Blind Channel Equalization Research Articles

Fast Blind Channel Equalization Based on Online Deep Neural Network

Fast Blind Channel Equalization Based on Online Deep Neural Network

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.

Modified gate activation functions of Bi-LSTM-based SC-FDMA channel equalization

Abstract In recent years, artificial neural networks (ANNs) have grown a lot and helped solve numerous problems in wireless communication systems. We have evaluated the performance of the Bidirectional-Long-Short-Term-Memory (Bi-LSTM) recurrent neural networks (RNNs) for joint blind channel equalization and symbol detection using a variety of activation functions (Afs) for the gate units (sigmoid) of Bi-LSTMs without requiring any prior knowledge of channel state information (CSI). The performance of Bi-LSTM networks with different AFs found in the literature is compared. This comparison was carried out with the assistance of three different learning algorithms, namely Adam, rmsprop, and SGdm. The research findings clearly show that performance, as measured by equalization accuracy, can be improved. Furthermore, demonstrate that the sigmoid gate activation function (GAF), which is commonly used in Bi-LSTMs, does not significantly contribute to optimal network behavior. In contrast, there are a great many less well-known AFs that are capable of outperforming the ones that are most frequently utilized.

Adaptive algorithms for blind channel equalization in impulsive noise

The unsupervised adaptive mitigation of intersymbol interference in an additive impulsive noise environment, modeled as generalized Gaussian, is dealt in this work. The theory of statistical invariance, Wijsman’s theorem, is used to develop a maximal-invariant test to discriminate equally-likely pulsed signals against impulsive disturbance leading to an admissible cost function for blind equalization. The cost function is optimized to realize two adaptive equalizers capable of not only mitigating intersymbol interference but also robust to impulsive disturbance. Numerical simulations, obtained on a baseband digital microwave radio system for amplitude-phase shift keying signaling in an additive (generalized Gaussian and symmetric-alpha stable) impulsive environment, confirm the admissibility of the proposed equalizers in terms of robustness and steady convergence.

Modified constant modulus algorithm based on bat algorithm

In this work, modified constant modulus algorithm based on bat algorithm is proposed for wireless sensor communications systems. The bat algorithm is a swarm intelligence optimization algorithm, which mainly used to solve optimization problems. The proposed algorithm focused on modified constant modulus algorithm, which is also applicable to the constant modulus algorithm. The error function of blind equalization algorithm is used as the evaluation function of the bat algorithm, and then the initial value of the weight vector is calculated adaptively by the bat algorithm. Theoretical analysis is provided to illustrate that the proposed algorithm has a faster convergence speed than the original one and is suitable for almost all blind channel equalization algorithms. The simulation results support the newly proposed improved algorithm. The proposed algorithm could be applied to some more complex wireless channel environments to improve the reception performance of sensor communication systems.

Blind Modulation Identification of Underwater Acoustic MPSK Using Sparse Bayesian Learning and Expectation Maximization

This paper presents a likelihood-based algorithm for identifying different phase shift keying (PSK) modulations, i.e., BPSK, QPSK, and 8PSK. This algorithm selects the modulation type that maximizes a loglikelihood function that is based on the known original constellation associated with the constellation of the received signals for the candidate modulation types. However, there are two problems in non-cooperative underwater acoustic Multiple Phase Shift Keying (MPSK) modulation identification based on the likelihood method. One is the original constellation, which as prior information is unknown. The other is the underwater acoustic multipath channel makes the constellation distort seriously. In this paper, we solved these problems by combining sparse bayesian learning (SBL) with expectation maximization (EM). The specific steps are as follows. Firstly, blind channel equalization can be achieved by channel impulse response (CIR), which is estimated by sparse bayesian learning in single input multi output (SIMO) underwater acoustic channel. Subsequently, we used expectation maximization to compensate amplitude attenuation and phase offset, as the original constellation of MPSK is unknown. Finally, modulation can be successfully identified by the Quasi Hybrid Likelihood Ratio Test (QHLRT). The simulation results show that the channel estimation method based on SBL can eliminate the influence of channel effectively, and the EM algorithm can make the received constellation converge to the preset constellation in the case of unknown original transmit constellation, which effectively solves these two problems. We use the proposed SBL-EM-QHLRT method to achieve an identification rate of more than 95% in underwater acoustic multipath channels with Signal to Noise Ratio (SNR) higher than 15 dB, which provides a new idea for modulation identification of non-cooperative underwater acoustic MPSK.

Unsupervised Linear and Nonlinear Channel Equalization and Decoding Using Variational Autoencoders

A new approach for blind channel equalization and decoding, variational inference, and variational autoencoders (VAEs) in particular, is introduced. We first consider the reconstruction of uncoded data symbols transmitted over a noisy linear intersymbol interference (ISI) channel, with an unknown impulse response, without using pilot symbols. We derive an approximate maximum likelihood estimate to the channel parameters and reconstruct the transmitted data. We demonstrate significant and consistent improvements in the error rate of the reconstructed symbols, compared to existing blind equalization methods such as constant modulus, thus enabling faster channel acquisition. The VAE equalizer uses a convolutional neural network with a small number of free parameters. These results are extended to blind equalization over a noisy nonlinear ISI channel with unknown parameters. We then consider coded communication using low-density parity-check (LDPC) codes transmitted over a noisy linear or nonlinear ISI channel. The goal is to reconstruct the transmitted message from the channel observations corresponding to a transmitted codeword, without using pilot symbols. We demonstrate improvements compared to the expectation maximization (EM) algorithm using turbo equalization. Furthermore, unlike EM, the computational complexity of our method does not have exponential dependence on the size of the channel impulse response.

Signal Detection for Underwater IoT Devices With Long and Sparse Channels

Underwater acoustic communication often suffers from extended channel impulse response (CIR) and large Doppler spread such that signals become difficult to detect and decode. For the underwater Internet-of-Things (IoT) applications, the challenges are even bigger, because the IoT devices usually transmit very short messages due to severe power constraints, and the length of pilots are often shorter than that of CIR. Therefore, conventional pilot-assisted channel estimation and equalization approaches are incapable of detecting the information data. Moreover, the existing blind channel equalization algorithms, which do not require pilots, are not able to detect information data either, because the number of transmitted symbols is too small to approximate the expected loss with empirical loss, where the loss refers to as the error of estimated signal envelopes. In this article, a new equalization and decoding algorithm is proposed for the underwater IoT devices under harsh communication environments. Inspired by the recent blind deconvolution and compressive sensing techniques, we construct an optimization problem with the objective function rewarding sparsity of the estimated CIR using l4-norm and convexify the feasible set of the problem while guarantee the same solution. Then, we develop a pruned tree search initialization method and use gradient descent to find an optimal solution efficiently. The new algorithm is first verified by simulations, which show that the proposed algorithm outperforms conventional methods, such as the linear minimum mean square error (LMMSE) equalizer and a constant modulus algorithm (CMA). The proposed algorithm, along with a practical procedure for compensating large Doppler spread and carrier frequency offset, is further employed to process the real-world underwater IoT data collected in a fish-tag project. It shows that the proposed algorithm can equalize and detect the IoT data which were corrupted by channels whose lengths are longer than that of pilots, but the existing algorithms, such as LMMSE equalizer and CMA-based blind equalizer are not able to accomplish. It also shows that the proposed algorithm can provide a very impressive improvement compared to raw detection (no equalization or decoding) and decoding-only approaches.

MIMO OFDM Blind Channel Equalization using Multilayer Neural Network in Impulsive Noise Environment

Multiple Input Multiple Output (MIMO) system has several input and output antennas for executing the data transmission. Channel Estimation (CE) is required in MIMO, to achieve the effective signal transmission over the various amount of antennas. By using CE over the MIMO, the noiseless data transmission is performed. Hence in this paper, a Multi-layer Neural Network (MNN) is used for identifying the CE and this system is named as Multi-layer Neural Network-MIMO-Digital Filter (MNN-MIMO-CE) is proposed for blind channel equalization. The MNN-MIMO-CE has Feed forward Artificial Neural Network (FANN) with back propagation in Levenberg-Marquardt (LM) algorithm and it has two processes MNN training and MNN testing. LM algorithm is used to train the MNN. These processes are used to provide the CE for different combination of antennas. The performance of the MNN-MIMO-CE method is evaluated in comparison with the existing method [25] through simulations using BER as the performance measure.

Moving Target Indication for Dual-Channel Circular SAR/GMTI Systems.

In a dual-channel circular synthetic aperture radar (CSAR) and ground moving target indication (GMTI) system, the antenna baseline is not parallel with the flight path due to a yaw angle. The angle causes a varying group-phase shift between the dual-channel signals and therefore degrades the correlation between the image pair. Therefore, the group-phase shift needs to be removed before channel equalization. To resolve the problem, the interferometric phase term was deduced and analyzed based on the geometry of a dual-channel CSAR system. Then, the varying phase term with respect to the Doppler frequency and the varying group-phase shift over the range were compensated for in the channel registration. Furthermore, blind channel equalization, including two-dimensional calibration and amplitude equalization, was applied to eliminate the amplitude and residual phase differences between the channels. Finally, the amplitude image obtained using a displaced phase center antenna (DPCA) was multiplied by the phase image obtained with along-track interferometry (ATI) to detect moving targets. The experimental results verified the effectiveness of the method for both uniform and non-uniform clutter suppression.

Rprop and improved Rprop+ based constant modulus type (RCMT) blind channel equalization algorithm for QAM signal

The aim of paper is to address the issues such as poor convergence, moderate BER, residual ISI associated with unsupervised (blind) weight adaptation technique employed for channel equalization. Two noble algorithms based on resilient back propagation framework have been proposed as solution for QAM signal. The widely accepted gradient descent based Constant Modulus algorithm suffers from poor convergence issues, high residual ISI and Moderate BER. Proposed solution assimilate Constant Modulus Algorithm (CMA) like error function into a general Rprop algorithm having two distinctive approaches of with/ without weight backtracking capability, taking into consideration of frequency selective nature of channels and additive gaussian noise. The algorithms exploit the advantage of Rprop mechanism, thus improving the convergence rate and have better ISI (inter symbol interference) suppression capability. Simulation of the proposed Rprop and improved Rprop+ based CM type (RCMT) algorithm proves their advantageously enhanced capabilities in terms of convergence, complexity, and residual ISI in comparison to the CMA and its variants. Proposed algorithm can also been used for M-PSK signal for which it shows similar performance.

CMA adaptive equalization in subspace pre-whitened blind receivers

In blind channel equalization, the use of whitening transformation (WT) preceding the constant modulus algorithm (CMA), referred to as the pre-whitened CMA, may accelerate the rate of convergence of using the CMA alone. In this work, we develop a novel subspace pre-whitened CMA (SP-CMA) using the subspace WT. By allowing the channel matrix to be non-square, this approach for the subspace WT offers greater flexibility in the design of the WT than the conventional per-whitened CMA does. The similarities and differences between the SP-CMA and the conventional CMA were first examined and analyzed in terms of their convergence behaviors from a theoretical viewpoint. The convergence behavior of the SP-CMA was analyzed under the whiteness assumption in which the input of the blind equalizer has been whitened beforehand by the subspace WT. The upper bound of the improvement in convergence of the SP-CMA over its CMA counterpart was developed. This analysis can be readily extended to other existing pre-whitened CMA schemes. Computer simulations using two highly dispersive multipath channels confirmed the superior convergence of the SP-CMA.

Blind Channel Equalization of Star QAM using Dual Dispersion MCMA Algorithm

An algorithm for blind channel equalization is presented for 16 and 32 Star QAM, namely, Dual Dispersion MCMA algorithm. The algorithm taking the concept from MCMA, uses the Dual Dispersion minimization approach for blind channel equalization. As Star QAM constellation contains two rings, so instead of one, dual dispersion minimization approach is used for its both rings. With modification in MCMA cost function, the new algorithm results improved performance in convergence rate of Residual ISI and MSE against MCMA algorithm. By incorporating decision directed approach, the performance increases drastically. Simulation results show effectiveness of proposed algorithm in removing the ISI and correcting the errors in symbols of received signal.

Passive Vector Sensing for Non-Cooperative Emitter Localization in Indoor Environments

Indoor emitter localization is a topic of continued interest for improving wireless security as wireless technologies continue to become more advanced. Conventional methods have focused on the localization of devices relative to multi-sensor systems owing to ease of implementation with pre-existing infrastructures. This work, however, focuses on enhancing wireless security via non-cooperative emitter localization in scenarios where only a single receiver can be employed. A vector sensor is simulated and experimentally developed that extracts three-dimensional signal characteristics for room-based emitter localization and is compared to conventional methodologies such as Received Signal Strength (RSS), Time of Arrival (ToA), and Direction of Arrival (DoA). The proposed method generates time-frequency fingerprints and extracts features through dimensionality reduction. A second stage extracts spatial parameters consisting of Channel State Information (CSI) and DoAs that are analyzed using a Gaussian Mixture Model (GMM) to segregate fine-grained regions of interest within each room where the non-cooperative emitter resides. Blind channel equalization cascaded with a least squares channel estimate is used for acquiring the CSI, whereas the DoAs are obtained by unique trigonometric properties of the vector sensing antenna. The results demonstrate that a vector sensor can improve non-cooperative emitter localization and enhance wireless security in indoor environments.

Design of Supervised and Blind Channel Equalizer Based on Moth-Flame Optimization

With the increase in demand of high-speed data, the communication channels are suffering from inter-symbol interference, nonlinearity and noise. In this paper, digital channel equalizers are developed for finite impulse response (FIR) and infinite impulse response (IIR) channels. Supervised learning based on minimum mean square error is opted for FIR channels affected by noise and nonlinearity. For IIR channel, blind equalization based on constant modulus technique is employed. The weights of both type of equalizers are determined by a recently developed nature-inspired algorithm moth-flame optimization (MFO). The performance is compared with the same structure of equalizer trained with standard algorithms like: artificial immune system, adaptive particle swarm optimization, binary genetic algorithm and least mean square algorithm. Simulation studies are demonstrated for equalizers designed to compensate the response of two FIR channels, and both are affected by two nonlinearities with noise and three IIR channels. Superior performance by the proposed MFO equalizer is reported based on frequency response analysis, mean square error during training and BER plots during testing.

Blind Equalization in the Presence of Co-channel Interference Based on Higher-Order Statistics

An improved blind channel equalization method is proposed based on the generalized eigenvector algorithm (GEA) in this paper. This new method can blindly equalize the desired signal in the presence of strong co-channel interference. The basic idea underlying the improved GEA method is that higher-order cumulants can be sensitive to frequency offset. By exploiting this property of higher-order statistics, blind equalizer can be designed to equalize the desired signal with known frequency offset while suppressing the interference with a different frequency offset. Simulation results are shown to demonstrate the effectiveness of the proposed method.

Logarithmic cost-based improved constant modulus type blind channel equalisation algorithm for M-QAM/M-PSK signal

In this paper, authors have proposed the blind channel equalisation algorithm based on logarithmic cost function for QAM/PSK signal which is widely used in the digital communication system. Constant modulus algorithm (CMA) and modified constant modulus algorithm (MCMA), the two widely referenced algorithms for blind equalisation of a QAM/PSK signal, exhibit very slow convergence rates and large steady-state mean square error. The proposed algorithm attains faster convergence speed and low steady state mean square error by incorporating the improved logarithmic cost-based error function in the resilient back propagation-based framework. This makes the weight adaption of equaliser simple. Simulation results show that the proposed algorithm has better convergence rate and lower steady state error in comparison to CMA and MCMA algorithms.

Blind System Identification Using Symbolic Dynamics

In this paper, a chaos-based approach is proposed for system identification with binary random signal. A chaos-based approach is developed to model random binary sequence and is applied to blind system identification. The Cramer Rao Lower Bound (CRLB)-based on the chaos representation is derived. The theoretical mean square error of the proposed approach is also derived. It is shown that the proposed blind approach achieves the CRLB asymptotically. The proposed technique is applied to blind channel equalization of a quadrature amplitude modulation communication system. The equalizer is based on expected maximization and unscented Kalman filtering and smoother. Our proposed method shows superior performance in comparison with conventional blind equalization techniques. The significance of this research is to extend the advantages of chaos to random signals for the blind system identification.

Logarithmic cost-based improved constant modulus type blind channel equalisation algorithm for M-QAM/M-PSK signal

In this paper, authors have proposed the blind channel equalisation algorithm based on logarithmic cost function for QAM/PSK signal which is widely used in the digital communication system. Constant modulus algorithm (CMA) and modified constant modulus algorithm (MCMA), the two widely referenced algorithms for blind equalisation of a QAM/PSK signal, exhibit very slow convergence rates and large steady-state mean square error. The proposed algorithm attains faster convergence speed and low steady state mean square error by incorporating the improved logarithmic cost-based error function in the resilient back propagation-based framework. This makes the weight adaption of equaliser simple. Simulation results show that the proposed algorithm has better convergence rate and lower steady state error in comparison to CMA and MCMA algorithms.

An Equalization Initialization Procedure for MDM Systems Based on Orthogonal Matching Pursuit

In this letter, a new initialization procedure is proposed for channel equalization in the mode division multiplexing (MDM) systems. The initialization procedure is based on the orthogonal matching pursuit (OMP) algorithm. With the proposed method, it is possible to use a short training sequence (TS) to estimate the initial tap values for the constant modulus algorithm (CMA), and the CMA provides further channel equalizer optimization afterward. It is found that with the aid of the OMP algorithm, the length of the TS can be as short as 256 symbols for an MDM system with 35-ns delay spread, which is only 1/16 of the TS length required by the least square algorithm. The OMP based semi-blind algorithm has shorter TS length and a lower computational cost in comparison to the full TS-based channel equalization approaches and a better convergence performance in comparison to the full blind channel equalization algorithms.