Number Of Source Signals Research Articles

Frequency-Domain Blind Source Separation of Many Speech Signals Using Near-Field and Far-Field Models

We discuss the frequency-domain blind source separation (BSS) of convolutive mixtures when the number of source signals is large, and the potential source locations are omnidirectional. The most critical problem related to the frequency-domain BSS is the permutation problem, and geometric information is helpful as regards solving it. In this paper, we propose a method for obtaining proper geometric information with which to solve the permutation problem when the number of source signals is large and some of the signals come from the same or a similar direction. First, we describe a method for estimating the absolute DOA by using relative DOAs obtained by the solution provided by independent component analysis (ICA) and the far-field model. Next, we propose a method for estimating the spheres on which source signals exist by using ICA solution and the near-field model. We also address another problem with regard to frequency-domain BSS that arises from the circularity of discrete-frequency representation. We discuss the characteristics of the problem and present a solution for solving it. Experimental results using eight microphones in a room show that the proposed method can separate a mixture of six speech signals arriving from various directions, even when two of them come from the same direction.

Resolution of signal sources via spectral moment estimation

In different practical situations it is desired to estimate the number of signal sources and their positions in space or in frequency domain. The first problem is known as the detection or the order estimation and the second one as the resolution. For the resolution problem techniques such as nonlinear least squares (NLSM), high-order Yule-Walker method (HOYW), multiple signal classification (MUSIC), Pisarenko harmonic retrieval method, min-norm method, estimation of signal parameters by rotational invariance technique (ESPRIT), were proposed (Marple, 1987 and Stoica and Moses, 1997). All these high-resolution methods are based on the analysis of the signal covariance matrix. But the covariance matrix is not the only choice to represent the signal spectrum. In different applications (weather radars, synthetic aperture radar (SAR) signal processing, ultrasound imaging in medicine, atmospheric turbulence measurements) the signal spectrum can be modeled through its algebraic moments. Recently a number of efficient nonparametric methods have been proposed to estimate the algebraic spectral moments (Monakov, 1999). The presented paper is an attempt to solve the direction of arrival (DOA) problem via estimation of the algebraic spectral moments. A method proposed in the article is comparable in its accuracy with the MUSIC method. At the same time its computational burden is much lower. The method permits to estimate the signal power of sources easily to complete the full spectral line analysis. Additionally the method shows good robustness in situations when signal sources have noticeable spatial extend

Robust adaptive blind signal estimation algorithm for underdetermined mixture

In general, existing blind source separation (BSS) algorithms have been designed based on assumptions that there are at least an equal number of sources and sensors and/or there is no noise present. These ideal situations rarely exist and hence the algorithms do not produce optimum results where either one or both of the assumptions have been violated. Underdetermined mixtures where the number of source signals is greater than the number of observed signals are encountered in neural signal detection from a small number of sensors, image modelling, EEG data and biomedical applications. A new algorithm to estimate unknown source signals from fewer observed signals and simultaneously reduce noise is proposed. The proposed algorithm is based upon a model that addresses the issue of noise and offers greater accuracy with standard assumptions relaxed. It offers an attractive solution with no pre-requisites on the nature of the signals and noise for the algorithm to be applicable. Most BSS algorithms adopt batch processing and are only applicable to orthogonal mixtures. The proposed algorithm does not require the mixing matrix to be orthogonal and can be implemented in an adaptive format to track time-varying mixtures. Results supporting the algorithm's superiority and comparisons with results from other algorithms are also presented to prove the tracking capability of our adaptive algorithm. Synthetic and real-time simulations demonstrate the improvement in convergence and accuracy of estimated signals with fewer restrictions in terms of its applicability.

Model-order selection

The parametric (or model-based) methods of signal processing often require not only the estimation of a vector of real-valued parameters but also the selection of one or several integer-valued parameters that are equally important for the specification of a data model. Examples of these integer-valued parameters of the model include the orders of an autoregressive moving average model, the number of sinusoidal components in a sinusoids-in-noise signal, and the number of source signals impinging on a sensor array. In each of these cases, the integer-valued parameters determine the dimension of the parameter vector of the data model, and they must be estimated from the data.

Direction-of-Arrival Tracking Scheme for DS/CDMA Systems: Direction Lock Loop

In this paper, a new direction-of-arrival (DOA) tracking algorithm, direction lock loop (DiLL), is proposed for wireless direct-sequence code-division multiple-access systems. It has a similar concept to the delay lock loop that is used for timing synchronization. It may track the DOA of sources by iterations. Its computational requirements are NK+O(K) for coherent DiLL and 2NK+O(K) for noncoherent DiLL, where N is the number of antenna elements and K is the number of signal sources, which is less than that of the projection approximation subspace tracking with deflation algorithm. The DOA tracking accuracy is demonstrated by analysis and computer simulations.

重畳パルス列の信号分離のための時間-周期解析法

This paper presents a new method for signal separation of interleaved pulse trains consisting of several pulse trains emitted from independent signal sources, some of which may only exist for a short time. The separation is based on the differences in the pulse repetition intervals (PRIs) of the signal sources. To detect each pulse train, we derive a map from the input signal to a function of two variables: time and PRI, which we call the PRI map. By taking the absolute value of the PRI map, we obtain a short-time PRI spectrum from which we can use thresholding to estimate the number of signal sources, their time duration, and the PRIs. The PRI map is an extension of PRI transform, which we previously proposed. The extension is based on time-period analysis. The construction of the PRI map resembles a wavelet transform. The difference is that a PRI map is a nonlinear transform, while the wavelet transform is linear. Simulation results are presented on the performance of the signal separation of interleaved pulse trains using the PRI map. Finally, performance analysis shows the detection ability of the PRI map for short pulse trains.

Detection-estimation of more uncorrelated gaussian sources than sensors in nonuniform linear antenna arrays-part II: partially augmentable arrays

Previous studies dealing with direction-of-arrival (DOA) estimation for uncorrelated planes waves incident on nonuniform M-sensor arrays assumed that the number of signal sources m was known or had already been estimated. In the case (m<M), traditional detection techniques such as Akaike's information criterion (AIC) and minimum description length (MDL) that are based on the equality of several smallest eigenvalues in the covariance matrix may be applied, although we demonstrate that these results can be misleading for nonuniform arrays. In the case (m/spl ges/M), these standard techniques are not applicable. We introduce a new approach to the detection problem for fully augmentable arrays (whose set of intersensor differences is complete). We show that the well-known direct augmentation approach applied to the sample covariance matrix is not a solution by itself since the resulting Toeplitz matrix is generally not positive definite for realistic sample volumes. We propose a transformation of this augmented matrix into a positive definite Toeplitz matrix T/sub /spl mu// with the proper number of equal minimum eigenvalues that are appropriate for the candidate number of sources /spl mu/. Comparison of the results of these best-fit transformations over the permissible range of candidates then allows us to select the most likely number of sources m/spl circ/ using traditional criteria and yields uniquely defined DOAs. Simulation results demonstrate the high performance of this method. Since detection techniques for superior scenarios have not been previously described in the literature, we compare our method with the standard AIC and MDL techniques in a conventional case with similar Cramer-Rao bound (CRB) and find that it has a similar detection performance.

A Self-Localization Method for Wireless Sensor Networks

We consider the problem of locating and orienting a network of unattended sensor nodes that have been deployed in a scene at unknown locations and orientation angles. This self-calibration problem is solved by placing a number of source signals, also with unknown locations, in the scene. Each source in turn emits a calibration signal, and a subset of sensor nodes in the network measures the time of arrival and direction of arrival (with respect to the sensor node's local orientation coordinates) of the signal emitted from that source. From these measurements we compute the sensor node locations and orientations, along with any unknown source locations and emission times. We develop necessary conditions for solving the self-calibration problem and provide a maximum likelihood solution and corresponding location error estimate. We also compute the Cramer-Rao bound of the sensor node location and orientation estimates, which provides a lower bound on calibration accuracy. Results using both synthetic data and field measurements are presented.

Spectral estimation for interleaved pulse trains with short-length elements

This paper presents a new method for the signal separation of interleaved pulse trains consisting of several independent signal sources, some of which possibly exist for only a short period of time. The separation is based on the differences in the pulse repetition intervals (PRIs) of the signal sources. To detect each signal source, we derive a map from the input signal to a function of two variables: time and PRI, which we call the PRI map. By taking the absolute value of the PRI map, we obtain a short-time PRI spectrum, from which we can use thresholding to estimate the number of signal sources, their time duration, and the PRIs. The PRI map is an extension of the PRI transform, which was proposed by the author previously. The construction of the PRI map is similar to that of a wavelet transform. The difference is that the PRI map is a nonlinear transform, while the wavelet transform is a linear one. Simulation results are presented on the performance of the signal separation of interleaved pulse trains using the PRI map.

Detection-estimation of more uncorrelated Gaussian sources than sensors in nonuniform linear antenna arrays .I. Fully augmentable arrays

Previous studies dealing with direction-of-arrival (DOA) estimation for uncorrelated planes waves incident on nonuniform M-sensor arrays assumed that the number of signal sources m was known or had already been estimated. In the "conventional" case (m<M), traditional detection techniques such as Akaike's information criterion (AIC) and minimum description length (MDL) that are based on the equality of several smallest eigenvalues in the covariance matrix may be applied, although we demonstrate that these results can be misleading for nonuniform arrays. In the "superior" case (m/spl ges/M), these standard techniques are not applicable. We introduce a new approach to the detection problem for "fully augmentable" arrays (whose set of intersensor differences is complete). We show that the well-known direct augmentation approach applied to the sample covariance matrix is not a solution by itself since the resulting Toeplitz matrix is generally not positive definite for realistic sample volumes. We propose a transformation of this augmented matrix into a positive definite Toeplitz matrix T/sub /spl mu// with the proper number of equal minimum eigenvalues that are appropriate for the candidate number of sources /spl mu/. Comparison of the results of these best-fit transformations over the permissible range of candidates then allows us to select the most likely number of sources m/spl circ/ using traditional criteria and yields uniquely defined DOAs. Simulation results demonstrate the high performance of this method. Since detection techniques for superior scenarios have not been previously described in the literature, we compare our method with the standard AIC and MDL techniques in a conventional case with similar Cramer-Rao bound (CRB) and find that it has a similar detection performance.

Statistical characteristics of the AIC and MDL criteria in the problem of estimating the number of sources of multivariate signals in the case of a short sample

At present, there are many methods for estimating the number of signal sources detected by an antenna array. The most well-known methods are based on the AIC (Akaike Information Criterion) and MDL (Minimum Description Length) criteria. The statistical characteristics of these methods have been analyzed in a large number of papers. However, the results obtained in these papers are valid for an unknown internal-noise intensity, and the found theoretical estimates are asymptotic. In the case of short samples, the characteristics of these methods are usually analyzed on the basis of numerical simulations. In this paper, we find the AIC and MDL statistical characteristics in the case of a known internal-noise intensity of the antenna array. It is shown that within the framework of such a formulation of the problem, the characteristics of the estimate of the number of multivariate-signal sources obtained by these methods can be calculated analytically on the basis of the formulas derived by the authors of this paper for the distribution of the maximum noise eigenvalue of the sample correlation matrix of Gaussian input signals. Analytical expressions for the probability of overvaluation of the number of signal sources are obtained for any size of the sample.

Acoustic model generating method for speech recognition

The acoustic model generating method for speech recognition enables a high representation effect on the basis of the minimum possible model parameters. In an initial model having a smaller number of signal sources, the acoustic model for speech recognition is generated by selecting the splitting processing or the merging processing for the signal sources successively and repeatedly. The merging processing is executed prior to the splitting processing. In the merging processing, when the merged result is not appropriate, the splitting processing is executed for the model obtained before merging processing (without use of the merged result). Further, the splitting processing includes three methods at the same time, as (1) a method of splitting the signal source into two and reconstructing a shared structure between a plurality of states having common signal sources to be split, (2) a method of splitting one state into two states corresponding to different phoneme context categories in phoneme context direction, (3) a method of splitting one state into two states corresponding to different speech sections in time direction. One of the three methods is selected by obtaining three pieces of maximum likelihood for the three splitting steps and judging which one is the biggest to select the splitting step for which the biggest likelihood is obtained.

A method of blind separation for convolved non-stationary signals

This paper proposes a method of “blind separation” which extracts non-stationary signals (e.g., speech signals, music) from their convolutive mixtures (observed signals). The function is acquired by modifying a network's parameters so that a cost function takes the minimum at any time. The cost function is the one introduced by Matsuoka et al. (Neural Networks 8 (3) (1995) 411–419). The learning rule is derived from the natural gradient (Amari et al., 1998, IEEE Trans. Signal Processing, submitted) minimization of the cost function. The validity of the proposed method is confirmed by computer simulation. The proposed method is applied to the case of N o (the number of observed signals)= N s (the number of source signals) and N o> N s.

Cascade neural networks for multichannel blind deconvolution

The authors present a new simple but efficient and powerful extension of Bussgang-type blind equalisation algorithms which can extract multiple source signals from their unknown convolutive mixtures. A cascade neural network is proposed, where each module consists of an equalisation subnetwork and a deflation subnetwork. This approach can adopt any blind equalisation algorithm (which has been developed for the equalisation of a single channel). It can also be applied when the number of source signals is not known in advance. Extensive computer simulation results confirm the validity and high efficiency of the proposed method.

Eigenanalysis interference cancellers with robust capabilities

The maximum rejection of interference in the presence of steering angle error for adaptive array processing is considered. It has been shown that eigenanalysis interference cancellers (EICs) possess the advantage of providing maximal suppression of undesired interference with fast convergence over conventional adaptive beamformers. However, the performance of EICs is also very sensitive to steering angle error when the number of signal sources is overestimated. We present an artificial source injection technique to make EICs have robust capabilities against steering angle error. Modifications for enhancing the proposed technique are also presented. It is shown that the proposed technique can alleviate the drawback like the loss of degrees of freedom when using existing EICs. Simulation examples are provided for illustrating the effectiveness of the proposed technique.

On estimating the direction of arrival when the number of signal sources is unknown

A new problem, estimation of the direction of arrival (DOA) without knowing (or assuming) the number of signal sources, is addressed. In this paper we propose a method which is related to both the multiple signal classification (MUSIC) and Capon's methods. The performance of the proposed method when the number of signal sources is unknown is shown to be almost the same as that of the MUSIC method when the number of signal sources is exactly known. In addition, from the statistical properties, it is observed that the estimation error of the proposed method has almost the same variance as the MUSIC method, although the proposed method yields a slightly biased estimate.

A combined determination-estimation method for direction of arrival estimation

A combined determination-estimation method is proposed for direction finding of multiple source locations in this paper. The method is based on the conditional mean multiple signal classification (MUSIC) null-spectrum, and does not require a priori decision on the number of signal sources. It is shown that the shapes of the MUSIC and conditional mean MUSIC null-spectra are not quite different. To see the resolution performance, the probability of resolution (PR) of the MUSIC null-spectrum and that of the conditional mean MUSIC null-spectrum are obtained by computer simulation, from which it is seen that the PRs of these two null-spectra are almost the same. In addition it is found that the information theoretic criterion and Bayesian approach (maximum a posteriori estimation method) for determining the number of signal sources would give the same result.

Internal structure of black boxes with multiple stochastic output

Black boxes can be modelled by a finite number of signal sources strictly related to input signals and of noise sources. The internal organisation structure within the black box can be constructed in a detail dependent upon the dimensionality of the output vector. This structure describes overlap of signal sources and noise sources which are operational in the system while it is forming different response components. Two examples of practical systems are worked out.

Signal separation theory using adaptive arrays

AbstractThe signal separation technique using adaptive arrays is a new area in array data processing. The model considered in this paper is that of an array consisting of N elements; the number of signal sources, which are separated in spatial location, is M and M ≥ N. In the case of narrow band signals, the pre‐envelope form of the incident signal can be obtained from the original signal and its Hilbert transform. The directional bearing‐angle matix G is formed in terms of the conventional beam‐forming system. By using a special implementation, the inverse matrix of G is derived. Finally, a matrix transform is operated on the received signal so that the output signal is separable, i.e. each output channel has only one incident signal. In the case of wide band signals, the DFT of the input signal or heterodyne is required. The block diagrams of the signal separation technique are given and some important results of this technique are derived. The results of system simulation experiments in digital computers prove that this theory is effective for separating signals.

Acoustic signal interpretation: Reasoning with non-specific and uncertain information

An expert system approach to identifying the sources of underwater acoustic signals is described. Much of the information about ocean vessels, which is derived from acoustic features, is non-specific (i.e. pointing only to general classes of vessels). As well, there is often uncertainty both in the accuracy of the feature identification and in the applicability of the rules in the knowledge base. In order to deal with non-specific and uncertain evidence in the presence of an unknown number of signal sources, we develop an inference network approach which is based on the Dempster-Shafer theory of evidence.