Adaptive Nonlinear Equalizer Research Articles

Adaptive two-stage nonlinear feedforward equalizer and decision feedback equalizer for a visible-light communication and ultra-large effective area pure silica fiber seamless integrated system

We proposed an adaptive two-stage nonlinear feedforward equalizer and decision feedback equalizer to minimize the negative influence of nonlinear distortions. A data rate of 960 Mbit/s is experimentally achieved on the guided visible-light transparent transmission over a 100-m ultra-large effective area pure silica fiber. The experimental results verified the effectiveness and improvement of the proposed method compared with the traditional feedforward post-equalizers.

Adaptive Nonlinear Equalization Combining Sparse Bayesian Learning and Kalman Filtering for Visible Light Communications

Nonlinear post equalization (NPE) based on Volterra series (VS) is considered as an effective way to mitigate the severe light emitting diode (LED) nonlinearity and multipath effect in a visible light communication (VLC) system. However, it is restricted by kernel complexity in practical applications. In this paper, we formulate the kernel extraction of VS-based NPE to be a sparse recovery problem, and propose an efficient sparsity-aware approach, using combined sparse Bayesian learning (SBL) and Kalman filtering (KF) to extract the active VS kernels and thus to reduce the redundancy of NPE. First, from the view of probability, a Bayesian strategy is applied to select the dominant regressors from the original measurement matrices by exploiting the learning of hyperparameters, which encourages the sparseness of VS kernels with an imposed prior. Then, based on the specified regression matrix, the improved KF iteration is used in the estimation of the kernel coefficients to overcome the system instability in a dynamic noise environment. With this methodology, the active VS kernels can be effectively extracted and the corresponding kernel quantity is significantly reduced at least by 65%. Moreover, the system can still work effectively in the case of a lower size of training samples. The simulation results show that the proposed scheme is beneficial to both the nonlinearity compensation and multipath interference mitigation, and exhibits better overall performance than some existing methods, which demonstrates the potential and validity of kernel extraction in VS-based NPE.

Adaptive Nonlinear Equalization for Digital Array Receivers

As low-cost fully digital array technology becomes more commercialized, techniques need to be developed to be able to deal with many of the inherent problems of these systems. This article focuses on mitigating the intermodulation distortion (IMD) caused by the low-input third-order intercept point (IIP3) of the low-noise amplifier (LNA) in a digital array element's channel. The performance of solid-state electronics also varies with the temperature of the device, thus changing the device's nonlinear characteristics. This article proposes an adaptive solution for nonlinear equalization (NLEQ) with the use of the least mean-square (LMS) algorithm. Data from a modern digital array channel are corrected using the proposed method; the channel nonlinearities are also characterized for further simulations. A simulation using these nonlinear coefficients shows that NLEQ can effectively mitigate the IMD of two strong interferers that had previously distorted the weak signal of interest. Finally, a nine-element fully digital array is simulated, showing the correlation of IMD with specific, predictable directions, and the decorrelation of these spurs after NLEQ is applied to each element of the array.

Analysis of BER Improvement of Adaptive Equalizer using CE and STB code

In a wireless communication channel, when the modulation bandwidth is exceeding the coherence bandwidth ISI takes place as the transmitted pulses are spread into the adjacent symbols. To combat the effects of ISI and noise and to reconstruct the signal and minimize Bit Error Rate (BER), the adaptive channel equalizer is used at the receiver end. Various kinds of interferences in a communication channel exists like Inter symbol Interference, Multipath Interference and Additive Interference which deals with the design of an Adaptive Equalizer. The idea of the equalizer is to build filter in the receiver that counter acts the effect of the channel. In essence, the equalizer must “unscatter” the impulse response and can be stated as the goal of designing the equalizer E so that the impulse response of the combined channel and equalizer CE has a single spike. We investigate channel equalization and introduce hierarchical and adaptive nonlinear channel equalization algorithms that are highly efficient and provide significantly enhanced bit error rate (BER) performance. Due to the high complexity of nonlinear equalizers and poor performance of linear ones, to equalize highly difficult channels, we employ piecewise linear equalizers.

Literature Review on BER Improvement of Adaptive Equalizer

Channel equalization is an important aspect in high speed digital communication required for efficient and reliable data recovery and reception when the data is transmitted over band-limited channel subjected to noise and interference. We investigate channel equalization and introduce hierarchical and adaptive nonlinear channel equalization algorithms that are highly efficient and provide significantly improved bit error rate (BER) performance. Due to the high complexity of nonlinear equalizers and poor performance of linear ones, to equalize highly difficult channels, we employ piecewise linear equalizers.

3 × 104 Gb/s Single-λ Interconnect of Mode-Division Multiplexed Network With a Multicore Fiber

In this paper, we study the use of silicon microring modulators in an integrated mode-division multiplexing (MDM) network for short-reach interconnects using discrete multitone (DMT) modulation. A fiber grating coupler array is used as a high-speed optical interface between the on-chip mode channels and off-chip multicore fiber (MCF). The whole link has a crosstalk level lower than –23.1 dB. The MDM network can work without the crosstalk compensation of digital signal processing. We present experimental results of the linearity of the silicon microring modulator in terms of spurious-free dynamic range (SFDR). The third-order intermodulation distortion SFDR is 93.4 dB/Hz 2/3 at 20 GHz. We can improve system performance by using adaptive nonlinear equalizer at the DMT receiver to mitigate transmitter and transmission impairments. An aggregate bitrate above 312 Gb/s is achieved with a bit error ratio of 3.8 × 10−3. With the addition of nonlinear equalizer, the line rates of the MDM network can be further increased to about 330 Gb/s. The experimental results demonstrate the feasibility of single wavelength DMT transmission in MDM network with MCF.

Adaptive and efficient nonlinear channel equalization for underwater acoustic communication

We investigate underwater acoustic (UWA) channel equalization and introduce hierarchical and adaptive nonlinear (piecewise linear) channel equalization algorithms that are highly efficient and provide significantly improved bit error rate (BER) performance. Due to the high complexity of conventional nonlinear equalizers and poor performance of linear ones, to equalize highly difficult underwater acoustic channels, we employ piecewise linear equalizers. However, in order to achieve the performance of the best piecewise linear model, we use a tree structure to hierarchically partition the space of the received signal. Furthermore, the equalization algorithm should be completely adaptive, since due to the highly non-stationary nature of the underwater medium, the optimal mean squared error (MSE) equalizer as well as the best piecewise linear equalizer changes in time. To this end, we introduce an adaptive piecewise linear equalization algorithm that not only adapts the linear equalizer at each region but also learns the complete hierarchical structure with a computational complexity only polynomial in the number of nodes of the tree. Furthermore, our algorithm is constructed to directly minimize the final squared error without introducing any ad-hoc parameters. We demonstrate the performance of our algorithms through highly realistic experiments performed on practical field data as well as accurately simulated underwater acoustic channels.

The Rainfall Intensity Effects on 1–13 GHz UWB-Based 5G System for Outdoor Applications

This paper reports a research contribution on tropical outdoor channel characterization in 1–13 GHz band for 5G systems. This 1–13 GHz ultra-wideband (UWB) channel characterization is formulated with rain intensity as the most important variable, from 20 mm/h to 200 mm/h. Tropical rain will cause pulse broadening and distorts the transmitted symbols, so the probability of symbol errors will increase. In this research, the bit error rate (BER) performance evaluation is done using both matched filtering or correlator-based receivers. At no rain conditions, BER 10−6 will be attained at signal to noise ratio (SNR) 5 dB, but at rainfall intensity 200 mm/h, the BER will fall to 10−2 for matched filter and 5×10-2 for correlator-based receivers. For improving the BER performance, an adaptive nonlinear phase equalizer is proposed which adopts multiple allpass biquad infinite impulse response (IIR) filters combined with low-order finite impulse response (FIR) filter to mitigate the nonlinearity phase and differential attenuation of magnitude responses due to antenna and tropical outdoor UWB channel effects. Our simulation results show that the proposed equalizer has worked successfully with BER 10−6 on the rain rate that is exceeded for 0.01% of the time (R0.01) rain intensity or 99.99% availability. In addition, at rainfall rate 120 mm/h, the proposed nonlinear phase equalizer can give 9 dB signal improvement.

Hybrid time-frequency domain equalization for LED nonlinearity mitigation in OFDM-based VLC systems.

A novel hybrid time-frequency domain equalization scheme is proposed and experimentally demonstrated to mitigate the white light emitting diode (LED) nonlinearity in visible light communication (VLC) systems based on orthogonal frequency division multiplexing (OFDM). We handle the linear and nonlinear distortion separately in a nonlinear OFDM system. The linear part is equalized in frequency domain and the nonlinear part is compensated by an adaptive nonlinear time domain equalizer (N-TDE). The experimental results show that with only a small number of parameters the nonlinear equalizer can efficiently mitigate the LED nonlinearity. With the N-TDE the modulation index (MI) and BER performance can be significantly enhanced.

Adaptive Nonlinear Equalizer Using a Mixture of Gaussian-Based Online Density Estimator

This paper introduces a new adaptive nonlinear equalizer relying on a radial basis function (RBF) model, which is designed based on the minimum bit error rate (MBER) criterion, in the system setting of the intersymbol interference channel plus cochannel interference (CCI). Our proposed algorithm is referred to as the online mixture of Gaussian-estimator-aided MBER (OMG-MBER) equalizer. Specifically, a mixture of Gaussian-based probability density function (pdf) estimator is used to model the pdf of the decision variable, for which a novel online pdf update algorithm is derived to track the incoming data. With the aid of this novel online mixture of Gaussian-based sample-by-sample updated pdf estimator, our adaptive nonlinear equalizer is capable of updating its equalizer's parameters sample by sample to aim directly at minimizing the RBF nonlinear equalizer's achievable bit error rate (BER). The proposed OMG-MBER equalizer significantly outperforms the existing online nonlinear MBER equalizer, known as the least bit error rate equalizer, in terms of both the convergence speed and the achievable BER, as is confirmed in our simulation study.

Adaptive nonlinear Volterra equalizer for mitigation of chirp-induced distortions in cost effective IMDD OFDM systems

We report experimental validations of an adaptive 2nd order Volterra equalization scheme for cost effective IMDD OFDM systems. This equalization scheme was applied to both uplink and downlink transmission. Downlink settings were optimized for maximum bitrate where we achieved 34 Gb/s over 10 km of SSMF using an EML with 10 GHz bandwidth. For the uplink, maximum reach was optimized achieving 14 Gb/s using a low-cost DML with 2.5 GHz bandwidth.

A novel joint-processing adaptive nonlinear equalizer using a modular recurrent neural network for chaotic communication systems

To eliminate nonlinear channel distortion in chaotic communication systems, a novel joint-processing adaptive nonlinear equalizer based on a pipelined recurrent neural network (JPRNN) is proposed, using a modified real-time recurrent learning (RTRL) algorithm. Furthermore, an adaptive amplitude RTRL algorithm is adopted to overcome the deteriorating effect introduced by the nesting process. Computer simulations illustrate that the proposed equalizer outperforms the pipelined recurrent neural network (PRNN) and recurrent neural network (RNN) equalizers.

Adaptively Combined FIR and Functional Link Artificial Neural Network Equalizer for Nonlinear Communication Channel

This paper proposes a novel computational efficient adaptive nonlinear equalizer based on combination of finite impulse response (FIR) filter and functional link artificial neural network (CFFLANN) to compensate linear and nonlinear distortions in nonlinear communication channel. This convex nonlinear combination results in improving the speed while retaining the lower steady-state error. In addition, since the CFFLANN needs not the hidden layers, which exist in conventional neural-network-based equalizers, it exhibits a simpler structure than the traditional neural networks (NNs) and can require less computational burden during the training mode. Moreover, appropriate adaptation algorithm for the proposed equalizer is derived by the modified least mean square (MLMS). Results obtained from the simulations clearly show that the proposed equalizer using the MLMS algorithm can availably eliminate various intensity linear and nonlinear distortions, and be provided with better anti-jamming performance. Furthermore, comparisons of the mean squared error (MSE), the bit error rate (BER), and the effect of eigenvalue ratio (EVR) of input correlation matrix are presented.

Functional link neural network cascaded with Chebyshev orthogonal polynomial for nonlinear channel equalization

Nonlinear intersymbol interference (ISI) leads to significant error rate in nonlinear communication and digital storage channel. In this paper, therefore, a novel computationally efficient functional link neural network cascaded with Chebyshev orthogonal polynomial is proposed to combat nonlinear ISI. The equalizer has a simple structure in which the nonlinearity is introduced by functional expansion of the input pattern by trigonometric polynomial and Chebyshev orthogonal polynomial. Due to the input pattern and nonlinear approximation enhancement, the proposed structure can approximate arbitrarily nonlinear decision boundaries. It has been utilized for nonlinear channel equalization. The performance of the proposed adaptive nonlinear equalizer is compared with functional link neural network (FLNN) equalizer, multilayer perceptron (MLP) network and radial basis function (RBF) along with conventional normalized least-mean-square algorithms (NLMS) for different linear and nonlinear channel models. The comparison of convergence rate, bit error rate (BER) and steady state error performance, and computational complexity involved for neural network equalizers is provided.

Adaptive nonlinear channel equalization based on combination neural network for chaos-based communication systems

For nonlinear channel distortions of chaos-based communication systems，based on the analysis of the theory of chaotic signal reconstruction and the characteristics of transversal filter and functional link neural network (FLNN)，a novel nonlinear adaptive equalizer with the architecture of combination of transversal filter and functional link neural network (CFFLNN) is proposed in this paper. The novel nonlinear equalizer fully utilizes faster convergence characteristics of transversal filter and the nonlinear approximation capability of FLNN by function expansion due to enhanced input space. Furthermore，the performance of the novel nonlinear adaptive equalizer is also improved. Finally，the proposed equalizer is designed and its adaptive algorithm is deduced by the low complexity normalized least mean square (NLMS) method. And an analysis of stability and convergence for the derived algorithm is provided. To illustrate the analysis，results obtained from the computer simulation are also provided for both linear and nonlinear channels in chaos-based communication system.

Adaptive neural Legendre orthogonal polynomial nonlinear channel equalization for chaos-based communications systems

The performance of chaos-based communications systems is greatly affected by many sorts of nonlinear distortions. If nonlinear distortions in the channel can be removed, the performance of chaos-based communications systems can be improved. According to analysis of Volterra filter, a novel structure of neural network Legendre orthogonal polynomial equalizer is proposed based on the theory of chaotic signal reconstruction. Combining the characteristic of single layer neural network and structure of Legendre orthogonal polynomial, the equalizer is designed and realized after the analysis of a few parameter nonlinear filters, and adaptive algorithm is deduced using the normalized least mean square algorithm. To support the analysis, simulation results for nonlinear chaos-based communication channel are provided.

Adaptive Pre- and Post-Compensation of Nonlinear Distortions for High-Level Data Modulations

In this letter, we show how different signal processing techniques can be combined to optimize the performance of a typical wideband nonlinear satellite link with spectrally efficient high-level modulation techniques. In particular, we follow two concurrent approaches: on one side, we pursue signal optimization in the form of special amplitude and phase shift keying (APSK) constellations to reduce the effect of nonlinear distortions, while on the other, we analyze the feasibility of adaptive data predistortion (DP) at the transmitter and adaptive nonlinear equalization (NLE) at the receiver. We demonstrate that the use of such optimized constellations relieves the complexity of the nonlinearity compensation techniques, and we also show that by clever adoption of these techniques the sensitivity to nonlinear distortion of both uncoded and turbo coded quadrature amplitude modulation and APSK constellations is greatly reduced.

Fuzzy techniques for adaptive nonlinear equalization

This paper presents a review of the application of fuzzy filters to nonlinear channel equalization problem. The paper presents the development of fuzzy filters for channel equalization applications first. The close relationship between the fuzzy equalizers and the equalizer based on maximum a posteriori probability principle (MAP) is derived. The MAP equalizers are also called Bayesian equalizers since their decision function is based on Bayes’ decision theory. It is shown that the fuzzy implementation of the MAP equalizer provides major computational advantages. The structure of this fuzzy equalizer also provides scope for co-channel interference (CCI) suppression in the presence of inter symbol interference (ISI) and additive white Gaussian noise (AWGN) with the help of a pre-processor. The advantages associated with the fuzzy equalizers can make them a candidate for mobile communication applications.

Combined channel estimation and data detection using soft statistics for frequency-selective fast-fading digital links

A novel adaptive nonlinear equalizer for fast time-varying multipath channels that combines the channel estimation and data detection tasks is presented. The a posteriori probabilities (APPs) of the states of the intersymbol interference (ISI) channel are recursively computed from the received data by a symbol-by-symbol (SbS) detector and are then employed by a Kalman-type nonlinear channel estimator. Robust channel tracking and good data-detection performance are obtained, with a reasonable receiver complexity.

Adaptive nonlinear equalizer with reduced computational complexity

This paper presents an approach of adaptive nonlinear equalization having much less computational complexity than existing nonlinear equalizers. The proposed equalizer first estimates many local regions in the symbol decision space, and then performs a biased finite impulse response filtering in each estimated local region. The final estimate of the transmitted symbol is obtained by a weighted average of the local results. By using a self-organizing and localized linear tuning methods, the proposed nonlinear equalizer can achieve an almost optimal decision making capability like the existing nonlinear equalizers. Simulation results show that the proposed equalizer can be effectively applied to on-line adaptation environments due to its reduced computational complexity, making complexity similar to that of a linear equalizer.