Neural Equalizer Research Articles

Long Short-Term Memory Neural Equalizer

A trainable neural equalizer based on Long Short-Term Memory (LSTM) neural network architecture is proposed in this paper to recover the channel output signal. The current widely used solution for the transmission line signal recovery is generally realized through a decision feedback equalizer (DFE) or forward-feedback equalizer (FFE-DFE) combination. The novel learning-based equalizer is suitable for highly non-linear signal restoration thanks to its recurrent design. The effectiveness of the LSTM equalizer (LSTME) is shown through an advance design system (ADS <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^@$</tex-math></inline-formula> ) simulation channel signal equalization task including a quantitative and qualitative comparison with an FFE-DFE combination. The LSTM neural network shows good equalization results compared to that of the FFE-DFE combination. The advantage of a trainable LSTM equalizer lies in its ability to learn its parameters in a flexible manner and to tackle complex scenarios without any hardware modification. This can reduce the equalizer implantation cost for variant transmission channels and bring additional portability in practical applications.

BER Analysis of Neural Equalizer in OFDM systems

Digital communication gives larger data capacity and best communication speed. The signal transmitted through the wireless channels in digital communication affected by nonlinearities like noise. Inter Symbol Interference (ISI) dominantly causes huge data loss. It is caused due to multipath propagation, band-limited channels noise. Equalization, a process of inducing inverse channel response to compensate the effects of ISI is used to combat these effects. Orthogonal Frequency Division Multiplexing (OFDM) system supports high data rates and offers resistance towards the channel effect. Adding equalizer to OFDM systems make it more robust.In real time situations the response of channel is not known in prior. So, adaptive equalizers are implemented to compensate channel effects with the help of pilot symbols which are used to estimate the channel response and equalize the signal accordingly. Minimum Mean Square Error (MMSE), Least Square (LS) are some of the existing algorithms used to implement the equalizers. These conventional algorithms require some statistical properties of channel which is not possible in real time scenarios. Also, Linear Transverse equalizer failed to provide satisfactory results in the case of Non Minimum Phase channel. Neural Networks is capable to perform this task and can be used as an alternative to these algorithms.Back Propagation Neural Networks (BPNN) and Deep Neural Networks (DNN) can achieve better results when compared to conventional algorithms. Here, Deep Neural Networks with Adam optimization is proposed to enhance the performance of equalization. DNN can be used in both linear and non-linear channels. Also, Adam optimization used with Back Propagation uses variable and adaptive learning rate which reduces slow convergence and increases the efficiency of neural network unlike stochastic gradient descent which uses fixed learning rate.In this work the performance of proposed equalizer in OFDM systems is analyzed over flat and frequency selective fading of Rayleigh channels. The performance is measured in terms of Bit Error rate over SNR range -30dB to 25 dB. The results are compared with that of MMSE and it is observed that over the mentioned range of SNR the proposed equalizer achieved acceptable results and has low Bit error rate than that of MMSE in both flat and frequency selective fading channels.

Dynamic evolving neural fuzzy inference system equalization scheme in mode division multiplexer for optical fiber transmission

The performance of optical mode division multiplexer (MDM) is affected by inter-symbol interference (ISI), which arises from higher-order mode coupling and modal dispersion in multimode fiber (MMF). Existing equalization algorithms in MDM can mitigate linear channel impairments, but cannot tackle nonlinear channel impairments accurately. Therefore, mitigating the noise in the received signal of MDM in the presence of ISI to recover the transmitted signal is important issue. This paper aims at controlling the broadening of the signal from MDM and minimizing the undesirable noise among channels. A dynamic evolving neural fuzzy inference system (DENFIS) equalization scheme has been used to achieve this objective. Results illustrate that nonlinear DENFIS equalization scheme can improve the received distorted signal from an MDM with better accuracy than previous linear equalization schemes such as recursive‐least‐square (RLS) algorithm. Desirably, this effect allows faster data transmission rate in MDM. Additionally, the successful offline implementation of DENFIS equalization in MDM encourages future online implementation of DENFIS equalization in embedded optical systems.

Butterfly neural equalizer applied to optical communication systems with two-dimensional digital modulation.

This article aims to present, analyze and evaluate a new equalizer architecture, inspired by the butterfly equalizer used in optical communication, based on Artificial Neural Networks (ANN) of the Multi-Layer Perceptron (MLP) type for nonlinear systems with two-dimensional modulation named the Butterfly Neural Equalizer (NE-Butterfly). The NE-Butterfly is intended to equalize any channel that has real or complex taps, whether linear or nonlinear. Simulation results are presented for different types of nonlinear fiber optic channels with complex and real taps, also containing inter symbolic interference and additive noise. The results are compared with other neural equalizers in the literature with the objective of validating the performance of the NE-Butterfly, which stands out as having the overall best performance against the ones it was compared to.

Nonlinearities compensator based on SORBFNN in ultra-long-haul high-capacity CO-OFDM systems

Radial basis function neural network is recognized as being the most useful type of neural network for a nonlinear equalizer in the CO-OFDM system. In the history of nonlinear equalizers, the focus has always been on mitigation of nonlinearity. Despite this interest, no one to the best of our knowledge has studied ultra-long-haul transmission length. Previous work has been limited to normal transmission length, i.e., up to 1400 km. In ultra-long-haul optical fiber communication systems, the optical signal becomes very much complex at longer distance, i.e., around over 8000 km. It has not yet been established whether radial basis function neural network can do the same improvement in performance at ultra-long-haul transmission length. A basic issue of a customary radial basis function neural system is its low performance at such a long distance. This paper presents a new approach to compensating nonlinearities in ultra-long-haul optical fiber communication CO-OFDM systems. In this new approach, a radial basis function with nonlinear equalizer (first hidden layer with automatically adjusted structure, i.e., number of neuron nodes in the hidden layer and the different parameters of the structure through learning, and second hidden layer with fixed structure) based on two hidden layers has been recommended. The aim of this study is to examine the performance of a self-organizing radial basis function neural network-based nonlinear equalizer (SORBFNN-NLE) for the mitigation of nonlinearities in ultra-long-haul CO-OFDM systems. Better performance of the SORBFNN is attributed due to self-organizing structure and training of network. From this study, it has been observed that the proposed SORBFNN-NLE performs well regarding Q-factor and OSNR at an ultra-long distance.

Application of functional link artificial neural network for mitigating nonlinear effects in coherent optical OFDM

Artificial Neural Networks are developed as an important technique for equalization and have been widely used to mitigate the nonlinear effects in coherent optical systems. For the compensation of nonlinearities in coherent optical orthogonal frequency division multiplexing technique, the most popular artificial neural network model is a multilayer perceptron (MLP), as it is able to perform complex mapping between input and output spaces with significant success. However due to the complexity of multilayer perceptron nonlinear equalizer (MLP-NLE) model training of neural network is difficult. To overcome computational complexity issues of MLP-NLE, a single neuron based functional link artificial neural network nonlinear equalizer (FLANN-NLE) has been developed in this paper. Better performance of an equalizer is attributed to the usage of aPSO-BP algorithm for training the FLANN-NLE. The proposed FLANN-NLE surpasses the existing works both in terms of Q-Factor and computational complexity. For a fiber length of 1000 km and at launch power of −6 dBm, the improvement in Q-Factor is approximately equal to 3.3 and 1 dB in contrast to the previously reported values of approximately 3 and 0.7 dB at bit rate of 40 and 80 Gbps respectively.

A novel support vector machine robust model based electrical equaliser for coherent optical orthogonal frequency division multiplexing systems

Classifiers, such as artificial neural networks non-linear equaliser (ANN-NLE), Wiener–Hammerstein non-linear equaliser, Volterra non-linear equaliser (Volterra-NLE) and support vector machine non-linear equaliser (SVM-NLE), can play a significant role in compensating non-linear imperfections in the optical communications context. Using classifiers to mitigate the non-linear effects in coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems is an interesting idea to be investigated. In this study, a novel support vector machine robust version, specifically adapted to a 100 Gb/s CO-OFDM data structure for long haul distance, is proposed. Firstly, the authors demonstrate that SVM-NLE upgrades the system performance by about 10−1 in terms of bit-error rate compared to Volterra-NLE at optical signal-to-noise ratio equal to 14 dB. Then, they show that it can double the transmission distance up to 1600 km over single mode fibre channel. Furthermore, a performance comparison is performed using 16 quadrature amplitude modulation and 40 Gb/s bit rate for SVM-NLE, ANN-NLE and inverse Volterra series transfer function non-linear equaliser, respectively.

An improved back propagation algorithm for training neural network-based equaliser for signal restoration in digital communication channels

An improved back propagation algorithm for training neural network-based equaliser for signal restoration in digital communication channels

An improved back propagation algorithm for training neural network-based equaliser for signal restoration in digital communication channels

The back propagation BP algorithm has been very successful in training multilayer perceptron-based equalisers; despite its success BP convergence is still too slow. Within this paper we present a new approach to enhance the training efficiency of the multilayer perceptron-based equaliser MLPE. Our approach consists on modifying the conventional back propagation algorithm, through creating an adaptive nonlinearity in the activation function. Experiment results evaluates the performance of the MLPE trained using the conventional BP and the improved back propagation with adaptive gain IBPAG. Due to the adaptability of the activation function gain the nonlinear capacity and flexibility of the MLP is enhanced significantly. Therefore, the convergence properties of the proposed algorithm are more improved compared to the BP. The proposed algorithm achieves the best performance in the entire simulation experiments.

Neural equalization applied to systems with bidimensional digital modulation

A new equalization model for digital communication systems is proposed, based on a multi-layer perceptron (MLP) artificial neural network with a backpropagation algorithm. Unlike earlier techniques, the proposed model, called the bidimensional neural equalizer, is composed of two independent MLP networks that operate in parallel for each dimension of the digital modulation scheme. A heuristic method to combine the errors of the two MLP networks is also proposed, with the aim of reducing the convergence time. Simulations performed for linear and nonlinear channels demonstrated that the new model could improve performance in terms of the bit error rate and the convergence time, compared to existing models.

Fast Fading Channel Neural Equalization Using Levenberg-Marquardt Training Algorithm and Pulse Shaping Filters

Artificial Neural Network (ANN) equalizers have been successfully applied to mitigate Inter symbolic Interference (ISI) due to distortions introduced by linear or nonlinear communication channels. The ANN architecture is chosen according to the type of ISI produced by fixed, fast or slow fading channels. In this work, we propose a combination of two techniques in order to minimize ISI yield by fast fading channels, i.e., pulse shape filtering and ANN equalizer. Levenberg-Marquardt algorithm is used to update the synaptic weights of an ANN comprise only by two recurrent perceptrons. The proposed system outperformed more complex structures such as those based on Kalman filtering approach.

A low complexity Hopfield neural network turbo equalizer

In this article, it is proposed that a Hopfield neural network (HNN) can be used to jointly equalize and decode information transmitted over a highly dispersive Rayleigh fading multipath channel. It is shown that a HNN MLSE equalizer and a HNN MLSE decoder can be merged in order to realize a low complexity joint equalizer and decoder, or turbo equalizer, without additional computational complexity due to the decoder. The computational complexity of the Hopfield neural network turbo equalizer (HNN-TE) is almost quadratic in the coded data block length and approximately independent of the channel memory length, which makes it an attractive choice for systems with extremely long memory. Results show that the performance of the proposed HNN-TE closely matches that of a conventional turbo equalizer in systems with short channel memory, and achieves near-matched filter performance in systems with extremely large memory.

Instantaneous Gradient Based Dual Mode Feed-Forward Neural Network Blind Equalization Algorithm

To further improve the performance of feed-forward neural network blind equalization based on Constant Modulus Algorithm (CMA) cost function, an instantaneous gradient based dual mode between Modified Constant Modulus Algorithm (MCMA) and Decision Directed (DD) algorithm was proposed. The neural network weights change quantity of the adjacent iterative process is defined as instantaneous gradient. After the network converges, the weights of neural network to achieve a stable energy state and the instantaneous gradient would be zero. Therefore dual mode algorithm can be realized by criterion which set according to the instantaneous gradient. Computer simulation results show that the dual mode feed-forward neural network blind equalization algorithm proposed in this study improves the convergence rate and convergence precision effectively, at the same time, has good restart and tracking ability under channel burst interference condition.

T/2 Fractionally Spaced Based on Wavelet Neural Network Blind Equalization Algorithm

T/2 Fractionally Spaced Based on Wavelet Neural Network Blind Equalization Algorithm

Efficient classification algorithm and a new training mode for the adaptive radial basis function neural network equaliser

The study presents a new classification algorithm and a new online training mode used for learning the parameters of a Bayesian RBFNN (radial basis function neural network) equaliser in a non-linear time-varying channel. The classification algorithm is used to determine the centres of the hidden layer neurons that are equal to the channel states. This proposed unsupervised classification algorithm is based on both the K-means and the rival penalised competitive algorithms. Its main advantage is neither an initialisation phase nor a knowledge of the channel states number is required. The connections of weights and the spread of the hidden neurons are learned by the gradient descent algorithm, which applies a new proposed training mode. This training mode combines the advantages of both the online and the offline training modes such as stability and good speed of convergence. The performances of the RBFNN equaliser trained by the proposed method are shown in comparison with the performances of the optimal Bayesian equaliser and those of the same equaliser trained by other known training modes. All these performances are studied by using different types of channels.

SCFNN-Based Decision Feedback Equalization Robust to Frequency Offset and Phase Noise

This paper proposes a self-constructing fuzzy neural network-based decision feedback equalizer (SCFNN DFE). An online learning algorithm containing the structure and parameter learning phases is employed in training the SCFNN DFE. Specifically, the feedforward input vector classification and a gradient-descent method are both used in this online learning algorithm. We show by simulations that the proposed SCFNN DFE offers improvement compared to the traditional DFE methods in the presence of frequency offset and phase noise.

Fuzzy Neural Network Blind Equalization Algorithm Based on Signal Transformation

To recover QAM signals at the receiver of blind equalizer, a Fuzzy C-means clustering Neural Network Blind Equalization Algorithm based on Signal Transformation (ST-FNN-BEA) is proposed. The proposed algorithm uses signal transformation method to debase the computational complexity of equalizer input signals and speed up the convergence rate, and makes use of fuzzy c-means clustering algorithm dividing the equalizer input signals into each cluster center with different membership values to improve the equalization performance. The proposed ST-FNN-BEA outperforms Neural Network Blind Equalization Algorithm (NN-BEA) and Neural Network Blind Equalization Algorithm based on Signal Transformation (ST-NN-BEA) in improving convergence rates and reducing mean square error. The performance of ST-FNN-BEA is proved by the computer simulation with underwater acoustic channels.

A novel concept of embedding orthogonal basis function expansion block in a neural equalizer structure for digital communication channel

The proposed neural equalizer structure is based on a novel orthogonal basis function (OBF) expansion technique, motivated by genetic evolutionary concept, which utilizes a self-breeding approach t...

Performance of fuzzy logic-based slope tuning of neural equaliser for digital communication channel

Adaptive equalisation in digital communication systems is a process of compensating the disruptive effects caused mainly by intersymbol interference in a band-limited channel and plays a vital role for enabling higher data rate in modern digital communication system. Designing efficient equalisers having low structural complexity and faster learning algorithms is also an area of much research interest in the present scenario. This paper presents a novel technique of improving the performance of conventional multilayer perceptron (MLP)-based decision feedback equaliser (DFE) of reduced structural complexity by adapting the slope of the sigmoidal activation function using fuzzy logic control technique. The adaptation of the slope parameter increases the degrees of freedom in the weight space of the conventional feedforward neural network (CFNN) configuration. Application of this technique provides faster learning with less training samples and significant performance gain. This research work also proposes adaptive channel equalisation techniques on recurrent neural network framework. Exhaustive simulation studies carried out prove that by replacing the conventional sigmoid activation functions in each of the processing nodes of recurrent neural network with multilevel sigmoid activation functions, the bit error rate performance has significantly improved. Further slopes of different levels of the multilevel sigmoid have been adapted using fuzzy logic control concept. Simulation results considering standard channel models show faster learning with less number of training samples and performance level comparable to the their conventional counterparts. Also, there is scope for parallel implementation of slope adaptation technique in real-time implementation, which saves the computational time.

Parameter Estimation of Recurrent Neural Equalizers Using the Derivative-Free Kalman Filter

For the last decade, recurrent neural networks (RNNs) have been commonly applied to communications channel equalization. The major problems of gradient-based learning techniques, employed to train recurrent neural networks are slow convergence rates and long training sequences. In high-speed communications system, short training symbols and fast convergence speed are essentially required. In this paper, the derivative-free Kalman filter, so called the unscented Kalman filter (UKF), for training a fully connected RNN is presented in a state-space formulation of the system. The main features of the proposed recurrent neural equalizer are fast convergence speed and good performance using relatively short training symbols without the derivative computation. Through experiments of nonlinear channel equalization, the performance of the RNN with a derivative-free Kalman filter is evaluated.