scholarly journals Edgeworth Expansion Based Model for the Convolutional Noise pdf

2014 ◽  
Vol 2014 ◽  
pp. 1-19
Author(s):  
Yonatan Rivlin ◽  
Monika Pinchas
Keyword(s):  
Probability Density Function ◽  
Lagrange Multipliers ◽  
Conditional Expectation ◽  
Edgeworth Expansion ◽  
Entropy Density ◽  
Approximation Technique ◽  
Density Approximation ◽  
Mean Square ◽  
Simulation Results ◽  
Probability Density Function Pdf

Recently, the Edgeworth expansion up to order 4 was used to represent the convolutional noise probability density function (pdf) in the conditional expectation calculations where the source pdf was modeled with the maximum entropy density approximation technique. However, the applied Lagrange multipliers were not the appropriate ones for the chosen model for the convolutional noise pdf. In this paper we use the Edgeworth expansion up to order 4 and up to order 6 to model the convolutional noise pdf. We derive the appropriate Lagrange multipliers, thus obtaining new closed-form approximated expressions for the conditional expectation and mean square error (MSE) as a byproduct. Simulation results indicate hardly any equalization improvement with Edgeworth expansion up to order 4 when using optimal Lagrange multipliers over a nonoptimal set. In addition, there is no justification for using the Edgeworth expansion up to order 6 over the Edgeworth expansion up to order 4 for the 16QAM and easy channel case. However, Edgeworth expansion up to order 6 leads to improved equalization performance compared to the Edgeworth expansion up to order 4 for the 16QAM and hard channel case as well as for the case where the 64QAM is sent via an easy channel.

scholarly journals A New Efficient Expression for the Conditional Expectation of the Blind Adaptive Deconvolution Problem Valid for the Entire Range ofSignal-to-Noise Ratio

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 72 ◽  
Author(s):  
Monika Pinchas
Keyword(s):  
Probability Density Function ◽  
Closed Form ◽  
Maximum Entropy ◽  
Conditional Expectation ◽  
Entropy Density ◽  
Approximation Technique ◽  
Density Approximation ◽  
Signal To Noise ◽  
Computational Burden ◽  
Blind Adaptive

In the literature, we can find several blind adaptive deconvolution algorithms based on closed-form approximated expressions for the conditional expectation (the expectation of the source input given the equalized or deconvolutional output), involving the maximum entropy density approximation technique. The main drawback of these algorithms is the heavy computational burden involved in calculating the expression for the conditional expectation. In addition, none of these techniques are applicable for signal-to-noise ratios lower than 7 dB. In this paper, I propose a new closed-form approximated expression for the conditional expectation based on a previously obtained expression where the equalized output probability density function is calculated via the approximated input probability density function which itself is approximated with the maximum entropy density approximation technique. This newly proposed expression has a reduced computational burden compared with the previously obtained expressions for the conditional expectation based on the maximum entropy approximation technique. The simulation results indicate that the newly proposed algorithm with the newly proposed Lagrange multipliers is suitable for signal-to-noise ratio values down to 0 dB and has an improved equalization performance from the residual inter-symbol-interference point of view compared to the previously obtained algorithms based on the conditional expectation obtained via the maximum entropy technique.

scholarly journals 16QAM Blind Equalization via Maximum Entropy Density Approximation Technique and Nonlinear Lagrange Multipliers

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
R. Mauda ◽  
M. Pinchas
Keyword(s):  
Maximum Entropy ◽  
Lagrange Multipliers ◽  
Signal To Noise Ratio ◽  
Minimum Mean Square Error ◽  
Blind Equalization ◽  
Entropy Density ◽  
High Signal ◽  
Approximation Technique ◽  
Density Approximation ◽  
Simulation Results

Recently a new blind equalization method was proposed for the 16QAM constellation input inspired by the maximum entropy density approximation technique with improved equalization performance compared to the maximum entropy approach, Godard’s algorithm, and others. In addition, an approximated expression for the minimum mean square error (MSE) was obtained. The idea was to find those Lagrange multipliers that bring the approximated MSE to minimum. Since the derivation of the obtained MSE with respect to the Lagrange multipliers leads to a nonlinear equation for the Lagrange multipliers, the part in the MSE expression that caused the nonlinearity in the equation for the Lagrange multipliers was ignored. Thus, the obtained Lagrange multipliers were not those Lagrange multipliers that bring the approximated MSE to minimum. In this paper, we derive a new set of Lagrange multipliers based on the nonlinear expression for the Lagrange multipliers obtained from minimizing the approximated MSE with respect to the Lagrange multipliers. Simulation results indicate that for the high signal to noise ratio (SNR) case, a faster convergence rate is obtained for a channel causing a high initial intersymbol interference (ISI) while the same equalization performance is obtained for an easy channel (initial ISI low).

scholarly journals A Novel Technique for Achieving the Approximated ISI at the Receiver for a 16QAM Signal Sent via a FIR Channel Based Only on the Received Information and Statistical Techniques

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 708
Author(s):  
Hadar Goldberg ◽  
Monika Pinchas
Keyword(s):  
Edgeworth Expansion ◽  
Finite Impulse Response ◽  
Signal To Noise Ratio ◽  
Signal Transmission ◽  
Entropy Density ◽  
Approximation Technique ◽  
Novel Technique ◽  
Input Multiple Output ◽  
Source Signal ◽  
Single Input

A single-input-multiple-output (SIMO) channel is obtained from the use of an array of antennas in the receiver where the same information is transmitted through different sub-channels, and all received sequences are distinctly distorted versions of the same message. The inter-symbol-interference (ISI) level from each sub-channel is presently unknown to the receiver. Thus, even when one or more sub-channels cause heavy ISI, all the information from all the sub-channels was still considered in the receiver. Obviously, if we know the approximated ISI of each sub-channel, we will use in the receiver only those sub-channels with the lowest ISI level to get improved system performance. In this paper, we present a systematic way for obtaining the approximated ISI from each sub-channel modelled as a finite-impulse-response (FIR) channel with real-valued coefficients for a 16QAM (16 quadrature amplitude modulation) source signal transmission. The approximated ISI is based on the maximum entropy density approximation technique, on the Edgeworth expansion up to order six, on the Laplace integral method and on the generalized Gaussian distribution (GGD). Although the approximated ISI was derived for the noiseless case, it was successfully tested for signal to noise ratio (SNR) down to 20 dB.

Evolutionary Oppositional Moth Flame Optimization for Renewable and Sustainable Wind Energy Based Economic Dispatch

2019 ◽  
Vol 10 (4) ◽  
pp. 65-84 ◽  
Author(s):  
Sunanda Hazra ◽  
Provas Kumar Roy
Keyword(s):  
Wind Speed ◽  
Probability Density Function ◽  
Wind Energy ◽  
Fossil Fuel ◽  
Economic Load Dispatch ◽  
Opposition Based Learning ◽  
The Social ◽  
Simulation Results ◽  
Fossil Fuel Energy ◽  
Probability Density Function Pdf

Fossil fuel power has limited its penetration into the power system network for the intermittency and unpredictability coordination. That's why, renewable wind energy incorporating load dispatch becomes a promising system. In this regard, this article proposes an economic load dispatch (ELD) in the existence of renewable wind technology for consuming less fossil fuel energy. For the stochastic scenery of wind speed, the Weibull probability density function (PDF) is used. To boost up the convergence swiftness and advance the simulation results, opposition-based learning (OBL) is integrated with the basic moth flame optimization (MFO) technique, which depends on the social dealings of the moth in nature. The performance of OMFO is evaluated through four cases and each case consists of three different load demands. The simulation results by these methods along with various other existing algorithms in the literature are presented to demonstrate the validity and usefulness of the proposed OMFO.

scholarly journals Improved Approach for the Maximum Entropy Deconvolution Problem

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 547
Author(s):  
Shay Shlisel ◽  
Monika Pinchas
Keyword(s):  
Maximum Entropy ◽  
Density Function ◽  
Edgeworth Expansion ◽  
Entropy Density ◽  
Point Of View ◽  
Convergence Time ◽  
Approximation Technique ◽  
Gaussian Density ◽  
Deconvolution Problem ◽  
Equalization Method

The probability density function (pdf) valid for the Gaussian case is often applied for describing the convolutional noise pdf in the blind adaptive deconvolution problem, although it is known that it can be applied only at the latter stages of the deconvolution process, where the convolutional noise pdf tends to be approximately Gaussian. Recently, the deconvolutional noise pdf was approximated with the Edgeworth Expansion and with the Maximum Entropy density function for the 16 Quadrature Amplitude Modulation (QAM) input but no equalization performance improvement was seen for the hard channel case with the equalization algorithm based on the Maximum Entropy density function approach for the convolutional noise pdf compared with the original Maximum Entropy algorithm, while for the Edgeworth Expansion approximation technique, additional predefined parameters were needed in the algorithm. In this paper, the Generalized Gaussian density (GGD) function and the Edgeworth Expansion are applied for approximating the convolutional noise pdf for the 16 QAM input case, with no need for additional predefined parameters in the obtained equalization method. Simulation results indicate that improved equalization performance is obtained from the convergence time point of view of approximately 15,000 symbols for the hard channel case with our new proposed equalization method based on the new model for the convolutional noise pdf compared to the original Maximum Entropy algorithm. By convergence time, we mean the number of symbols required to reach a residual inter-symbol-interference (ISI) for which reliable decisions can be made on the equalized output sequence.

scholarly journals Adaptive filters for color image processing

1999 ◽  
Vol 4 (6) ◽  
pp. 529-538 ◽  
Author(s):  
V. Papanikolaou ◽  
K. N. Plataniotis ◽  
A. N. Venetsanopoulos
Keyword(s):  
Image Processing ◽  
Probability Density Function ◽  
Adaptive Filters ◽  
Color Image ◽  
A Priori ◽  
Color Image Processing ◽  
Gaussian Probability Density Function ◽  
Simulation Results ◽  
Color Filters ◽  
Probability Density Function Pdf

The color filters that are used to attenuate noise are usually optimized to perform extremely well when dealing with certain noise distributions. Unfortunately it is often the case that the noise corrupting the image is not known. It is thus beneficial to knowa priorithe type of noise corrupting the image in order to select the optimal filter. A method of extracting and characterizing the noise within a digital color image using the generalized Gaussian probability density function (pdf) (B.D. Jeffs and W.H. Pun,IEEE Transactions on Image Processing,4(10), 1451–1456, 1995 andProceedings of the Int. Conference on Image Processing,465–468, 1996), is presented. In this paper simulation results are included to demonstrate the effectiveness of the proposed methodology.

scholarly journals Adaptive modulation based on steady-state mean square error for underwater acoustic communication

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zhiyong Liu ◽  
Zhoumei Tan ◽  
Fan Bai
Keyword(s):  
Steady State ◽  
Mean Square Error ◽  
Adaptive Modulation ◽  
Blind Equalization ◽  
Training Sequence ◽  
Transmission Efficiency ◽  
Underwater Acoustic Communication ◽  
Mean Square ◽  
Modulation Mode ◽  
Simulation Results

AbstractTo improve the transmission efficiency and facilitate the realization of the scheme, an adaptive modulation (AM) scheme based on the steady-state mean square error (SMSE) of blind equalization is proposed. In this scheme, the blind equalization is adopted and no training sequence is required. The adaptive modulation is implemented based on the SMSE of blind equalization. The channel state information doesn’t need to be assumed to know. To better realize the adjustment of modulation mode, the polynomial fitting is used to revise the estimated SNR based on the SMSE. In addition, we also adopted the adjustable tap-length blind equalization detector to obtain the SMSE, which can adaptively adjust the tap-length according to the specific underwater channel profile, and thus achieve better SMSE performance. Simulation results validate the feasibility of the proposed approaches. Simulation results also show the advantages of the proposed scheme against existing counterparts.

scholarly journals Dynamic Reliability Analysis Method of Degraded Mechanical Components Based on Process Probability Density Function of Stress

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Peng Gao ◽  
Liyang Xie
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Solar Array ◽  
Dynamic Reliability ◽  
Reliability Models ◽  
Practical Engineering ◽  
Mechanical Components ◽  
Reliability Computation ◽  
Probability Density Function Pdf

It is necessary to develop dynamic reliability models when considering strength degradation of mechanical components. Instant probability density function (IPDF) of stress and process probability density function (PPDF) of stress, which are obtained via different statistical methods, are defined, respectively. In practical engineering, the probability density function (PDF) for the usage of mechanical components is mostly PPDF, such as the PDF acquired via the rain flow counting method. For the convenience of application, IPDF is always approximated by PPDF when using the existing dynamic reliability models. However, it may cause errors in the reliability calculation due to the approximation of IPDF by PPDF. Therefore, dynamic reliability models directly based on PPDF of stress are developed in this paper. Furthermore, the proposed models can be used for reliability assessment in the case of small amount of stress process samples by employing the fuzzy set theory. In addition, the mechanical components in solar array of satellites are chosen as representative examples to illustrate the proposed models. The results show that errors are caused because of the approximation of IPDF by PPDF and the proposed models are accurate in the reliability computation.

An improved energy envelope stochastic averaging method and its application to a nonlinear oscillator

2016 ◽  
Vol 23 (1) ◽  
pp. 119-130 ◽  
Author(s):  
Yaping Zhao
Keyword(s):  
Steady State ◽  
Probability Density Function ◽  
Probability Density ◽  
Averaging Method ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
System Response ◽  
Mean Square ◽  
Fpk Equation ◽  
The Mean

An improved stochastic averaging method of the energy envelope is proposed, whose application sphere is extensive and whose implementation is convenient. An oscillating system with both nonlinear damping and stiffness is taken into account. Its averaged Fokker-Planck-Kolmogorov (FPK) equation in respect of the transition probability density function of the energy envelope is deduced by virtue of the method mentioned above. Under the initial and boundary conditions, the joint probability density function as to the displacement and velocity of the system is worked out in closed form after solving the averaged FPK equation by right of a technique based on the integral transformation. With the aid of the special functions, the transient solutions of the probabilistic characteristics of the system response are further derived analytically, including the probability density functions and the mean square values. A simple approach to generate the ideal white noise is drastically ameliorated in order to produce the stationary wide-band stochastic external excitation for the Monte Carlo simulating investigation of the nonlinear system. Both the theoretical solution and the numerical solution of the probabilistic properties of the system response are obtained, which are extremely coincident with each other. The numerical simulation and the theoretical computation all show that the time factor has a certain influence on the probability characteristics of the response. For example, the probabilistic distribution of the displacement tends to be scattered and the mean square displacement trends toward its steady-state value as time goes by. Of course the transient process to reach the steady-state value will obviously be shorter if the damping of the system is greater.

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