Adaptive Blind Equalization Research Articles

Optimizing Instrument Transformer Performance through Adaptive Blind Equalization and Genetic Algorithms

In real-world scenarios, deviations in the frequency response of instrumentation transformers can lead to distorted harmonic measurements, highlighting the critical role harmonic measurement plays in assessing power quality. The blind channel equalization technique offers a potential solution to improve the frequency response of a large number of instrumentation transformers already installed in substations. These transformers were designed to accurately measure only the fundamental phasor component. Therefore, in order to use them for harmonic phasor measurement, methodologies for reducing frequency distortion must be applied. In this work, we propose a novel approach to improve the frequency response of the instrument transformer using adaptive blind equalization. The blind technique can compensate for distortions caused by voltage and current transducers without requiring prior knowledge of input signals or circuit characteristics. The proposed methodology uses a Linear Prediction Filter to convert the colored noise present at the channel output into white noise. Furthermore, a genetic algorithm is used to find a pole to cancel possible zeroes present in the frequency response of some transducers. The main advantage of blind equalization with the genetic algorithm is its independence, operating without clear information about the channel or the input signal. Through extensive experimentation, we demonstrate the effectiveness of the proposed methodology in significantly reducing the absolute error in ratio and phase caused by current and voltage transformers. Simulated and laboratory experiments are presented in this paper.

Parallel Blind Adaptive Equalization of Improved Block Constant Modulus Algorithm With Decision-Directed Mode

Parallel Blind Adaptive Equalization of Improved Block Constant Modulus Algorithm With Decision-Directed Mode

Blind Equalization and Channel Estimation in Coherent Optical Communications Using Variational Autoencoders

We investigate the potential of adaptive blind equalizers based on variational inference for carrier recovery in optical communications. These equalizers are based on a low-complexity approximation of maximum likelihood channel estimation. We generalize the concept of variational autoencoder (VAE) equalizers to higher order modulation formats encompassing probabilistic constellation shaping (PCS), ubiquitous in optical communications, oversampling at the receiver, and dual-polarization transmission. Besides black-box equalizers based on convolutional neural networks, we propose a model-based equalizer based on a linear butterfly filter and train the filter coefficients using the variational inference paradigm. As a byproduct, the VAE also provides a reliable channel estimation. We analyze the VAE in terms of performance and flexibility over a classical additive white Gaussian noise (AWGN) channel with inter-symbol interference (ISI) and over a dispersive linear optical dual-polarization channel. We show that it can extend the application range of blind adaptive equalizers by outperforming the state-of-the-art constant-modulus algorithm (CMA) for PCS for both fixed but also time-varying channels. The evaluation is accompanied with a hyperparameter analysis.

The Residual ISI for Which the Convolutional Noise Probability Density Function Associated with the Blind Adaptive Deconvolution Problem Turns Approximately Gaussian.

In a blind adaptive deconvolution problem, the convolutional noise observed at the output of the deconvolution process, in addition to the required source signal, is—according to the literature—assumed to be a Gaussian process when the deconvolution process (the blind adaptive equalizer) is deep in its convergence state. Namely, when the convolutional noise sequence or, equivalently, the residual inter-symbol interference (ISI) is considered small. Up to now, no closed-form approximated expression is given for the residual ISI, where the Gaussian model can be used to describe the convolutional noise probability density function (pdf). In this paper, we use the Maximum Entropy density technique, Lagrange’s Integral method, and quasi-moment truncation technique to obtain an approximated closed-form equation for the residual ISI where the Gaussian model can be used to approximately describe the convolutional noise pdf. We will show, based on this approximated closed-form equation for the residual ISI, that the Gaussian model can be used to approximately describe the convolutional noise pdf just before the equalizer has converged, even at a residual ISI level where the “eye diagram” is still very closed, namely, where the residual ISI can not be considered as small.

A Full-Digital M-CAP Receiver With Synchronisation and Adaptive Blind Equalisation for Visible Light Communications

With an emphasis on the real-time implementation of a practical carrier-less amplitude and phase (CAP) receiver for visible light communication (VLC), this paper proposes a full-digital architecture for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> -CAP receiver with synchronisation and adaptive blind equalisation. The architecture is mainly based on the observation that a CAP signal can be demodulated using a quadrature and amplitude (QAM) receiver with an added counterclockwise rotation operation. The proposed CAP receiver employs two digital phase-locked loops (DPLL) to realise the symbol timing and carrier synchronisation, which are the most critical issues in practical systems. With the constant-modulus algorithm (CMA) offering the benefit of decoupling carrier and symbol timing synchronisation, the receiver can blindly equalise the distorted signal at the output of symbol timing synchronisation. Finally, the performance of 4/16/64-CAP receivers, which are designed using this architecture and operates at 80/160/240 Mbit/s through a low-pass light-emitting diode (LED) with a 3-dB bandwidth of 7 MHz cascaded with three measured optical wireless channels, is evaluated by Monte Carlo simulations. Results show that the receiver architecture can successfully solve the symbol timing and carrier synchronisation problems and mitigate inter-symbol interference caused by LED and/or wireless channels. The design framework for a full-digital CAP receiver has been laid out in this paper.

Blind adaptive identification and equalization using bias-compensated NLMS methods

Blind adaptive identification and equalization using bias-compensated NLMS methods

Adaptive blind equalization for multi‐level QAM signals in impulsive noise environment

A maximum correntropy criterion-blind clustering multi-modulus algorithm (MCC-BCMMA) is proposed to equalize multi-level quadrature amplitude modulation (QAM) channels in impulsive noise environment. The novel cost function is based on the maximum correntropy criterion (MCC), theoretical analysis shows that this criterion is useful when the noise is impulsive. Moreover, this cost function is decomposed into in-phase term and orthogonal term to eliminate the phase ambiguity, treats high-order QAM signal to classical QAM4 signal to reduce the error, and calculates the weight coefficients by a simple way. Simulation results show that the newly proposed algorithm MCC-BCMMA can be used to equalize multi-level QAM signals in both Gaussian and impulsive noise environments, and it shows better equalization performance under impulsive noise. The relationship between the kernel size of MCC, the convergence speed and accuracy is also analysed.

A new multipath channel estimation and mitigation using annihilation filter combined tracking loop implementation in software GPS receivers

The multipath effect causes severe degradation in the positioning of commercial GPS receivers. Due to multipath error, the positioning accuracy could reach a few of 10 m. If the cumulative Multipath delay is less than 0.1–0.35 chips, then it is difficult to mitigate in GPS receivers. This causes severe degradation in GPS signals and can cause a measurement bias. To alleviate this problem, the estimation of multipath parameters using annihilating filter and its mitigation in the GPS tracking loop is proposed in this work. The estimation of randomly generated multipath signals can be performed in the receiver with a lower sampling rate when compared to the larger bandwidth of the GPS baseband signal. Here, the frequency components of the multipath signal in superimposed complex exponentials have been transformed from the time delay and the amplitude of the path observables. The Rayleigh fading model in the urban scenario has been simulated in which the amplitude and the phase of the number of paths (i.e. the frequency component of superimposed complex exponentials) are set and this fading signal is convolved with GPS signal that forms the multipath faded signal. In the GPS receiver post-processing stage, with the help of the annihilation filter, the multipath components are estimated, then an inverse/adaptive filter and compensation technique are further applied to mitigate the multipath component. The mean square error with the different number of paths with noisy environments is analyzed utilizing the cadzow denoising algorithm. The simulation results of the proposed technique employed in the tracking module of the software GPS receiver under severe multipath conditions indicate a substantial enhancement in the performance of the GPS receiver with minimal code and carrier phase error when compared to the least squares and adaptive blind equalization channel techniques. Moreover, the positioning accuracy is also calculated with the inclusion of multipath components in two satellites out of six satellites used in the simulation, the results showed that the annihilation filter improved the mean position accuracy up to 9.3023 m.

Blind Adaptive Equalization for Aerospace Communication Channels

In some communication systems, it is desirable for the receiver to synchronize to the received signal and to adjust the equalizer without having knowledge of a training sequence. Blind equalization uses the initial adjustment of the coefficients without making use of a training sequence. Different adaptive blind equalization algorithms have been developed over the past four decades. In this paper, we investigate the effect of blind equalization on space communication channels. The space channel under investigation is considered to be a multipath frequency selective channel having four paths. The channel is subjected to the phenomenon of InterSymbol Interference (ISI) which severely degrades the performance of the space communication system. Two blind algorithms are used in equalizer adjustment. The impulse responses of the space channel, the blind equalizer and the combination of channel and equalizer for QPSK and 16-QAM transmission are shown. The scatter diagrams for the transmitted sequence, received sequence, and the output of the equalizer using two of the blind algorithms are shown.

Adaptive blind equalization of fast time‐varying channel with frequency estimation in impulsive noise environment

In this paper, a novel source signal recovery method for fast time-varying channels described by complex exponential-basis expansion model (CE-BEM) in the impulsive noise environment is proposed. This method consists of two phases. The first phase is the equalization of fast time-varying channels, in this phase, a novel algorithm FSE-FLOS-CMA is proposed. The convergence performance of this newly proposed algorithm is much better than that of existing fractionally spaced equalizer-constant modulus algorithm (FSE-CMA) in impulsive noise environment. In the second phase, a novel frequency estimation method is proposed. The estimated frequency in impulsive noise environment is obtained by calculating a specific p-order fractional low-order cyclic moment of the equalized signal. Simulation results show that the proposed FSE-FLOS-CMA and frequency estimation method can effectively estimate the source signals transmitted through the fast time-varying channels in impulsive noise environment.

Performance Analysis of MSAGF-MMA Adaptive Blind Equalization Algorithm with Variable Step Size Using Input Power Signal and Decision-Directed Error Signal

Performance Analysis of MSAGF-MMA Adaptive Blind Equalization Algorithm with Variable Step Size Using Input Power Signal and Decision-Directed Error Signal

Blind Adaptive Low-Complexity Time-Domain Equalizer for 100-Gb/s Direct-Detection Optical OFDM Systems Over Long-Reach SSMF

In this article, we report a low-complexity blind adaptive time-domain equalizer (TEQ) to reduce the cyclic prefix (CP) length for 100-Gb/s direct-detection optical orthogonal frequency-division multiplexing (OFDM) system combined with wavelength-division multiplexing system over 400-km standard single-mode fiber length. We show that a significant complexity reduction can be achieved by designing a modified cost function of multicarrier equalization based on orthogonality restoration (MERO) algorithm on one hand, and on deploying the symmetrical TEQ property on the other hand. Our article shows that the reduction of the system adaptation complexity can be realized up to 50% when designing and optimizing the stated system parameters. Our low-complexity MERO simulation model exhibits better performance, for a shorter CP length equal to $0.39$ % of the OFDM symbol duration, than the existing conventional algorithms in term of bit error rate versus optical signal-to-noise ratio with a much lower complexity.

Adaptive blind equalization for a MIMO chaotic communication system

There exist few blind solutions for chaotic MIMO channel equalization. In this work, a chaotic MIMO channel equalization framework is proposed. The objective function to be minimized in the proposed solution is obtained by adopting the objective function developed for chaotic SISO channel equalization. Furthermore, an optimum filter that minimizes the proposed cost function is designed to recover chaotic input signals assuming that the channel is known. The stationary point of the adaptive solution is equal to the optimal filter if the adaptive filter coefficients change sufficiently slowly. The adaptive solution is contrasted with the optimum filter in terms of mean-square error and bit error rate performances. In addition, the proposed solution reconstructs chaotic input signals at the same time. Consequently, it can be applied to multiple signal separation problems as well.

Digital Signal Processing Optimization Algorithm for Terahertz Communication Based on Short Convolution Iterative Algorithm and Adaptive Blind Equalization Algorithm

This paper systematically studies the crosstalk problem caused by the low parallelization rate and tail-to-back tailing in the high-speed digital signal parallel processing in terahertz communication. First, in order to improve the parallelization rate in system application, a high-speed digital signal in the network is filtered in parallel based on a short convolution iterative algorithm for the input signal. Second, an adaptive blind equalization algorithm is proposed to solve the problem crosstalk is used to restore the original signal. Finally, the effectiveness of the equalization algorithm is verified by MATLAB, and the designed algorithm is implemented by Labview simulation software. The effectiveness of the designed algorithm is verified by simulation analysis. The high-speed signal after parallel filtering and equalization can restore the information of the original signal well.

Wide range rate adaptation of QAM-based probabilistic constellation shaping using a fixed FEC with blind adaptive equalization.

We investigate the rate adaptability of quadrature amplitude modulation (QAM)-based probabilistic constellation shaping (PCS) using a fixed forward error correction (FEC) scheme over a wide range of information rates (IRs). Blind adaptive equalization that does not sacrifice any of the IRs was adopted. We show that the conventional decision directed least mean square (DDLMS) algorithm can cause a problem of mis-convergence when it is applied to the PCS of a low IR. To avoid the mis-convergence of DDLMS, we propose a DDLMS-based algorithm that simultaneously minimizes the error between the average symbol power of filter outputs and that of a transmitted PCS signal. Using this technique, we conducted a wavelength-division multiplexed transmission experiment with 32-Gbaud 16/64QAM-based PCS and a fixed FEC of a low-density parity-check code for DVBS-2, where the IR of PCS was optimized at each transmission distance. We confirmed that the data rate of PCS with a fixed FEC and DSP configuration could be improved up to 1.9 times compared with that of QAM-only rate adaptation and that 64QAM-based PCS could provide a wider range of transmission distance and IR while almost covering that of the 16QAM-based one.

Performance analysis of the multiuser Shalvi-Weinstein algorithm

Performance analyses of blind adaptive equalizers provide valuable insights on their behavior, thus being fundamental in the design process. In the literature, interesting theoretical results to predict the steady-state performance of well-known constant-modulus-based algorithms were obtained under rather idealized equalization conditions. In practice, however, the communication channel is often noisy and perfect equalization can be unachievable. In this paper, we employ a linear regression model, commonly used in supervised adaptive filtering, to consider imperfect equalization conditions in the steady-state analysis of constant-modulus-based algorithms. Due to the nonlinear nature of blind algorithms, this analysis extension is a rather challenging, but rewarding, task. In particular, we apply the extended analysis model to the multiuser Shalvi–Weinstein algorithm, chosen due to its inherent advantages in adaptive blind equalization, namely high convergence rate and numerical robustness. As a result, we obtain a theoretical expression for its excess mean-square error (EMSE) at steady state. Interestingly enough, the resulting EMSE expression allows for the identification of distinct performance degradation causes, such as effects due to high-order statistics of the transmitted constellation, imperfect equalization, and multiuser cross-correlation penalty. In spite of the many assumptions considered throughout the EMSE expression derivation, simulation results validate it under realistic operating conditions.

Efficient Blind Adaptive CSE to Reduce Cyclic Prefix Length in Direct Detection Optical OFDM Systems

Abstract Direct detection optical orthogonal frequency division multiplexing (DDO-OFDM) systems for a long-reach of standard single mode fiber (SSMF) require a large length of cyclic prefix (CP) to avoid the inter-symbol interference (ISI) effect caused by group velocity dispersion (GVD). Unfortunately, this method is inefficient due to the energy wasted in CP samples. In order to reduce the CP length and to mitigate the residual ISI, a novel blind adaptive channel shortening equalizer (CSE) is proposed in this paper. Based on the orthogonality between subcarriers in the fast Fourier transform (FFT) property, the proposed algorithm attempts to minimize the sum-squared correlation (SSCM) between each sample located in a well-defined window to update the CSE coefficients. Thus, the combined channel-CSE response is shortened. Therefore, it can cancel the residual ISI effect due to the GVD and the short CP length. The performance of the system is evaluated on basis of bit error rate (BER) versus optical signal to noise ratio (OSNR) for different CP lengths. The simulation results validate the new algorithm SSCM and show that it can reduce the CP length with a much better system improvement than existing algorithms.

A Performance Comparison of CCA and RMMA Algorithm for Blind Adaptive Equalization

A Performance Comparison of CCA and RMMA Algorithm for Blind Adaptive Equalization

Performance Evaluation of MSAG-SCS-MMA-I Adaptive Blind Equalization Algorithm with dual step-size

Performance Evaluation of MSAG-SCS-MMA-I Adaptive Blind Equalization Algorithm with dual step-size

Space-time multichannel adaptive filtering scheme for VLC color cross-talk equalization.

In the emerging framework of visible light communications, the limitation of modulation bandwidth of light emitting diodes (LEDs) transmitters is counterbalanced by the use of red-green-blue (RGB) LEDs since they exhibit higher modulation bandwidth. Using RGB LEDs allows to exploit the spatial multiplexing aspects, that is obtaining parallel channels for transmission. In this context, we used at the receiver RGB-tuned photodiodes (PDs). Hence each PD can, in principle, detect only the information its tuning is matched to. The drawback of increasing spectral efficiency is the presence of cross-talk at the single PD due to the signals emitted by the remaining colors when a perfect color filtering is not applied. In this paper we consider amplitude shift keying (ASK) modulation, investigate the issue of the spatial (color) interference and we present a blind multichannel adaptive equalizer able to mitigate the temporary intersymbol interference (ISI) and also the spatial (color) ISI, this latter partially suppressed using suitable color filters. We analyze also the convergence of the adaptive algorithm and compare its performance with the literature.