Minimax estimation of unknown deterministic signals in colorednoise

The estimation of a deterministic signal corrupted by random noise is considered. The strategy is to find a linear noncausal estimator which minimizes the maximum mean square error over an a priori set of signals. This signal set is specified in terms of frequency/energy constraints via the discrete Fourier transform. Exact filter expressions are given for the case of additive white noise. For the case of additive colored noise possessing a continuous power spectral density, a suboptimal filter is derived whose asymptotic performance is optimal. Asymptotic expressions for the minimax estimator error are developed for both cases. The minimax filter is applied to random data and is shown to solve asymptotically a certain worst-case Wiener filter problem     

A constrained weighted least squares approach for time-frequencydistribution kernel design

In most applications of time-frequency (t-f) distributions, the t-f kernel is of finite extent and applied to discrete time signals. This paper introduces a matrix-based approach for t-f distribution kernel design. In this new approach, the optimum kernel is obtained as the solution of a linearly constrained weighted least squares minimization problem in which the kernel is vectorial and the constraints form a linear subspace. Similar to FIR temporal and spatial constrained least squares (LS) design methods, the passband, stopband, and transition band of an ideal kernel are first specified. The optimum kernel that best approximates the ideal kernel in the LS error sense, and simultaneously satisfies the multiple linear constraints, is then obtained using closed-form expressions. This proposed design method embodies a well-structured procedure for obtaining fixed and data-dependent kernels that are difficult to obtain using other design approaches     

时频子空间拟合波达方向估计

本文提出了一种基于信号空时特征结构的时频子空间拟合方法,利用双线性时频分布构造时频相关矩阵 C _x代替传统的阵列相关矩阵 R _x,通过 C _x的特征分解实现了信号子空间与噪声子空间的分离.该方法在空域和二维时频域同时进行处理,能够区分具有不同时频特征的信号,既适用于平稳信号的场合又适用于时变、非平稳信号的情形,属于空时多维处理的范畴.可以证明,基于平稳信号假设的经典子空间方法是该方法的低维特例.由于包含了时变滤波的过程,因此该方法具有信号选择性以及抗干扰和抗噪声的能力.仿真结果证实了该方法的有效性.     

Time-frequency projection filters and time-frequency signalexpansions

We consider the problems of designing a linear, time-varying filter with a specified “time-frequency (TF) pass region” and of constructing an orthonormal basis for the parsimonious expansion of signals located in a given TF support region. These problems of TF filtering and TF signal expansion are reduced to the problem of designing a “TF subspace”, i.e., a linear signal space comprising all signals located in a given TF legion. Specifically, the TF filter is taken to be the orthogonal projection operator on the TF subspace. We present an optimum design of TF subspaces that is based on the Wigner distribution of a linear signal space and is an extension of the well-known signal synthesis problem. The optimum TF subspace is shown to be an “eigenspace” of the TF region, and some properties of eigenspaces are discussed. The performance of TF projection filters and TF signal expansions is studied both analytically and via computer simulation     

Optimal information fusion distributed smoother for discrete multichannel ARMA signals

Based on the multisensor optimal information fusion criterion weighted by matrices in the linear minimum variance sense, using estimators of white measurement noise, an optimal information fusion distributed Kalman smoother is given for discrete time multichannel autoregressive moving average (ARMA) signals with correlated noise. It has a three-layer fusion structure with a fault tolerant property. The first and the second fusion layers both have netted parallel structures to determine cross-covariance matrices between any two faultless sensors. The third fusion layer is the fusion centre to determine the optimal weights and obtain the optimal fusion smoother. The fusion smoother has higher precision than that of any local smoother. Its effectiveness is shown by applying it to a double-channel signal system with three sensors.     

Structurally Constrained Receivers for Signal Detection and Estimation

A general approach to the problem of designing structurally constrained receivers for signal detection and estimation is proposed. The approach is based on the constrained Bayesian methodology wherein risk-minimizing inference (or decision) rules are modified (constrained) by replacement of true posterior probabilities with estimated posterior probabilities. The estimators are structurally constrained minimum-mean-squared-error (MMSE) estimators for random posterior probabilities. This methodology is, in essence, an extension and generalization of the well-known linear MMSE estimation methodology. The approach is employed to design linearly constrained coherent receivers for signals in additive and multiplicative noise, and quadratically constrained noncoherent receivers for signals in additive noise. An analysis of these receivers shows that they are very similar to those that are optimum for additive Gaussian noise. The methodology provides a unified theory of receiver design based on the constrained MMSE criterion. This unification yields new insight into this old approach, clarifying both strengths and weaknesses of the approach.     

A transform domain SVD filter for suppression of muscle noise artefacts in exercise ECG's

The proposed filter assumes the noisy electrocardiography (ECG) to be modeled as a signal of deterministic nature, corrupted by additive muscle noise artefact. The muscle noise component is treated to be stationary with known second-order characteristics. Since noise-free ECG is shown to possess a narrow-band structure in discrete cosine transform (DCT) domain and the second-order statistical properties of the additive noise component is preserved due to the orthogonality property of DCT, noise abatement is easily accomplished via subspace decomposition in the transform domain. The subspace decomposition is performed using singular value decomposition (SVD). The order of the transform domain SVD filter required to achieve the desired degree of noise abatement is compared to that of a suboptimal Wiener filter using DCT. Since the Wiener filter assumes both the signal and noise structures to be statistical, with a priori known second-order characteristics, it yields a biased estimate of the ECG beat as compared to the SVD filter for a given value of mean-square error (mse). The filter order required for performing the subspace smoothing is shown to exceed a certain minimal value for which the mse profile of the SVD filter follows the minimum-mean-quare error (mmse) performance warranted by the suboptimal Wiener filter. The effective filter order required for reproducing clinically significant features in the noisy ECG is then set by an upper bound derived by means of a finite precision linear perturbation model. A significant advantage resulting from the application of the proposed SVD filter lies in its ability to perform noise suppression independently on a single lead ECG record with only a limited number of data samples.     

Locally optimum rank detection of correlated random signals inadditive noise

Nonparametric detection of a zero-mean random signal in additive noise is considered. The locally optimum detector based on signs and ranks of observations is derived, for good weak-signal detection performance under any specified noise probability density function. This detector is shown to have interesting similarities to the locally optimum detector for random signals. It may also be viewed as a generalization of the locally optimum rank detector for known signals. Examples of the test statistic of the detector are given for some specific noise probability density functions. Asymptotic and finite sample-size performance of the locally optimum rank detector is also considered     

Optimum differentiation using Kalman filter theory

Consideration is given to the construction of an optimum differentiator to give the minimum-variance unbiased estimate of the first derivatives of random signals corrupted by white noise. It is assumed that the signals are differentiable and are the outputs of a known linear finite-dimensional (possibly time-varying) system excited by white noise. Extension of the results to consider higher-order differentiation is straightforward.     

异步DS-CDMA系统盲空时信道估计及多用户检测

该文提出了适用于频率选择性瑞利衰落信道中的异步DS-CDMA系统盲空时信道估计及多用户检测算法。通过研究多径信号码空间和数据矢量空间,采用噪声子空间技术进行异步DS-CDMA系统盲空时信道参数估计,同时利用了多径传播和接收机同步失调的特性,以利于把盲线性滤波优化技术应用于稳健的干扰抑制。使用一种修改的ULV更新算法进行噪声子空间跟踪,该算法不需要相关矩阵的秩估计,直接估计噪声子空间,不进行信号子空间跟踪。并且研究了线性约束最小方差(LCMV)盲空时多用户检测及其基于Householder变换约束最小均方算法(HCLMS)的自适应实现。仿真结果验证了该文算法的有效性。     

The linear prediction of deterministic signals

A method is presented for linear estimations of functionals of deterministic signals containing additive noise. The method is based on statistical decision theory and assumes discrete observations. In general terms a deterministic signal, with the noise subtracted, is a member of a class of functions with no probability distribution over the members of the class. In this paper the class is restricted to real one-dimensional functions parametrized by a real vector. The linear minimax estimate of the function to be estimated is proposed and the problem of computing it shown to be equivalent to a quadratic programming problem which can be solved exactly when the class of true signals is finite and sometimes when the class is infinite. In the latter case the problem can be solved approximately, subject to some mild restrictions on the signal. The exact algebraic solution is given for prediction of linear signals for up to three observations and is compared with the solution based on Wiener's theory.     

一种用于未知噪声背景中相干源二维波达方向估计的新方法

本文提出了一种用于相干源二维波达方向（DOA）估计的新方法。在该方法中，通过构造一种特别形式的阵列数据协方差矩阵，并利用一次最小平方过程从中提取一个线性算子用以估计噪声子空间，使算法不受信号源相关性的影响，且避免了矩阵的特征值分解。基于噪声的相关性是空间带限的合理假设，新方法选用了一种简单而又特殊的平面阵列结构，用以估计信号源入射的方位角和仰角，使算法不需要特定的传感器加性噪声模型。由于该新方法具有上述优点，因而使其更面向于实时应用。     

A general likelihood-ratio formula for random signals in Gaussian noise

It is shown that the likelihood ratio for the detection of a random, not necessarily Gaussian, signal in additive white Gaussian noise has the same form as that for a known signal in white Gaussian noise. The role of the known signal is played by the casual least-squares estimate of the signal from the observations. However, the "correlation" integral has to be interpreted in a special sense as an Itô stochastic integral. It will be shown that the formula includes all known explicit formulas for signals in white Gaussian noise. However, and more important, the formula suggests an "estimator-correlator" philosophy for engineering approximation of the optimum receiver. Some extensions of the above result are also discussed, e.g., additive finite-variance, not necessarily Gaussian, noise plus a white Gaussian noise component. Purely colored Gaussian noise can be treated if whitening filters can be specified. The analog implementation of Itô integrals is briefly discussed. The proofs of the formulas are based on the concept of an innovation process, which has been useful in certain related problems of linear and nonlinear least-squares estimation, and on the concept of covariance factorization.     

Multiple signal extraction by multiple interference attenuation in the presence of random noise in seismic array data

A vector of digital filters is derived for the multichannel processing of the signals acquired by an array of sensors with the objective of extracting multiple desired signals by the attenuation of multiple interferences and random noise. The signals and interferences are assumed to have arbitrary waveforms with no a priori knowledge of these waveforms. The time duration of the recorded array data is assumed to be long enough to incorporate all time delayed propagated waveforms at the sensors of the array. The derivation is for the general case of an arbitrary array geometric configuration and is not confined to the special case of a linear array of equispaced sensors. The rationale adopted in the derivation of the filters is to give first priority at each discrete frequency to passing the signals, a second priority to canceling the interferences, and a third priority to attenuating the random noise. This rationale well suits the case of seismic data that are dominantly corrupted by strong interferences rather than random noise. Solving a constrained minimization problem derives the vector of array filters. The computation of this vector requires the application of a powerful matrix decomposition technique for the detection of any redundant and/or inconsistent constraints at each discrete frequency. The simulation results demonstrate the extraction ability of the derived filters in both the multiple input single output and the multiple input multiple output processing schemes.     

The structure of least-mean-square linear estimators for synchronousM-ary signals (Corresp.)

Several authors have shown that the structure of the least-mean-square linear estimator of the sequence of random amplitudes in a synchronous pulse-amplitude-modulated signal that suffers intersymbol interference and additive noise is a matched filter whose output is periodically sampled and passed through a transversal filter (tapped delay line). It is our purpose in this paper to generalize this result to synchronousm-ary signals (e.g., FSK, PSK, PPM signals). We prove that the structure of the least-mean-square linear estimator of the sequence of random parameters in a synchronousm-ary signal, which suffers intersymbol interference and additive noise, is a parallel connection ofmmatched filters followed by tapped delay lines. A similar structure is derived for the continuous waveform estimator of a synchronousm-ary signal. Finally, we present a structure for estimation-decision detection of synchronousm-ary signals, which is based on least-mean-suare linear estimates of aposterioriprobabilities.     

一种新的子空间跟踪方法在DOA估计中的应用

介绍了一种新的子空间跟踪方法(双迭代最小二乘(Bi—LS)子空间跟踪方法)在DOA估计中的应用。特征子空间方法的关键是对信号或噪声子空间的估计。在实际中，有些信号的统计特性是时变的，为得到参数的即时估计值，需要随时根据新的阵列接受数据对信号或噪声子空间进行更新。将Bi—LS子空间跟踪算法和自适应ESPRIT算法相结合，形成一种快速递推的自适应ESPRIT算法，对时变信号DOA进行跟踪估计。其计算复杂度小，仿真结果验证了该算法的有效性。     

基于小波包变换的非高斯噪声信号结构分析

该文利用小波包变换的时频局部分析能力,研究了非高斯分布平稳随机噪声的统计特性,揭示了 非高斯噪声信号的信号结构。在此基础上,将经典最优检测器的结论推广到背景噪声为非高斯分布的情况, 提出了一种基于小波包变换的非高斯噪声下的信号检测方法。仿真实验验证了该方法是正确的。     

Single-trial subspace-based approach for VEP extraction

A signal subspace approach for extracting visual evoked potentials (VEPs) from the background electroencephalogram (EEG) colored noise without the need for a prewhitening stage is proposed. Linear estimation of the clean signal is performed by minimizing signal distortion while maintaining the residual noise energy below some given threshold. The generalized eigendecomposition of the covariance matrices of a VEP signal and brain background EEG noise is used to transform them jointly to diagonal matrices. The generalized subspace is then decomposed into signal subspace and noise subspace. Enhancement is performed by nulling the components in the noise subspace and retaining the components in the signal subspace. The performance of the proposed algorithm is tested with simulated and real data, and compared with the recently proposed signal subspace techniques. With the simulated data, the algorithms are used to estimate the latencies of P(100), P(200), and P(300) of VEP signals corrupted by additive colored noise at different values of SNR. With the real data, the VEP signals are collected at Selayang Hospital, Kuala Lumpur, Malaysia, and the capability of the proposed algorithm in detecting the latency of P(100) is obtained and compared with other subspace techniques. The ensemble averaging technique is used as a baseline for this comparison. The results indicated significant improvement by the proposed technique in terms of better accuracy and less failure rate.     

基于小波包变换的双模噪声中信号的检测

以一类非高斯噪声———双模噪声为背景噪声,利用小波包变换良好的时频分析能力,对双模噪声的统计特性进行了研究,在此基础上,将经典最优检测器的结论推广到背景噪声为双模噪声的情况,提出了基于小波包变换的双模噪声中信号的检测方法。他是对传统的双模噪声中信号处理的完善与补充,仿真结果表明,该方法要明显优于经典检测。     

Analog communication over randomly-time-varying channels

The problem of analog communication over a randomly-time-varying channel is considered. An analog source generates a message which is assumed to be a sample function from a Gaussian random process. The message is passed through a linear realizable system before modulation. (This corresponds to the pre-emphasis network in FM.) The output of this system is the modulating signal for a no-memory modulator which, in general, will be nonlinear. The modulated signal is transmitted over a time-varying channel We restrict ourselves to Gaussian multiplicative channels. At the channel output, noise is added. The specific problem of interest is to find the optimum estimate of the message. The principle results are: begin{enumeratge} item An integral equation whose solution is the optimum estimate. item A feedback demodulator whose output is the optimum estimate over a certain range of signal-to-noise ratios. item A proof that the optimum demodulator corresponds to a joint channel and message estimator. This result is the continuous analog of the estimator-correlator result in digital systems. Some related problems and possible extensions are discussed briefly. end{enumerate}