Wide Range Of Turbulence Conditions Research Articles

Transformer neural networks for closed-loop adaptive optics using nonmodulated pyramid wavefront sensors

Context. The pyramid wavefront sensor (PyWFS) provides the required sensitivity for demanding future adaptive optics (AO) instruments. However, the PyWFS is highly nonlinear and requires the use of beam modulation to successfully close an AO loop under varying atmospheric turbulence conditions. This comes at the expense of a loss in sensitivity. Aims. We trained, analyzed, and compared the use of deep neural networks (NNs) as nonlinear estimators for the nonmodulated PyWFS, identifying the most suitable NN architecture for a reliable closed-loop AO. Methods. We developed a novel training strategy for NNs that seeks to accommodate for changes in residual statistics between open and closed loops, plus the addition of noise for robustness purposes. Through simulations, we tested and compared several deep NNs from classical to new convolutional neural networks (CNNs), plus the most recent transformer neural network (TNN; global context visual transformer, GCViT), first for an open loop and then for a closed loop. By identifying and properly retraining the most adequate deep neural net, we tested its simulated performance first in an open loop and then for closing an AO loop at a variety of noise and turbulence conditions. We finally tested the trained NN ability to close a real AO loop for an optical bench. Results. Using open-loop simulated data, we observe that a TNN (GCViT) largely surpasses any CNN in estimation accuracy in a wide range of turbulence conditions. Moreover, the TNN performs better in a simulated closed loop than CNNs, avoiding estimation issues at the pupil borders. When closing the loop at strong turbulence and low noise, the TNN using nonmodulated PyWFS data is able to close the loop, similar to a PyWFS with 12λ/D of modulation. When the noise is increased, only the TNN is able to close the loop, while the standard linear reconstructor fails even when a modulation is introduced. Using the GCViT, we closed a real AO loop in the optical bench and achieved a Strehl ratio between 0.28 and 0.77 for turbulence conditions corresponding to Fried parameters ranging from 6 to 20 cm, respectively. Conclusions. Through a variety of simulated and experimental results, we demonstrate that a TNN is the most suitable architecture for extending the dynamic range without sacrificing sensitivity for a nonmodulated PyWFS. It opens the path for using nonmodulated Pyramid WFSs in an unprecedented range of atmospheric and noise conditions.

An experimental study on the settling velocity of inertial particles in different homogeneous isotropic turbulent flows

We propose an experimental study on the gravitational settling velocity of dense, sub-Kolmogorov inertial particles under different background turbulent flows. We report phase Doppler particle analyser measurements in a low-speed wind tunnel uniformly seeded with micrometre scale water droplets. Turbulence is generated with three different grids (two consisting of different active-grid protocols while the third is a regular static grid), allowing us to cover a very wide range of turbulence conditions in terms of Taylor-scale-based Reynolds numbers ( $Re_\lambda \in [30\unicode{x2013}520]$ ), Rouse numbers ( $Ro \in [0\unicode{x2013}5]$ ) and volume fractions ( $\phi _v \in [0.5\times 10^{-5}\unicode{x2013}2.0\times 10^{-5}]$ ). We find, in agreement with previous works, that enhancement of the settling velocity occurs at low Rouse number, while hindering of the settling occurs at higher Rouse number for decreasing turbulence energy levels. The wide range of flow parameters explored allowed us to observe that enhancement decreases significantly with the Taylor–Reynolds number and is significantly affected by the volume fraction $\phi _v$ . We also studied the effect of large-scale forcing on settling velocity modification. The possibility of changing the inflow conditions by using different grids allowed us to test cases with fixed $Re_\lambda$ and turbulent intensity but with different integral length scale. Finally, we assess the existence of secondary flows in the wind tunnel and their role on particle settling. This is achieved by characterising the settling velocity at two different positions, the centreline and close to the wall, with the same streamwise coordinate.

Neural Successive Cancellation Polar Decoder With Tanh-Based Modified LLR Over FSO Turbulence Channel

The neural successive cancellation (NSC) decoder with tanh-based modified log-likelihood ratio (LLR) is proposed for reducing the decoding latency of polar codes over free space optical (FSO) turbulence channel. The conventional successive cancellation (SC) decoder is partitioned into multiple sub-blocks, which are replaced by multiple sub neural network (NN) decoders with tanh-based modified LLR. The recursive characteristic of the polar sequences reliability ranking given in 5G standard enables the sub-NN decoder to be uniquely determined by code length and the number of information bits. Confirmed by the simulation, the bit error rate (BER) performance of NSC decoder with tanh-based modified LLR is close to the conventional SC decoder over turbulence channel for the practical-length polar codes. Regarding turbulence-stability, the NSC decoder trained in moderate and strong turbulence conditions have stable performance in a wide range of turbulence conditions. Moreover, in comparison of decoding latency, the NSC decoder with tanh-based modified LLR takes less than 25% time steps of SC decoder in the same code length.

Parameter Estimation of the Lognormal-Rician Channel Model Using Saddlepoint Approximation

In this article, the challenges of effective channel estimation for the lognormal-Rician turbulence model are addressed. We present a novel maximum likelihood estimation algorithm involving a saddlepoint approximation (SAP) method to estimate the shaping parameters of the lognormal-Rician distribution. An additional parameter k needs to be estimated in addition to r and σ z 2 under the SAP representation. The accuracy of the proposed estimator is investigated by using the mean square error and normalized mean square error. The simulated results show that the proposed estimator exhibits satisfactory performance over a wide range of turbulence conditions, and it can be easily applied to both noiseless and noisy situations. The effect of the estimated shaping parameters errors on the bit error rate (BER) for the on-off key (OOK) modulation is also investigated; it is shown that the BER performance derived with the SAP estimator becomes closer to the system performance with perfect shaping parameters as r increases. In particular, we present a qualitative comparison between the proposed SAP estimator and other algorithms available in the literature.

Performance analysis for a mixed RF and multihop FSO communication system in 5G C-RAN

In this paper, we investigate the performance of a mixed radio frequency (RF) and multihop free space optical (FSO) system in a fifth-generation cloud radio access network (C-RAN) architecture. To cope with the practical channel characteristics, the RF link is assumed to experience the $ \kappa - \mu $ shadowed fading that has recently been proposed to model the small-scale multipath fading as well as line-of-sight shadowing. For FSO links, we adopt the exponentiated Weibull distribution, which can represent irradiance fluctuations at the finite receiving aperture over a wide range of turbulence conditions. Furthermore, we consider the pointing error between the FSO end devices. We first derive a novel probability density function (PDF) expression for the $ \kappa - \mu $ shadowed fading so that the $ \kappa $, $ m $, and $ \mu $ can be equal to the arbitrary positive real value. Then, we study the outage probability and the average symbol error rate (ASER) of the considered system. Our analysis is based on a decode-and-forward (DF) relaying scheme. We choose M-ary quadrature amplitude modulation (M-QAM) for the RF link and binary pulse position modulation (BPPM) for the FSO links. Finally, to provide more insights, we present the asymptotic approximate expressions in high signal-to-noise ratio regimes. Our research shows that the performance of the mixed RF and multihop FSO system can be improved by the large receiving aperture and the increasing number of hops.

SIMO subcarrier PSK FSO links with phase noise and non‐zero boresight pointing errors over turbulence channels

Terrestrial free-space optical (FSO) communication systems with subcarrier intensity modulation have experienced a particular research attention in the recent past. However, their performance strongly degrades in the presence of atmospheric turbulence, pointing errors, and phase noise impairments. In order to overcome these limitations, the authors consider a receiver diversity scheme of a typical subcarrier phase-shift keying (PSK) system and investigate the performance by means of the average symbol error probability (ASEP). They assume a wide range of turbulence conditions, non-zero boresight pointing errors, and phase noise strengths described through the gamma-gamma, Beckmann, and Tikhonov distributions, respectively. Novel approximate ASEP expressions are derived for single-input single-output and single-input multiple-output (SIMO) configurations. Appropriate numerical results are depicted and validated by Monte Carlo simulations.

Performance of decode-and-forward mixed RF/FSO system over [formula omitted] shadowed and Exponentiated Weibull fading

In this paper, we investigate the performance of decode-and-forward dual-hop mixed RF/FSO system in fifth-generation (5G) cloud radio access network. To describe the 5G channel characteristics properly, we assume that the RF link follows κ−μ shadowed fading which has been recently proposed to model small-scale multipath fading as well as line-of-sight (LOS) shadowing. For the FSO link, we adopt the Exponentiated Weibull distribution which can represent irradiance fluctuations at the finite receiving aperture over a wide range of turbulence conditions. We first derive the cumulative distribution function in terms of Meijer’s G function, and then use it to obtain the analytical expressions of the outage probability, average bit error rate and ergodic capacity. The system performances are analyzed with different κ−μ shadowed fading parameters, turbulence strength and receiver aperture sizes. The analytical results show an accurate match to the Monte-Carlo simulation.

Performance investigation of the polar coded FSO communication system over turbulence channel.

In this paper, for the first time, to the best of our knowledge, polar codes are introduced and experimentally implemented in a free space optical (FSO) communication system to combat atmospheric turbulence induced fading. By analyzing the characteristics of the turbulence channel, a method of evaluating the channel state information for polar decoding is proposed that can achieve good trade-off between the performance and the computational complexity of this polar coded system. To verify our scheme, an intensity modulation direct detection FSO communication experimental platform with a turbulence chamber is established. For the weak turbulence condition, comparing with the low-density parity check codes, the experimental results show that our proposed scheme has stronger error correcting capacity and lower computational complexity in combating the turbulence induced fading. Moreover, for moderate and strong turbulence conditions, the gamma-gamma turbulence model is adopted for constructing the Monte Carlo simulation. The results of the experiment and simulation both show that our proposed scheme can effectively combat atmospheric turbulence induced fading with a relatively low computational complexity in a wide range of turbulence conditions.

Power Input Measurements in Stirred Bioreactors at Laboratory Scale.

The power input in stirred bioreactors is an important scaling-up parameter and can be measured through the torque that acts on the impeller shaft during rotation. However, the experimental determination of the power input in small-scale vessels is still challenging due to relatively high friction losses inside typically used bushings, bearings and/or shaft seals and the accuracy of commercially available torque meters. Thus, only limited data for small-scale bioreactors, in particular single-use systems, is available in the literature, making comparisons among different single-use systems and their conventional counterparts difficult.This manuscript provides a protocol on how to measure power inputs in benchtop scale bioreactors over a wide range of turbulence conditions, which can be described by the dimensionless Reynolds number (Re). The aforementioned friction losses are effectively reduced by the use of an air bearing. The procedure on how to set up, conduct and evaluate a torque-based power input measurement, with special focus on cell culture typical agitation conditions with low to moderate turbulence (100 < Re < 2·104), is described in detail. The power input of several multi-use and single-use bioreactors is provided by the dimensionless power number (also called Newton number, P0), which is determined to be in the range of P0 ≈ 0.3 and P0 ≈ 4.5 for the maximum Reynolds numbers in the different bioreactors.

Power Input Measurements in Stirred Bioreactors at Laboratory Scale

The power input in stirred bioreactors is an important scaling-up parameter and can be measured through the torque that acts on the impeller shaft during rotation. However, the experimental determination of the power input in small-scale vessels is still challenging due to relatively high friction losses inside typically used bushings, bearings and/or shaft seals and the accuracy of commercially available torque meters. Thus, only limited data for small-scale bioreactors, in particular single-use systems, is available in the literature, making comparisons among different single-use systems and their conventional counterparts difficult. This manuscript provides a protocol on how to measure power inputs in benchtop scale bioreactors over a wide range of turbulence conditions, which can be described by the dimensionless Reynolds number (Re). The aforementioned friction losses are effectively reduced by the use of an air bearing. The procedure on how to set up, conduct and evaluate a torque-based power input measurement, with special focus on cell culture typical agitation conditions with low to moderate turbulence (100 < Re < 2·104), is described in detail. The power input of several multi-use and single-use bioreactors is provided by the dimensionless power number (also called Newton number, P0), which is determined to be in the range of P0 ≈ 0.3 and P0 ≈ 4.5 for the maximum Reynolds numbers in the different bioreactors.

Modeling of the gas-phase combustion of a grate-firing biomass furnace using an extended approach of Eddy Dissipation Concept

The ability of the standard Eddy Dissipation Concept (EDC) approach to account for the chemical kinetic rates during the interaction between chemistry and turbulent flow field made it a suitable scheme for simulating gas-phase combustion. However, its application poses a challenge for modeling weakly turbulent reacting flow conditions, as well as reacting flows with comparable flow and chemical time scales. A modified version of EDC (referred to here as extended EDC) has recently been developed for predominantly non-premixed turbulent flames. This led to significant improvement in the predictions of species and temperature fields of biomass-derived gas jet flames over a wide range of turbulence conditions (from weakly to highly turbulent flow conditions). The present study examines the application of this extended EDC approach for the simulation of a small-scale updraft biomass combustor. The predictions of the model are compared with those of the standard EDC and their counterparts’ experimental temperature and species concentrations. In addition, the pathway of formation/destruction of gas-fuel species and pollutants (e.g., NOx) is investigated. The findings of the present study reveal a significant improvement in the predictions of temperature field and species of the gas-phase of grate-firing biomass combustion.

Block Markov superposition transmission with pulse position modulation over free-space optical links

In FSO (Free-Space Optical) communications, performance of the communication systems is severely degraded by atmospheric turbulence. PPM (Pulse Position Modulation) is widely used in FSO communication systems owing to its high power effciency. In this paper, we present a combination of the BMST (Block Markov Superposition Transmission) technique and the PPM scheme to improve the reliability of the transmission over FSO links. Based on analyzing an equivalent system, a lower bound on the bit-error-rate of the proposed scheme is presented. Extensive simulations are performed which show that the BMST-PPM system performs well under a wide range of turbulence conditions and improves the performance of the basic code. Simulation results also show that, the performance of the system with the sliding-window detection/decoding algorithm matches well with the lower bound in the low-error-rate region.

Multiscale permutation entropy analysis of laser beam wandering in isotropic turbulence

We have experimentally quantified the temporal structural diversity from the coordinate fluctuations of a laser beam propagating through isotropic optical turbulence. The main focus here is on the characterization of the long-range correlations in the wandering of a thin Gaussian laser beam over a screen after propagating through a turbulent medium. To fulfill this goal, a laboratory-controlled experiment was conducted in which coordinate fluctuations of the laser beam were recorded at a sufficiently high sampling rate for a wide range of turbulent conditions. Horizontal and vertical displacements of the laser beam centroid were subsequently analyzed by implementing the symbolic technique based on ordinal patterns to estimate the well-known permutation entropy. We show that the permutation entropy estimations at multiple time scales evidence an interplay between different dynamical behaviors. More specifically, a crossover between two different scaling regimes is observed. We confirm a transition from an integrated stochastic process contaminated with electronic noise to a fractional Brownian motion with a Hurst exponent H=5/6 as the sampling time increases. Besides, we are able to quantify, from the estimated entropy, the amount of electronic noise as a function of the turbulence strength. We have also demonstrated that these experimental observations are in very good agreement with numerical simulations of noisy fractional Brownian motions with a well-defined crossover between two different scaling regimes.

Wave optics simulations of synthetic aperture ladar performance through turbulence.

This paper utilizes a combination of theory and simulations to examine synthetic aperture imaging across a wide range of turbulence conditions. Extensive wave optics simulations are used to validate existing theory and to investigate the use of a common measurement technique. It demonstrates the applicability of earlier synthetic aperture laser radar (ladar) (SAL) research across a wide range of turbulence conditions, and examines the metric approaches and limitations for the imaging conditions normally seen in practical SAL systems. To examine the full impact of turbulence on SAL, the derivations, simulations, and analyses include three different resolution metrics as well as a commonly used contrast metric: the integrated sidelobe ratio. This paper demonstrates the integrated effects of turbulence on SAL imaging. Finally, suggestions are given for measuring the true resolving power of operational SAL systems.

Generalized block Markov superposition transmission over free-space optical links

In free-space optical (FSO) communications, the performance of the communication systems is severely degraded by atmospheric turbulence. Channel coding and diversity techniques are commonly used to combat channel fading induced by atmospheric turbulence. In this paper, we present the generalized block Markov superposition transmission (GBMST) of repetition codes to improve time diversity. In the GBMST scheme, information sub-blocks are transmitted in the block Markov superposition manner, with possibly different transmission memories. Based on analyzing an equivalent system, a lower bound on the bit-error-rate (BER) of the proposed scheme is presented. Simulation results demonstrate that, under a wide range of turbulence conditions, the proposed scheme improves diversity gain with only a slight reduction of transmission rate. In particular, with encoding memory sequence (0, 0, 8) and transmission rate 1/3, a diversity order of eleven is achieved under moderate turbulence conditions. Numerical results also show that, the GBMST systems with appropriate settings can approach the derived lower bound, implying that full diversity is achievable.

MIMO FSO communication using subcarrier intensity modulation over double generalized gamma fading

Atmospheric turbulence-induced fading is known to have a serious detrimental effect on the performance of free-space optical (FSO) communication. The involvement of multiple lasers and photodetectors in FSO systems offers an effective way to overcome fading. Very recently, a new generic fading model, called double-generalized gamma (double GG), is developed for accurately describing irradiance fading over a wide range of turbulence conditions. Therefore, for a general and exact study of the multiple-input multiple-output (MIMO) FSO system, the double GG fading model is adopted in this paper. We investigate the MIMO FSO systems using subcarrier intensity modulation. Two typical transmit diversity schemes, repetition code (RC) and orthogonal space-time block code (OSTBC), are considered. We first propose a new power series expression for the probability density function of the double GG fading. Then we derive the average error rate expressions for both schemes in terms of double power series. The truncated forms of the derived power series enable the rapid and accurate numerical computation of the error rates. Furthermore, we present the asymptotic error rate analyses at high electrical signal-to-noise ratio (SNR) for both schemes. Closed-form diversity order and coding gain for both schemes are also obtained. Our numerical results, verified by simulation, confirm that RC outperforms OSTBC for MIMO FSO systems with subcarrier intensity modulation in double GG fading. The asymptotic coding gain of the RC scheme over the OSTBC scheme is analytically quantified for varying degrees of the fading strength.

Ergodic capacity analysis for DF strategies in cooperative FSO systems.

This paper focuses on the ergodic capacity analysis in the context of cooperative free-space optical (FSO) systems when the line of sight is available. Novel asymptotic closed-form expressions for the ergodic capacity corresponding to two different decode-and-forward (DF) strategies are obtained for a cooperative FSO communication system. Here, the atmospheric turbulence is modeled by a gamma-gamma distribution of parameters α and β which allows to study a wide range of turbulence conditions (moderate-to-strong) as well as the effect of the misalignment with zero boresight. It is demonstrated that cooperative communications are able to achieve not only a better performance in terms of the error rate performance as well as outage probability than direct transmission, but also in terms of the channel capacity in the context of FSO systems without much increase in hardware. In this way, a 3-way FSO communication setup is considered, in which the cooperative protocol can be applied to achieve a greater ergodic capacity compared to a direct transmission. It can be concluded that a greater and robust capacity strongly dependent on the relay location is achieved compared to a direct transmission without cooperative communication when line of sight is available. Here, the line of sight is taken into account in order to achieve a significant robustness under different turbulence conditions and more severe pointing errors regardless of the relay location. Simulation results are further demonstrated to confirm the accuracy and usefulness of the derived results.

Maximum Likelihood Estimation of the Lognormal-Rician FSO Channel Model

In this letter, the on-going challenges are addressed for the application of the lognormal-Rician turbulence model to free-space optical communication systems. Maximum likelihood estimation is applied to characterize the lognormal-Rician turbulence model parameters, and the expectation-maximization algorithm is used to compute maximum likelihood estimates of the unknown parameters. The performance is investigated, by way of the mean square error, and it is found that the proposed technique can accurately characterize free-space optical communication channels over a wide range of turbulence conditions, with reduced demand on the quantity of data samples.

Turbulence-induced persistence in laser beam wandering.

We have experimentally confirmed the presence of long-memory correlations in the wandering of a thin Gaussian laser beam over a screen after propagating through a turbulent medium. A laboratory-controlled experiment was conducted in which coordinate fluctuations of the laser beam were recorded at a sufficiently high sampling rate for a wide range of turbulent conditions. Horizontal and vertical displacements of the laser beam centroid were subsequently analyzed by implementing detrended fluctuation analysis. This is a very well-known and widely used methodology to unveil memory effects from time series. Results obtained from this experimental analysis allow us to confirm that both coordinates behave as highly persistent signals for strong turbulent intensities. This finding is relevant for a better comprehension and modeling of the turbulence effects in free-space optical communication systems and other applications related to propagation of optical signals in the atmosphere.

A Novel Statistical Channel Model for Turbulence-Induced Fading in Free-Space Optical Systems

In this paper, we propose a new probability distribution function which accurately describes turbulence-induced fading under a wide range of turbulence conditions. The proposed model, termed double-generalized gamma (double GG), is based on a doubly stochastic theory of scintillation and developed via the product of two generalized gamma distributions. The proposed double GG distribution generalizes many existing turbulence channel models and provides an excellent fit to the published plane and spherical waves simulation data. Using this new statistical channel model, we derive closed form expressions for the outage probability and the average bit error as well as corresponding asymptotic expressions of free-space optical communication systems over turbulence channels. We demonstrate that our derived expressions cover many existing results in the literature earlier reported for gamma-gamma, double-Weibull and K channels as special cases.