Cumulant-based blind identification of linearmulti-input-multi-output systems driven by colored inputs

The blind identification problem of a linear multi-input-multi-output (MIMO) system is widely noticed by many researchers in diverse fields due to its relevance to blind signal separation. However, such a problem is ill-posed and has no unique solution. Therefore, we can only find a solution of the problem within an equivalence class. We address the blind identification problem of the linear MIMO system driven by unobservable colored inputs using higher order statistics (HOS), particularly the fourth-order cumulants, of the outputs, where the unobservable inputs are mutually independent but temporally colored linear processes. We first define the set, which is denoted by S, of stable scalar transfer functions and then define the notion of a generalized permutation matrix (which is abbreviated by a g-matrix) over S. Then, it is shown that the transfer function matrix of an unknown system is identified only up to post-multiplication by a g matrix. This result is applied to identifying FIR systems for blind signal separation     

Blind equalization of MIMO-FIR channels driven by white but higherorder colored source signals

The goal of the article is to find a minimal amount of statistical information (or a much weaker condition) about source signals for which blind equalization is possible for multiple-input multiple-output finite-impulse response (MIMO-FIR) channels. First, a sufficiently broad framework is set up within which such a theoretical problem is well posed. Within this framework, it is shown that second-order statistics (SOS) alone are not sufficient for blind equalization when the source signals are white. Additional higher order statistics (HOS) are needed. Then we show that the only additional higher order statistical information needed is spatial fourth-order cumulants. Though it has not yet been proved to be minimal, it is interesting to note that this is the same as the weakest known condition on the source signals even for an instantaneous mixture. We then show a necessary and sufficient condition for blind equalization when the source signals are white and spatially fourth-order uncorrelated. Based on this condition, criterion (A) for blind equalization of MIMO-FIR channels is developed by exploiting the temporal fourth-order statistics. Finally, based on this criterion, a new necessary and sufficient condition in terms of cumulants for the blind equalization of MIMO-FIR channels is obtained     

Efficient calculation of partial derivatives in nonlinear conductances driven by periodic input signals

Expressions for calculating current derivatives efficiently with respect to voltage in nonlinear conductances under periodic excitation are derived. The validity of Egami's approach for computing these derivatives is discussed.     

EVAM: an eigenvector-based algorithm for multichannel blinddeconvolution of input colored signals

A new algorithm is proposed for the deconvolution of an unknown, possibly colored, Gaussian or nonstationary signal that is observed through two or more unknown channels described by rational system transfer functions. More specifically, not only the root (pole and zero) locations but also the orders of the channel transfer functions are unknown. It is assumed that the channel orders may be overestimated. The proposed algorithm estimates the orders and root locations of the channel transfer functions, therefore it can also be used in multichannel system identification problems. The input signal is allowed to be nonstationary and the channel transfer functions may be a nonminimum phase as well as noncausal, hence the proposed algorithm is particularly suitable for applications such as dereverberation of speech signals recorded through multiple microphones. Several experimental results indicate improvement compared to the existing methods in the literature     

Blind identification of FIR systems driven by Markov-like inputsignals

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     

The bispectrum of complex signals: definitions and properties

The symmetry properties and the relationship between all forms of third-order cumulants of complex signals are investigated. It is shown that all cumulants (for different position of the complex conjugate) are related by simple transformations. Autoregressive modeling of complex-valued signals using third-order cumulants is also investigated. It is shown that modeling of complex-valued signals requires a different approach from modeling of real-valued signals     

Blind identification and deconvolution of linear systems driven bybinary random sequences

The problem of blind identification and deconvolution of linear systems with independent binary inputs is addressed. To solve the problem, a linear system is applied to the observed data and adjusted so as to produce binary outputs. It is proved that the system coincides with the inverse of the unknown system (with scale and shift ambiguities), whether it is minimum or nonminimum phase. These results are derived for nonstationary independent binary inputs of infinite or finite length. Based on these results, an identification method is proposed for parametric linear systems. It is shown that under some mild conditions, a consistent estimator of the parameter can be obtained by minimizing a binariness criterion for the output data. Unlike many other blind identification and deconvolution methods, this criterion handles nonstationary signals and does not utilize any moment information of the inputs. Three numerical examples are presented to demonstrate the effectiveness of the proposed method     

Performance of a quadricorrelator driven by modulated signals

An analysis is presented of a balanced quadricorrelator driven by a digital-modulated signal with thermal noise. The aim is to assess its performance as a frequency difference detector. The circuit output is decomposed into a signal term and a disturbance referred to as noise. Exprssions are given for the signal and for the power spectral density of the noise as a function of the various system parameters. Design criteria are provided to minimize the output noise for zero frequency offset. In particular, it is found that at high signal-to-noise ratios the noise level can be made vanishingly small by the proper choice of the quadricorrelator filters. A similar result has been recently discovered for another frequency difference detector, the dual-filter detector. It is shown that a balanced quadricorrelator and a dual-filter detector can be made totally equivalent     

加性信号调制下色关联噪声驱动的单模激光的光强关联时间

采用线性化近似,计算了加性信号调制下色关联噪声驱动的单模激光增益模型的光强关联时间T,发现当两噪声间关联程度λ为正时,T-D和T-I0曲线中出现极大值(即出现共振);当λ为负时,T-D曲线中出现极小值(即出现抑制),T-I0曲线出现两个极值(一个极小值一个极大值);当λ为零时,T随量子噪声强度D和定态光强I0的增加而单调增加.另外,无论λ取何值,T随周期信号振幅A和衰减系数γ的增大都单调减小.同时通过研究周期信号频率Ω和噪声互关联时间τ3对T-D、T-I0、T-A以及T-γ曲线的影响,发现Ω的取值对这四种曲线的影响不大,而τ3的取值对T-D、T-I0和T-A曲线的影响较大,对T-γ曲线的影响较小.     

Linear systems identification from random threshold binary data

A new identification problem of estimating parameters of linear dynamic systems from random threshold binary observations of its output and input is stated. The only available data are collected as a result of checking whether a signal reached a randomly specified threshold at a randomly chosen instant of time. The proposed estimation algorithm is based on the celebrated von Neumann theorem, which was earlier used mainly for generating random numbers. Strong consistency of parameters estimate from low-cost output binary observations is proved, assuming deterministic input signal of a finite duration. Possibilities of relaxing the assumption used in the theoretical part of the paper are considered by means of simulations     

Direct adaptive control of nonminimum phase systems using integralaction

A direct adaptive control scheme is proposed for nonminimum-phase systems in which controller parameters are estimated from the recursive least-squares algorithm and additional auxiliary parameters are obtained from the proposed polynomial identity. A local convergence is guaranteed without any extra condition. Integral action is incorporated into the adaptive controller to eliminate the steady-state error and to satisfy a condition of the unique solution for the polynomial identity. The control law used in this scheme is based on the set-point-on-I-only proportional-integral-derivative (PID) structure     

Blind input, initial state, and system identification of SIMO Laguerre systems

Laguerre filters have infinite impulse responses (IIRs) but with finite tapped delay-line parameterizations. This paper investigates subspace-based blind identification of Laguerre filter tap coefficients, the internal filter state, and the input, given only noisy observations of the output. This paper deals only with single-input, multiple-output (SIMO) Laguerre models. A state space model for the SIMO Laguerre system is derived from which blind estimation algorithms are developed. As in the finite impulse response (FIR) case, the Laguerre filter taps coefficients can be estimated from the column space of a certain Hankel matrix constructed from noisy output observations, whereas the internal state and input can be estimated from the row space by exploiting state space structure. While not exactly uniquely identifiable, conditions are given for which the tap coefficients, the internal state, and the input can be determined to within a multiplicative scalar factor.     

Adaptive identification of nonminimum phase ARMA models usinghigher order cumulants alone

An adaptive identification algorithm for causal nonminimum phase ARMA models in additive colored Gaussian noise is proposed. The algorithm utilizes higher order cumulants of the observed signal alone. It estimates the AR and MA parameters successively in each iteration without computing the residual time series. The steepest descent method is used for parameter updating     

Linear multiuser detectors for incompletely known symmetric signals in CDMA systems

In this paper, we consider a synchronous code-division multiple-access (CDMA) system with a multiuser receiver. All users are assumed to have symmetric signature sequences, but the presence of a subset of the users is unknown to the receiver. We first calculate the signal-to-interference ratio (SIR) in this environment for the matched-filter receiver, the decorrelating receiver, and the linear minimum mean-square error (MMSE) detector. We then identify the user capacity for a single-class system, and the effective bandwidth for a multiple-class system. The result is compared to the case of random sequences and of optimum sequences. For symmetric sequences, the effective bandwidth cannot be expressed by a scalar as in , because two constraints have to be satisfied simultaneously to satisfy the SIR requirement. We introduce a two-dimensional (2-D) vector notion of effective bandwidth with and without unknown users. For both the decorrelator and the MMSE detector, the user capacity is 1 when all users are known to the receivers and is reduced to (1-N/L) when N users are unknown (with L the processing gain). The performance of these three linear detectors, with and without unknown users, is compared.     

Identification of nonminimum phase FIR systems via fourth-order cumulants and genetic algorithm

In this paper, the problem of estimating the parameters of an FIR system from only the fourth-order cumulants of the noisy system output is considered. The FIR system is driven by a symmetric, independent, and identically distributed (i.i.d) non-Gaussian sequence. We propose a new formula called Weighted Overdetermined C(q, k) (WOC(q, k)) by extending the conventional C(q, k) formula. The optimal selection of the weights in WOC(q, k) is performed by using the Genetic Algorithm (GA) optimization method which minimizes a nonlinear error function based on the fourth-order cumulants alone. Simulations are provided to reveal the effectiveness and the superiority of this novel technique over the C(q, k) and other existing techniques.     

The cross-bicepstrum: definition, properties, and application forsimultaneous reconstruction of three nonminimum phase signals

The recovery of three signals from their cross-bispectrum (or the identification of the impulse responses of three parallel linear time-invariant (LTI) systems from the cross-bispectrum of their system outputs) by computing the complex cepstrum of the cross-bispectrum, as long as the signals (or impulse responses) have no zeros on the unit circle, is discussed. It is shown that the three signals can be separated completely and (approximately) recovered in the cross-bicepstrum domain, except for their magnitude and linear phase factors. The computation of the cross-bicepstrum can be seen as a method for the simultaneous computation of the ordinary complex cepstra of three nonminimum-phase signals without the need for phase unwrapping. Both least-squares and fast Fourier-transform (FFT)-based methods for computing the bicepstral coefficients are presented. Simulation examples of signal reconstruction in Gaussian white and nonGaussian colored noise and of system identification are included. The results are extended to nth-order cross-spectra, and the factorization problem for these spectra is discussed     

音圈电机激光扫描器的线性扫描控制

建立了音圈电机驱动的激光扫描器的模型并进行了参数辨识。由于音圈电机驱动的激光扫描器反馈回路的高频噪声较大,利用光电精密跟踪的传统方法,如改进型PID控制算法,以及理想闭环特性(最佳二阶特性)的逆向设计方法,系统并不能稳定工作,易振荡。分析了造成振荡的原因,采用前馈复合控制方法,避开了振荡因子同时又减小了稳态误差,解决了稳态误差和振荡的矛盾。结合反馈回路噪声大的特点,将滤波器加入反馈回路中,使激光扫描器不仅能稳定工作,消除了扫描时候的抖动,同时减少了线性扫描时候的磁滞现象。     

Receivers AM input signals probability characteristics and qualityestimation

Different structures of universal and automated integral monitoring systems (AIMS) for broadcasting are discussed. A procedure determining the probability characteristics of broadcasting receivers input signal levels is investigated, and useful statistic distribution laws are obtained. The results enable us to propose an integral quality estimation for an amplitude modulated broadcasting system operating in the 0.15 to 30 MHz frequency range. This method can be applied to various modulation methods and frequency ranges     

Linear prediction of subband signals

The performance of linear prediction of fullband and subband signals is described in terms of the respective prediction gain. The subband prediction gain is characterized in terms of the fullband signal power spectral density and the frequency response of the subband filters. For Gaussian fullband signals, the asymptotic subband prediction gain can never be larger than the asymptotic fullband prediction gain. Simulation results compare fixed and adaptive fullband and subband prediction gains for Gaussian sources and speech. For speech, the subband prediction gain can exceed the fullband prediction gain     

Blind channel identification with colored sources by exploiting properties of companion matrices

This paper proposes a new second-order statistics-based method for blind multiple-input multiple-output (MIMO) finite-impulse-response (FIR) channel estimation driven by colored sources. It is assumed that the second-order statistics (SOS) of the input sources are known a priori. By exploiting the new derived properties of the companion matrices, an original proof for the uniqueness of the system solution is provided, which serves as a theoretical basis for the proposed new method that admits a closed-form solution. The corresponding identifiability conditions and the computational complexity of the proposed method are discussed and compared with other existing method. Numerical simulation results are presented to illustrate the performance of the proposed algorithm.