Showing papers on "Volterra series published in 2021"

Soft-Demapping for Short Reach Optical Communication: A Comparison of Deep Neural Networks and Volterra Series

Abstract: In optical fiber communication, optical and electrical components introduce nonlinearities, which require effective compensation to attain highest data rates. In particular, in short reach communication, components are the dominant source of nonlinearities. Volterra series are a popular countermeasure for receiver-side equalization of nonlinear component impairments and their memory effects. However, Volterra equalizer architectures are generally very complex. This article investigates soft deep neural network (DNN) architectures as an alternative for nonlinear equalization and soft-decision demapping. On coherent 92GBd dual polarization 64QAM back-to-back measurements performance and complexity is experimentally evaluated. The proposed bit-wise soft DNN equalizer (SDNNE) is compared to a 5th order Volterra equalizer at a 15% overhead forward error correction (FEC) limit. At equal performance, the computational complexity is reduced by 65%. At equal complexity, the performance is improved by 0.35 dB gain in optical signal-to-noise-ratio (OSNR).

200-m/500-Mbps underwater wireless optical communication system utilizing a sparse nonlinear equalizer with a variable step size generalized orthogonal matching pursuit.

Abstract: Linear and nonlinear impairments in underwater wireless optical communication (UWOC) systems caused by the limited bandwidth and nonlinearity of devices severely degrade the system performance. In this paper, we propose a sparse Volterra series model-based nonlinear post equalizer with greedy algorithms to mitigate the nonlinear impairments and the inter-symbol interference (ISI) in a UWOC system. A variable step size generalized orthogonal matching pursuit (VSgOMP) algorithm that combines generalized orthogonal matching pursuit (gOMP) and adaptive step size method is proposed and employed to compress the Volterra equalizer with low computational cost. A maximum data rate of 500 Mbps is realized with the received optical power of −32.5 dBm in a 7-m water tank. In a 50-m swimming pool, a data rate of 500 Mbps over 200-m underwater transmission is achieved with a BER lower than the forward error correction (FEC) threshold of 3.8 × 10−3. The number of kernels of the sparse Volterra equalizer is reduced to 70% of that of the traditional Volterra equalizer without significant BER performance degradation. Compared with orthogonal matching pursuit (OMP) scheme and regularized orthogonal match pursuit (ROMP) scheme, the VSgOMP scheme reduces the running time by 68.6% and 29.2%, respectively. To the best of our knowledge, this is the first time that a sparse Volterra equalizer combined with VSgOMP algorithm is employed for the nonlinear equalization in a long-distance high-speed UWOC system.

On Bilinear Time-Domain Identification and Reduction in the Loewner Framework

Abstract: The Loewner framework (LF) in combination with Volterra series (VS) offers a non-intrusive approximation method that is capable of identifying bilinear models from time-domain measurements. This method uses harmonic inputs which establish a natural way for data acquisition. For the general class of nonlinear problems with VS representation, the growing exponential approach allows the derivation of the generalized kernels, namely, symmetric generalized frequency response functions (GFRFs). In addition, the homogeneity of the Volterra operator determines the accuracy in terms of how many kernels are considered. For the weakly nonlinear setup, only a few kernels are needed to obtain a good approximation. In this direction, the proposed adaptive scheme is able to improve the estimations of the computationally nonzero kernels. The Fourier transform associates these measurements with the derived GFRFs and the LF makes the connection with system theory. In the linear case, the LF associates the so-called S-parameters with the linear transfer function by interpolating in the frequency domain. The goal of the proposed method is to extend identification to the case of bilinear systems from time-domain measurements and to approximate other general nonlinear systems (by means of the Carleman bilinearizarion scheme). By identifying the linear contribution with the LF, a considerable reduction is achieved by means of the SVD. The fitted linear system has the same McMillan degree as the original linear system. Then, the performance of the linear model is improved by augmenting a special nonlinear structure. In a nutshell, we learn reduced-dimension bilinear models directly from a potentially large-scale system that is simulated in the time domain. This is done by fitting first a linear model, and afterward, by fitting the corresponding bilinear operator.

Discrete-Time Signatures and Randomness in Reservoir Computing

Abstract: A new explanation of the geometric nature of the reservoir computing (RC) phenomenon is presented RC is understood in the literature as the possibility of approximating input-output systems with randomly chosen recurrent neural systems and a trained linear readout layer Light is shed on this phenomenon by constructing what is called strongly universal reservoir systems as random projections of a family of state-space systems that generate Volterra series expansions This procedure yields a state-affine reservoir system with randomly generated coefficients in a dimension that is logarithmically reduced with respect to the original system This reservoir system is able to approximate any element in the fading memory filters class just by training a different linear readout for each different filter Explicit expressions for the probability distributions needed in the generation of the projected reservoir system are stated, and bounds for the committed approximation error are provided

Bayesian Optimization for Nonlinear System Identification and Pre-Distortion in Cognitive Transmitters

Abstract: We present a digital signal processing (DSP) scheme that performs hyperparameter tuning (HT) via Bayesian optimization (BO) to autonomously optimize memory tap distribution of Volterra series and adapt parameters used in the synthetization of a digital pre-distortion (DPD) filter for optical transmitters. Besides providing a time-efficient technique, this work demonstrates that the self-adaptation of DPD hyperparameters to correct the component-induced nonlinear distortions as different driver amplifier (DA) gains, symbol rates and modulation formats are used, leads to an improvement in transmitter performance. The scheme has been validated in back-to-back (b2b) experiments using dual-polarization (DP) 64 and 256 quadrature amplitude modulation (QAM) formats, and symbol rates of 64 and 80 GBd. For DP-64QAM at 64 GBd, it is shown that the DPD scheme reduces the required optical signal-to-noise ratio (OSNR) at a bit error ratio of 10-2 by 0.9 dB and 0.6 dB with respect to linear DPD and a heuristic nonlinear DPD approach, respectively. Moreover, we show that the proposed approach also reduces filter complexity by 75% in conjunction with the use of memory polynomials (MP), while achieving a similar performance to Volterra pre-distortion filters.

Model order reduction for bilinear control systems with inhomogeneous initial conditions

Abstract: This work focuses on the model order reduction problem for bilinear control systems with nonzero initial conditions. Based on the Volterra series analysis, the system response can be decomposed int...

Integral Equations Related to Volterra Series and Inverse Problems: Elements of Theory and Applications in Heat Power Engineering

Abstract: The paper considers two types of Volterra integral equations of the first kind, arising in the study of inverse problems of the dynamics of controlled heat power systems. The main focus of the work is aimed at studying the specifics of the classes of Volterra equations of the first kind that arise when describing nonlinear dynamics using the apparatus of Volterra integro-power series. The subject area of the research is represented by a simulation model of a heat exchange unit element, which describes the change in enthalpy with arbitrary changes in fluid flow and heat supply. The numerical results of solving the problem of identification of transient characteristics are presented. They illustrate the fundamental importance of practical recommendations based on sufficient conditions for the solvability of linear multidimensional Volterra equations of the first kind. A new class of nonlinear systems of integro-algebraic equations of the first kind, related to the problem of automatic control of technical objects with vector inputs and outputs, is distinguished. For such systems, sufficient conditions are given for the existence of a unique, sufficiently smooth solution. A review of the literature on these problem types is given.

Incoherent Laser Heterodyned Long-Reach 60-GHz MMWoF Link With Volterra Filtered 16-QAM OFDM Beyond 13 Gbps

Abstract: By remotely heterodyning two independent laser carriers, the long-reach 60-GHz millimeter-wave-over-fiber (MMWoF) link is demonstrated for the Volterra series filtered quadrature amplitude modulation orthogonal frequency division multiplexing (QAM-OFDM) transmission with nonlinear noise suppression, which enables 13-Gbps data delivery through 50-km single-mode fiber (SMF) and 3-m free-space links A wavelength tunable colorless laser diode transmits the Volterra filter equalized QAM-OFDM data to remotely couple with a localized single-mode laser carrier at the optical receiving end of the MMWoF system Such an incoherently coupled dual-mode carrier facilitates the optical single-carrier modulation to suppress chromatic dispersion induced power fading effect of the SMF transmitted QAM-OFDM data The 2nd+3rd-order nonlinear noise induced by direct modulation, heterodyne conversion, and phase fluctuation of the incoherently coupled dual-mode carrier is corrected with the Volterra filter equalization to upgrade the decoded signal-to-noise ratio (SNR) by >2 dB After remotely heterodyning the downstream and the localized carriers with mutual incoherence in between, the 16-QAM OFDM transmission at a data rate up to 132 Gbps is successfully delivered over 3-m wireless link, which reveals the FEC certificated error vector magnitude of 141%, SNR of 17 dB, and bit error rate of 17 × 10−3

A bivariate Volterra series approach to modeling and linearization of power amplifiers

Abstract: A bivariate Volterra series perspective is adopted for a generic power amplifier (PA) modeling. This approach is motivated by the presence of a PA mechanism responsible of an internal signal generation. The bivariate resulting model extends a conventional Volterra model by including terms containing cross products of the input signal and the new internal variable. The approach is developed considering a simple univariate Volterra model and the signal envelope as the internal variable. The enriched structure incorporates new terms with the envelope raised to odd powers. A particular case of this bivariate Volterra series approach is the generalized memory polynomial model. The convenience of the bivariate terms in the model structure of a class J PA is experimentally demonstrated for the amplifier driven by a 30-MHz 5G New Radio signal, over a range of more than 13 dB output power levels. Results for the digital predistortion of the class J PA are also provided, illustrating as well the benefits of the bivariate model for the linearization performance.

Phase-based order separation for Volterra series identification

Abstract: This article addresses the identification of nonlinear systems represented by Volterra series. To improve the robustness of some existing methods, we propose a pre-processing stage that separates n...

A Circuit-Inspired Digital Predistortion of Supply Network Effects for Capacitive RF-DACs

Abstract: This article presents a novel digital predistortion (DPD) approach to compensate for nonlinear dynamic distortions caused by the supply network of capacitive radio frequency digital-to-analog converters (RF-DACs). The developed DPD concept recreates the voltage distortion on the RF-DAC’s supply network and modulates the input signal such that the effects on the output signal of the RF-DAC are canceled. In contrast to conventional DPD approaches such as pruned Volterra series or memory polynomials, the complexity of the proposed concept is reduced to a feasible level, allowing for implementation in integrated circuits. Furthermore, the derived DPD model allows to use linear estimation algorithms for coefficient training. The presented DPD is demonstrated by measurements of two different capacitive RF-DAC designs and compared with conventional DPD approaches. EVM and adjacent channel power ratio (ACPR) can be improved by up to 6 and 7 dB, respectively, outperforming conventional approaches.

An Efficient QAM Detector via Nonlinear Post-Distortion Based on FDE Bank Under PA Impairments

Abstract: In this paper, we propose a receiver structure for single-carrier uplink transmission with frequency domain equalization (FDE) that is exposed to power amplifier (PA) nonlinearities. A two-stage approach is adopted, in which linear communication channel is equalized at the first stage, and it is followed by post-distortion, where nonlinear distortion is reduced. In the literature, nonlinear processing techniques are proposed, which perform memoryless compensation of nonlinear distortion together with FDE. However, in this study, we show that even if memoryless nonlinearity exists, the received signal is impaired by nonlinear inter-symbol-interference. Therefore, we propose a class of symbol rate post-distortion techniques, which use neighboring received symbols to suppress the nonlinear interference. Three different post-distortion methods, Gaussian process regression (GPR), neural network (NN) and Volterra series (VS) based post-distorters, are considered. Also, a combiner, which intelligently combines the outputs of fractional delayed bank of FDE’s after post-distortion, is proposed to overcome performance degradation of FDE for frequency selective channels under nonlinear distortion. Performances of the proposed techniques are compared with state-of-the-art approaches in terms of bit error rate (BER) and achievable information rate (AIR) metrics. Simulation results demonstrate that post-distortion methods together with bank of FDE outperform state-of-the-art techniques.

A Higher Order Manifold-Valued Convolutional Neural Network with Applications to Diffusion MRI Processing.

Abstract: In this paper, we present a novel generalization of the Volterra Series, which can be viewed as a higher-order convolution, to manifold-valued functions. A special case of the manifold-valued Volterra Series (MVVS) gives us a natural extension of the ordinary convolution to manifold-valued functions that we call, the manifold-valued convolution (MVC). We prove that these generalizations preserve the equivariance properties of the Euclidean Volterra Series and the traditional convolution operator. We present novel deep network architectures using the MVVS and the MVC operations which are then validated via two experiments. These include, (i) movement disorder classification from diffusion magnetic resonance images (dMRI), and (ii) fiber orientation distribution function (fODF) reconstruction from compressed sensed dMRIs. In both the experiments, MVVS and MVC networks outperform the state-of-the-art.

Convolution and Volterra Series Approach to Reduced-Order Modeling of Unsteady Aerodynamic Loads

Abstract: A combined approach of linear convolution and higher-order Volterra series (VS) to reduced-order modeling of unsteady transonic aerodynamic loads is presented. Our framework offers a simple method ...

Identification and Parameter Estimation of Asymmetric Nonlinear Damping in a Single-Degree-of-Freedom System Using Volterra Series

Abstract: Most of the dynamic systems are inherently nonlinear either with stiffness nonlinearity or with damping nonlinearity. Presence of nonlinearity often leads to characteristic behaviours in response such as jump phenomenon, limit cycle and super-harmonic resonances. Such behviours can be accurately predicted only if the nonlinearity structure and related parameters are properly known. A majority of identification works is based on a-priori knowledge of nonlinearity structure and most of them consider only stiffness nonlinearities. Not much work has been reported on identification and parameter estimation in the area of damping nonlinearities. This paper presents a systematic classification of asymmetric damping nonlinearity and develops a parameter estimation algorithm using harmonic excitation and response amplitudes in terms of higher order Frequency Response Functions. The asymmetry in damping nonlinearity is modeled as a polynomial function containing square and cubic nonlinear terms and then Volterra series is employed to derive the response amplitude formulation for different harmonics using synthesied higher order Frequency Response Functions. Detailed numerical study is carried out with different combinations of square and cubic nonlinearity parameters to investigate appropriate excitation level and frequency so as to get measurable signal strength of second and third harmonics and at the same time keeping the Volterra series approximation error low. The estimation algorithm is first presented for nonlinear parameters and then it is extended for estimation of linear parameters including damping ratio. It is demonstrated through numerical simulation that nonlinear damping parameters can be accurately estimated with proper selection of excitation level and frequency.

A New Block-Oriented Model for Reduced Complexity Digital Predistortion in Wideband Applications

Abstract: Power Amplifier (PA) linearization by Digital Pre-Distortion (DPD) using baseband signals is one of the most popular methods for improving wireless transmission systems' efficiency. This research addresses this problem by focusing on reducing the DPD complexity without compromising the linearization system's efficiency. This contribution consists of a DPD structure with memory effects based on the Feed-backed Wiener (FW) system, which results in a pruned Volterra series. A FIR filter is used as a feedback path to compensate for the PA memory effects. The proposed structure is used to linearize an LDMOS PA (50 W - 500 MHz to 2.5 GHz) in the case of LTE/4G signals with different bandwidths and output powers. A comparison in terms of DPD identification and PA linearization performances between the proposed model and the Generalized Memory Polynomial (GMP) model shows that the proposed model presents similar performances, with the advantage of reduced complexity.

Hysteresis Modeling of Magnetic Shape Memory Alloy Actuator Based on Volterra Series

Abstract: Magnetic shape memory alloy-based actuator (MSMA-BA) has the capability to generate the micro–nano-scale precision positioning, which has unparalleled virtue in contrast with the traditional motion driving mechanism. Nevertheless, the output displacement of the MSMA-BA exhibits complex hysteresis nonlinearity, which hinders its utility in the high-precision positioning field. In this article, an online Volterra series model based on wavelet neural network (VSM-WNN) is proposed to describe the rate-dependent hysteresis of the MSMA-BA. The kernel function of the VSM is extracted with a WNN, in which the feasibility of this extraction is proved in theory via Taylor expansion of the wavelet function. Finally, the validity of the proposed model is confirmed by means of experiments. Experimental results indicate that the VSM-WNN has a remarkable performance in describing the traits of hysteresis behavior of the MSMA-BA.

Input/output reduced model of a damped nonlinear beam based on Volterra series and modal decomposition with convergence results

Abstract: This paper addresses the model reduction and the simulation of a damped Euler–Bernoulli–von Karman pinned beam excited by a distributed force. This nonlinear problem is formulated as a PDE and reformulated as a well-posed state-space system. The model order reduction and simulation are derived by combining two approaches: a Volterra series expansion and truncation and a pseudo-modal truncation defined from the eigenbasis of the linearized problem. The interest of this approach lies in the large class of input waveshapes that can be considered and in the simplicity of the simulation structure. This structure only involves cascades of finite-dimensional decoupled linear systems and multilinear functions. Closed-form bounds depending on the model coefficients and the truncation orders are provided for the Volterra convergence domain and the approximation error. These theoretical results are generalized to a large class of nonlinear models, and refinement of bounds are also proposed for a large sub-class. Numerical experiments confirm that the beam model is well approximated by the very first Volterra terms inside the convergence domain.

Robust Flow Field Signal Estimation Method for Flow Sensing by Underwater Robotics

Abstract: The flow field is difficult to evaluate, and underwater robotics can only partly adapt to the submarine environment. However, fish can sense the complex underwater environment by their lateral line system. In order to reveal the fish flow sensing mechanism, a robust nonlinear signal estimation method based on the Volterra series model with the Kautz kernel function is provided, which is named KKF-VSM. The flow field signal around a square target is used as the original signal. The sinusoidal noise and the signal around a triangular obstacle are considered undesired signals, and the predicting performance of KKF-VSM is analyzed after introducing them locally in the original signals. Compared to the radial basis function neural network model (RBF-NNM), the advantages of KKF-VSM are not only its robustness but also its higher sensitivity to weak signals and its predicting accuracy. It is confirmed that even for strong nonlinear signals, such as pressure responses in the flow field, KKF-VSM is more efficient than the commonly used RBF-NNM. It can provide a reference for the application of the artificial lateral line system on underwater robotics, improving its adaptability in complex environments based on flow field information.

Sum-capacity of Uplink Multiband Satellite Communications with Nonlinear Impairments

Abstract: A compact and closed-form expression of capacity is derived for an uplink multiband satellite system in the presence of nonlinear interference. The nonlinear effect comes from the satellite high-power amplifier modeled by a Volterra series expansion. The derivations reveal that the nonlinear interference can provide a constructive power contribution that could be used to increase the transmission rate. Consequently, decoders designed by viewing this interference as only an additional noise are suboptimal. Numerical results confirm this claim and also show that an appropriate power allocation amongst the subbands may be of interest.

Nonlinear model standardization for the analysis and design of nonlinear systems with multiple equilibria

Abstract: In engineering practice, a nonlinear system stable about several equilibria is often studied by linearizing the system over a small range of operation around each of these equilibria, and allowing the study of the system using linear system methods. Theoretically, for operations beyond a small range but still within the stable regime of an equilibrium, the system behaves nonlinearly, and can be described and investigated using the Volterra series approach. However, there is still no available approach that can systematically transform the model of a nonlinear system into a form that can be studied over the whole stable regime about an equilibrium so as to facilitate the system study using the Volterra series approach. This transformation is, in the present study, referred to as nonlinear model standardization, which is the extension of the well-known concept of linearization to the nonlinear case. In this paper, a novel approach to nonlinear model standardization is proposed for nonlinear systems that can be described by a Nonlinear AutoRegressive model with eXogeneous input (NARX) or a nonlinear differential equation (NDE) model. The proposed approach is then used in three case studies covering the applications in nonlinear system analysis, nonlinear system design, and nonlinearity compensation, respectively, demonstrating the significance of the proposed nonlinear model standardization in a wide range of engineering practices.