Additive Colored Gaussian Noise Research Articles

A Novel Subspace Decomposition with Rotational Invariance Technique to Estimate Low-Frequency Oscillatory Modes of the Power Grid

This paper proposes modified Karhunen–Loeve transform with total least square estimation of signal parameters using rotational in-variance technique (MKLT-TLS-ESPRIT) to approximate the low-frequency oscillatory modes. MKLT decreases the impact of highly correlated additive colored Gaussian noise (ACGN) from the signal by differentiating the correlation matrix w.r.t from the final time instance. A quantitative study of the suggested method with other estimation methods is used to evaluate the effectiveness of the proposed method. Monte Carlo simulations with 50,000 runs are conducted to test the robustness of the estimation scheme for MKLT-TLS-ESPRIT. The evaluation of the efficiency of the proposed method in real-time perspective, the two-area system, and New England sixty-eight bus test system has been considered. The analysis shows that the suggested methodology correctly measures the interarea modes and lowers their mean and standard deviation to a minimum value.

Optimal Tracking Control of Networked Systems Subject to Model Uncertainty and Additive Colored Gaussian Noise

For control systems with communication links, the various communication parameters can bring negative effects on system’s performance. Taking tracking problem for example, it is extremely difficult to achieve accurate tracking, that is, the tracking error can not be zero because of these communication constraints, such as model uncertainties originate from plant and channel, and additive colored Gaussian noise (ACGN). In this brief, by employing unit feedback controller (UFC) and two-parameters controller (TPC), the output tracking control (OTC) performance of networked systems subject to model uncertainties and ACGN is investigated. Consequently, two exact expressions of OTC performance limitations are derived with UFC and TPC. These results clearly show that OTC performance tightly depends on non-minimum phase zeros (NMPZs) and unstable poles (UPs) of the given plant. Moreover, the existence of uncertainties and ACGN can result in the poor OTC performance.

Blind estimation of noise level based on pixels values prediction

Noise parameters estimation is needed for many tasks of digital image processing. Many efficient algorithms of noise variance estimation were proposed during last two decades. However, most of those estimators are efficient only for a specific kind of noise for which they were designed. For example, methods of estimation of variance of white additive Gaussian noise (AWGN) fail in the case of additive colored Gaussian noise (ACGN) or for noises with other distributions. In this paper a new fully blind method of noise level estimation is proposed. For a given image, a distorted image with a removed part of pixels (around 10%) is generated. Then an inpainting (or impulse noise removal) method is used to recover missed pixels values. The difference between true and recovered values is used for a robust estimation of noise level. The algorithm is applied for different image scales to estimate noise spectrum. In the paper we propose a convolutional neural network PIXPNet for effective prediction of values of missing pixels. A comparative analysis shows that the proposed PIXPNet provides smallest error of recovered pixels values among all existing methods. A good efficiency of usage of the proposed approach in both AWGN and spatially correlated noise suppression is demonstrated.

A New Technique for ARMA-System Identification Based on QR-Decomposition of Third Order Cumulants Matrix

In this paper a new technique to estimate the coefficients of a general Autoregressive Moving Average (ARMA) (p, q) model is proposed. The ARMA system is excited by an un-observable independently identically distributed (i.i.d) non-Gaussian process. The proposed ARMA coefficients estimation method uses the QR-Decomposition (QRD) of a special matrix built with entries of third order cumulants (TOC) of the available output data only. The observed output may be corrupted with additive colored or white Gaussian noise of unknown power spectral density. The proposed technique was compared with several good methods such as the residual time series (RTS) and the Q-slice algorithm (QSA) methods. Simulations for several examples were tested. The results for these examples confirm the good performance of the proposed technique with respect to existing well-known methods.

New results on the trade-off performance of LTI system with colored noise and encoder-decoder strategy

This paper studies the trade-off performance between tracking performance and control input energy of the multi-input multi-output(MIMO), linear and time-invariant(LTI) system over an additive coloured Gaussian noise(ACGN) channel and the encoder-decoder strategies. The restriction that filter in the encoder-decoder strategy must be diagonal matrix is not necessary. And some new results are derived according to the inner-outer factorization. The results show that the trade-off performance is correlated to the unstable pole, non-minimum phase zero of the system. Also new poles and zeros generated by the non-diagonal encoder-decoder strategies may affect the trade-off performance. At last, two examples with different filters and different encoder-decoder strategies are discussed to validate the conclusions. The various encoder-decoder strategies revealed by the simulations may enhance or deteriorate the trade-off performance proposed in this paper.

Signal-to-noise ratio constrained feedback control: Robust stability analysis

The explicit consideration of a communication channel model in a feedback control loop is known to be constrained by a fundamental limitation for stabilizability on the channel signal-to-noise ratio (SNR) when the linear time invariant (LTI) plant model is unstable. The LTI modelling approach for real, usually nonlinear, processes compromises accuracy versus complexity of the resulting model. This in turn introduces a gap between the proposed model and the real process, which is known as the model uncertainty. In this paper we then study SNR limitations by considering the continuous-time scenario and the case of an additive coloured Gaussian noise (ACGN) channel with bandwidth limitation, for which we then quantify the infimal SNR subject to the simultaneous presence of plant, channel and noise model uncertainties. We observe, for the special case of memoryless additive white Gaussian noise (AWGN) channels, that the obtained SNR limitation subject to plant model uncertainty can be redefined as a channel capacity limitation for stabilization.

Enhancing proximity measure between residual and noise for image denoising

Sparse representation and dictionary learning-based image denoising algorithms approximate the clean image patch by linear combination of few dictionary atoms. Clearly, residue after completion of denoising must be similar to the contaminating noise. Ideally, clean image patch is perfectly recovered if residue is exactly contaminating noise. Hence, for better denoising, residue must be enforced to possess characteristics similar to the contaminating noise. In this paper, we model residue such that proximity between residue and contaminating noise is increased. The proposed mathematical model makes sure that the residue is as random in nature as contaminating noise. This is achieved by unique sparse coding and dictionary update stages developed based on modelling of randomness in residue. The proposed algorithm is tested on additive white Gaussian noise (AWGN), additive coloured Gaussian noise (ACGN) and Laplacian noise. Since performance of the image denoising algorithms also depend on image effective bandwidth, therefore, in this paper we have generated synthetic images with known effective image bandwidths. These images are generated using the discrete cosine transform (DCT). The proposed algorithm is also tested on these images. The proposed algorithm is compared with state-of-the-art algorithms. The comparison on the bases of peak signal-to-noise ratio (PSNR), structure similarity index measure (SSIM) and feature similarity index measure (FSIM) indicate that the proposed algorithm is able to produce often better and competitive results.

Optimal tracking performance of control systems with two-channel constraints

This paper focuses on the tracking performance limitation for a class of networked control systems (NCSs) with two-channel constraints. In communication channels, we consider bandwidth, energy constraints and additive colored Gaussian noise (ACGN) simultaneously. In plant, non-minimal zeros and unstable poles are considered; multi-repeated zeros and poles are also applicable. To obtain the optimal performance, the two-parameter controller is adopted. The theoretical results show that the optimal tracking performance is influenced by the non-minimum phase zeros, unstable poles, gain at all frequencies of the given plant, and the reference input signal for NCSs. Moreover, the performance limitation is also affected by the limited bandwidth, additive colored Gaussian noise, and the corresponding multiples for the non-minimum phase zeros and unstable poles. Additionally, the channel minimal input power constraints are given under the condition ensuring the stability of the system and acquiring system performance limitation. Finally, simulation examples are given to illustrate the theoretical results.

Step reference tracking in signal-to-noise ratio constrained feedback control

In this paper we address the problem of step reference tracking in the context of signal-to-noise ratio (SNR) constrained feedback control. We study the presence of a channel model in the feedback loop either over the measurement path, between the plant and the controller, or the control path, between the controller and the plant. We start the analysis by considering the memoryless additive white Gaussian noise (AWGN) channel model, and follow-up with the additive coloured Gaussian noise (ACGN) channel with memory model. We observe that the standard SNR constrained feedback loop configuration, when tracking step references, will result in an infinite channel SNR. We show that this situation can be ameliorated by extending the feedback loop configuration with an encoder and decoder. The proposed configurations result in a finite SNR that converges back to the infimal SNR for regulation when the amplitude of the reference signal tends to zero.

CMI analysis and precoding designs for correlated multi-hop MIMO channels

Conditional mutual information (CMI) analysis and precoding design for generally correlated wireless multi-hop multi-input multi-output (MIMO) channels are presented in this paper. Although some particular scenarios have been examined in existing publications, this paper investigates a generally correlated transmission system having spatially correlated channel, mutually correlated source symbols, and additive colored Gaussian noise (ACGN). First, without precoding techniques, we derive the optimized source symbol covariances upon mutual information maximization. Secondly, we apply a precoding technique and then design the precoder in two cases: maximizing the mutual information and minimizing the detection error. Since the optimal design for the end-to-end system cannot be analytically obtained in closed form due to the non-monotonic nature, we relax the optimization problem and attain sub-optimal designs in closed form. Simulation results show that without precoding, the average mutual information obtained by the asymptotic design is very close to the one obtained by the optimal design, while saving a huge computational complexity. When having the proposed precoding matrices, the end-to-end mutual information significantly increases while it does not require resources of the system such as transmission power or bandwidth.

Secrecy Capacity of Wiretap Channels with Additive Colored Gaussian Noise

Wyner has shown in his seminal paper on (discrete memoryless) wiretap channels that if the channel between the sender and an eavesdropper is a degraded version of the channel between the sender and the legitimate receiver, then the sender can reliably and securely transmit a message to the receiver, while the eavesdropper obtains absolutely no information about the message. Later, Leung-Yan-Cheong and Hellman extended Wyner's result to the case where the noise is white Gaussian. In this paper we extend the white Gaussian wiretap channel to the colored Gaussian case and show the finite block length secrecy capacity of colored Gaussian wiretap channels. We also show an asymptotic lower bound on the secrecy capacity of a specific colored Gaussian wiretap channel for which optimum power allocation can be found by water filling.

Optimal Tracking Performance Limitation of Networked Control Systems With Limited Bandwidth and Additive Colored White Gaussian Noise

This paper studies optimal tracking performance issues for multi-input-multi-output linear time-invariant systems under networked control with limited bandwidth and additive colored white Gaussian noise channel. The tracking performance is measured by control input energy and the energy of the error signal between the output of the system and the reference signal with respect to a Brownian motion random process. This paper focuses on two kinds of network parameters, the basic network parameter-bandwidth and the additive colored white Gaussian noise, and studies the tracking performance limitation problem. The best attainable tracking performance is obtained, and the impact of limited bandwidth and additive colored white Gaussian noise of the communication channel on the attainable tracking performance is revealed. It is shown that the optimal tracking performance depends on nonminimum phase zeros, gain at all frequencies and their directions unitary vector of the given plant, as well as the limited bandwidth and additive colored white Gaussian noise of the communication channel. The simulation results are finally given to illustrate the theoretical results.

Digital Output Feedback Control over Signal-to-Noise Ratio Limited Communication Channels

AbstractIn this paper we address the problem of finding a stabilizing feedback controller for a linear time invariant (LTI) plant model when measurement is performed over a communication channel model subject to channel input logarithmic quantization and a signal-to-noise ratio (SNR) constraint. The location of the communication channel is therefore on the measurement path, that is between the plant and the controller, nevertheless similar results can be obtained for the alternative location over the control path.In our first approach the communication channel model itself is selected to be an additive white Gaussian noise (AWGN) channel. We then describe the spectral power density of the channel density as a function of the power spectral density of the channel additive white Gaussian noise and the uniform distributed process model arising from a logarithmic quantization. The infimal channel SNR is then obtained through the definition for the channel input power, together with an interpretation of a bound on the logarithmic quantization relative error as a multiplicative modeling error.In our second approach we extend the proposed analysis to the class of additive colored Gaussian noise (ACGN) channels with memory. The infimal SNR is then obtained again through the definition for the channel input power. Finally, an extension to the case of sampled-data systems is proposed.

Signal-to-noise ratio fundamental constraints in discrete-time linear output feedback control

In the present paper we study the fundamental limitations on stability that arise when an additive coloured Gaussian noise (ACGN) channel is explicitly considered in a linear time invariant (LTI) control feedback loop. By considering a linear setting we can express the fundamental limitation on stability as a lower bound in closed-form on the ACGN channel signal-to-noise ratio (SNR). Outside the context of networked control, the obtained lower bound can be interpreted as an H 2 performance limitation.

Signal-to-Noise Ratio Fundamental Limitations in Continuous-Time Linear Output Feedback Control

In the present technical note we study the fundamental limitation on stability that arise when an additive coloured Gaussian noise (ACGN) channel is explicitly considered over either the control or measurement paths of a linear time invariant (LTI) feedback loop. By considering a linear setting we can naturally express the fundamental limitation as a lower bound on the channel signal-to-noise ratio (SNR) required for stabilisability. We start by first obtaining a closed-form expression for the squared <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm of a partial fraction expansion with repeated poles in the Laplace domain. We then use the squared <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm result to obtain the closed-form expression for the infimal SNR required for stabilisability. The proposed closed-form includes the case of repeated unstable plant poles and non minimum phase (NMP) zeros.

Asymptotic Equivalence Between the UML and the Extended SLN Symbol Timing Estimation on an Additive Colored Gaussian Noise Channel

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> It has recently been reported that the unconditional maximum likelihood (UML) symbol-timing estimation is asymptotically equivalent to the square-law nonlinearity (SLN) on an additive white Gaussian noise (AWGN) channel. By introducing a whitened matched filter (WMF), we propose an extended SLN and prove the asymptotical equivalence between the UML and the extended SLN on an additive colored Gaussian noise. Simulation results show the same behavior asymptotically when a mixture of an AWGN and a flicker noise is adopted as a noise source. </para>

Infimal Feedback Capacity for a Class of Additive Coloured Gaussian Noise Channels

In this paper we consider the infimal signal-to-noise ratio (SNR) required for stabilisation of a linear time invariant (LTI) scalar unstable plant over a class of additive coloured Gaussian noise channels. We apply recent results in the literature to obtain the feedback capacity of such a class of channels. We prove that the infimal SNR constrained LTI solution, when dealing with a scalar unstable plant, does achieve a channel feedback capacity equal to the infimal rate of transmission required for stability. The optimality of such channel feedback capacity is a non trivial result since we consider additive 1st order moving average (MA) and autoregressive moving average (ARMA) coloured noise.

Multicarrier spread spectrum techniques for downstream power‐line communications on low voltage grid

AbstractIn this paper different spread spectrum systems are proposed for broadband downstream power‐line communications (PLCs). Orthogonal frequency division multiplexing (OFDM) technique permits to greatly enhance the system throughput but can be strongly damaged by ‘hidden nodes’ situations. The introduction of suitable hybrid schemes, such as MT‐CDMA, allows to efficiently face this inconvenience by increasing system robustness.The performance of the systems considered is expressed in terms of bit error rate (BER), derived by simulations under the assumptions of frequency‐selective multipath fading channel and additive coloured gaussian noise according to the in‐building networks model, under the same overall working conditions of bandwidth occupation, transmitted power and global data rate. Copyright © 2003 John Wiley &amp; Sons, Ltd.

Duality theorems for joint source-channel coding

We consider joint source-channel coding for a memoryless Gaussian source and an additive white Gaussian noise (AWGN) channel. For a given code defined by an encoder-decoder pair (/spl alpha/, /spl beta/), its dual code is obtained by interchanging the encoder and decoder: (/spl beta/, /spl alpha/). It is shown that if a code (/spl alpha/, /spl beta/) is optimal at rate p channel uses per source sample and if it satisfies a certain uniform continuity condition, then its dual code (/spl beta/, /spl alpha/) is optimal for rate 1//spl rho/ channel uses per source sample. Further, it is demonstrated that there is a code which is optimal but its dual code is not optimal. Finally, using random coding, we show that there is an optimal code which has an optimal dual. The duality concept is also presented for the cases of (i) binary memoryless equiprobable source and binary-symmetric channel (BSC), and (ii) colored Gaussian source and additive colored Gaussian noise (ACGN) channel.

Wavelet parameter and phase estimation using cumulant slices

A simple, closed-form expression relates one-dimensional output cumulant statistics with the parameters of a known-order moving-average wavelet. Based on this relationship the author obtains unique parameter and phase estimates of autoregressive moving-average seismic wavelets. The input reflectivity sequence is assumed to be non-Gaussian, independent, and identically distributed. The wavelet is not assumed to be minimum phase and is allowed to include all-pass factors. The seismogram is contaminated by additive-colored Gaussian noise. Simulations demonstrate that the algorithm works well for moderate-size data records with a relatively low signal-to-noise ratio. >