非线性网络Volterra级数表示的代数求解算法

本文基于非线性网络Volterra级数表示的辅助代数方法,提出了非线性网络n阶Volterra核和n阶非线性传递函数的代数编列算法。求取了非线性网络的规范形、三角形、对称形n阶Volterra核及相应的n阶非线性传递函数,同时也降低了非线性网络Volterra级数表示编列算法的复杂性。     

非线性ROF系统的分析和建模

在分析ROF(radio over fiber)系统组成与传输非线性的基础上,提出了用Volterra泛函级数为非线性ROF系统建立模型.研究了非线性ROF系统的Volterra级数表述、最小均方和最小二乘两种确定Volterra级数核的自适应算法在非线性ROF系统建模中的应用.通过一个用Volterra泛函级数对非线性ROF系统建模的实例,比较了Volterra LMS和Volterra RLS算法在建模中的效果,证明了用Volterra级数对非线性ROF系统建模的有效性.     

Algorithm for solving a class of phase-lock-loop equations

An algorithm for solving the nonlinear Volterra equation of an nth-order phase-lock loop having all poles simple is presented. The proposed formulas are quite general with respect to the phase-detector nonlinearity and require little computational effort.     

非线性动态网络的离散算法及仿真

在非线性网络响应分析中,采用Volterra级数法可以导出与线性系统传递函数相似的非线性传递函数,能使非线性系统用线性化和系统化方法达到精确分析.文中给出了非线性网络响应的Volterra级数解的连续算式,为解决连续算式计算麻烦的问题,提出用方波脉冲技术处理用Volterra级数表示法描述的非线性网络响应与激励之间关系的一组广义卷积积分的迭加计算,从而得到非线性网络响应求解的Volterra级数解的离散算式.仿真表明该算法求出的非线性网络响应与真实模型曲线十分逼近,证明了它的有效性.     

Averaging and Cancellation Effect of High-Order Nonlinearity of a Power Amplifier

Nonlinear distortion of a power amplifier (PA) due to the nonlinear input-output transfer function is studied. The high-order nonlinearity or Fourier components of the output, due to the mixing of input signals, are found to be related to an average integral related to the transfer function, thus giving insight to the cancellation effect of the nonlinearity. A simple formula has been derived to relate the nth-order Fourier component of a nonlinear transfer function with a sinusoidal input to an average integral of the nth-order derivative of the transfer function. The large signal nonlinear distortion of the nth-order can therefore be regarded as a weighted average of the nth-order derivative of the transfer function. For PAs, the averaging effect gives rise to local minima in the intermodulation distortion terms during power sweep because of the cancellation of the positive part and the negative part of the derivative during averaging. We have applied the formula to InGaP heterojunction bipolar transistors PAs and are able to explain most of the observed nonlinear phenomena of the amplifiers.     

Optimal Volterra kernel estimation algorithms for a nonlinearcommunication system for PSK and QAM inputs

A fifth-order Volterra kernel estimation algorithm, which is optimal in the least mean square error sense, for a bandpass nonlinear system is derived. The algorithm is based on some characteristics of i.i.d. circularly symmetric zero-mean complex-valued Gaussian random variables. The proposed algorithm can be used to identify a nonlinear system under uniformly i.i.d. rectangular M-QAM input and under uniformly i.i.d. M-PSK input (M⩾4) with modest modification. The same approach has been used to derive an optimal Volterra kernel estimation algorithm up to the third order. However, in some cases, a third-order model is not of “high enough order” to capture the nonlinear system characteristics. A simulation example is given to show the necessity of deriving a fifth-order Volterra kernel estimation algorithm and to test for the correctness of the algorithm     

Nonlinear Transient and Distortion Analysis via Frequency Domain Volterra Series

This paper presents a novel approach for transient and distortion analyses for time-invariant and periodically time-varying mildly nonlinear analog circuits. Our method is based on a frequency domain Volterra series representation of nonlinear circuits. It computes the nonlinear responses using a nonlinear current method that recursively solves a series of linear Volterra circuits to obtain linear and higher-order responses of a nonlinear circuit. Unlike existing approaches, where Volterra circuits are solved mainly in the time domain, the new method solves the linear Volterra circuits directly in the frequency domain via an efficient graph-based technique, which can derive transfer functions for any large linear network efficiently. As a result, both frequency domain characteristics, like harmonic and intermodulation distortion, and time domain waveforms can be computed efficiently. The new algorithm takes advantage of identical Volterra circuits for second- and higher-order responses, which results in significant savings in driving the transfer functions. Experimental results for two circuits—a low-noise amplifier and a switching mixer—are obtained and compared with SPICE3 to validate the effectiveness of this method.     

MIMO非线性系统辨识：Volterra级数法

本文讨论了一般ＭＩＭＯ非线性系统的Ｖｏｌｔｅｒｒａ级数表示,给出并证明了Ｖｏｌｔｅｒｒａ核矩阵存在的条件。提出了两种辨识Ｖｏｌｔｅｒｒａ核矩阵的方法,即随机响应法与脉冲响应法。给出了利用系统的输入输出信号计算Ｖｏｌｔｅｒｒａ核矩阵的公式。最后,利用仿真实例验证上述方法的有效性。     

非线性电路和系统的灵敏度分析非线性传递函数法

本文研究了非线性传递函数的性质,提出了n阶稳定性、n阶零极点,n阶频率响应、n阶零灵敏度等新概念和非线性系统灵敏度分析的新理论和方法。     

高频段频谱占用的Volterra预测方法研究

为了能够给高频用户提供较为可靠的空闲频段,需要对高频段频谱占用的情况进行预测。本文提出一种基于自适应Volterra滤波理论的预测方法,通过对频谱占用因子时间序列进行状态空间重构,并采用递推形式的自适应递归最小二乘算法实时调整Volterra模型的核系数。实际数据处理结果表明,该预测方法能够很好地跟踪频谱占用因子的非线性变化,具有预测误差小,训练计算复杂度低等优点。      

Relationship between Volterra series and generalized power series

The relationship between the Volterra nonlinear transfer functions of a system and the elements of its generalized power series is established. A formula is derived which enables the Volterra nonlinear transfer functions to be obtained from the power series expansion of the nonlinear system.     

毫米波谐波振荡器的Volterra级数分析法

本文基于Ｖｏｌｔｅｒｒａ级数法和非线性转移函数理论，提出了一种分析毫米波谐波振荡器的新方法，给出了描述其非线性特性的决定方程，通过求解一组非线性代数方程，便可计算出谐波振荡器的振荡频率和幅度。文中给出了具体分析实例，并与谐波平衡法等进行了比较，结果表明：这种方法具有理论严密、准确性高、适用范围广等特点，特别是利用一次决定方程的结果作为其它非线性数值分析方法的初始估值，则可大大地节约计算时间，并容易     

隐相空间的DUPSO-RPSOVF语音预测模型研究

提出了一种基于二阶Volterra级数的语音信号非线性预测模型.为克服传统的最小均方（Least Mean Square,LMS）算法在模型核系数更新时的固有缺点,引入耗散均匀搜索粒子群优化算法（Dissipative Uniform Particle Swarm Optimization,DUPSO）求解核系数,并构建了DUPSO-SOVF预测模型;为避免传统方法中相空间的重构过程,构建了隐相空间DUPSO-SOVF预测模型,在求解模型核系数时动态地求解出最优嵌入维数和延迟时间;为降低模型复杂度,在误差允许范围内进行模型关键项的提取,从而减少了核系数个数,构建了少参数的DUPSO-RPSOVF（Reduced Parameter SOVF,RPSOVF）预测模型.将英语音素、单词和短语作为实验样本数据进行仿真,结果表明：隐相空间DUPSO-SOVF模型能够准确的计算出相空间重构参数,DUPSO-SOVF和DUPSO-RPSOVF两种预测模型对单帧和多帧语音信号均具有较高的预测精度,优于PSO-SOVF和LMS-SOVF预测模型,并且能够很好地反映语音序列变化的趋势和规律,可以满足语音序列预测的要求.     

弱非线性动态系统Volterra核自动测试系统的研究

本文讨论弱非线性动态系统Ｖｏｌｔｅｒｒａ核自动测试系统的研制，应用Ｖｏｌｔｅｒｒａ泛函级数和计算机技术于非线性系统，本文结合频率域多点测量弱非线性系统前二阶核的算法ＱＭＭＰ２及测量前三阶核的算法ＱＭＭＰ３，设计了自动测试系统。本文给出应用该系统的两个测量实例。     

Linear multichannel blind equalizers of nonlinear FIR Volterrachannels

Truncated Volterra expansions model nonlinear systems encountered with satellite communications, magnetic recording channels, and physiological processes. A general approach for blind deconvolution of single-input multiple-output Volterra finite impulse response (FIR) systems is presented. It is shown that such nonlinear systems can be blindly equalized using only linear FIR filters. The approach requires that the Volterra kernels satisfy a certain coprimeness condition and that the input possesses a minimal persistence-of-excitation order. No other special conditions are imposed on the kernel transfer functions or on the input signal, which may be deterministic or random with unknown statistics. The proposed algorithms are corroborated with simulation examples     

A mixed-domain method for identification of quadratically nonlinearsystems

A new mixed-domain method for identifying Volterra transfer functions of a nonlinear system, which can be represented by a second-order truncated Volterra series, is presented in this paper. This method is built on a discrete mixed-domain Volterra model derived from analyzing both discrete time- and frequency-domain Volterra models of quadratically nonlinear systems. It is shown that the conventional discrete frequency-domain Volterra model can be derived from the discrete mixed-domain Volterra model by making certain approximations. In this sense, the frequency-domain model can be considered to be a cough version of the mixed-domain model and thus cannot outperform the mixed-domain model in terms of modeling capability. In addition, the new method is shown to be able to properly identify the Volterra transfer functions even when the output of the quadratically nonlinear system is aliased. Based on this insight, a new anti-aliasing frequency-domain method, which is immune from the output aliasing problem, is developed. The superiority of these new methods over the conventional method is demonstrated by using them to analyze known quadratically nonlinear systems     

Modified Volterra series transfer function method

In this letter, we offer a modified version of the Volterra series transfer function (VSTF) method that has been previously proposed as an analytical solution to the nonlinear Schrodinger equation for single-mode fibers. The modified VSTF provides a simple closed-form expression of the output of a mildly nonlinear fiber. It gives orders more accurate result than the original VSTF method and can successfully solve the energy divergence problem experienced by the original method. The result is a stronger analytical tool for modeling signal propagation in optical communication systems     

Volterra series transfer function of single-mode fibers

A nonrecursive Volterra series transfer function (VSTF) approach for solving the nonlinear Schrodinger (NLS) wave equation for a single-mode optical fiber is presented. The derivation of the VSTF is based on expressing the NLS equation In the frequency domain and retaining the most significant terms (Volterra kernels) in the resulting transfer function. Due to its nonrecursive property and closed-form analytic solution, this method can excel as a tool for designing optimal optical communication systems and lumped optical equalizers to compensate for effects such as linear dispersion, fiber nonlinearities and amplified spontaneous emission (ASE) noise from optical amplifiers. We demonstrate that a third-order approximation to the VSTF model compares favorably with the split-step Fourier (recursive) method in accuracy for power levels used in current optical communication systems. For higher power levels, there is a potential for improving the accuracy by including higher-order Volterra kernels at the cost of increased computations. Single-pulse propagation and the interaction between two pulses propagating at two different frequencies are also analyzed with the Volterra method to verify the ability to accurately model nonlinear effects. The analysis can be easily extended to include inter-channel interference in multi-user systems like wavelength-division multiple-access (WDM), time-division multiplexed (TDM), or code-division multiplexed (CDM) systems     

Convergence of Volterra series in simulation of nonlinear processes in electronic circuits

Physical and mathematical reasons for the divergence of functional Volterra series in calculation of nonlinear electronic circuits described by algebraic differential equations are considered. It is shown that the main reason is the character of the feedbacks involving nonlinear elements and leading to a high level of repeated combinational interactions. On model examples, the disruption of the iterative process due to the loss of continuity and differentiability of nonlinear operators on the real axis or on the complex plane is demonstrated.     

OFDM功率放大器线性化快速算法

针对OFDM功率放大器线性化问题,本文采用数字预失真的方法来补偿功率放大器的非线性失真。预失真器采用Volterra序列来逼近,并提出一种重置BFGS算法来训练非线性预失真器。通过设定切换条件,使参数学习在梯度下降法与拟牛顿法之间切换。这既增加了新算法的数值稳定性,又可提高收敛速度。仿真采用数字基带预失真器对OFDM信号的功率放大器进行预失真,结果表明了新算法的高效性。并且,增加数字预失真模块可大大改善OFDM功率放大器的性能。