Showing papers on "Volterra series published in 2015"

Decomposed Vector Rotation-Based Behavioral Modeling for Digital Predistortion of RF Power Amplifiers

Abstract: A new behavioral model for digital predistortion of radio frequency (RF) power amplifiers (PAs) is proposed in this paper. It is derived from a modified form of the canonical piecewise-linear (CPWL) functions using a decomposed vector rotation (DVR) technique. In this model, the nonlinear basis function is constructed from piecewise vector decomposition, which is completely different from that used in the conventional Volterra series. Theoretical analysis has shown that this model is much more flexible in modeling RF PAs with non-Volterra-like behavior, and experimental results confirmed that the new model can produce excellent performance with a relatively small number of coefficients when compared to conventional models.

Enhanced Performance of a High-Speed WDM CAP64 VLC System Employing Volterra Series-Based Nonlinear Equalizer

Abstract: The light-emitting diode nonlinearity in visible light communication (VLC) systems is considered to be a major problem that deteriorates system performance. In this paper, we experimentally demonstrate a high-speed WDM CAP64 VLC system employing a Volterra series-based nonlinear equalizer to mitigate the nonlinear effect. A modified cascaded multimodulus algorithm (M-CMMA) is utilized to calculate the error function and update the weights of the nonlinear equalizer without using training symbols. An aggregate data rate of 4.5 Gb/s is successfully achieved over 2-m indoor free-space transmission with a bit error rate (BER) below the 7% forward error correction limit of 3.8 × 10 -3 . With the Volterra nonlinear equalizer, the Q factor of the VLC system is 1. 6 dB better than that without using the nonlinear equalizer, and the transmission distance is also increased by about 110 cm at the BER of 3.8 × 10 -3 . To the best of our knowledge, this is the first time that the Volterra nonlinear equalizer is utilized for high-speed carrierless amplitude and phase (CAP) modulation-based VLC systems.

Multipoint Volterra Series Interpolation and $\mathcal{H}_2$ Optimal Model Reduction of Bilinear Systems

Abstract: In this paper, we focus on model reduction of large-scale bilinear systems. The main contributions are threefold. First, we introduce a new framework for interpolatory model reduction of bilinear systems. In contrast to the existing methods where interpolation is forced on some of the leading subsystem transfer functions, the new framework shows how to enforce multipoint interpolation of the underlying Volterra series. Then, we show that the first-order conditions for optimal $\mathcal{H}_2$ model reduction of bilinear systems require multivariate Hermite interpolation in terms of the new Volterra series interpolation framework; thus we extend the interpolation-based first-order necessary conditions for $\mathcal{H}_2$ optimality of LTI systems to the bilinear case. Finally, we show that multipoint interpolation on the truncated Volterra series representation of a bilinear system leads to an asymptotically optimal approach to $\mathcal{H}_2$ optimal model reduction, leading to an efficient model reduction...

Frequency Domain Analysis and Design of Nonlinear Systems based on Volterra Series Expansion: A Parametric Characteristic Approach

Abstract: 1 Introduction.- 2 The Generalized Frequency Response Functions and Output Spectrum of Nonlinear Systems.- 3 Output Frequency Characteristics of Nonlinear Systems.- 4 Parametric Characteristic Analysis (PCA).- 5 The Parametric Characteristics of the GRFRs and the Parametric Characteristics Based Analysis.- 6 The Parametric Characteristics of Nonlinear Output Spectrum and Applications.- 7 The Parametric Characteristics Based Output Spectrum Analysis.- 8 Determination of Nonlinear Output Spectrum Based on its Parametric Characteristics --- Some Theoretical Issues.- 9 Nonlinear Characteristic Output Spectrum for Nonlinear Analysis and Design.- 10 Using Nonlinearity for Output Vibration Suppression: An Application Study.- 11 Mapping from Parametric Characteristics to the GFRFs and Output Spectrum.- 12 Nonlinear Influence in the Frequency Domain: Alternating Series.- 13 Magnitude Bound Characteristics of Nonlinear Frequency Response Functions.- 14 Parametric Convergence Bounds of Volterra-Type Nonlinear Systems.- 15 Summary and Overview.- References. 2 The Generalized Frequency Response Functions and Output Spectrum of Nonlinear Systems.- 3 Output Frequency Characteristics of Nonlinear Systems.- 4 Parametric Characteristic Analysis (PCA).- 5 The Parametric Characteristics of the GRFRs and the Parametric Characteristics Based Analysis.- 6 The Parametric Characteristics of Nonlinear Output Spectrum and Applications.- 7 The Parametric Characteristics Based Output Spectrum Analysis.- 8 Determination of Nonlinear Output Spectrum Based on its Parametric Characteristics --- Some Theoretical Issues.- 9 Nonlinear Characteristic Output Spectrum for Nonlinear Analysis and Design.- 10 Using Nonlinearity for Output Vibration Suppression: An Application Study.- 11 Mapping from Parametric Characteristics to the GFRFs and Output Spectrum.- 12 Nonlinear Influence in the Frequency Domain: Alternating Series.- 13 Magnitude Bound Characteristics of Nonlinear Frequency Response Functions.- 14 Parametric Convergence Bounds of Volterra-Type Nonlinear Systems.- 15 Summary and Overview.- References.

SSBI Mitigation in A-RF-Tone-Based VSSB-OFDM System With a Frequency-Domain Volterra Series Equalizer

Abstract: The analog domain generated radio frequency-tone (A-RF-tone)-based virtual single sideband (VSSB) direct detection (DD) optical orthogonal frequency division multiplexing (OFDM) scheme is employed to eliminate the residual RF-tone image and substantially improve the signal quality after digital-to-analog converter. The VSSB signal is generated by electrically combining the baseband OFDM signals with sinusoidal waves without a frequency guard band to maximize the electrical and optical spectral efficiencies. The input–output relationship of the VSSB DD-OFDM system is represented and modeled as a second-order nonlinear kernel function by using the theory of Volterra series for the first time. The theory of Volterra inverse for the nonlinear system is introduced to analyze and mitigate subcarriers-to-subcarriers beating interference. In this paper, we further compare and analyze the inherent relationship between the iteration interference cancellation technique and Volterra postinverse equalizer, and that between symbol predistortion algorithm and Volterra preinverse equalizer. The analysis results show that the iteration interference cancellation technique can be considered as a second-order Volterra postinverse equalizer with iterative decision feedback, and symbol predistortion algorithm as a special designed second-order Volterra preinverse equalizer with iteration and step size control.

Fully Blind Linear and Nonlinear Equalization for 100G PM-64QAM Optical Systems

Abstract: We demonstrate fully blind processing and reduced-complexity nonlinear equalization (NLE) of a 100G PM-64QAM optical channel in a 50 GHz WDM grid, achieving a maximum reach of 1524 km over pure silica core fiber at a bit error rate of $2.7\times 10^{-2}$ . The equalization of linear polarization-dependent effects is performed by a radius-directed constant modulus algorithm (RD-CMA), enabled by a multiradii training stage, yielding a very small penalty ( $Q$ 2 factor) relatively to data-aided CMA. Applying a simplified Volterra series nonlinear equalizer (simVSNE), operating in the frequency domain, we demonstrate a reach extension of $\sim$ 27% relatively to linear equalization. Due to its lower spatial resolution requirements, the simVSNE technique is shown to provide a more efficient NLE than the well-known back-propagation split-step Fourier method, both in terms of latency and number of complex multiplications per sample. The potential benefit of NLE for fully blind processing of high-order QAM optical signals is demonstrated by an incremental reduction of the RD-CMA penalty to <0.04 dB.

Adaptive high-order nonlinear function approximation using time-domain volterra series to provide flexible high performance digital pre-distortion

Abstract: A method is described for predistorting an input signal to compensate for non-linearities caused to the input signal in producing an output signal. The method comprises: providing an input for receiving a first input signal as a plurality of signal samples, x [n], to be transmitted over a non-linear element; providing at least one digital predistortion block comprising, a plurality of IQ predistorter cells coupled to the input, each comprising a lookup table (LUT) for generating an LUT output The at least one digital predistortion block block is configured to apply interpolation between LUT entries for the, plurality of LUTs; and generate an output signal, y [n], by each of the plurality of IQ predistorter cells by adaptively modifying the first input signal using interpolated LUT entries to compensate for distortion effects in the non-linear element. A combiner may be provided configured to combine the output signal samples, y Q , from the plurality of IQ predistorter cells into a combined signal to generate the output signal, y [n], for transmission to the non-linear element. An error calculation block may be coupled to a digital predistortion adaptation block to determine and modify a predistortion performance.

Time-Domain Volterra-Based Digital Backpropagation for Coherent Optical Systems

Abstract: We propose a novel closed-form time-domain (TD) Volterra series nonlinear equalizer (VSNE) for the mitigation of Kerr-related distortions in polarization-multiplexed (PM) coherent optical transmission systems. The proposed TD-VSNE is obtained from the inverse Fourier analysis of a frequency-domain VSNE based on a frequency-flat approximation. Employing novel TD approximations, we demonstrate the equivalency between the VSNE algorithms formulated in time and frequency domains. In order to enhance the computational efficiency, we insert a power weighting time window in the TD-VSNE, yielding the weighted VSNE (W-VSNE) algorithm. We demonstrate that the convergence of the W-VSNE to its maximum performance is much faster than that of the TD-VSNE, thus requiring fewer parallel filters. Through numerical simulation of a 224-Gb/s PM-16QAM optical channel, we compare the performance/complexity tradeoff of the W-VSNE with the well-known split-step Fourier method (SSFM) and with the computationally optimized weighted SSFM (W-SSFM). Enabled by the use of fewer iterations and only two parallel W-VSNE filters, we demonstrate a reduction of up to $\sim$ 45% on computational effort and $\sim$ 70% on latency, in comparison with the W-SSFM.

Behavioral Modeling of Concurrent Dual-Band Transmitters Based on Radially-Pruned Volterra Model

Abstract: This paper presents a radially-pruned multi-dimensional Volterra model for the modeling and linearization of concurrent dual-band transmitters. The proposed model accounts for the impact of cross-band intermodulation distortions of the dual-band power amplifier (PA) and also the effect of quadrature modulator (QM) imperfections. The performance of the proposed model is validated using a broadband class AB PA driven concurrently by two independent LTE signals at a separation frequency of around 60 MHz, in the presence of in-phase/quadrature $(I/Q) $ modulator imperfections. The measurement results validate the accurate linearization performance of the proposed model in suppressing the adjacent channel power (ACP) , as well as the QM impairments, as compared to other state-of-the-art models.

Distortion Analysis Using Volterra Series and Linearization Technique of Nano-Scale Bulk-Driven CMOS RF Amplifier

Abstract: The distortion analysis of nano-scale bulk-driven (BD) CMOS RF amplifier is presented based on Volterra series. The first three-order Volterra kernels are computed; and the closed-form expressions of the second-order and third-order harmonic distortion (HD) are derived. These expressions give good accuracy comparing with the simulation results, and can provide insight into the nonlinearity of nano-scale BD amplifier. These expressions unveil and demonstrate that the nano-scale BD MOSFET has distinct nonlinear characteristics. Also, distortion-aware design guidelines for nano-meter CMOS BD amplifier are provided. A modified second-order intermodulation $({\rm IM}_{2})$ injection technique is presented to suppress the third-order intermodulation $({\rm IM}_{3})$ product. This modified technique which consumes only 64 $\mu{\rm A}$ current employs phase adjustment of the low-frequency ${\rm IM}_{2}$ ; and up to 20 dB ${\rm IM}_{3}$ reduction is achieved over 1 MHz–20 MHz two-tone spacing range without gain reduction or noise penalty.

An SIMO Nonlinear System Approach to Analysis and Design of Vehicle Suspensions

Abstract: Vehicle suspension (or vibration control) systems are usually inherently nonlinear and can be modeled as single input multiple output (SIMO) system. In this paper, parametric convergence bounds for Volterra series expansion of nonlinear systems described by a SIMO nonlinear auto-regressive with exogenous inputs model are studied in the frequency domain, which can clearly indicate the parametric range in which a given nonlinear system has a convergent Volterra series expansion, referred to as parametric bound of convergence (PBoC). With the resulting PBoC of characteristic parameters, nonlinear systems with a nonlinear multiobjective performance (MOP) function can then be analyzed in the frequency domain using a nonlinear characteristic output spectrum method based on the Volterra series expansion. To demonstrate the results and method above, a vehicle suspension system, which is taken as a typical SIMO nonlinear system with a MOP function to optimize, is investigated. The results demonstrate a systematic and novel method for nonlinear analysis and design.

A Combinatorial Impairment-Compensation Digital Predistorter for a Sub-GHz IEEE 802.11af-WLAN CMOS Transmitter Covering a 10x-Wide RF Bandwidth

Abstract: A new combinatorial impairment-compensation digital predistorter (DPD) for a sub-GHz IEEE 802.11af-WLAN CMOS transmitter (TX) is proposed. For the TX to cover a 10x-wide bandwidth, the DPD implements a modified dynamic deviation reduction (DDR)-based Volterra series to jointly nullify the frequency-dependent I/Q imbalance, counter-intermodulation (CIM) of mixers, and nonlinearities of power amplifier (PA) with memory effect. The interactions of those impairments are firstly analyzed using two Volterra series. After applying the tandem properties of Volterra series, interactions of all impairments can be described in one Volterra series by bonding those impairments in parallel. Coefficients of the DPD are extracted with the Least- Square (LS) estimator, achieving lower running complexity than the existing DPDs, which were developed to handle the PA nonlinearities only. Verifications are based on both system-level simulations and silicon measurements of a 65-nm CMOS TX prototype. When the TX delivers a 6-MHz bandwidth, 2048-point, 64-QAM OFDM signal at $>+$ 10 dBm output power, the measured EVM is $ 3.7% and adjacent channel leakage ratio (ACLR) is $ 40.2 dBc under individual DPD applied at each RF. A novel one-shot calibration for reuse in the entire TV-band is demonstrated also, showing EVM $ 4.2% and ACLR $ 39.8 dBc.

Validation of Volterra Series Approach for Modelling Parametric Rolling of Ships

Abstract: Parametric motion is the phenomenon where a structure is excited into large amplitude motion even when there is no direct excitation. A well-known example of this type of motion is the parametric roll of ships in head or following seas. Parametric roll of container ships in head seas is relatively a new problem which has gained much importance after the catastrophic incidence of APL China in 1998. Although a lot of analytical techniques are available on the assessment of parametric roll in regular excitation, not many investigations have explored its occurrence in irregular seas. A consensus on the stability criteria to assess the danger due to this phenomenon in actual ocean has not yet been reached making it an active area of investigation.A precursor to the development of stability criteria is a simple model to capture the phenomenon of parametric rolling. However, it is important that the model is not over simplified and ignores important dynamics of the process. Therefore it is necessary to perform validation studies between the simplified model and the complete nonlinear model capturing all the physics of the phenomenon.This paper provides the validation studies of a 1-DOF (degree of freedom) simplified model for roll motion against a standard 6-DOF time domain simulation approach. The 1-DOF model is based on the Volterra series representation of the hydrostatic stiffness in waves while accounting for the heave and pitch motions of the model. It also includes a nonlinear damping model capturing the radiation and the viscous damping. The 6-DOF model solves for the nonlinear equations of motion based on Euler angles and also includes the nonlinear Froude Krylov excitations and nonlinear hydrostatic forces on the vessel. Details of the modeling in the two approaches are described and comparisons are performed to assess the validity of 1-DOF simplified model.Copyright © 2015 by ASME

Volterra series theory: A state-of-the-art review

Abstract: Because many real-world systems are inherently nonlinear in nature, nonlinear problems have received considerable interest and attention from engineers, physicists, mathematicians, and other scientists Many mathematical theories and methods have been developed to model, solve, and analyze nonlinear problems and systems One such method uses the Volterra series, which describes the nonlinear relationship between system input and output This is a powerful mathematical tool for the analysis of nonlinear systems, and is essentially an extension of the standard convolution description of linear systems This paper introduces the basic definition of the Volterra series, together with some frequency domain concepts derived from the Volterra series The connection between the Volterra series and other nonlinear system description models and nonlinear problem solving methods is discussed, including the Taylor series, Wiener series, NARMAX model, Hammerstein model, Wiener model, Wiener-Hammerstein model, harmonic balance method, perturbation method, and Adomian decomposition method Challenging problems and the state-of-the-art in series convergence research and kernel identification studies are comprehensively introduced

Noise Estimation in Electroencephalogram Signal by Using Volterra Series Coefficients.

Abstract: The Volterra model is widely used for nonlinearity identification in practical applications. In this paper, we employed Volterra model to find the nonlinearity relation between electroencephalogram (EEG) signal and the noise that is a novel approach to estimate noise in EEG signal. We show that by employing this method. We can considerably improve the signal to noise ratio by the ratio of at least 1.54. An important issue in implementing Volterra model is its computation complexity, especially when the degree of nonlinearity is increased. Hence, in many applications it is urgent to reduce the complexity of computation. In this paper, we use the property of EEG signal and propose a new and good approximation of delayed input signal to its adjacent samples in order to reduce the computation of finding Volterra series coefficients. The computation complexity is reduced by the ratio of at least 1/3 when the filter memory is 3.

Nonparametric volterra kernel estimation using regularization

Abstract: Modeling of nonlinear dynamic systems constitutes one of the most challenging topics in the field of system identifi- cation. One way to describe the nonlinear behavior of a process is by use of the nonparametric Volterra Series representation. The drawback of this method lies in the fact that the number of parameters to be estimated increases fast with the number of lags considered for the description of the several impulse responses. The result is that the estimated parameters admit a very large variance leading to a very uncertain description of the nonlinear system. In this paper, inspired from the regularization techniques that have been applied to one-dimensional (1-D) impulse responses for a linear time invariant (LTI) system, we present a method to estimate efficiently finite Volterra kernels. The latter is achieved by constraining the estimated parameters appropriately during the identification step in a way that prior knowledge about the to-be-estimated kernels is reflected on the resulting model. The enormous benefit for the identification of Volterra kernels due to the regularization is illustrated with a numerical example.

A widely nonlinear approach to compensate impairments in I/Q modulators

Abstract: A novel approach to model impairments in I/Q modulators is presented. The proposal is based on the use of double Volterra series for the I and Q branches. The new model has been shaped as a digital predistorter that can be applied to the compensation of I/Q imbalance, and it has been experimentally validated on a commercial I/Q modulator with superimposed artificial impairments. Measurement results with LTE test signals are compared with other approaches and confirm that the proposed method effectively accomplishes the reduction of carrier leakage, spectral regrowth, and in-band distortion. Performance metrics are within the state-of-the-art, but nearly halving the coefficients of the reference method.

A convex approach for NMPC based on second order Volterra series models

Abstract: Summary In model predictive control (MPC), the input sequence is computed, minimizing a usually quadratic cost function based on the predicted evolution of the system output In the case of nonlinear MPC (NMPC), the use of nonlinear prediction models frequently leads to non-convex optimization problems with several minimums This paper proposes a new NMPC strategy based on second order Volterra series models where the original performance index is approximated by quadratic functions, which represent a lower bound of the original performance index Convexity of the approximating quadratic cost functions can be achieved easily by a suitable choice of the weighting of the control increments in the performance index The approximating cost functions can be globally minimized by convex optimization techniques in order to compute the input sequence The minimization of the performance index is carried out by an iterative optimization procedure, which guarantees convergence to the solution Furthermore, for a nominal prediction model, asymptotic stability for the proposed NMPC strategy can be shown In the case of considering an estimation error in the prediction model, input-to-state practical stability is assured The control performance of the NMPC strategy is illustrated by experimental results Copyright © 2014 John Wiley & Sons, Ltd

Using a modified Modal Series to analyse weakly nonlinear circuits

Abstract: In this paper, a modified Modal Series to model and analyse weakly nonlinear circuits is introduced. This method not only provides an analytical expression for the response to input signals, as does Volterra Series, the popular method for the analysis of nonlinear circuits, but also provides the response to initial conditions as well as interaction between the initial conditions and the input signals, which Volterra Series does not. The extension of this method to multi-input circuits is straightforward. The method is applied to analyse three examples: a single-stage amplifier, a typical track and hold sampler, and the Colpitts oscillator. The results are discussed and compared with existing methods.