二阶Volterra变数据块长LMS算法

二阶Volterra数据块LMS算法利用当前时刻及其以前时刻更多输入信号和误差信号的信息提高了算法的收敛速度,但由于其固定数据块长取值的不同导致了算法的收敛速度和稳态误差此消彼长。针对这个问题,本文提出一种二阶Volterra变数据块长LMS算法,通过时刻改变输入信号数据块长度提高算法性能。本算法首先采用两个并行的二阶Volterra滤波器,其输入信号数据块长差值始终保持一个单位;然后将其各自的输出误差信号同时输入到数据块长判决器,通过判决器得到下一时刻各个滤波器输入信号的数据块长度;最后以第1个二阶Volterra滤波器的输出作为整个滤波系统的输出,从而改善了算法性能。将本算法应用于非线性系统辨识,计算机仿真结果表明,高斯噪声背景下本算法的收敛速度和稳态性能都得到了明显的提高。      

Artifacts in Wiener kernels estimated using Gaussian white noise

Wiener's nonlinear system identification theory characterizes a system function with a set of kernels of integrals. One method of determining these Wiener kernels is the cross-correlation technique proposed by Lee and Schetzen, which uses Gaussian white noise as the input to the unknown system. Because a test stimulus is only an approximation of infinitely long Gaussian white noise, it is possible that artifacts are generated during the estimation of the kernels. To help identify and characterize these artifacts, Wiener kernel estimates for two simple nonlinear model systems were made using a pseudorandom Gaussian white noise sequence. The results showed that because of the approximation of a Gaussian distribution, artifacts appear in the estimated kernels due to a form of aliasing. These artifacts can be reduced by increasing the sequence length of the input noise.     

Higher-order statistics-based input/output system identification and application to noise cancellation

Higher-than-second-order statistics-based input/output identification algorithms are proposed for linear and nonlinear system identification. The higher-than-second-order cumulant-based linear identification algorithm is shown to be insensitive to contamination of the input data by a general class of noise including additive Gaussian noise of unknown covariance, unlike its second-order counterpart. The nonlinear identification is at least as optimal as any linear identification scheme. Recursive-least-squares-type algorithms are derived for linear/nonlinear adaptive identification. As applications, the problems of adaptive noise cancellation and time-delay estimation are discussed and simulated. Consistency of the adaptive estimator is shown. Simulations are performed and compared with the second-order design.Part of the results of this paper were presented at the workshop on HOSA, Vail, CO, June 1989, and at the International Conference on ASSP, Albuquerque, NM, April 1990. The work of G. B. Giannakis in this paper was supported by LabCom Contract 5-25254.     

高斯过程混合模型在含噪输入预测策略下的煤矿瓦斯浓度柔性预测

高斯过程回归是机器学习中解决非线性回归的一种典型回归方法。然而,单一的高斯过程难以拟合非平稳、多模态的时序数据。另外,在实际应用中需要预测的输入数据会受到噪声的干扰。为了克服这些问题,本文提出了含噪输入预测策略下的高斯过程混合回归预测方法（niMGP）,并针对煤矿瓦斯浓度数据进行了参数学习和柔性预测。与其它传统回归方法相比,这种柔性预测方法是在测试输入数据具有噪声干扰的情况下进行预测,使其结果更为鲁棒和准确。本文首先通过模拟实验验证了在具有固定信噪比的测试输入数据上,高斯过程混合模型在含噪输入预测策略下的回归结果在稳定性上优于其传统预测策略下的回归结果。本文进一步选取松藻煤矿中打通一矿的333944号传感器获取的实际瓦斯浓度数据片段,对其进行了适当的数据增强之后,通过实际数据的实验进一步表明,高斯过程混合模型采用含噪输入预测策略在数据回归分析的预测上相比传统预测策略具有更好的稳定性。实际中还可以通过调节测试输入数据中噪声分布的方差来调节预测的灵敏度,达到分级预警的效果。      

基于高斯核显性映射的核归一化解相关仿射投影P范数算法

为了降低核仿射投影P范数(KAPP)算法的计算量和存储容量,提高在输入信号强相关时KAPP算法的收敛速度和稳态性能,该文提出基于高斯核显性映射的核归一化解相关APP(KNDAPP-GKEM)算法。该算法利用归一化解相关方法预先解除输入信号的相关性;利用高斯核显式映射方法近似得到显式核函数,消除了对历史数据的依赖,解决了KAPP算法因结构不断生长导致的计算量和存储容量过大的问题。α稳定分布噪声背景下的非线性系统辨识仿真结果表明,在输入信号强相关时KNDAPP-GKEM算法收敛速度快,非线性系统辨识稳态均方误差小,训练所需时间呈线性缓慢增长,有利于实际非线性系统辨识的应用。     

The Effect of a Bandpass Nonlinearity on Signal Detectability

When an angle-modulated signal plus noise constitute the input to a bandpass device exhibiting a nonlinear input-output power characteristic and AM to PM conversion, the noise component of the output has altered first- and second-order statistics. A method of evaluating the two-dimensional first-order statistics of this noise is presented. The effect on signal detectability of a nonlinearity inserted between two channel noise sources is studied; expressions for the mean square received phase error and probability of error (for coherent digital phase modulation) are derived. The hard limiting satellite channel, with Gaussian noise on the up and down links, is examined in detail, and it is demonstrated that the limiter can significantly affect signal detectability.     

Second-order adaptive Volterra system identification based ondiscrete nonlinear Wiener model

The authors present the nonlinear LMS adaptive filtering algorithm based on the discrete nonlinear Wiener (1942) model for second-order Volterra system identification application. The main approach is to perform a complete orthogonalisation procedure on the truncated Volterra series. This allows the use of the LMS adaptive linear filtering algorithm for calculating all the coefficients with efficiency. This orthogonalisation method is based on the nonlinear discrete Wiener model. It contains three sections: a single-input multi-output linear with memory section, a multi-input, multi-output nonlinear no-memory section and a multi-input, single-output amplification and summary section. For a white Gaussian noise input signal, the autocorrelation matrix of the adaptive filter input vector can be diagonalised unlike when using the Volterra model. This dramatically reduces the eigenvalue spread and results in more rapid convergence. Also, the discrete nonlinear Wiener model adaptive system allows us to represent a complicated Volterra system with only few coefficient terms. In general, it can also identify the nonlinear system without over-parameterisation. A theoretical performance analysis of steady-state behaviour is presented. Computer simulations are also included to verify the theory     

A computationally efficient and interference tolerant nonparametricalgorithm for LTI system identification based on higher ordercyclostationarity

A new nonparametric algorithm for the identification of linear time-invariant systems is proposed. The method is based on the cyclic correlations of the input and output signals with a nonlinear transformation of the input signal. Consequently, although it exploits the higher order cyclostationarity properties of the input and output signals, its computational complexity is comparable with that of methods based on second-order statistics. The proposed estimator of the system transfer function is inherently immune to the presence of noise and interference on both input and output signal measurements and turns out to be asymptotically unbiased and consistent. Moreover, bias and variance of the estimate exhibit a rate of convergence to zero equal to that of estimates based on second-order statistics. Finally, simulation results show that the proposed algorithm significantly outperforms, in terms of both bias and variance of the estimates, several nonparametric identification algorithms previously presented in the literature     

一种利用多音激励估算非线性失真的方法

针对射频通讯电路中的非线性失真,将非线性电路简化为三阶无记忆模型.利用信号的互补累积分布函数,讨论不同音数的多音信号同窄带高斯白噪声的关系.通过时域随机相位平均的原理,得到了较少音数(K<100)情况下进行非线性参数精确仿真和测试的方法,减少了由于多音音数较少而引起的仿真误差和波动.     

Estimating second-order Volterra system parameters from noisy measurements based on an LMS variant or an errors-in-variables method

This paper deals with the identification of a nonlinear SISO system modelled by a second-order Volterra series expansion when both the input and the output are disturbed by additive white Gaussian noises. Two methods are proposed. Firstly, we present an unbiased on-line approach based on the LMS. It includes a bias correction scheme which requires the variance of the input additive noise. Secondly, we suggest solving the identification problem as an errors-in-variables issue, by means of the so-called Frisch scheme. Although its computational cost is high, this approach has the advantage of estimating the Volterra kernels and the variances of both the additive noises and the input signal, even if the signal-to-noise ratios at the input and the output are low.     

Second-order analysis of the output of a discrete-time Volterra system driven by white noise

The second-order analysis of the output of a discrete-time nonlinear system described by a truncated Volterra series whose input consists of a sequence of independent random variables (white noise)is considered. The main result consists of an explicit formula for the mean value of the output process in terms of the cumulants of the input and of Volterra kernels. This formula, with suitable modifications, allows the calculation of the output correlation as well as of the continuous and discrete components of the spectral distribution. Several applications are considered, and in particular the Gaussian white noise case is worked out in detail. Finally, the computational aspects of the analysis are discussed with the aim of showing that in several situations closed-form results can be obtained.     

A fast recursive least squares adaptive second order Volterrafilter and its performance analysis

A fast, recursive least squares (RLS) adaptive nonlinear filter modeled using a second-order Volterra series expansion is presented. The structure uses the ideas of fast RLS multichannel filters, and has a computational complexity of O(N³) multiplications, where N-1 represents the memory span in number of samples of the nonlinear system model. A theoretical performance analysis of its steady-state behaviour in both stationary and nonstationary environments is presented. The analysis shows that, when the input is zero mean and Gaussian distributed, and the adaptive filter is operating in a stationary environment, the steady-state excess mean-squared error due to the coefficient noise vector is independent of the statistics of the input signal. The results of several simulation experiments show that the filter performs well in a variety of situations. The steady-state behaviour predicted by the analysis is in very good agreement with the experimental results     

一种改进的电力线通信系统脉冲噪声抑制方法

为了抑制脉冲噪声对电力线正交频分复用（OFDM）通信系统的影响,最常用的方法之一是在接收端OFDM解调器之前前置一个置零非线性单元,即传统置零法。然而,由于引入了非线性失真,其性能并不理想。针对传统置零法引起的非线性失真问题,提出了一种基于迭代消除非线性失真的改进置零法。首先,对接收到的时域OFDM信号进行脉冲噪声检测和置零处理;然后,在频域利用已检测的符号来重构时域置零处理引入的非线性失真,并通过迭代提高重构的准确性;最后,从频域接收信号中减去重构的非线性失真。仿真结果表明,所提改进算法与传统置零法相比,有非常大的性能提升,增强了电力线OFDM通信系统对脉冲噪声的抵抗能力。     

Multiple Edge Responses for Fast and Accurate System Simulations

High-speed input/output (I/O) link performance is limited by random noise as well as signal integrity issues such as dispersion, reflections, and crosstalk. Hence, accurate prediction of system performance including these random and deterministic noise is crucial in high-speed link design. This paper presents a novel, fast, and accurate method to simulate the time-domain system response. The presented method calculates the system response using multiple edge responses (MER) based on linear superposition. Being able to take into account system nonlinearity more accurately, the presented method significantly improves simulation accuracy compared with the other published fast simulation techniques based on either single bit response (SBR) or double edge responses (DER), while at the same time maintaining equivalent numerical efficiency. Furthermore, peak distortion analysis, which is commonly used to find the worst-case data pattern based on SBR, is extended for DER and MER using dynamic programming. A multiphase worst-case data pattern approach is also introduced in this paper in order to determine the worst-case system performance under both timing and voltage consideration.      

Identification of cubically nonlinear systems using undersampleddata

A practical technique for identification of cubically nonlinear systems using higher order spectra of the discrete data samples of the system input and output is proposed. This technique differs from the conventional one in that it only requires the sampling frequency for the system output to be equal to twice the bandwidth of the system input, instead of six times the bandwidth of the system input. This means the demand for high speed processing and a large amount of data in the conventional approach can be greatly relieved, Two methods are developed: one is suitable for systems with a Gaussian random input, the other is suitable for systems with a non-Gaussian random input. The advantages of the two methods over their conventional counterparts are demonstrated via computer simulation     

A novel robust filtering strategy for systems with Non-Gaussian noises

For estimating the states of moving targets in the nonlinear system with non-Gaussian noise, the combination of Gaussian Sum Filter (GSF) and other nonlinear filters has been chosen as the filtering algorithm conventionally. The Smooth Variable Structure Filter (SVSF) is a new predictor-corrector method used for state and parameter estimation, which has good stability and robustness. In this paper we propose a new strategy called the modified GS-EKF-SVSF, which inherits good robustness of Gaussian Sum and Smooth Variable Structure Filter (GS-SVSF) and high accuracy of Gaussian Sum and Extended Kalman Filter (GS-EKF). A nonlinear system with non-Gaussian noise for target tracking is used to test the proposed new strategy. The simulation results demonstrate that our proposed strategy has higher accuracy and better robustness when there are modelling uncertainties existing in the system.     

UFMC系统中基于Volterra滤波器的非线性失真补偿方案

为实现通用滤波多载波(UFMC)通信系统高效、可靠的通信性能,需在最大程度上补偿由记忆型高功率放大器(HPA)引起的非线性失真.为解决HPA造成的失真问题,本文提出了一种基于Volterra滤波器的非线性失真补偿(V-NLDC)技术.该技术利用了Volterra级数的稀疏特性和能够模拟任意精度非线性系统的性质以逐次逼近的方式对信号进行预失真.将预失真后的信号传送至HPA,然后采用噪声消除器做进一步噪声消除处理,以达到更小失真度的目的.同时,本研究采用收敛速度快、性能稳定的自适应最小二乘法(RLS),可根据环境变化自适应地计算Volterra滤波器和噪声消除器的系数.通过大量蒙特卡罗仿真实验证实了所提出的非线性失真补偿技术可以很好的补偿由记忆型HPA非线性失真所造成的影响,从而优化系统性能.     

A Modified Barrett-Lampard Expansion and Its Application to Bandpass Nonlinearities with Both AM-AM and AM-PM Conversion

A two-dimensional Barrett-Lampard expansion is developed to handle two-dimensional nonlinear systems with random Gaussian inputs. The theory is applied to the problem of evaluating the mean signal and the inphase and quadrature noise correlation functions at the output of a TWT nonlinearity exhibiting arbitrary AM-AM and AM-PM characteristics, when the input consists of a narrow-band signal and Gaussian noise. As a specialized application, the classical problem of determining the coherent and incoherent noise correlation functions at the output of a power-law bandpass nonlinearity is also considered. The results are of interest in assessing the performance of coherent satellite communication channels. The theory developed is accompanied by numerical examples of practical interest.     

Binary Signaling over Channels Containing Quadratic Nonlinearities

This paper examines the transmission of binary data signals over channels which contain quadratic nonlinearities and additive Gaussian noise. We consider the case where the channel is nonlinear with memory and where the signal is passed through an input receiver filter and sampled once every signaling interval. The samples are represented by a discrete Volterra series and a special case where the received sample contains a single quadratic distortion term is examined. The optimum (maximum-likelihood) receiver (processor) is derived and upper and lower performance bounds obtained. The performance of a practical, suboptimum receiver is examined by means of computer simulation and is shown to be very close to the lower bound of the optimum receiver. Next we examine the case where the received sample contains two quadratic distortion terms. Again, upper and lower performance bounds are obtained. The performance of a suboptimum receiver which uses nonlinear decision feedback is evaluated by computer simulation. Its performance is shown to be superior to an optimum linear receiver.     

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