Finite Impulse Response System Identification Research Articles

Performance Analysis for Subband Identification

The so-called subband identification method has been introduced recently as an alternative method for identification of finite-impulse response systems with large tap sizes. It is known that this method can be more numerically efficient than the classical system identification method. However, no results are available to quantify its advantages. This paper offers a rigorous study of the performance of the subband method. More precisely, we aim to compare the performance of the subband identification method with the classical (fullband) identification method. The comparison is done in terms of the asymptotic residual error, asymptotic convergence rate, and computational cost when the identification is carried out using the prediction error method, and the optimization is done using the least-squares method. It is shown that by properly choosing the filterbanks, the number of parameters in each subband, the number of subbands, and the downsampling factor, the two identification methods can have compatible asymptotic residual errors and convergence rate. However, for applications where a high order model is required, the subband method is more numerically efficient. We study two types of subband identification schemes: one using critical sampling and another one using oversampling. The former is simpler to use and easier to understand, whereas the latter involves more design problems but offers further computational savings.

Blind identification of FIR systems driven by Markov-like input signals

We propose a new algorithm for the blind identification and equalization of finite impulse response (FIR) systems using the second-order statistics of the received signal. The new algorithm is set in the same context as the algorithms of Tong et al. (1994) and Moulines et al. (1995), however, unlike those earlier approaches it is designed to allow correlated input signals. Specifically, the algorithm accommodates finite memory sources and sources whose autocorrelation function decays exponentially. Numerical simulations compare the equalization performance of the new algorithm to those of Tong and Moulines. It is shown that our algorithm yields consistently lower bit-error rates at a wide variety of signal-to-noise ratios and at various equalizer lengths. Moreover, the algorithm maintains this advantage even if it has no a priori information of source correlation or if source symbols are uncorrelated.

Subspace method for blind identification of multichannel FIR systems in noise field with unknown spatial covariance

We present a new subspace-based method for blind identification of multichannel finite impulse response (FIR) systems. Instead of assuming spatially white additive noise as commonly used, we consider the case where the noise spatial covariance matrix is unknown. We show how a standard subspace method can be simply modified so that the channel estimate does not depend on the zero-lag correlation coefficient of the observation vector and, thus, is independent of the spatial covariance matrix of the additive noise.

A new FIR system identification method based on fourth-order cumulants: Application to blind equalization

Recently, numerous Finite Impulse Response (FIR) system identification methods based on High Order Statistics (HOS) have been proposed in the literature. These methods can be classified into three categories: closed-form solutions, linear algebra solutions and nonlinear optimization based solutions. Because of their simplicity, closed-form and linear algebra solutions are the ones most used in practice. In this paper, we propose a new explicit solution based on fourth-order cumulants. Compared to existing closed-form solutions, the proposed solution uses more statistics and compared to linear algebra solutions it needs less arithmetical operations. This solution is based on a Cholesky type decomposition of a positive definite Hermitian matrix made up of fourth-order cumulants. An efficient algorithm is given to estimate this matrix. Then, the proposed FIR system identification method is applied to estimate the impulse response (i.r.) coefficients of a radio communication channel in order to “open the eyes” of the channel by minimizing the Mean-Square Error (MSE) criterion. The performance of the proposed method is illustrated by some simulation results.

FIR system identification using third- and fourth-order cumulants

A new set of equations relating the coefficients of a finite-impulse-response (FIR) system and the third- and fourth-order cumulants of the system output are derived. Based on these equations, two new methods to estimate FIR parameters are presented. Simulation results show that these methods perform better than other recently published linear methods in the additive coloured Gaussian noise case. This improvement is due to the fact that they do not make use of any correlation information and that they employ several slices of third- and fourth-order cumulants.

Blind identification of FIR systems using third order cumulants

A variety of real systems can be represented (either completely or in part) by the finite impulse response (FIR) systems. The parameters of such a system as well as the phase are often required in many practical situations. Non-minimum phase (NMP) systems may be identified correctly from the higher order cumulants which contain the non-minimum phase information. Five estimators based on third-order cumulants are discussed for the identification of (minimum or nonminimum phase) FIR systems from the observed noisy output which has been contaminated by zero-mean symmetric white noise of unknown variance. Two of these algorithms employ both non-linear optimisation and third-order cumulant matching techniques, and the other three are based on the method of least squares but using a specific relation between the third-order cumulants and the parameters of FIR systems. Results from extensive simulations are presented to highlight the salient features and to make comparison with some published results.

Blind identification of FIR systems excited by discrete-alphabet inputs

An algorithm for the identification of finite-impulse-response (FIR) system parameters from output measurements, for systems excited by discrete-alphabet inputs, is described. The approach taken is algebraic. It does not rely directly on the statistical properties of the measurements, but rather it essentially solves the nonlinear equations appearing in the problem by converting them to equivalent linear equations, using the discrete-alphabet property of the input signal. The proposed algorithm was tested by computer simulations and some of these simulations are illustrated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Linear bispectrum of signals and identification of nonminimum phase FIR systems driven by colored input

The identification of non-minimum-phase finite-impulse-response (FIR) systems driven by third-order stationary colored signals that are not linear processes is addressed. Modeling the linear part of the bispectrum of a signal is discussed. The bispectrum of a signal is decomposed into two multiplicative factors. The linear bispectrum is defined as the factor of the bispectrum that can exactly be modeled using a third-order white-noise-driven linear shift-invariant (LSI) system. The linear bispectrum of the output of the unknown LSI system is represented using an ARMA (autoregressive moving average) model, where the MA parameters correspond to the unknown FIR system impulse response coefficients, and the AR parameters model the linear bispectrum of the input signal. An algorithm for identifying the MA and AR parameters is given. How the proposed method is different from fitting an ARMA model directly to the bicumulants or the bispectrum of the system output is discussed. The method is applied to blur identification. >

Adaptive deconvolution and identification of nonminimum phase FIR systems based on cumulants

A novel adaptive deconvolution and system identification scheme is introduced for a linear, non-minimum-phase finite-impulse-response (FIR) system driven by non-Gaussian white noise. The adaptive scheme is based on approximating the FIR system by noncausal autoregressive (AR) models and using higher order cumulants of the system output. As such, it is a blind equalization (deconvolution) scheme. The set of updated AR parameters is obtained by using a gradient-type algorithm and by using higher order cumulants instead of time samples of the output signal. It is demonstrated by means of extensive simulations that the adaptive scheme works well for both stationary and nonstationary cases. As expected, it outperforms the autocorrelation-based gradient method for nonminimum-phase system identification and deconvolution. Performance comparisons to existing methods are given, using as figures of merit the probability of errors in the restored input sequence, computational complexity, and convergence rate. >

Performance of a Fast Algorithm for FIR System Identification Using Least-Squares Analysis

A wide variety of procedures have been proposed for identifying a finite impulse response (FIR) linear system from the input and output of the system. Most recently, a fast, efficient, least-squares method was proposed by Marple, and was shown to require less computation and storage than any other known procedure for identifying moderate to large FIR systems. In this paper we measure the actual performance of the newly proposed fast system identification algorithm by using it to estimate a variety of FIR systems excited by either white noise or a speech signal. It is shown that essentially theoretically ideal performance is achieved for white noise inputs; however, for speech signals poor performance was obtained because of the lack of certain frequency bands in the excitation. A simple modification to the estimation procedure is proposed and is shown to provide substantial performance improvements. Using the spectrally modified speech signal, the performance of the fast system identification algorithm was found to be acceptable for a wide variety of applications.

Efficient least squares FIR system identification

If finite impulse response (FIR) system identification is performed by minimizing the squared error between the measured system output and an estimate from an FIR system output, a set of least squares normal equations to be solved for the FIR system coefficients is obtained. If the assumed FIR system is of duration M samples, the usual solution for the M least squares simultaneous equations requires a number of computational operations proportional to M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> and storage of normal equation coefficients proportional to M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . The set of normal equations has an underlying structure, however, that can be exploited to yield a solution with computational operations proportional to M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and storage proportional to M. Such an efficient algorithmic solution is presented here.

Short-time Fourier analysis tecniques for FIR system identification and power spectrum estimation

A wide variety of methods have been proposed for system modeling and identification. To date, the most successful of these methods have been time domain procedures such as least squares analysis, or linear prediction (ARMA models). Although spectral techniques have been proposed for spectral estimation and system identification, the resulting spectral and system estimates have always been strongly affected by the analysis window (biased estimates), thereby reducing the potential applications of this class of techniques. In this paper we propose a novel short-time Fourier transform analysis technique in which the influences of the window on a spectral estimate can essentially be removed entirely (an unbiased estimator) by linearly combining biased estimates. As a result, section (FFT) lengths for analysis can be made as small as possible, thereby increasing the speed of the algorithm without sacrificing accuracy. The proposed algorithm has the important property that as the number of samples used in the estimate increases, the solution quickly approaches the least squares (theoretically optimum) solution. The method also uses a fixed Fourier transform length independent of the amount of data being analyzed, allowing the estimate to be recursively updated as more data is made available. The method assumes that the system is a finite impulse response (FIR) system.

FIR system modeling and identification in the presence of noise and with band-limited inputs

System identification, that is, the modeling and identification of a system from knowledge of its input and output signals, is a subject that is of considerable importance in many areas of signal and data processing. Because of the diversity of applications, a number of different methods for system identification with different advantages and disadvantages have been described and used in the literature. In this paper we investigate the performance of three well-known system identification methods based on an FIR (finite impulse response) model of the system. The methods will be referred to in this paper as the least squares analysis (LSA) method, the least mean squares adaptation algorithm (LMS), and the short-time spectral analysis (SSA) procedure. Our particular interest in this paper concerns the performance of these algorithms in the presence of high noise levels and in situations where the input signal may be band-limited. Both white and nonwhite random noise signals as well as speech signals are used as test signals to measure the performance of each of the system identification techniques as a function of the signal-to-noise ratio of the systems output. Quantitative results in terms of an accuracy measure of system identification are presented and a simple analytical model is used to explain the measured results.