Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613531
T. Kaiser, J. Mendel
Cumulants have been successfully applied in the area of narrowband array signal processing. This motivates a performance analysis to find out the strengths and the weaknesses of each new algorithm. Hitherto, most of the known performance analyses are based on the asymptotic covariance of sample cumulants and are therefore called asymptotic performance analyses. Recently, explicit formulas for the finite-sample covariances of second-, third-, and fourth-order sample cumulants for any kind of signal, any kind of noise, any array shape and arbitrary sensors have been derived. These formulas enable a finite-sample performance analysis. In the single source case the steering vector is proportional to a vector built up by a product of second-order cumulants or by fourth-order cumulants. This means that the finite-sample (co)variance of the steering vector can be investigated by using the formulas for the finite-sample covariance of the second- and fourth-order sample cumulant. Hence, the open question "Which cumulants should be selected for steering vector estimation ?"-is addressed in this paper.
{"title":"Which cumulants should be selected for steering vector estimation?","authors":"T. Kaiser, J. Mendel","doi":"10.1109/HOST.1997.613531","DOIUrl":"https://doi.org/10.1109/HOST.1997.613531","url":null,"abstract":"Cumulants have been successfully applied in the area of narrowband array signal processing. This motivates a performance analysis to find out the strengths and the weaknesses of each new algorithm. Hitherto, most of the known performance analyses are based on the asymptotic covariance of sample cumulants and are therefore called asymptotic performance analyses. Recently, explicit formulas for the finite-sample covariances of second-, third-, and fourth-order sample cumulants for any kind of signal, any kind of noise, any array shape and arbitrary sensors have been derived. These formulas enable a finite-sample performance analysis. In the single source case the steering vector is proportional to a vector built up by a product of second-order cumulants or by fourth-order cumulants. This means that the finite-sample (co)variance of the steering vector can be investigated by using the formulas for the finite-sample covariance of the second- and fourth-order sample cumulant. Hence, the open question \"Which cumulants should be selected for steering vector estimation ?\"-is addressed in this paper.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"194 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127853454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613568
H. Ong, D. R. Iskander, A. Zoubir
Tugnait (1993) has used the cross bispectrum to detect non-Gaussian signals common to two sensors when the noise in each sensor is either mutually independent or has vanishing bispectra. However the detection methods presented assume enough data are available for asymptotic results to apply. If this assumption is not valid then the performance of the detection methods will be degraded. In this paper we propose a detection scheme based on the bootstrap that handles the small data size case. Unlike other bispectrum based techniques, the proposed scheme maintains the nominal test level while achieving high power. Simulation examples are given and the performance of the bootstrap based method is compared with a method proposed by Tugnait.
{"title":"Detection of a common non-Gaussian signal in two sensors using the bootstrap","authors":"H. Ong, D. R. Iskander, A. Zoubir","doi":"10.1109/HOST.1997.613568","DOIUrl":"https://doi.org/10.1109/HOST.1997.613568","url":null,"abstract":"Tugnait (1993) has used the cross bispectrum to detect non-Gaussian signals common to two sensors when the noise in each sensor is either mutually independent or has vanishing bispectra. However the detection methods presented assume enough data are available for asymptotic results to apply. If this assumption is not valid then the performance of the detection methods will be degraded. In this paper we propose a detection scheme based on the bootstrap that handles the small data size case. Unlike other bispectrum based techniques, the proposed scheme maintains the nominal test level while achieving high power. Simulation examples are given and the performance of the bootstrap based method is compared with a method proposed by Tugnait.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127893097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613567
B. Pesquet-Popescu, P. Larzabal
Self-similar processes have received increasing attention in the signal processing community, due to their wide applicability in modeling natural phenomena which exhibit "1/f" spectra and/or long-range dependence. On the other hand the wavelet decomposition became a very useful tool in describing nonstationary self-similar processes. In this paper we first investigate the existence and the properties of higher-order statistics of self-similar processes with finite variance. Then, we consider some self-similar processes with infinite variance and study the statistical properties of their wavelet coefficients.
{"title":"Higher and lower-order properties of the wavelet decomposition of self-similar processes","authors":"B. Pesquet-Popescu, P. Larzabal","doi":"10.1109/HOST.1997.613567","DOIUrl":"https://doi.org/10.1109/HOST.1997.613567","url":null,"abstract":"Self-similar processes have received increasing attention in the signal processing community, due to their wide applicability in modeling natural phenomena which exhibit \"1/f\" spectra and/or long-range dependence. On the other hand the wavelet decomposition became a very useful tool in describing nonstationary self-similar processes. In this paper we first investigate the existence and the properties of higher-order statistics of self-similar processes with finite variance. Then, we consider some self-similar processes with infinite variance and study the statistical properties of their wavelet coefficients.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"11 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124279060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613542
Yifeng Zhou, H. Leung
In this paper, we present a minimum entropy fusion approach for multisensor data fusion in non-Gaussian environments. We represent the fused data in the form of the weighted sum of the multisensor outputs and use the varimax norm as the information measure. The optimum weights are obtained by maximizing the varimax norm of the fused data. The minimum entropy fusion solution only depends on the empirical distribution of the sensor data and makes no specific distribution assumptions about the sensor data. Numerical simulation results are provided to show the effectiveness of the proposed fusion approach.
{"title":"Minimum entropy approach for multisensor data fusion","authors":"Yifeng Zhou, H. Leung","doi":"10.1109/HOST.1997.613542","DOIUrl":"https://doi.org/10.1109/HOST.1997.613542","url":null,"abstract":"In this paper, we present a minimum entropy fusion approach for multisensor data fusion in non-Gaussian environments. We represent the fused data in the form of the weighted sum of the multisensor outputs and use the varimax norm as the information measure. The optimum weights are obtained by maximizing the varimax norm of the fused data. The minimum entropy fusion solution only depends on the empirical distribution of the sensor data and makes no specific distribution assumptions about the sensor data. Numerical simulation results are provided to show the effectiveness of the proposed fusion approach.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131069474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613511
C. Bourin, P. Bondon
Bilinear systems are useful to model nonlinear time series. They can be described by a nonlinear recursive equation involving a finite number of parameters. Their analysis and particularly the estimation of the parameters is of central interest. In this paper we establish difference equations between lagged moments and cumulants up to third-order of a simple bilinear model, and show how to use these relations to estimate the parameters.
{"title":"On the identifiability of bilinear stochastic systems","authors":"C. Bourin, P. Bondon","doi":"10.1109/HOST.1997.613511","DOIUrl":"https://doi.org/10.1109/HOST.1997.613511","url":null,"abstract":"Bilinear systems are useful to model nonlinear time series. They can be described by a nonlinear recursive equation involving a finite number of parameters. Their analysis and particularly the estimation of the parameters is of central interest. In this paper we establish difference equations between lagged moments and cumulants up to third-order of a simple bilinear model, and show how to use these relations to estimate the parameters.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132451317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613563
A. Zoubir, C.L. Brown, B. Boashash
A modification to a previously developed characteristic function based Gaussianity test is proposed. The power of the test is consequently improved. This test is then extended to the multivariate case, allowing it to be applied to correlated data. Monte Carlo simulations are performed to compare power with two other tests for multivariate Gaussianity, with encouraging results.
{"title":"Testing multivariate Gaussianity with the characteristic function","authors":"A. Zoubir, C.L. Brown, B. Boashash","doi":"10.1109/HOST.1997.613563","DOIUrl":"https://doi.org/10.1109/HOST.1997.613563","url":null,"abstract":"A modification to a previously developed characteristic function based Gaussianity test is proposed. The power of the test is consequently improved. This test is then extended to the multivariate case, allowing it to be applied to correlated data. Monte Carlo simulations are performed to compare power with two other tests for multivariate Gaussianity, with encouraging results.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115987846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613523
Jitendra Tugnait
The problem considered is that of identification of unknown parameters of multivariable, linear "errors-in-variables" models, i.e., linear systems where measurements of both input and output of the system are noise contaminated. Attention is focused on frequency-domain approaches where the integrated polyspectrum (bispectrum or trispectrum) of the input and the integrated cross-polyspectrum, respectively, of the given time-domain input-output data are exploited. We first develop (computable) expressions for the covariance matrix of the system transfer function estimate and show that the system transfer function matrix estimate is asymptotically complex Gaussian. Then we propose and analyze a pseudo-maximum likelihood (PML) estimator of system parameters using the developed statistics of the system transfer function estimate. Finally two simulation examples are presented.
{"title":"Identification of multivariable stochastic linear systems using integrated polyspectrum given noisy input-output data","authors":"Jitendra Tugnait","doi":"10.1109/HOST.1997.613523","DOIUrl":"https://doi.org/10.1109/HOST.1997.613523","url":null,"abstract":"The problem considered is that of identification of unknown parameters of multivariable, linear \"errors-in-variables\" models, i.e., linear systems where measurements of both input and output of the system are noise contaminated. Attention is focused on frequency-domain approaches where the integrated polyspectrum (bispectrum or trispectrum) of the input and the integrated cross-polyspectrum, respectively, of the given time-domain input-output data are exploited. We first develop (computable) expressions for the covariance matrix of the system transfer function estimate and show that the system transfer function matrix estimate is asymptotically complex Gaussian. Then we propose and analyze a pseudo-maximum likelihood (PML) estimator of system parameters using the developed statistics of the system transfer function estimate. Finally two simulation examples are presented.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115726156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613536
T. Kaiser, J. Mendel
In this paper we provide explicit formulas for the covariances of second-third-, and fourth-order sample cumulants as used in narrowband array processing. These covariances provide a basis for analysing the performance of cumulant based algorithms for finite-sample length, which is in contrast to usual asymptotic performance analyses. The use of these formulas, which consist of several thousand terms, will be demonstrated, and a rough idea of their applicability to a performance analysis for finite numbers of samples will be given.
{"title":"Covariance of finite-sample cumulants in array-processing","authors":"T. Kaiser, J. Mendel","doi":"10.1109/HOST.1997.613536","DOIUrl":"https://doi.org/10.1109/HOST.1997.613536","url":null,"abstract":"In this paper we provide explicit formulas for the covariances of second-third-, and fourth-order sample cumulants as used in narrowband array processing. These covariances provide a basis for analysing the performance of cumulant based algorithms for finite-sample length, which is in contrast to usual asymptotic performance analyses. The use of these formulas, which consist of several thousand terms, will be demonstrated, and a rough idea of their applicability to a performance analysis for finite numbers of samples will be given.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123392328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613527
A. Tesei, R. Bozzano, C. Regazzoni
This paper focuses on the problem of multilevel digital signal estimation in the presence of generic noise in a communication system. Noise is assumed unimodal, independent identically distributed, generically non Gaussian, that is eventually asymmetric, impulsive or not. The proposed solution is based on a previously developed estimator which requires the analytical probability density function model of the noise. The selected estimator was originally applied under the assumption of S/spl alpha/S noise distribution. In this paper the asymmetric generalized Gaussian (agg) model is selected as a suitable model to describe the noise processes: hence, it is discussed and compared with the S/spl alpha/S distributions in terms of decoding performances. Tests were performed on simulated binary sequences corrupted by interference generated as S/spl alpha/S processes. Test results outlines comparable performances of the two families of parametric noise models.
{"title":"Comparison between asymmetric generalized Gaussian (AGG) and symmetric-/spl alpha/-stable (S/spl alpha/S) noise models for signal estimation in non Gaussian environments","authors":"A. Tesei, R. Bozzano, C. Regazzoni","doi":"10.1109/HOST.1997.613527","DOIUrl":"https://doi.org/10.1109/HOST.1997.613527","url":null,"abstract":"This paper focuses on the problem of multilevel digital signal estimation in the presence of generic noise in a communication system. Noise is assumed unimodal, independent identically distributed, generically non Gaussian, that is eventually asymmetric, impulsive or not. The proposed solution is based on a previously developed estimator which requires the analytical probability density function model of the noise. The selected estimator was originally applied under the assumption of S/spl alpha/S noise distribution. In this paper the asymmetric generalized Gaussian (agg) model is selected as a suitable model to describe the noise processes: hence, it is discussed and compared with the S/spl alpha/S distributions in terms of decoding performances. Tests were performed on simulated binary sequences corrupted by interference generated as S/spl alpha/S processes. Test results outlines comparable performances of the two families of parametric noise models.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114371791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613525
Hyoungill Kim, Bum-Ki Jeon, Taewon Yang, K. Sung
A recursive estimation algorithm for FIR systems is proposed using the 3rd and 4th order cumulants. From the 3rd and 4th order cumulants relationship, we construct a certain matrix form whose entry consists of the system output sequence. Using this matrix form, the proposed recursive algorithm is developed by the overdetermined recursive instrumental variable (ORIV) method. The proposed algorithm provides improved estimation accuracy when additive Gaussian noise is present and can be applied to a time varying system as well. Simulation results are presented to compare the performance with other HOS-based algorithms.
{"title":"Recursive estimation algorithm for FIR systems using the 3rd and 4th order cumulants","authors":"Hyoungill Kim, Bum-Ki Jeon, Taewon Yang, K. Sung","doi":"10.1109/HOST.1997.613525","DOIUrl":"https://doi.org/10.1109/HOST.1997.613525","url":null,"abstract":"A recursive estimation algorithm for FIR systems is proposed using the 3rd and 4th order cumulants. From the 3rd and 4th order cumulants relationship, we construct a certain matrix form whose entry consists of the system output sequence. Using this matrix form, the proposed recursive algorithm is developed by the overdetermined recursive instrumental variable (ORIV) method. The proposed algorithm provides improved estimation accuracy when additive Gaussian noise is present and can be applied to a time varying system as well. Simulation results are presented to compare the performance with other HOS-based algorithms.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"131 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124258044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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