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 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.

Nonlinearity of the maximum entropy method in resolution enhancement

1992 ◽  
Vol 70 (12) ◽  
pp. 2887-2894 ◽  
Author(s):  
J. K. Kauppinen ◽  
D. J. Moffatt ◽  
H. H. Mantsch
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Linear Prediction ◽  
Signal To Noise Ratio ◽  
Resolution Enhancement ◽  
Nonlinear Behavior ◽  
Entropy Method ◽  
Spectral Lines ◽  
High Signal ◽  
Intensity Pattern

The nonlinear behavior of the filter-type Maximum Entropy Method (MEM) was investigated from a theoretical and a practical point of view. The integrated intensity of the output spectral lines of MEM was probed as a function of the input intensity pattern, the filter length, and the S/N ratio of the input spectrum. The nonlinear behavior of MEM has been explained and the results compared with those derived by another method, LOMEP (Lineshape Optimized Maximum Entropy linear Prediction). The study was carried out with the aim of resolution enhancement of spectra that have high signal-to-noise ratio.

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.

Automatic Variable K Module Design of Digital Phase-Locked Loop

2012 ◽  
Vol 263-266 ◽  
pp. 20-24
Author(s):  
Yan Peng Sun ◽  
Xia Yu Yang
Keyword(s):  
Signal To Noise Ratio ◽  
Phase Locked Loop ◽  
High Signal ◽  
Signal To Noise ◽  
Module Design ◽  
Digital Phase ◽  
Capture Time ◽  
Simulation Results ◽  
Noise Ratio

PLL lock signal, there is contradictions in the capture time and capture bandwidth, also in the capture bandwidth and high signal-to-noise ratio. The article adopted the method of timely change bandwidth to resolve these conflicts, and used the VHDL to design a auto-change K module to adjust the bandwidth. Simulation results verify the validity of the module in the side of resolving conflicts between capture time and capture bandwidth, and capture bandwidth and high signal-to-noise ratio too.

scholarly journals Fast Two-Step Energy Detection for Spectrum Sensing

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Meiling Lai ◽  
Shengliang Peng ◽  
Xi Yang ◽  
Lin Zhou
Keyword(s):  
Spectrum Sensing ◽  
Signal To Noise Ratio ◽  
Energy Detection ◽  
Sampling Time ◽  
Point Of View ◽  
High Signal ◽  
Sampling Process ◽  
Simulation Results ◽  
Theoretical Analyses ◽  
Detection Speed

Spectrum sensing is one of the key tasks in cognitive radio. This paper proposes a fast two-step energy detection (FED) algorithm for spectrum sensing via improving the sampling process of conventional energy detection (CED). The algorithm adaptively selectsN-point or 2N-point sampling by comparing its observed energy with prefixed double thresholds, and thereby is superior in sampling time and detection speed. Moreover, under the constraint of constant false alarm, this paper optimizes the thresholds from maximizing detection probability point of view. Theoretical analyses and simulation results show that, compared with CED, the proposed FED can achieve significant gain in detection speed at the expense of slight accuracy loss. Specifically, within high signal-to-noise ratio regions, as much as 25% of samples can be reduced.

scholarly journals The Maximum Entropy Method in Ultrasonic Non-Destructive Testing—Increasing the Resolution, Image Noise Reduction and Echo Acquisition Rate

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 621
Author(s):  
Evgeny Bazulin
Keyword(s):  
Maximum Entropy ◽  
Model Experiment ◽  
Signal To Noise Ratio ◽  
Low Noise ◽  
High Signal ◽  
Structural Noise ◽  
Signal To Noise ◽  
Flat Bottom ◽  
Noise Ratio ◽  
Code Division Multiple

The use of linear methods, for example, the Combined Synthetic Aperture Focusing Technique (C–SAFT), does not allow one to obtain images with high resolution and low noise, especially structural noise in all cases. Non-linear methods should improve the quality of the reconstructed image. Several examples of the application of the maximum entropy (ME) method for ultrasonic echo processing in order to reconstruct the image of reflectors with Rayleigh super-resolution and a high signal-to-noise ratio are considered in the article. The use of the complex phase-shifted Barker code signal as a probe pulse and the compression of measured echoes by the ME method made it possible to increase the signal-to-noise ratio by more than 20 dB for the image of a flat-bottom hole with a diameter of 1 mm in a model experiment. A modification of the ME method for restoring the reflector image by the time-of-flight diffraction (TOFD) method is considered, taking into account the change of the echo signal shape, depending on the depth of the reflector. Using the ME method, 2.5D-images of models of dangling cracks in a pipeline with a diameter of 800 mm were obtained, which make it possible to determine their dimensions. In the object with structural noise, using the ME method, it was possible to increase the signal-to-noise ratio of the reflector image by more than 12 dB. To accelerate the acquisition of echoes in the dual scan mode, it is proposed to use code division multiple access (CDMA) technology based on simultaneous emission by all elements of the array of pseudo-orthogonal signals. The model experiment showed the effectiveness of applying the ME method.

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 Design, Analysis of 4×4 and 8×8 MIMO System with ZF, MMSE and BF Techniques

2017 ◽  
Vol 17 (2) ◽  
pp. 16-19 ◽  
Author(s):  
Arun Kumar ◽  
Piyush Vardhan ◽  
Manisha Gupta
Keyword(s):  
Signal Detection ◽  
Mimo System ◽  
Signal To Noise Ratio ◽  
Minimum Mean Square Error ◽  
Digital Signal ◽  
Base Station ◽  
Beam Forming ◽  
High Signal ◽  
Zero Forcing ◽  
Signal Processors

AbstractThis work focuses on studying signal detection using three different equalization techniques, namely: Zero Forcing (ZF), Minimum Mean Square Error (MMSE) and Beam Forming (BF), for a 4×4 MIMO-system. Results show that ZF equalization is the simplest technique for signal detection, However, Beam Forming (BF) gives better Bit Error Rate (BER) performances at high Signal to Noise Ratio (SNR) values with some complexity in design. For more antennas at the base station, it is too complex to design the weight matrix for ZF, however, it is suitable for BF with the help of good quality digital signal processors. Performance of MIMO-system, with 8 antennas at the base station using BF equalization, is analysed to get BER values at different SNR. Results show a considerable improvement in BER for 8 antennas at the base station.

scholarly journals A Low-Complexity Pilot-Based Frequency-Domain Channel Estimation for ICI Mitigation in OFDM Systems

Electronics ◽  
2021 ◽  
Vol 10 (12) ◽  
pp. 1404
Author(s):  
Francisco J. Martín-Vega ◽  
Gerardo Gómez
Keyword(s):  
Channel Estimation ◽  
Frequency Domain ◽  
Signal To Noise Ratio ◽  
Minimum Mean Square Error ◽  
Estimation Method ◽  
Low Complexity ◽  
High Signal ◽  
Ofdm Systems ◽  
Coupling Matrix ◽  
Pilot Pattern

A low-complexity pilot pattern and a frequency-domain channel estimation method for Inter-Carrier Interference (ICI) mitigation is proposed for Orthogonal Frequency Division Multiple Access (OFDM) systems. The proposed method exploits the band structure of the coupling matrix to perform an ICI-free channel estimation in the frequency domain. This ICI-free estimation relies on some conditions imposed over the pilot pattern that simplify the complexity of channel estimation significantly, since its complexity is the same as classical least squares (LS) channel estimation used in low mobility scenarios. Then, the ICI is removed by using a modified version of Minimum Mean Square Error (MMSE) equalization, which reduces the computational complexity considerably. This modified MMSE equalization relies on the sparse and banded structure of the coupling matrix and on a low complexity variant of the Cholesky decomposition, which is named LDLH factorization. It is shown that the proposed method greatly improves the Bit Error Rate (BER) in the high Signal-to-Noise Ratio (SNR) regime.

Sign in / Sign up

Export Citation Format

Share Document