Nonlinear Communication Channels Research Articles

Nonlinear Spectrum of Conventional OFDM and WDM Return-to-Zero Signals in Nonlinear Channel

The nonlinear Schrödinger equation (NLSE) is often used as a master path-average model for fiber-optic links to analyze fundamental properties of such nonlinear communication channels. Transmission of a signal in nonlinear channels is conceptually different from linear communications. We use here the NLSE channel model to explain and illustrate some new unusual features introduced by nonlinearity. In general, NLSE describes the co-existence of dispersive (continuous) waves and localized (here in time) waves: soliton pulses. The nonlinear Fourier transform method allows one to compute for any given temporal signal the so-called nonlinear spectrum that defines both continuous spectrum (analog to conventional Fourier spectral presentation) and solitonic components. Nonlinear spectrum remains invariant during signal evolution in the NLSE channel. We examine conventional orthogonal frequency-division multiplexing (OFDM) and wavelength-division multiplexing (WDM) return-to-zero signals and demonstrate that both signals at certain power levels have soliton component. We would like to stress that this effect is completely different from the soliton communications studied in the past. Applying Zakharov-Shabat spectral problem to a single WDM or OFDM symbol with multiple sub-carriers, we quantify the effect of statistical occurrence of discrete eigenvalues in such an information-bearing optical signal. Moreover, we observe that at signal powers optimal for transmission, an OFDM symbol with high probability has a soliton component.

Investigation of Nonlinear Communication Channel with Small Dispersion via Stochastic Correlator Approach

We consider the optical fiber channel modelled by the nonlinear Schrödinger equation with additive white Gaussian noise and with large signal-to-noise ratio. For the small dispersion case we present the approach to analyze the stochastic nonlinear Schrödinger equation. Taking into account the averaging procedure (frequency filtering) of the output signal detector we find the first corrections in small dispersion parameter to the correlators of the input signal recovered by the backward propagation. These correlators are the important ingredients for the calculation of the channel capacity and the optimal input signal distribution. We assert that the information channel characteristics essentially depend on the procedures of the output signal filtering and the recovery of the transmitted signal.

Self-Interference Cancellation for Shared Band Transmission in Nonlinear Satellite Communication Channels

Self-Interference Cancellation for Shared Band Transmission in Nonlinear Satellite Communication Channels

Calculation of mutual information for nonlinear communication channel at large signal-to-noise ratio.

Using the path-integral technique we examine the mutual information for the communication channel modeled by the nonlinear Schrödinger equation with additive Gaussian noise. The nonlinear Schrödinger equation is one of the fundamental models in nonlinear physics, and it has a broad range of applications, including fiber optical communications-the backbone of the internet. At large signal-to-noise ratio we present the mutual information through the path-integral, which is convenient for the perturbative expansion in nonlinearity. In the limit of small noise and small nonlinearity we derive analytically the first nonzero nonlinear correction to the mutual information for the channel.

고차 QAM 시스템에서 AV-MMA 적응 등화 알고리즘의 성능 평가

This paper relates with the eualization performance of Adaptive Varying-MMA (AV-MMA) in order to the minimization of intersymbol interference that is occurs in the nonlinear communication channel. In order to obtain the error signal in the tap coefficient updating process of adaptive equalization algorithm, the present MMA uses the constant modulus. But in AV-MMA, the adaptively varying modulus are used according to the equalizer output, it is possible to reduce the error signal and possbile to improving the overall equalization performance. In order to improved equalization performance of the AV-MMA in the 64-QAM signal, the present MMA performance were compared. For this, the output signal constellation of equalizer, residual isi, maximum distortion, MSE and SER curves are applied. As a result of computer simulation, the AV-MMA has more better performance in the every performance index than MMA, and the SER performance shows that it has more robustness in high SNR environmnet compared to MMA.

Identification of Fifth-order Wiener and Hammerstein Channels based on the Estimation of an Associated Volterra Kernel

In this paper, we consider the problem of identification of fifthorder Wiener and Hammerstein nonlinear communication channels using the estimation of an associated Volterra kernel. We exploit the special form of the fifth-order associated Volterra kernel for deriving two algorithms that allow to estimate the parameters of the linear part of these channels. In the case of a Wiener channel, the associated Volterra kernel is a tensor satisfying a rank-one PARAFAC decomposition whose the parameters can be estimated by means of an alternating least squares (ALS) algorithm. In the case of a Hammerstein channel, its associated Volterra kernel is a diagonal tensor, which leads to a closed-form solution for estimating the parameters of the linear block. The coefficients of the nonlinear block modeled as a fifth degree polynomial are then estimated by means of the standard non recursive least squares (LS) algorithm. The performance of the proposed identification methods is illustrated by means of Monte Carlo simulation results.

Information-theoretic analysis of iterated Bayesian acoustic source localization in a static ocean waveguide.

Fundamental constructs of information theory are applied to quantify the performance of iterated (sequential) Bayesian localization of a time-harmonic source in a range- and time-invariant acoustic waveguide using the segmented Fourier transforms of the received pressure time series. The nonlinear relation, defined by acoustic propagation, between the source location and the received narrowband spectral components is treated as a nonlinear communication channel. The performance analysis includes mismatch between the acoustic channel and the model channel on which the Bayesian inference is based. Source location uncertainty is quantified by the posterior probability density of source location, by the posterior entropy and associated uncertainty area, by the information gain (relative entropy) at each iteration, and by large-ensemble limits of these quantities. A computational example for a vertical receiver array in a shallow-water waveguide is presented with acoustic propagation represented by normal modes and ambient noise represented by a Kuperman-Ingenito model. Performance degradation due to noise-model mismatch is quantified in an example. Potential extensions to uncertain and stochastic environments are discussed.

QAM 시스템에서 Constellation Matching-MMA 적응 등화 알고리즘의 성능 평가

This paper relates with the eualization performance of Constellation Matching-MMA (CM-MMA) in order to the consists of optimum receiver for the minimization of intersymbol interference and additive noise effects that is occurs in the nonlinear communication channel. The error signal were obtained that combines the Constellation Matching technique that inserts the zero point between the signal point of equalizer for improving the residual isi and convergence speed compared to the currently used MMA algorithm. In the initial state of adaptive equalization, it depends on the MMA characteristics mainly. And in the steady state, it depends on the CM characteristics mainly. In order to analyzing the equalization performance, the output signal constellation, residual isi, maximum distortion, MSE and SER were applied, then it were compared with the present MMA algorithm. As a result of computer simulation, the CM-MMA has more better performance in the every performance index, and it was also confirmed that the constellation matching effect can be obtained in the greater than 20dB signal to noise ratio.

QAM 신호에서 Constellation Reduction을 이용한 MMA 적응 등화 알고리즘의 성능 개선

This paper related with the CR-MMA which is possible to improving the equalization performance by applying the concept of constellation reduction in the MMA adaptive equalization alogorithm in order to reduce the intersymbol interference that is occurred in the nonlinear communication channel. In the updating process of MMA adaptive equalizer, the error signal is being obtained by using the equalizer output, and the performance will be degraded by the increase the error signal in the high order QAM constellation. But by using the constellation reduction, the high order QAM signal will be changed to the 4-QAM signal constellation and then the error signal will be obtained. By doing so, the error signal will be minimized and it is possible to improve the equalization performance in the high order QAM transmitted signal. The Computer simulation was performed in order to compare the performance of the proposed CR-MMA algorithm and original MMA algorithm in the same communication channel and noise environment. For this, the recoverd signal constellation which is the output of equalizer, residual isi and MD (Maximum Distortion) learning curve which is represents the convergence performance and SER which is represents the roburstness of noise were used. As a result of simulation, the CR-MMA has more superior to the MMA. And it was confirmed that the CR-MMA has roburstness to the noise in the SER performance.

Nonlinear inverse synthesis and eigenvalue division multiplexing in optical fiber channels.

We scrutinize the concept of integrable nonlinear communication channels, resurrecting and extending the idea of eigenvalue communications in a novel context of nonsoliton coherent optical communications. Using the integrable nonlinear Schrödinger equation as a channel model, we introduce a new approach-the nonlinear inverse synthesis method-for digital signal processing based on encoding the information directly onto the nonlinear signal spectrum. The latter evolves trivially and linearly along the transmission line, thus, providing an effective eigenvalue division multiplexing with no nonlinear channel cross talk. The general approach is illustrated with a coherent optical orthogonal frequency division multiplexing transmission format. We show how the strategy based upon the inverse scattering transform method can be geared for the creation of new efficient coding and modulation standards for the nonlinear channel.

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.

QAM 시스템에서 DSE-MMA 블라인드 등화 알고리즘의 성능 평가

Abstract This paper related with the DSE-MMA (Dithered Sign-Error MMA) that is the simplification of computational arithmetic number in blind equalization algorithm in order to compensates the intersymbol interference which occurs the passing the nonlinear communication channel in the presence of the band limit and phase distortion. The SE-MMA algorithm has a merit of H/W implementation for the possible to reduction of computational arithmetic number using the 1 bit quantizer in stead of multiplication in the updating the equalizer tap weight. But it degradates the overall blind equalization algorithm performance by the information loss at the quantization process compare to the MMA. The DSE-MMA which implements the dithered signed-error concepts by using the dither signal before qualtization are added to MMA, then the improved SNR performance which represents the roburstness of equalization algorithm are obtained. It has a concurrently compensation capability of the amplitude and phase distortion due to intersymbol interference like as the SE-MMA and MMA algorithm. The paper uses the equalizer output signal, residual isi, MD, MSE learning curve and SER curve for the performance index of blind equalization algorithm, and the computer simulation were performed in order to compare the SE-MMA and DSE-MMA applying the same performance index. As a result of simulation, the DSE-MMA can improving the roburstness and the value of every performance index after steady state than the SE-MMA, and confirmed that the DSE-MMA has slow convergence speed which meaning the reaching the seady state from initial state of adaptive equalization filter.

On nonlinear amplifier modeling and identification using baseband Volterra-Parafac models

The baseband Volterra–Parafac model is a useful tool to represent a nonlinear communication channel with a parametric complexity reduced with respect to the full Volterra model. In this paper we include additional symmetry properties of real power amplifier kernels in the equivalent baseband Volterra-Parafac approach in order to gain a further reduction in the number of parameters. To illustrate the new proposal, the parameters of the equivalent baseband Volterra–Parafac representation for a power amplifier are estimated using the complex least mean square algorithm. Comparison of the measured amplifier output and the model prediction for the case of an orthogonal frequency division multiplexing input signal demonstrates a notable model performance.

QAM 시스템에서 SE-MMA 블라인드 적응 등화 알고리즘의 성능

This paper related with the performance of SE-MMA (Signed-Error MMA) that is the reduction of computational operation number in algorithm than MMA blind eualization algorithm which are possible to elimination of intersymbol interferance in the band limited and time dispersive nonlinear communication channel. In MMA algorithm which are possible to reduction of amplitude and phase rotation by intersymbol interference that is occurred in channel without using the training sequence, it uses the error signal that is the difference of the equalizer output and constant modulus, the statisticlly characteristic of transmitted signal. But in SE-MMA, it uses the polarity of the error signal, then it is possible to reduce the updating the tap coefficient and to simplify the H/W implementation. The computer simulation were performed in order to compare the performance of SE-MMA and conventional MMA algorithm. For this, the recovered signal constellation that is the output of the equalizer, the convergence performance by MSE, MD (maximum distortion) and residual isi characteristic learning curve, SER were used. As a result of simulation, the SE-MMA has more fast convergence speed than the MMA. But in the other index after reaching the seady state, it gives more worst performance values in the used index.

Nonlinear communication channels with capacity above the linear Shannon limit

We prove that, under certain conditions, the capacity of an optical communication channel with in-line, nonlinear filtering (regeneration) elements can be higher than the Shannon capacity for the corresponding linear Gaussian white noise channel.

Nonlinear channel modeling and identification using baseband Volterra–Parafac models

Baseband Volterra models are very useful for representing nonlinear communication channels. These models present the specificity to include only odd-order nonlinear terms, with kernels characterized by a double symmetry. The main drawback is their parametric complexity. In this paper, we develop a new class of Volterra models, called baseband Volterra–Parafac models, with a reduced parametric complexity, by using a doubly symmetric Parafac decomposition of high order Volterra kernels viewed as tensors. Three adaptive algorithms are then proposed for estimating the parameters of these models. Some Monte Carlo simulation results are presented to compare the performance of the proposed estimation algorithms, in the case of third-order baseband Volterra systems excited by PSK and QAM inputs.

Estimation of cubic nonlinear bandpass channels in orthogonal frequency-division multiplexing systems

Modeling and compensation of nonlinear communication channels has long been an important research topic in digital communications. A nonlinear bandpass channel is commonly modeled by a baseband equivalent Volterra series which relates the complex envelopes of the channel input and output. In this paper, we propose a novel method to estimate the frequency-domain baseband equivalent Volterra kernels of cubically nonlinear bandpass channels in orthogonal frequencydivision multiplexing (OFDM) systems. We recognize that the input signal for an OFDM system employing QAM or PSK modulations satisfies the properties of a kind of random multisine signal. By exploring the higher-order auto-moment spectra of the random multisine signal, a computationally efficient algorithm for determining the frequency-domain baseband equivalent Volterra kernels is derived. The obtained kernel estimates are optimal in the minimum mean square error (MMSE) sense. The proposed method can be used to estimate nonlinear bandpass channels for OFDM systems employing pure QAMs, pure PSKs, or a mixture of QAMs and PSKs. The effectiveness of the proposed method is demonstrated by applying it to estimate the nonlinear bandpass channel of an example OFDM system. Nonlinear channel compensators based on the Volterra model can benefit from the proposed method.

MIMO Volterra Modeling for Nonlinear Communication Channels

Multiple-input multiple-output (MIMO) Volterra models have applications in different areas, including telecommunications. An overview of the modeling of nonlinear communication channels using MIMO Volterra models is presented in this paper. First, the development of an equivalent baseband discrete-time representation of a single-input single-output (SISO) Volterra system is carried out. This development constitutes the basis for several versions of discrete-time equivalent baseband MIMO Volterra systems presented in the sequel. The spectral broadening provided by a Volterra system on the equivalent baseband received signals is shown by calculating the frequency domain representation of the Volterra channel output. Some important block structured nonlinear MIMO models are also described, with their link to MIMO Volterra models. Finally, some applications of such models for communication systems are briefly discussed.

Nonlinear channel equalization for wireless communication systems using Legendre neural networks

In this paper, we present a computationally efficient neural network (NN) for equalization of nonlinear communication channels with 4-QAM signal constellation. The functional link NN (FLANN) for nonlinear channel equalization which we had proposed earlier, offers faster mean square error (MSE) convergence and better bit error rate (BER) performance compared to multilayer perceptron (MLP). Here, we propose a Legendre NN (LeNN) model whose performance is better than the FLANN due to simple polynomial expansion of the input in contrast to the trigonometric expansion in the latter. We have compared the performance of LeNN-, FLANN- and MLP-based equalizers using several performance criteria and shown that the performance of LeNN is superior to that of MLP-based equalizer, in terms of MSE convergence rate, BER and computational complexity, especially, in case of highly nonlinear channels. LeNN-based equalizer has similar performance as FLANN in terms of BER and convergence rate but it provides significant computational advantage over the FLANN since the evaluation of Legendre functions involves less computation compared to trigonometric functions.

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.