Convergence analysis of the alternating RGLS algorithm for the identification of the reduced complexity Volterra model

In this paper we provide a convergence analysis of the alternating RGLS (Recursive Generalized Least Square) algorithm used for the identification of the reduced complexity Volterra model describing stochastic non-linear systems. The reduced Volterra model used is the 3rd order SVD-PARAFC-Volterra model provided using the Singular Value Decomposition (SVD) and the Parallel Factor (PARAFAC) tensor decomposition of the quadratic and the cubic kernels respectively of the classical Volterra model. The Alternating RGLS (ARGLS) algorithm consists on the execution of the classical RGLS algorithm in alternating way. The ARGLS convergence was proved using the Ordinary Differential Equation (ODE) method. It is noted that the algorithm convergence canno׳t be ensured when the disturbance acting on the system to be identified has specific features. The ARGLS algorithm is tested in simulations on a numerical example by satisfying the determined convergence conditions. To raise the elegies of the proposed algorithm, we proceed to its comparison with the classical Alternating Recursive Least Squares (ARLS) presented in the literature. The comparison has been built on a non-linear satellite channel and a benchmark system CSTR (Continuous Stirred Tank Reactor). Moreover the efficiency of the proposed identification approach is proved on an experimental Communicating Two Tank system (CTTS).     

Nonlinear adaptive algorithms for equalisation in mobile satellite communications

This paper considers the equalisation problem in Quadrature Phase-Shift Keying (QPSK) modulated signals which have been distorted by the passage through a transmission channel. The channel is modelled as a Rician fading channel to simulate the behaviour of the transmission channel in the mobile satellite context. The equalisation is treated as the generalisation of the channel behaviour, and some algorithms with the structure of an artificial neural network using the Multilayer Perceptron, Volterra Series and Radial Basis Function are described. Results for the BER performance of typical transversal equalisers, with Square-Root Kalman adaptation algorithm, and algorithms with artificial neural network structure are also reported and evaluated. Improved performance is exhibited by the artificial neural network approaches.     

On parity problems and the functional-link artificial neural network

This paper contains the proof of a theorem on the capability of functional-link artificial neural networks both to represent and to learn the n-dimensional parity problem. The result is obtained by an embedding of the problem into a space of dimension 2ⁿ — 1. It is shown that the Volterra expansion of the data in n-dimensions provides the necessary transformation. By computing the parity function, it is shown that a suitable set of neural network weights can be deduced. Finally, it is demonstrated that 2ⁿ — 1 is the minimum embedding dimension for the problem.The contribution of A Zuderell of the University of Innsbruck is acknowledged.     

毫米波谐波振荡器的多模Volterra级数分析

本文基于Ｖｏｌｔｅｒｒａ级数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一多模Ｖｏｌｔｅｒｒａ级数法，并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和幅度。文中给出了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，可大大地节约     

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     

非线性动态系统“黑箱”建模方法的研究

本文研究弱非线性动态系统“黑箱”建模的理论和方法，并简要给出根据此方法建模的结果。     

基于双阶跃信号输入的Volterra模型辨识

Volterra模型作为非线性领域的一种非线性模型,由于其对工业过程可以以任意精度逼近,使得该模型有很广泛的应用研究意义。在将该模型运用到实际控制系统中之前,模型的高精度辨识显得尤为重要。在以往针对Volterra模型的辨识算法中,基本上主要是采用通用辨识算法识别模型参数,比如最小二乘法及各种改进的最小二乘法。这些通用的辨识算法在辨识Volterra模型时,不能充分考虑其非线性特点,同样不能在辨识过程中充分利用该特点。本文在充分考虑Volterra模型非线性的前提下,提出了一种基于双阶跃信号输入的Volterra模型辨识算法,该算法辨识原理简单,计算量较小,论文最后将该辨识算法应用到典型非线性CSTR系统的的辨识中,辨识结果证明了算法的有效性。     

宽带功率放大器PGSC建模方法及预失真研究

针对宽带功率放大器的强记忆效应特性,提出一种功放建模和数字预失真方法——PGSC模型。利用广义记忆多项式(GMP)、特定交叉项(SCT)及记忆时刻信号交叉项(CIMT)3个基函数来构造功放行为模型及数字预失真器,并搭建实际测试平台对模型的精度及线性化效果进行验证。测试结果表明,与PMEC方法相比,PGSC方法建模时的归一化均方误差减少了2.1 dB,数字预失真时输出信号的三阶邻信道功率比降低了4.94/2.03 dB;与GMP方法相比,PGSC方法仅利用73%的系数即可得到更高的模型精度和更好的线性化效果。     

Non‐Parametric Identification Method of Volterra Kernels for Nonlinear Systems Excited by Multitone Signal

To solve the problem of Volterra frequency‐domain kernels (VFKs) of nonlinear systems, which can be difficult to identify, we propose a novel non‐parametric identification method based on multitone excitation. First, we have studied the output properties of VFKs of nonlinear systems excited by the multitone signal, and derived a formula for identifying VFKs. Second, to improve the efficiency of the non‐parametric identification method, we suggest an increase in the number of tones for multitone excitation to simultaneously identify multi‐point VFKs with one excitation. We also propose an algorithm for searching the frequency base of multitone excitation. Finally, we use the interpolation method to separate every order output of VFK and extract its output frequency components, then use the derived formula to calculate the VFKs. The theoretical analysis and simulation results indicate that the non‐parametric method has a high precision and convenience of operation, improving the conventional methods, which have the defects of being unable to precisely identify VFKs and identification results are limited to three‐order VFK.     

卫星通信双循环下Volterra滤波预失真算法

针对卫星功率放大器输出信号非线性化的问题,提出了一种简化预失真算法.该算法通过两个一阶截断Volterra滤波模型构建前馈循环和反馈循环,并结合两重循环调整预失真器系数来实现卫星通信发射信号线性化处理.在载波频率的提高或传输速度增大时,该算法仍可通过提高预失真器系数更新速度和精确度,从而保证卫星发射信号具有较好的线性特性,具有很好的使用价值和可操作性.