ON-LINE SEQUENTIAL MULTICHANNEL BLIND DECONVOLUTION:A DEFLATIONAPPROACHSeungjin CHOISchool of Electrical and Electronics Engineering Chungbuk National University48Kaeshin-dong,CheongjuChungbuk361-763,KOREAschoi@engine.chungbuk.ac.krAndrzej CICHOCKILab for Open Information Systems Brain Science Institute,RIKEN 2-1Hirosawa,Wako-shiSaitama351-01,JAPANcia@brain.riken.go.jpABSTRACTWe present a simple but efficient and powerful extension of standard Bussgang-type blind equalization algorithms that is able to extract multiple source signals from their unknown convolutive mixtures.The extraction of source signals one by one using a deflation approach is proposed.A new adap-tive deflation algorithm which can cancel the contribution of already extracted source signals,is derived.This approach can adopt any blind equalization algorithm(which can ex-tract a single source).Furthermore,it can be also applied to the case when we do not know the number of source signals in advance.Extensive computer simulation results confirm the validity and high efficiency of our proposed method.1.INTRODUCTIONMultichannel blind deconvolution has a variety of applica-tions in wireless communications,image processing,array processing,and some biomedical applications.In multi-channel blind deconvolution,an dimensional vector of received signals is assumed to be generated from an dimensional vector of spatially in-dependent,temporally i.i.d.unknown source signalsusing the multi-variate linear time invari-antfilters,i.e.,(1) or equivalently in the scalar form(2)Portion of this work was supported by Korea Science and Engineer-ing Foundation under the contract981-0913-063-1and by Brain Science Institute,RIKEN,Japan where(is an unknown ()polynomial matrix with,and is de-lay operator such that)represents the characteristics of FIR channel.The task of multichanneldeconvolution is to recover the source signals from the received signals,up to a scaled,permuted,and de-layed version of source signals,i.e.,the estimates of sources ,,where is a permutation matrix,is a nonsingular scaling di-agonal matrix,and is a diagonal matrix whose th diagonal element is given by.2.EXTRACTION OF SINGLE SOURCE SIGNALLet us consider an FIR equalizer whose the th node output is described by(3)where are FIR equalizer coefficients andare the th sensor output.For the sake of simplicity,we as-sume that source signals have unit constant modulus, i.e.,.A single source can be extracted from the minimization of the extension of the Constant Modulus (CM)criterion[7]which is described by(4)Taking stochastic gradient descent,one can have the updat-ing rule for for FIR equalizer coefficients which has the form of(5)