Impact Of Higher-order Statistics On Adaptive Algorithms For Blind Source Separation

Abstract

The paper is devoted to present an analysis of the impact of higher order statistics (HOS) in adaptive blind source separation criteria. Despite the well known fact that they are necessary to provide source separation in a general framework, their impact on the performance of adaptive solutions is a still open research field. The approach of probability density function (pdf) recovering is used. In order to verify the analysis, two constrained adaptive algorithms are investigated. Namely, the multiuser kurtosis algorithm (MUK) and the multiuser constrained fitting probability density function algorithm (MU-CFPA) are used due to the desired characteristics of different HOS involved in their design. Simulation results are carried out to basis our analysis. © 2004 IEEE.170174Hyvärinen, A., Oja, E., Independent component analysis: Algorithms and applications (2000) Neural Networks, 13 (4-5), pp. 411-430Hérault, J., Jutten, C., Ans, B., Détection de grandeurs primitives dans un message composite par une architecture de calcul neuromimétique en apprentissage non supervisé (1985) Actes du Xéme Colloque GRETSI, pp. 1017-1022. , Nice, France, MaiPapadias, C.B., Globally convergente blind source separation based on a multiuser kurtosis maximization criterion (2000) IEEE Transactions on Signal Processing, 48 (12), pp. 3508-3519. , DecemberHaykin, S., (2000) Unsupervised Adaptive Filtering, Ser. (Series on Adaptive and Learning Systems for Signal Processing, Communications and Control), 1. , John Wiley & Sons: Source SeparationDonoho, D., (1981) On Minimum Entropy Deconvolution, pp. 565-608. , Academic PressComon, P., Independent component analysis: A new concept? (1994) Signal Processing, 36 (3), pp. 287-314. , AprilPapadias, C.B., Paulraj, A.J., A constant modulus algorithm for multiuser signal separation in presence of delay spread using antenna array (1997) IEEE Signal Processing Letters, 4 (6), pp. 178-181. , JunePapadias, C.B., (2000) Blind Separation of Independent Sources Based on Multiuser Kurtosis Optimization Criteria, 2, pp. 147-179. , John-Wiley & Sons, ch. 4Cavalcante, C.C., Cavalcanti, F.R.P., Mota, J.C.M., Romano, J.M.T., A constrained version of fitting PDF algorithm for blind source separation (2003) Proceeding of IEEE Signal Processing Advances for Wireless Communications (SPAWC 2003), , Rome, Italy, June, 15-18Benveniste, A., Goursat, M., Ruget, G., Robust identification of a nonminimum phase system: Blind adjustment of a linear equalizer in data communications (1980) IEEE Transactions on Automatic Control, AC-25 (3), pp. 385-399. , JuneNadal, J.-P., Parga, N., Redundancy reduction and independent component analysis: Conditions on cumulants and adaptive approaches (1997) Neural Computation, 9, pp. 1421-1456Shalvi, O., Weinstein, E., New criteria for blind deconvolution of nonminimum phase systems (channels) (1990) IEEE Transactions on Information Theory, 36 (2), pp. 312-321. , MarchHaykin, S., (1998) Neural Networks: A Comprehensive Foundation, 2nd Ed., , Prentice HallLacoume, J.-L., Amblard, P.-O., Comon, P., (1997) Statistiques d'Ordre Supérieur pour le Traitement du Signal, , ser. (Traitement du Signal). Paris: MassonCavalcante, C.C., (2001) Neural Prediction and Probability Density Function Estimation Applied to Blind Equalization, , Master's thesis, Federal University of Ceará (UFC), Fortaleza-CE, Brasil, FebruaryCavalcante, C.C., Cavalcanti, F.R.P., Mota, J.C.M., Adaptive blind multiuser separation criterion based on log-likelihood maximisation (2002) IEE Electronics Letters, 38 (20), pp. 1231-1233. , SeptemberHaykin, S., (2000) Unsupervised Adaptive Filtering, , ser. (Series on Adaptive and Learning Systems for Signal Processing, Communications and Control). John Wiley & Sons, vol. II: Blind DeconvolutionCavalcante, C.C., Cavalcanti, F.R.P., Mota, J.C.M., A PDF estimation-based blind criterion for adaptive equalization (2002) Proceedings of IEEE Int. Symposium on Telecommunications (ITS 2002), , Natal, Brazil, SeptemberBishop, C.M., (1995) Neural Networks for Pattern Recognition, , UK: Oxford University Pres