Gaussian Noise Model Research Articles

Universal upper bounds for Gaussian information capacity

The most natural way to describe an information-carrying system containing a specific noise is an additive white Gaussian-noise (AWGN) channel. In bosonic quantum systems (especially the Gaussian case), although the classical information capacity for a phase-insensitive and thermal-noise channel is additive based on a proof of the minimum output entropy conjecture, several open questions remain. By generalizing the Gaussian noise model from thermal noise to general Gaussian noise, we rigorously revisit and calculate these strong upper bounds on the information capacity for single-mode with general Gaussian-noise channels. In this study, we use the quantum entropy power inequality (QEPI) approach. This framework gives a new formula for finding upper bounds on the information capacity of bosonic Gaussian channels.

Research on relay selection of armored formations wireless UV covert communication

In view of the end-to-end communication interruption problem of armored formations in complex battlefield environments, relay-assisted methods are often used to establish cooperative communications links, and the choice of relay is a key issue. In order to improve the communication coordination ability among formations, an optimal relay selection algorithm for armored formations based on wireless ultraviolet (UV) covert communication is proposed on the premise of decode-and-forward protocol, combined with the threshold decision idea. The algorithm combines the advantages of UV NLOS(non-line-of-sight) communication. The optimal relay selection is made for the formations according to the signal-to-noise ratio (SNR) threshold and channel characteristics selection strategy, and the bit error rate (BER) performance is analyzed under Gaussian noise model. The simulation results show that the optimal relay link can be obtained by selecting the appropriate cooperation threshold according to different SNR environments and relay number. Furthermore, adjusting the receiving and transmitting status of the relay, when the cooperative communications link changes dynamically, can effectively improve the communication quality of the cooperative relay link.

Application of Machine Learning in Fiber Nonlinearity Modeling and Monitoring for Elastic Optical Networks

Fiber nonlinear interference (NLI) modeling and monitoring are the key building blocks to support elastic optical networks (EONs). In the past, they were normally developed and investigated separately. Moreover, the accuracy of the previously proposed methods still needs to be improved for heterogenous dynamic optical networks. In this paper, we present the application of machine learning (ML) in NLI modeling and monitoring. In particular, we first propose to use ML approaches to calibrate the errors of current fiber nonlinearity models. The Gaussian-noise (GN) model is used as an illustrative example, and significant improvement is demonstrated with the aid of an artificial neural network (ANN). Further, we propose to use ML to combine the modeling and monitoring schemes for a better estimation of NLI variance. The following contents are the listed errors as mentioned in the comments for reasons of withdrawal. (1) The works, as mentioned as the title, should be addressed is about the elastic optical networks(EON), however, the simulation setup and the results section are focused on the conventional wavelength division multiplexing(WDM) networks. This error may confuse some researcher, getting the misleading decision for the researches about the elastic optical networks. (2) There exists some errors in the results rection, such as, Fig.9(b) and (c) with the wrong captions may result in misleading decision. (3) The split-step-Fourier-method(SSFM) presents good accuracy if the sufficiently small steps are adopted in the calculation, however this paper has not necessary contents and efforts to optimise the step-length of SSFM. This error may confuse the accuracy of simulation results. Therefore, we decide to withdraw this paper from arXiv. The correct and complete paper with the same title was published in journal of lightwave technology with doi: 10.1109/JLT.2019.2910143.

Projection Data Smoothing for Low-Dose CT Based on $$\ell _p$$ℓp Regularization

Projection data smoothing is a traditional technique for low-dose computed tomography. The projection data can be modeled as a piecewise smooth function. It’s well known that $$\ell _1$$ regularization of the image gradients tries to recover piecewise constant functions, while $$\ell _2$$ regularization recovers smooth functions. This motivates us to propose the $$\ell _p$$ regularization with $$1<p<2$$ for low-dose projection data smoothing. Besides, the non-stationary Gaussian noise model for the projection data is built into the regularization term. The resulting model is then linearized such that the fast split-Bregman algorithm can be applied. Experiments on simulated projection data as well as real data show that $$\ell _p$$ regularization with $$1<p<2$$ could achieve better reconstruction compared to $$\ell _{1}$$ regularization.

Theoretical analysis of long-haul systems adopting mode-division multiplexing

In this paper, we modify the Gaussian noise model (GN-model) to address the nonlinearity effects in few-mode fibers. Closed-form expressions for the nonlinear interference power in birefringent few-mode fibers (FMFs) are derived and the effect of differential mode group delay (DMGD) is investigated. Moreover, the nonlinearity accumulation through propagation in multiple-spans fiber and the birefringence effect are considered. In addition, we discuss the effect of the DMGD on the fiber nonlinearity in systems adopting mode-division multiplexing (MDM). The results show that the DMGD management degrades the system performance in weak coupling regime because the nonlinear interference is enhanced. However, strong coupling-based transmission outperforms weak coupling transmission regardless of the DMGD effect in the weak coupling regime. On the other hand, by taking the DMGD effect into account, the system performance in weak coupling regime is better than that in strong coupling regime. Furthermore, the impact of the nonlinearity on the maximum reach is discussed.

Accumulation of nonlinear interference noise in probabilistically shaped 64-quadrature amplitude modulation systems

An efficient procedure is presented for evaluating the effects of modulation format on the accumulation of nonlinear interference noise (NLIN) in probabilistically shaped 28 Gbaud 64-quadrature amplitude modulation (QAM) wavelength division multiplexed (WDM) systems. The shaped symbol sequences are generated by the rate adaptive scheme concatenating a constant composition distribution matcher and a systematic forward error correction encoder. A shaping distribution based on the Maxwell–Boltzmann and the uniform distribution with the same net bit rate is considered. The NLIN variance is emulated using the accurate enhanced modulation-dependent Gaussian noise model. Accounting for the impact of higher-order standardized moments of the modulation, the dependence of NLIN variance on probabilistic shaping is determined using the proposed procedure. In addition, an increase in NLIN variance for shaping over uniform input is demonstrated. For a dual polarization (DP) fully loaded C-band WDM optical fiber system with a channel spacing of 37.5 GHz, probabilistic shaping leads to a reduction of 0.036 in the ratio of intrachannel and interchannel contributions to nonlinear noise over uniform 64-QAM for a 1500-km distance. Finally, for nine channels with DP probabilistically shaped 64-QAM input over 1500-km transmission, distributed amplification enables a reduction of 2.54 dB in the accumulation of normalized NLIN power compared to lumped amplification.

DOA Estimation in heteroscedastic noise

The paper considers direction of arrival (DOA) estimation from long-term observations in a very noisy environment. The concern is to derive methods obtaining reasonable DOAs at very low SNR. The noise is assumed zero-mean Gaussian and its variance varies in time and space, causing stationary data models to fit poorly over long observation times. Therefore a heteroscedastic Gaussian noise model is introduced where the variance varies across observations and sensors. The source amplitudes are assumed independent zero-mean complex Gaussian distributed with unknown variances (i.e. the source powers), inspiring stochastic maximum likelihood (ML) DOA estimation. The DOAs of plane waves are estimated from multi-snapshot sensor array data using sparse Bayesian learning (SBL) where the noise is estimated across both sensors and snapshots. This SBL approach is more flexible and performs better than other high-resolution methods since they cannot estimate the heteroscedastic noise process. An alternative to SBL is simple data normalization, whereby only the phase across the array is utilized. Simulations in noisy environments demonstrate that taking the heteroscedastic noise into account causes the DOA estimation to fail at lower SNR, often at 20 dB lower SNR.

Time resolved retardation and orientation measurement by common path heterodyne interferometer

A common path heterodyne interferometer is developed for characterizing the temporal response of a liquid crystal variable retarder. The phase retardation and azimuthal angle of optic axis are determined simultaneously at 10 Hz and 100 Hz driving signals. The maximum likelihood estimation technique based on Gaussian noise model is used to retrieve the amplitudes and phases of the heterodyne signals. The low frequency variations of phase retardation and azimuthal angle are then calculated from the amplitude ratio and phase difference. The random noises resulted from light intensity instability and environmental disturbances are significantly reduced during the calculation.

Iterative Resource Allocation Algorithm for EONs Based on a Linearized GN Model

Elastic optical networks (EONs) rely on efficient resource planning to meet future communication needs and avoid resource overprovisioning. Estimation of physical-layer impairments (PLIs) in EONs plays an important role in the network planning stage. Traditionally, the transmission reach (TR) and Gaussian noise (GN) models have been broadly employed in the estimation of the PLIs. However, the TR model cannot accurately estimate PLIs, whereas the GN model is incompatible with state of the art linear optimization solvers. In this paper, we propose a physical-layer estimation model based on the GN model, referred to as the conservative linearized Gaussian noise (CLGN) model. To address the routing, spectrum, and regeneration assignment problem accounting for PLIs, we introduce a link-based mixed integer linear programming formulation employing the CLGN, whose heavy computational burden is relieved by a heuristic approach referred to as the sequential iterative optimization algorithm. We show through simulation that network resources such as spectrum and regeneration nodes can be saved utilizing the CLGN model rather than the TR model. Our proposed heuristic algorithm speeds up the optimization process and provides better resource usage compared to state of the art algorithms on benchmark networks.

A Closed-Form Approximation of the Gaussian Noise Model in the Presence of Inter-Channel Stimulated Raman Scattering

An accurate, closed-form expression evaluating the nonlinear interference (NLI) power in coherent optical transmission systems in the presence of inter-channel stimulated Raman scattering (ISRS) is derived. The analytical result enables a rapid estimate of the signal-to-noise ratio (SNR) and avoids the need for integral evaluations and split-step simulations. The formula also provides new insight into the underlying parameter dependence of ISRS on the NLI. The proposed result is applicable for dispersion unmanaged, ultra-wideband transmission systems that use optical bandwidths of up to 15 THz. The accuracy of the closed-form expression is compared to numerical integration of the ISRS Gaussian Noise model and split-step simulations in a point-to-point transmission, as well as in a mesh optical network scenario.

Investigation of Intermodal Nonlinear Signal Distortions in Few-Mode Fiber Transmission

We present an experimental investigation of the Q -factor penalty due to intra and intermodal nonlinear signal distortions on 24.5 GBaud 16-quadratic-amplitude modulation based spatial super channel in a 36 km few-mode fiber. The results show that intermodal nonlinear signal degradations, caused by interfering spectral components separated by more than 17 nm, lead to similar Q -factor penalties as intramodal nonlinear signal degradations, originating in spectral components of less than 1 nm separation. We further compare the experimentally observed intra and intermodal nonlinear signal degradations with an analytical nonlinear Gaussian noise model and find a strong agreement between the two, validating the model as a computationally inexpensive tool for the design of few-mode fiber-based transmission systems.

Preamble Detection for Underwater Acoustic Communications Based on Sparse Channel Identification

Preamble detection before data transmission is an important module for an underwater communication system, since false detections would bring undesirable consequences in terms of the lifetime and coexistence of underwater networks. This paper conducts a thorough investigation of preamble detection in adverse underwater acoustic channels in the presence of various external interference, such as narrowband interference, impulsive noise, partial-band partial-block-duration interference, and chirps from nearby systems—The Gaussian noise model is not sufficient. We propose two novel detection methods based on the inherent sparsity of underwater acoustic channels: The first method declares signal detection when a sparse signal reconstruction is successful, whereas the second method accumulates the correlation coefficients from multiple paths instead of just the strongest path. We study the performance of the proposed methods based on simulations and experimental data sets, where the detection thresholds are empirically obtained. Performance results testify to the clear advantages of the proposed detection methods relative to existing matched-filter based approaches in various interference conditions.

Influence of denoising of input signal on classification of object location by artificial neural network in ultrawideband radiointroscopy

Background: A wide usage of impulse ultrawideband subsurface radars for a number of practical approaches in archeology, construction and humanitarian demining is holding back because of presence of noises and clutters of high level in the reflected field. It often makes the object classification practically unreal for at not big depths and distances from receiving and transmitting antennas. Besides of using special antenna system designs to improve recognition results, it is interesting to apply modern digital signal filtering techniques. Objectives: To investigate the influence of denoising on the quality of artificial neural network recognition of subsurface objects and their coordinates for a model of additive gaussian noise of a different noise level. Materials and methods: In this paper the idea of improving the stability of recognition of hidden objects in the presence of outside noise by previous processing of input signals with the latest popular noise reduction methods, such as the caterpillar method and wavelet transform method is verified. To eliminate the randomness of the result of the neural network response for each realization of the additive noise of a given level, a sufficient number of attempts are calculated for each of the methods, and statistics are provided to illustrate the effectiveness of each of the approaches. To check the hypothesis of the efficiency of input signal denoising the numerical simulation of the model of a real ground surface with subsurface object is carried out by means of Finite Difference Time Domain method (FDTD). The artificial neural network is trained on the obtained ideal time dependences of the amplitudes of the reflected field to correctly recognize the position of the object. The training is subsequently checked on the same input signals with additional noise of a certain level. Recognition errors in the last case are compared with similar errors when popular noise reduction procedures are applied to noisy input signals. Results: It is demonstrated that artificial neural networks have good approximating properties capable to effectively resist the noises in the input signals It is shown that for all noise levels, the caterpillar method statistically degrades the quality of an object recognition. The wavelet-transform method statistically improves slightly the classification of objects than for absence of denoising, but this result is not stable. Conclusion: For effective application of methods of noise filtration in received signals of impulse radar it is nessusary to have previous knowledge about noise character or peculiarities of useful signal. Implementation of denoising techniques without the use of this knowledge cannot improve the recognition quality of surface objects.

A Compensated Multi-Anchors TOF-Based Localization Algorithm for Asynchronous Wireless Sensor Networks

Tag localization for asynchronous wireless sensor networks requires the development of a scheme for clock synchronization. This remains a difficult and open problem since the performance of tag localization can be adversely affected by complications such as reply time and relative clock skew. Joint clock synchronization and a tag localization algorithm that implements a multi-anchor compensated time-of-flight (TOF) to the asynchronous wireless sensor network is a possible and viable solution. Although previous methods that leverage TOF measurements are effective and easily conducted, their performance is not always superior due to the relative clock skew. In this paper, we propose to extend the joint clock/tag synchronization/localization algorithm by introducing a compensation factor that can cancel relative clock skews from multi-tag anchor pairs. We apply a least squares estimation (LSE) algorithm to both the time of emission (TOE) and time of arrival (TOA) for the clock synchronization step. Under the assumption of a Gaussian measurement noise model, the tag localization problem is approximately solved by maximum likelihood estimation (MLE). To assess the performance of our algorithm, we derive the mean square error (MSE) of both relative clock skew and tag location and numerically evaluate the Cramer–Rao lower bound (CRLB) as a benchmark. The simulation results show that the accuracy of the relative clock skew-based estimation and tag localization are significantly improved over traditional algorithms when the appropriate reply time is selected. This is what our proposed algorithm focuses on: it is robust to tag mobility to some extent. We test the performance of proposed algorithm using a well-designed experiment. Based on the experiment results, the localization algorithm can achieve high accuracy without an additional restriction on the reply time and the clock skew.

Nonconvex Low Rank Approximation With Phase Congruency Regularization for Mixed Noise Removal

Mixed noise removal from a natural image is a challenging task since the complex noise distribution usually is inestimable. Many noise removal methods based on the low rank approximation have an excellent image denoising performance and are effective for recovering the images corrupted by Gaussian noise. These methods based on the additive white Gaussian noise(AWGN) model are sensitive to the outliers and non-Gaussian noise, such as the salt-and-pepper impulse noise (SPIN) and random valued impulse noise (RVIN). Such methods for mixed noise removal, however, are less effective in preserving image structures and tend to undesired staircase artifacts. This paper presents a novel Nonconvex Low Rank Model with Phase congruency and overlapping Group sparsity regularization (NLRM-PG) for mixed noise removal. Moreover, an efficient optimization algorithm under the alternating direction method of multipliers and majorization minimization framework is proposed to solve the NLRM-PG model. We demonstrate that the proposed method is effective for preserving local irregular structures and it reduces staircase artifacts with the two types of mixture noise, namely, AWGN+SPIN and AWGN+RVIN. Both qualitative and quantitative experiment results on synthetic noisy images and real noisy images illustrate that the proposed method can remove mixture noise in images more efficiently than the existing methods can do. And the results also outperform those obtained by using the competing state-of-the-art methods, particularly for the removal of high-density impulse noise.

On the Probabilistic Shaping and Geometric Shaping in Optical Communication Systems

We introduce and compare typical shaping schemes suitable for optical communications. The geometrically shaped-quadrature amplitude modulation (GS-QAM) formats are characterized by the non-equidistant spacing of constellation points, transmitted uniformly, and applied to improve system capacity. On the other hand, the well-known constant composition distribution matcher (CCDM) is applied for the generation of probabilistically shaped QAM (PS-QAM) formats. Mutual information (MI) is used as a metric to analyze the performances of regular/GS/PS-MQAM formats. In a linear amplified spontaneous emission noise limited region, it can be proved by the numerical simulation that MI performances of the GS-8/16QAM are always better than regular 8/16QAM and PS-8/16QAM; the largest shaping gains can be separately reached by PS-32QAM and GS-32QAM. We continue with the experimental demonstration on the 16QAM-based transmission system, and find that GS-16QAM generally has the best MI performance. We also find that the modulation-dependent nonlinear noises of the GS-8/16/32QAM are comparable to that of the regular 8/16/32QAM and generally lower than PS-8/16/32QAM. By using the enhanced Gaussian noise model, we observe that the GS-8/16QAM formats have better performances than regular 8/16QAM and PS-8/16QAM over multi-span transmission. Meanwhile, PS-32QAM formats provide superior performance over a relatively long transmission distance.

Measurement and Characterization of Acoustic Noise in Water Pipeline Channels

Measurement and characterization of acoustic noise in water pipeline systems across the 10 Hz to 100 kHz acoustic frequency band are reported in this paper. The motivation for the noise characterization is to support the development of acoustic signal processing and communication systems for water pipeline systems. Measurements are reported from an urban water supply system in the city of Christchurch, New Zealand, using hydrophones inserted into the pipelines. These measurements are some of the first that have been reported for an operational water supply system. In addition, for comparison to a controlled baseline reference, measurements have also been performed in a 160 m pipeline laboratory testbed at The Hong Kong University of Science and Technology. A key finding is that the noise amplitude probability density function (PDF) is found to follow a heavy-tailed distribution and the α-stable distribution is proposed for its characterization. The resultant acoustic noise measurements have also been analyzed to determine their power spectral density (PSD) characteristics. The measured noise PSD is not flat and characteristic frequencies and power density levels are utilized to capture the features of the noise PSD. These findings could have a significant impact on the design of signal processing systems for water pipeline systems due to their deviation from the conventional added white Gaussian noise model. In addition, three different acoustic noise sources with individual power and distribution characteristics are also postulated. These postulated sources are used to propose a straightforward acoustic noise model for supporting the simulation of acoustic noise for signal processing system design in water pipelines.

Angle measurement accuracy of quadrant photodetector with non-ideal signals

Considering the effects of noise on laser quadrant photodetector(QPD) digital measurement, the influencing factors of QPD digital angle measurement accuracy were analyzed and studied in this paper. Based on the laser pulse signal captured by QPD, the model of ideal voltage pulse signal produced by the Transimpedance Amplifier (TIA) was established. Considering White Gaussian Noise model of the QPD detecting circuit, the statistical distributions of target position deviation angle and target direction deviation angle calculated by normalized sum-difference algorithm were studied based on Monte Carlo method. Factors such as different signal distribution types in time domain, different Full Widths at Half Maximum (FWHM) and different system total Signal-Noise Ratio (SNR) were analyzed. The results show that: The statistical average and standard deviation of the target position and direction deviation angle were influenced by the above three factors. When the laser spots centers locate far from the coordinate origin on QPD photosensitive surface, the statistical distributions of the target position and direction deviation angle were in accord with normal distributions. The statistical average of the target position deviation angle was less than the ideal angle measurement, and the statistical average of the target direction deviation angle was approximately equal to the ideal angle measurement.

An algorithm for image restoration with mixed noise using total variation regularization

We present here an effective scheme for image denoising based on total variation regularization. The proposed scheme allows to efficiently remove Poisson noise as well as Gaussian noise simultaneously with the help of a new kind of data fidelity term, suitable for the mixed Poisson - Gaussian noise model. The results show that the algorithm corresponding to our new scheme outperforms the existing methods for mixed Poisson - Gaussian noise removal.

Ultra‐low‐dose CT image denoising using modified BM3D scheme tailored to data statistics

It is important to enhance image quality for low-dose CT acquisitions to push the ALARA boundary. Current state-of-the-art block-matching three-dimensional (BM3D) denoising scheme assumes white Gaussian noise (WGN) model. This study proposes a novel filtering module to be incorporated into the BM3D framework for ultra-low-dose CT denoising, by accounting for its specific power spectral properties. In the current BM3D algorithm, the Wiener filtering is applied in the transform domain to a post-thresholding signal for enhanced denoising. However, unlike most natural/synthetic images, low-dose CTs do not obey the ideal Gaussian noise model. Based on the specific noise properties of ultra-low-dose CT, we derive the optimal transform-domain coefficients of Wiener filter based on the minimum mean-square-error (MMSE) criterion, taking the noise spectrum and the signal/noise cross spectrum into consideration. In the absence of ground-truth signal, the hard-thresholding denoising module in the previous stage is used as a plug-in estimator. We evaluate the denoising performance on thoracic CT image datasets containing paired full-dose and ultra-low-dose images simulated by a well-validated clinical engine (or pipeline). We also assess its clinical implication by applying the denoising methods to the emphysema quantification task. Our modified BM3D method is compared with the current one, using peak signal-to-noise ratio (PSNR) and emphysema scoring results as evaluation metrics. The noise in ultra-low-dose CT presented distinct non-Gaussian characteristics and was correlated with image intensity. Performance evaluation showed that the current Wiener filter in basic BM3D algorithm yielded little denoising enhancement on ultra-low-dose CT images. In contrast, the proposed Wiener filter achieved (1.46, 1.91)dB performance gain in mean and median peak signal-to-noise ratio (PSNR) for 5%-dose image denoising and (0.93, 0.95)dB improvement for 10% dose. A paired t-test of the PSNRs between denoising using the current and the proposed Wiener filters demonstrated statistically significant improvement, yielding P-values of 1.45E-12 and 1.34E-7 on 5% and 10%-dose images, respectively. In addition, emphysema quantification on the denoised images using the modified BM3D method also had statistically significant advantage over that using the current BM3D scheme, resulting in a P-value of 6.30E-5 with the commonly used measure. This work tailors the Wiener filter in BM3D algorithm to data statistics and demonstrates statistically significant performance improvement on ultra-low-dose CT image denoising and a subsequent emphysema quantification task. Such performance gain is more pronounced with a lower dose level. The development and rationale are generally enough for other image denoising tasks when the WGN assumption is violated.