Linear and nonlinear ARMA model parameter estimation using anartificial neural network

Addresses parametric system identification of linear and nonlinear dynamic systems by analysis of the input and output signals. Specifically, the authors investigate the relationship between estimation of the system using a feedforward neural network model and estimation of the system by use of linear and nonlinear autoregressive moving-average (ARMA) models. By utilizing a neural network model incorporating a polynomial activation function, the authors show the equivalence of the artificial neural network to the linear and nonlinear ARMA models. They compare the parameterization of the estimated system using the neural network and ARMA approaches by utilizing data generated by means of computer simulations. Specifically, the authors show that the parameters of a simulated ARMA system can be obtained from the neural network analysis of the simulated data or by conventional least squares ARMA analysis. The feasibility of applying neural networks with polynomial activation functions to the analysis of experimental data is explored by application to measurements of heart rate (HR) and instantaneous lung volume (ILV) fluctuations     

Channel estimation for OFDM systems using adaptive radial basis function networks

We propose a new scheme for pilot-symbol-aided channel estimation in orthogonal frequency-division multiplexing (OFDM) systems in multipath fading channels, that does not require knowledge of the channel statistics (e.g., Doppler or power spectrum). It is based on using the radial basis function (RBF) network to model the dynamics of the fading process. Both one-dimensional and two-dimensional RBF networks are proposed to exploit the channel correlation in the time domain and in the time-frequency domain. The proposed RBF networks are essentially nonlinear interpolators of the pilot channels. Compared with the existing OFDM channel estimation methods based on linear filtering, the proposed new techniques offer both robustness to fading rate, and a better performance especially in relatively fast fading channels.     

Autocorrelation model-based identification method for ARMA systems in noise

A novel method for parameter estimation of minimum-phase autoregressive moving average (ARMA) systems in noise is presented. The ARMA parameters are estimated using a damped sinusoidal model representation of the autocorrelation function of the noise-free ARMA signal. The AR parameters are obtained directly from the estimates of the damped sinusoidal model parameters with guaranteed stability. The MA parameters are estimated using a correlation matching technique. Simulation results show that the proposed method can estimate the ARMA parameters with better accuracy as compared to other reported methods, in particular for low SNRs.     

基于零极点预测模型的码激励线性预测语音编码算法

针对传统码激励线性预测（Code Excited Linear Predictive，CELP）语音编码器在预测模型和参数估计方面的不足，提出了一种基于零极点预测模型的CELP语音编码新算法。该算法采用零极点预测模型来更准确地描述语音信号的短时相关性，并采用梯度法来同时对零极点模型的参数和激励码本增益进行联合优化求解。实验结果表明所提语音编码算法可显著降低CELP编码器合成语音的归一化均方误差，有效提高合成语音的质量。     

Noncausal nonminimum phase ARMA modeling of non-Gaussian processes

A method is presented for the estimation of the parameters of a noncausal nonminimum phase ARMA model for non-Gaussian random processes. Using certain higher order cepstra slices, the Fourier phases of two intermediate sequences (h_min(n) and h_max(n)) can be computed, where h_min(n) is composed of the minimum phase parts of the AR and MA models, and h_max(n) of the corresponding maximum phase parts. Under the condition that there are no zero-pole cancellations in the ARMA model, these two sequences can be estimated from their phases only, and lead to the reconstruction of the AR and MA parameters, within a scalar and a time shift. The AR and MA orders do not have to be estimated separately, but they are by product of the parameter estimation procedure. Through simulations it is shown that, unlike existing methods, the estimation procedure is fairly robust if a small order mismatch occurs. Since the robustness of the method in the presence of additive noise depends on the accuracy of the estimated phases of h_min(n) and h_max(n), the phase errors due to finite length data are studied and their statistics are derived     

Nonlinear spectral-estimation methods for ground clutter analysis

A simple ground clutter model has been analysed using nonlinear methods of power spectral estimation and the performance of these methods has been studied. The methods considered are the maximum entropy method (MEM), the maximum likelihood method (MLM), the least-squares method (LSM), the autoregressive moving average (ARMA) method and Prony's energy spectral-density estimation (PESD). The performance of these power spectral-estimation methods has been studied for different data lengths and different model orders     

Blind channel approximation: effective channel order determination

A common assumption of blind channel identification methods is that the order of the true channel is known. This information is not available in practice, and we are obliged to estimate the channel order by applying a rank detection procedure to an “overmodeled” data covariance matrix. Information theoretic criteria have been widely suggested approaches for this task. We check the quality of their estimates in the context of order estimation of measured microwave radio channels and confirm that they are very sensitive to variations in the SNR and the number of data samples. This fact has prohibited their successful application for channel order estimation and hits created some confusion concerning the classification into under- and over-modeled cases. Recently, it has been shown that blind channel approximation methods should attempt to model only the significant part of the channel composed of the “large” impulse response terms because efforts toward modeling “small” leading and/or trailing terms lead to effective overmodeling, which is generically ill-conditioned and, thus, should be avoided. This can be achieved by applying blind identification methods with model order equal to the order of the significant part of the true channel called the effective channel order. Toward developing an efficient approach for the detection of the effective channel order, we use numerical analysis arguments. The derived criterion provides a “maximally stable” decomposition of the range space of an “overmodeled” data covariance matrix into signal and noise subspaces. It is shown to be robust to variations in the SNR and the number of data samples. Furthermore, it provides useful effective channel order estimates, leading to sufficiently good blind approximation/equalization of measured real-world microwave radio channels     

On codes with spectral nulls at rational submultiples of the symbol frequency

In digital data transmission (respectively, storage systems), line codes (respectively, recording codes) are used to tailor the spectrum of the encoded sequences to satisfy constraints imposed by the channel transfer characteristics or other system requirements. For instance, pilot tone insertion requires codes with zero mean and zero spectral density at tone frequencies. Embedded tracking/focus servo signals produce similar needs. Codes are studied with spectral nulls at frequenciesf=kf_{s}/n, wheref, is the symbol frequency andk, nare relatively prime integers withk leq n;in other words, nulls at rational submultiples of the symbol frequency. A necessary and sufficient condition is given for a null atfin the form of a finite discrete Fourier transform (DFT) running sum condition. A corollary of the result is the algebraic characterization of spectral nulls which can be simultaneously realized. Specializing to binary sequences, we describe canonical Mealy-type state diagrams (directed graphs with edges labeled by binary symbols) for each set of realizable spectral nulls. Using the canonical diagrams, we obtain a frequency domain characterization of the spectral null systems obtained by the technique of time domain interleaving.     

State-dependent vector hybrid linear and nonlinear ARMA modeling: Theory

A new model is proposed to represent a general vector nonstationary and nonlinear process by setting up a state-dependent vector hybrid linear and nonlinear autoregressive moving average (SVH-ARMA) model. The linear part of the process is represented by a vector ARMA model, the nonlinear part is represented by a vector nonlinear ARMA model employing a multilayer feedforward neural network, and the nonstationary characteristics are captured with a hidden Markov chain. Based on a unifiedQ-likelihood function, an expectation-maximization algorithm for model identification is derived, and the model parameters are estimated by applying a state-dependent training and nonlinear optimization technique iteratively, which finally yields maximum likelihood estimation of model parameters. This model can track the nonstationary varying of a vector linear and/or nonlinear process adaptively and represent a vector linear and/or nonlinear system with low order. Moreover, it is able to characterize and track the long-range, second-order correlation features of many time series and thus can be used for reliable multiple step ahead prediction. Some impressive applications of the SVH-ARMA model are being presented in the companion paper by Zheng et al., pp. 575–597, this issue.     

Block adaptive techniques for channel identification and datademodulation over band-limited channels

A new approach to the problem of data detection for communications over band-limited channels with unknown parameters is introduced. We propose a new way to implement the Viterbi algorithm (VA) for maximum-likelihood data sequence estimation (MLSE) in a known channel environment and utilize it to derive block adaptive techniques for joint channel and data estimation, when the channel-impulse response (CIR) is unknown. We show, via simulations, that we can achieve a probability of error very close to that of the known channel environment and nearly reach a mean-square error in the channel estimate as predicted by analytical bounds, operating on static channels, which exhibit deep nulls in their magnitude response and nonlinear phase. The proposed schemes accomplish channel acquisition after processing a few hundred symbols while operating without a training sequence, whereas linear blind equalizers, such as Sato's (1975) algorithm, fail to converge at all. The application of block processing to adaptive MLSE is also investigated for time-varying frequency-selective Rayleigh-fading channels, which are used for modeling mobile communication systems. In such environments it is shown that the proposed scheme exhibits improved performance compared to the conventional adaptive MLSE receiver using tentative delayed decisions     

ARMA spectral estimation of time series with missing observations

The problem of estimating the power spectral density of stationary time series when the measurements are not contiguous is considered. A new autoregressive moving-average (ARMA) method is proposed for this problem, based on nonlinear optimization of a weighted-squared-error criterion. The method can handle either regularly or randomly missing observations. As a special case, the method can handle the problem of missing sample covariances. The computational complexity is modest compared to exact maximum likelihood estimation of the same parameters. The performance of the algorithm is illustrated by some numerical examples and is shown to be statistically efficient in these cases.     

Bispectrum Reconstruction Method of UWB Echoes

Estimation of transient signal in additive noise is very important in radar object detection and recognition. This paper presents a new method for transient signal reconstruction based on bispectrum estimation techniques. The third-order cumulants of the received noisy ultra-wide band echoes are acquired first and an ARMA model is then fitted. The bispectrum of the output signal of the ARMA model will be used to reconstruct the transient signal. Simulation results show that the effect is very good even in lower signal-to-noise (SNR) situation.     

基于EGARCH过程的电磁频谱占用状态波动特性分析

针对传统频谱占用度自回归移动平均(ARMA)模型由于未考虑序列的条件二阶矩,导致无法准确描述频谱占用状态的非线性时变特性问题,该文提出一种基于指数广义自回归条件异方差(EGARCH)过程的频谱占用状态时间序列建模方法。首先通过对ARMA模型的剩余残差进行条件异方差性检验,表明频谱占用时间序列存在明显的时域波动集聚性;其次基于EGARCH过程构建频谱占用度时间序列模型以及对实测数据的分析,表明该模型相较ARMA模型对频谱占用度的拟合与预测精度更高;最后由EGARCH模型参数存在杠杆效应系数,表明频谱占用状态变化对电磁环境波动的影响具有非对称性。研究结果表明EGARCH模型能够量化反映频谱占用状态的复杂非线性时变过程。     

A new recursive pseudo least squares algorithm for ARMA filteringand modeling. II

For pt.I see ibid., vol.40, no.11, p.2766-74 (Nov. 1992). A recursive algorithm for ARMA (autoregressive moving average) filtering has been developed in a companion paper. These recursions are seen to have a lattice-like filter structure. The ARMA parameters, however, are not directly available from the coefficients of this filter. The problem of identification of the ARMA model from the coefficients of this filter is addressed here. Two new update relations for certain pseudoinverses are derived and used to obtain a recursive least squares algorithm for AR parameter estimation. Two methods for the estimation of the MA parameters are also presented. Numerical results demonstrate the usefulness of the proposed algorithms     

A New Method of Generating Spectral Nulls at the Transmitter in Cognitive Radio

In cognitive radio (CR), cognitive users can sense the wholes and white spectrum and generate spectrum notch in the spectrum bands occupied by primary users (PUs) or interference. Thus, the key technology in CR is to control the spectrum shape of the transmitted signal to avoid PUs and interference. In this paper, a new method of shaping the transmitted signal spectrum envelope by spectrum-spread technology is proposed. The proposed method can generate spectral nulls at the band of PUs or interference in the CR environment. Compared to the existing methods generating spectrum nulls, the proposed method can effectively generate spectral nulls to avoid interference or PUs only by designing the pseudo-random code waveform (PCW) based on direct sequence spread spectrum technology. The condition of electromagnetic spectrum occupation is detected by CR technology so as to construct an ideal spectrum template. Based on the spectrum template, we study the design of the baseband waveform. The bit error rate (BER) performance of the proposed method in different sorts of interferences, and the relation between the BER and the spectrum overlap degree (SOD) are derived, of which the concept of SOD is proposed. The expression between BER and SOD shows that BER is proportional to SOD, which shows the criterion to design the PCW. The signal spectrograms in the receiver in presence of tone jamming and BPSK jamming indicate that the proposed scheme can effectively generate spectrum nulls in the frequency band occupied by PUs or interference. Furthermore, the BER versus SNR and BER versus SIR simulation results both in presence of tone jamming and BPSK jamming show that the proposed method has a significantly improved the BER performance by generating spectral nulls to avoid PUs or interferences. Simulation results are carried out to corroborate our theoretical analysis.     

Nonlinear Bayesian Filtering Using the Unscented Linear Fractional Transformation Model

For nonlinear state space model involving random variables with arbitrary probability distributions, the state estimation given a sequence of observations is based on an appropriate criterion such as the minimum mean square error (MMSE). This leads to linear approximation in the state space of the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), which work reasonably well only for mildly nonlinear systems. We propose a Bayesian filtering technique based on the MMSE criterion in the framework of the virtual linear fractional transformation (LFT) model, which is characterized by a linear part and a simple nonlinear structure in the feedback loop. LFT is an exact representation for any differentiable nonlinear mapping, so the virtual LFT model is amenable to a wide range of nonlinear systems. Simulation results demonstrate that the proposed filtering technique gives better approximation and tracking performance than standard methods like the UKF. Furthermore, for highly nonlinear systems where UKF diverges, the LFT model estimates the conditional mean with reasonable accuracy.      

基于块稀疏恢复的高频雷达空间角谱和极化谱联合估计方法

高频地波雷达（high-frequency surface wave radar,HFSWR）中电离层杂波的存在,会极大地影响雷达系统的性能,降低对目标的探测能力.为了精确获得杂波参数,从而更好地抑制电离层杂波,提出了一种基于压缩感知（compressive sensing,CS）的单快拍参数估计方法,用于对电离层杂波的空域和极化域参数估计.该方法基于极化敏感阵列的块稀疏估计模型,应用块正交匹配追踪（block orthogonal matching pursuit,BOMP）算法实现距离-多普勒域的单快拍空间角度和极化参数联合估计,并进一步获得目标和杂波的空间角谱和极化谱.该方法适用于任意极化敏感阵列,在距离-多普勒域单快拍条件下,其估计性能优于传统方法,且计算复杂度极低,可以实现实时处理.仿真结果和某HFSWR系统实测数据处理结果表明了参数估计方法的有效性.     

Improvements of a state-space iterative noise reduction algorithmfor harmonic retrieval

When the model of a noisy sinusoidal process is autoregressive moving average (ARMA), then the AR spectrum is biased. However, since the AR spectrum contains all the second-order information of the process, it is possible to retrieve the noiseless predictor from the noisy one. An iterative algorithm enabling the computation of the ARMA parameters from the AR parameters and a new well-suited initialization scheme are presented. Simulations of the state-space iterative noise reduction algorithm (SINA) are performed using various AR estimators. The mean-square-error graph is plotted for all these estimators and performances of the methods are discussed     

ARMA Synthesis of Fading Channels

Computationally scalable and accurate estimation, prediction, and simulation of wireless communication channels is critical to the development of more adaptive transceiver algorithms. Previously, the application of autoregressive moving average (ARMA) modeling to fading processes has been complicated by ill-conditioning and nonlinear parameter estimation. This correspondence presents a numerically stable and accurate method to synthesize ARMA rational approximations of correlated Rayleigh fading processes from more complex higher order representations. Here, the problem is decomposed into autoregressive (AR) model matching followed by linear system identification. Performance is compared to that of AR, inverse discrete Fourier transform, and sum of sinusoids techniques. Also, for the first time, the finite-precision performance of different methods is compared.     

DOA estimation of wideband sources without estimating the number of sources

In this paper, we propose a new technique to estimate wideband source directions from the sensor snapshots without requiring to know the number of sources present in the scenario. This work is motivated by the fact that the existing model order estimation (number of sources) techniques for wideband source scenario are either inaccurate or computationally expensive. Direction-of-arrival (DOA) estimation is realized using a beamformer framework which imposes nulls in the spatial spectrum along the source directions. The null width along the frequency axis is widened by introducing a new data dependent term into the optimization problem, thus achieving wideband capability. Furthermore, the temporal processing of the data snapshots drastically reduces the number of snapshots required for wideband DOA estimation. The effectiveness of the proposed formulation is studied with simulated experiments.