF), and outage probability of the maritime communication channel are obtained analytically. The outage performance of a maritime communication link is given depending on various parameters of the maritime environment, the Gaussian beam, and the (FSO) communication system.

Experimental verification of fiber coupling characteristics for FSO downlinks from the International Space Station.

Free-space optical (FSO) systems are compulsory to realize high capacity and interference-free communication links from low-Earth orbit (LEO) satellite constellations as well as spacecraft and space stations to the Earth. To be integrated with high-capacity ground networks, the collected portion of the incident beam should be coupled into an optical fiber. To accurately evaluate the signal-to-noise ratio (SNR) and bit-error rate (BER) performance metrics, the probability density function (PDF) of fiber coupling efficiency (CE) must be determined. Previous studies have experimentally verified the CE PDF for a single-mode fiber, however, there is no such investigation for the CE PDF of a multi-mode fiber (MMF) in a LEO-to-ground FSO downlink. In this paper, for the first time, the CE PDF for a 200-μm MMF is experimentally investigated using data from an FSO downlink from the Small Optical Link for International Space Station (SOLISS) terminal to a 40-cm sub-aperture optical ground station (OGS) supported by a fine-tracking system. An average CE of 5.45 dB was also achieved given that the alignment between SOLISS and OGS was not optimal. In addition, using the angle-of-arrival (AoA) and received power data, the statistical characteristics such as channel coherence time, power spectral density, spectrogram, and PDFs of AoA, beam misalignments, and atmospheric turbulence-induced fluctuations are revealed and compared with the state-of-the-art theoretical background.

Research on uplink performance of MIMO terrestrial-satellite laser communication based on OSM-MBM joint modulation

This paper proposes a multiple-input multiple-output (MIMO) terrestrial-satellite laser communication uplink system based on optical spatial modulation with medium-based modulation (OSM-MBM) joint modulation. The Málaga(M) distribution is used to describe the combined effects of near-ground turbulent light intensity scintillation, beam wander and angle of arrival fluctuation. The closed expression of the bit error rate (BER) of the OSM-MBM joint modulation MIMO terrestrial-satellite laser communication uplink is derived. The simulation analyzes the influence of transmitting radius, receiving aperture, beam divergence, zenith angle and signal-to-noise ratio on the system error performance, and compares it with traditional modulation, media-based modulation and optical space modulation. Finally, the experiment is verified by Monte Carlo. This research provides a theoretical reference for the engineering realization of the modulation technology for the MIMO terrestrial-satellite laser communication uplink system.

Beaconless angle-of-arrival tracking with improved receiver sensitivity and tracking precision for free-space optical communications

One of the technically challenging issues of free-space optical communication systems is the mitigation of angle-of-arrival (AoA) fluctuations, mainly arising from the vibration of receiving end and atmospheric turbulence. A common approach is to employ an AoA tracking system at the receiver. Beacon-based AoA tracking requires the beacon light, thus the system could be complicated and bulky when implemented. Beaconless AoA tracking could help to minimize the optical components required. This tracking typically requires an optical beam splitter to direct the received optical signal both to the beam position sensor and data photo-detector (PD). However, the presence of beam splitter results in optical power loss and tracking imprecision. In this paper, we propose a design of AoA tracking system based on an integrated beam positioning sensor and data PD to obviate the need for beacon light and beam splitter. We carry out a proof-of-concept experimental demonstration of AoA tracking systems for a 10-Gb/s free-space optical link over 104 m, comparing its performance with that of the conventional system. The demonstration shows a loss reduction of >2.9 dB by using the proposed design. It also shows that the proposed design improves the tolerance to AoA fluctuation by more than a factor of 2 at a target bit-error ratio of 10−3. The tracking time is measured to be 171 ms at an AoA fluctuation of 250 μrad. We show that the loop controller and fast steering mirror bandwidths are the main factors limiting the tracking time.

Study of anisotropy of convective optical underwater turbulence and the effect of the mean water temperature in the presence of a varying temperature gradient on it

In this paper, the anisotropy of optical convective underwater turbulence is investigated in terms of the variance of angle of arrival (AOA) fluctuations of a narrow laser beam propagating through it in different sections of the medium. The collimated laser beam with a wavelength 532 nm and a diameter 1 cm, which passes through a convective underwater turbulence. The turbulence is generated in a water tank with dimensions of 20 cm × 36 cm × 20 cm, which is installed on a flat surface electrical heater. During the experiments, the mean water temperature (MWT) can be changed from room temperature to 34 ∘C by increasing the heater temperature. The use of the heater also generates a temperature gradient in the medium. The laser beam propagates along a horizontal path with a length of 20 cm inside the tank at different altitudes from the heater source, as well as at different distances from one of the side walls of the turbulent medium. After passing the laser beam through the turbulent medium, the fluctuations of the AOA components in the vertical and horizontal directions are measured. From the time series of the measured AOA fluctuations, their variances are determined. The anisotropy of the medium is investigated by comparing the variance of AOA components measured in the vertical and horizontal directions. We show that the variances of both of vertical and horizontal components of the AOA fluctuations are increased with the MWT, and they are saturated at higher MWTs. In addition, different anisotropic behaviors are observed for the variances of the measured AOA fluctuations at the vicinity of the lateral wall and upper surface of the water. At the vicinity of the lateral wall the variances of the AOA fluctuations in the horizontal component are larger, but at the vicinity of the upper surface the variances of the AOA fluctuations in the vertical component are dominant. This behavior may be caused by the change of the convection motion direction in the turbulent fluid.

Performance and Channel Modeling Optimization for Hovering UAV-Assisted FSO Links

Unmanned Aerial Vehicle (UAV)-assisted free-space optical (FSO) communication has become a promising solution in both civil and military applications. Nevertheless, hovering UAV-assisted FSO links suffer from several losses due to atmospheric turbulence, pointing errors (PEs), angle-of-arrival (AOA) fluctuations, and link attenuation related to various weather conditions. In this paper, we optimize the theoretical channel model for hovering UAV-assisted FSO links considering all the above destructive channel factors. Our optimized theoretical channel model agrees with the Monte-Carlo simulation results much better under the full range of channel coefficients compared to previous published works. Based on our optimized theoretical channel model, theoretical expressions of the link outage probability, ergodic and outage capacity, and bit error rate are derived. The impact of various parameters, such as Rytov variance, root-mean-squares (RMS) of PEs and AOA fluctuations, angle of field-of-view, rain rate, visibility, optical beam divergence angle, and transmitted power on the above performance metrics is analytically studied and corroborated by Monte-Carlo simulations. Simulation results also show that for a given receiving aperture, transmit power, and link length, the performance of the hovering UAV-assisted FSO links can be optimized by carefully designing the ratio of optical beam divergence angle to RMS of PEs.

Dynamic Adaptive Beam Control System Using Variable Focus Lenses for Laser Inter-Satellite Link

One of technical challenges in laser inter-satellite link (ISL) is the mitigation of performance degradation caused by pointing errors and angle-of-arrival (AoA) fluctuations arising unavoidably from satellite movements and vibrations. In this paper, we propose the dynamic adaptive beam control (ABC) technique implementable by using variable focus lenses (VFLs) at both the transmitter and receiver. In this technique, we monitor the instantaneous pointing error and AoA fluctuation induced by satellite vibrations and then provide feedback corrections to the VFL-based ABC system. The VFLs at the transmitter and receiver adjust their focal lengths adaptively to the amount of pointing error and AoA fluctuation, respectively, to minimize the link loss. VFLs operated by electro-wetting or electromagnetic actuator are fast enough to respond to the vibrations. We design the proposed dynamic ABC system for laser ISL by using the double-lens configuration and VFLs. An exemplary system design is presented when commercially available VFLs are utilized. Our simulation study shows that the proposed dynamic ABC technique offers improved transmission performance, compared to the static and the dynamic ABC technique applied to either the transmitter or receiver.

A study on angle of arrival fluctuations in a temperature-, salinity- and sweetness-induced underwater optical turbulence

In this paper, we report the measurement of fluctuations of two components of Angle of Arrival (AoA) of a narrow laser beam propagating through an underwater turbulence induced by a mixture of hot and cold waters having inhomogeneity at small scales, and consider the effect of the water mean temperature on the AoA fluctuations. The same studies on the AoA fluctuations are presented when a mixture of two volumes of water with different salinity and sweetness are used. The results show that the AoA fluctuations increase by increasing the difference in initial temperatures of the hot and cold waters. Comparison of the variances of the AoA fluctuations for two different propagation lengths, reveals that it is greater for the longer path. In addition, comparison of the AoA fluctuations in two directions for different initial temperatures of the cold and hot waters shows that the underwater turbulence is an anisotropic medium whose anisotropy increases with the mean temperature of the water. In the experiments with the mixture of two volumes of water with different salinity and sweetness, the AoA fluctuations are not seriously affected by the water salinity, while for the sweetness we see a small but interesting response.

Kalman filter spot centroid detection algorithm in optical wireless communication

Atmospheric turbulence creates a light spot on the focal plane of the receiving end scintillation and angle of arrival fluctuation in optical wireless communication. The combination of a spot centroid detection algorithm and Kalman filter (KF) is proposed for spot tracking. The theoretical calculated value of the spot circle fit is filtered to obtain an optimal estimate of the spot center. The root mean square error of the detected spot centroids is used as an evaluation metric to verify the conventional algorithm and KF algorithm for the real-time tracking of the laser spot at transmission distances of 1.3, 4.1, and 10.3 km. The results show that the root mean square error of the spot in the pitch direction decreases from 0.740, 2.537, and 7.256 pixels to 0.683, 1.792, and 4.756 pixels, respectively, whereas the root mean square error of the spot in the horizontal direction decreases from 0.481, 2.131, and 5.932 pixels to 0.463, 1.471, and 4.362 pixels, respectively, compared with the conventional algorithm at three transmission distances. The envelope fluctuation of the baseband signal at the receiving end is significantly improved using KF algorithm compared with the conventional algorithm, which improves the stability of the optical wireless communication link.

Research on the performance of SIMO RC-OFDM system with exponential Weibull distribution in the downlink satellite–terrestrial laser communication

In this paper, a repetition code (RC) coherent orthogonal frequency division multiplexing (OFDM) single input multiple output (SIMO) system based on the exponential Weibull distribution model is proposed for downlink satellite–terrestrial laser communication. The closed form expression of bit error rate (BER) of the SIMO RC-OFDM system is derived by considering the joint effect of downlink intensity scintillation and angle of arrival fluctuation (AOA). The relationship between the BER and signal-to-noise ratio (SNR) of uncoded system and SIMO RC-OFDM system is compared under weak, medium and strong atmosphere turbulence, and the influence of the number of receiver antennas on the SIMO RC-OFDM system is studied. At the same time, under the condition of weak turbulence, the influence of important indicators such as zenith angle, receiving aperture, optimal beam divergence angle, and optimal transmission radius on the satellite–terrestrial laser communication downlink SIMO RC-OFDM system is analyzed. The Monte Carlo (MC) principle uses randomness to solve integral problems, and the obtained results are verified by MC simulations. This work provides a theoretical basis for research on coding technology in satellite–terrestrial laser downlink communication SIMO systems.

Analytical Channel Model and Link Design Optimization for Ground-to-HAP Free-Space Optical Communications

Integrating high altitude platforms (HAPs) and free space optical (FSO) communications is a promising solution to establish high data rate aerial links for the next generation wireless networks. However, practical limitations such as pointing errors and angle-of-arrival (AOA) fluctuations of the optical beam due to the orientation deviations of hovering HAPs make it challenging to implement HAP-based FSO links. For a ground-to-HAP FSO link, tractable, closed-form statistical channel models are derived in this article to simplify optimal design of such systems. The proposed models include the combined effects of atmospheric turbulence regimes (i.e., log-normal and gamma-gamma), pointing error induced geometrical loss, pointing jitter variance caused by beam wander, detector aperture size, beam-width, and AOA fluctuations of the received optical beam. The analytical expressions are corroborated by performing Monte--Carlo simulations. Furthermore, closed-form expressions for the outage probability of the considered link under different turbulence regimes are derived. Detailed analysis is carried out to optimize the transmitted laser beam and the field-of-view of the receiver for minimizing outage probability under different channel conditions. The obtained analytical results can be applied to finding the optimal parameter values and designing ground-to-HAP FSO links without resorting to time-consuming simulations.

Impacts of the source temperature and its distance on the statistical behavior of the convective air turbulence

In this paper, anisotropy and inhomogeneity of an indoor convective air turbulence are studied using two-channel moire deflectometry by statistical analyzing of the angle of arrival (AA) fluctuations over about 1300 points on the wave front passing through the turbulent area. The beam of a laser source is expanded and collimated with a diameter of 18 cm by a telescopic system consisting of an aspheric lens and a telescope. This beam propagates horizontally through a turbulent area. A heater is used for generating a convection air turbulence. At the end of the turbulent medium, the distorted wave front enters the aperture of another telescope. By the aid of another telescopic system, the diameter of the beam is reduced to a value of 2 cm, and the beam enters to a two-channel moire deflectometer. This device is able to measure AA of the wave front being fluctuated due to the turbulence. By statistical analyzing of the AA fluctuations in two perpendicular directions on the transverse plane, the homogeneity and isotropy of the turbulent medium are investigated at different distances from the heater in the presence of different temperature gradients. Results show that the temperature gradient and the distance from the heat source have considerable impacts on the inhomogeneity and anisotropy of the convective air turbulence. With increasing the distance from the heat source and decreasing the temperature gradient, the homogeneity increases, while by increasing the temperature gradient and in high distances from the heater, it becomes more isotropic. Finally, we report a way for estimating the depth of boundary layer.

Influence of anisotropy of marine turbulence on the variance of optical wave AOA fluctuations.

The optical wave angle of arrival (AOA) fluctuations in marine turbulence severely degrade long-range imaging quality by introducing image distortion. Theoretical investigations of optical wave AOA fluctuations are critical to improve the performances of long-range imaging systems in marine turbulence conditions. In this work, analytic expressions for the variance of optical plane and spherical wave AOA fluctuations in anisotropic marine turbulence will be derived. Compared with the previous models that focus on the isotropic and Kolmogorov properties of marine turbulence, both the anisotropy and non-Kolmogorov features of marine turbulence are considered. The anisotropic factor, general spectral power law instead of constant value of 11/3, finite turbulence inner and outer scales, and variable wavelength are included in the models developed in this work. Also, comparative analyses are performed for the models derived separately in marine and terrestrial anisotropic turbulence conditions. It turns out the anisotropy of turbulence cells degrades the effects of marine turbulence on the optical wave AOA fluctuations. Also, the marine atmosphere humidity fluctuations increase the impacts of anisotropic marine turbulence on the final derived models.

Beam Size Optimization and Adaptation for High-Altitude Airborne Free-Space Optical Communication Systems

High-altitude airborne platforms interconnected by free-space optical communications (FSOCs) have recently emerged as a promising solution for establishing wireless networks for rural and remote areas. The performance of FSOC system is severely degraded by the angle-of-arrival (AoA) fluctuation and pointing error. The precise alignment between the optical transmitter and receiver can be achieved by using the pointing, acquisition, and tracking (PAT), but it should work within the tight constraints of airborne platforms on size, weight, and power. It is also highly desirable that the PAT operates rapidly (e.g., without iteration for optimization) since the airborne platforms can be on the fast move. We propose a rapid and computation power-efficient adaptive beam control technique, where the beam sizes are adjusted without iterations at both the transmitter and receiver using nonmechanical variable-focus lenses, to mitigate the deleterious effects of AoA fluctuation and pointing error simultaneously. For this purpose, we provide the closed-form expressions about the optimum beam sizes at the transmitter and receiver for the outage probability. We carry out Monte Carlo simulations to validate the accuracy of our theoretical derivations. We show that the airborne FSOC system using the adaptive beam control technique outperforms the system having fixed beam sizes over wide ranges of AoA fluctuation and pointing error.