A Novel Approach to Eliminating the Permutation and Scaling Indeterminacies of Block BSS

Transcription

1 We Zhao, Yuehong Shen, Pengcheng Xu, Zhgang Yuan, Ymn We, We Jan A ovel Approach to Elmnatng the Permutaton and Scalng Indetermnaces of Block BSS WEI ZAO, YUEOG SE, PEGCEG XU, ZIGAG YUA, YIMI WEI, WEI JIA College of Communcatons Engneerng PLA Unversty of Scence and Technology oubaoyng Road o.88, Qnhua Dstrct, 4, anng CIA gmaye@6.com Abstract: - Ths paper consders the permutaton and scalng ndetermnacy problem of blnd source separaton (BSS) n the case that the contnuously mxng sgnals are splt n tme and processed block by block. When tyng the separated sgnals n each tme block, the recovered whole sgnals dffer from the orgnal sources up to permutaton and scalng ndetermnaces. Inspred by prevous Permutaton Method of reconstructng source sgnals n tme doman, a novel approach s proposed to elmnate the nherent permutaton and scalng ndetermnaces when the block BSS s consdered. Ths new method reformulates the mxng sgnals by overlappng adacent sgnal blocks partally and utlzes the dependent correlaton of the overlappng sgnals n each adacent block to adust the permutaton and scalng parameters. Compared wth the Permutaton Method, ths new method s more effcent n terms of separaton qualty and s much qucker n terms of executon speed. The performance of ths novel approach s confrmed by computer smulatons and realstc experments performed on wreless communcaton system. Key-Words: - blnd source separaton; ndependent component analyss; permutaton and scalng ndetermnaces; adacent tme blocks; overlappng sgnals; permutaton method Introducton For the recent decades, blnd source separaton (BSS) has receved consderable attenton, manly due to ts wde panel of potental applcatons such as mage recognton, audo processng, bology, wreless communcatons, etc []. BSS shows sgnfcant advantages n recovery of unknown source sgnals over other frameworks where technques strongly depend on the nformaton of sgnal dversty, transfer functons and so on. In the case where source sgnals are lnearly and nstantaneously mxed, BSS corresponds to ndependent component analyss (ICA). The core assumpton n ICA s reduced to the statstcal mutually ndependence between sources []. owever, for BSS one problem s nhered from the property of the followng ambgutes as presented n [3]. The frst ambguty s the exstence of the unknown complex scalng factor, whch results n the ambguous phase and ampltude n separated sgnals. The other ambguty s the permutaton of the separated sgnals. These ambgutes cause problems when contnuously ncomng measurement data s splt n tme and when they are processed block by block. Tyng components at adacent blocks wthout permutaton and rescalng does not recover the orgnal sgnals correctly. In order to solve the problem, several methods have been contrved as follows. DOA type [3], [4] methods te sgnal blocks wth smlar DOA and requre an array manfold. Snce t requres an array manfold, t degrades permutaton accuracy by calbraton error. Correlaton based methods [], [6] compute the correlaton coeffcent of all possble combnaton of separated sgnals n adacent blocks. But they are not approprately used n practcal applcaton n terms of computatonal resource. Recently, a permutaton algnment scheme based on mcrophone array drectvty patterns for speech sgnals s proposed n [7], where nterestng connectons between BSS and deal beamformng s explored. A permutaton method based upon the smlarty of the column vectors of the mxng matrx and trackng flters s proposed to concatenate ICA separated source sgnal tme blocks [8]. owever, the trackng flter s dffcult to control and complex to desgn. A contrast functon for ICA wthout permutaton ambguty s proposed n [9], []. It s proved that a lnear combnaton of the separator output fourth-order margnal cumulants s a vald contrast functon for ICA under E-ISS: Volume,

2 We Zhao, Yuehong Shen, Pengcheng Xu, Zhgang Yuan, Ymn We, We Jan prewhtenng f the weghts have the same sgn as the source kurtoss []. If, n addton, the source kurtoss are dfferent and so are the lnear combnaton weghts, the contrast elmnates the permutaton ambguty typcal to ICA, as the estmated sources are sorted at the separator output accordng to ther kurtoss values n the same order as the weghts. Inspred from the Permutaton Method n [8], n ths paper, we propose a novel approach to elmnate the permutaton and scalng ndetermnaces of BSS n the case where contnuously mxng measurement data s splt n tme and processed block by block. We artfcally reformulate the mxng sgnals by makng adacent sgnal blocks overlap partally. Takng advantage of the dependent correlaton of separated components n the overlappng part of correspondng adacent blocks, the permutaton and scalng of the latter blocks are adusted to be dentcal to that of the former blocks. Computer smulatons and realstc experments are performed to valdate the performance of our new method. Ths paper s organzed as follows. The system model and assumptons are presented n Secton. Our novel approach s ntroduced n Secton 3. Computer smulatons and realstc experments are performed n Secton 4. Secton concludes ths paper. Model and Assumptons. System model In ths paper, the BSS system model we consder s shown n Fg.. The source sgnals are denoted by s() t = [ s (), t, s ()] t T, where T means the transpose. The mxng sgnals are denoted by x() t = [ x (), t, x ()] T M t. The relatonshp between source and mxture sgnals can be descrbed as s () t s () t s () t A x () t x () t x () t M W Fg.. BSS system model yt () y () t y () t x() t = As() t () where A s the mxng matrx of M, whch s composed of M row vectors,.e., Α = [ a, a,, a ] T M. Smlarly, the recovered sgnals are denoted by y () t = [ y () t,, y () t ] T. The relatonshp between mxture and separaton sgnals can be descrbed as y( t) = W x( t ) () where W s the separatng matrx of M, whch contans column,.e., W= [ w, w,, w ]. W means the ermtan of W, that s W s transposed and conugated. Wthout loss of generalty and for smplcty, we assume the number of sources equal to that of observed sgnals,.e., = M n ths paper.. Assumptons on the model In order to recover the source sgnals blndly and successfully, we make two assumptons on the BSS system model. A. The source sgnals are statonary and statstcally ndependent, and they have zero-mean and unt varance. A. The mxng system s lnear and nstantaneous. 3 ew Permutaton and Scalng Elmnaton Approach 3. Permutaton and scalng ndetermnaces Frst, we set the global matrx as G = W A. In fact, the recovered sgnals are the estmatons of sources up to permutaton and scalng ndetermnaces,.e., y = Gs y g g g s y g g g s = (3) y g g g s g where y = g s = g e s,, =,,,. ϕ The permutaton ndetermnacy exsts when and the scalng ndetermnacy, ampltude and phase, exst when g or ϕg. The ndetermnaces are common to all BSS methods; fortunately, they are nsgnfcant n most applcatons. owever, when the mxng data s splt n tme and processed block by block, tyng the separated sgnals n each tme block may not recover the orgnal sources correctly. More precsely, the separated sgnals of each adacent block may dffer n permutaton, ampltude and phase, whch may lead to ndetermnacy when they are ted together. As shown n Fg., t can be seen obvously that the ambguty problem exsts E-ISS: Volume,

3 We Zhao, Yuehong Shen, Pengcheng Xu, Zhgang Yuan, Ymn We, We Jan between source sgnals and recovered sgnals when tyng recovered sgnals block by block. Source sgnals Separated sgnals Tme Fg.. Ambgutes between source sgnals and recovered sgnals 3. Overlappng sgnals Second, we reformulate the mxng sgnals by overlappng adacent tme blocks partally, whch s called the overlappng sgnals. When the samples rate s fxed, we assume the samples of each block are T. The -th and (+)-th block of mxture sgnals are denoted by x = x (: T) = [ x (), x (),, x ( T)] and x = x (: T) = [ x (), x (),, x ( T)] = [ x ( T L+ ), x ( T L+ ),, x ( T), x ( L+ ), x ( L+ ),, x ( T)] (4) In (4), we can see clearly the frst L samples x ( T L+ ), x ( T L+ ),, x ( T) n the (+)- th block are the overlappng part between the -th and (+)-th block,.e., the overlappng sgnals. For smplcty, we assume T s dvsble by L n ths paper. The structural model of the -th and (+)-th mxture blocks and correspondng overlappng sgnals s shown n Fg. 3, n whch the length of overlappng sgnals s artfcally set by L. Fg. 3. The -th and (+)-th mxture blocks and correspondng overlappng sgnals wth length of L. For the sake of convenence, we denote the separated sgnals of the -th block of mxture sgnals by y = y (: T) = [ y (), y (),, y ( T)] Gs,.e., y g g g s y s g g g = () y s g g g 3.3 Our proposed method Thrd, based on the assumpton A, all the sources are zero-mean and wth unt varance. ence, we can elmnate the ampltude ndetermnacy by normalzng the ampltude of all the separated block sgnals. The remanng permutaton and phase ndetermnaces are elmnated by usng our proposed method shown as follows: For =,,. ( ), + BSS BSS( + y = x y = x ) +. Φ = ( y ( T L+ : T).*( y (: L)) ) L 3. For =,,, (a). [ temp, mark] = max( abs( Φ (,:))) (b). ψ = y, y = y, y = ψ mark mark + ( ( : ) (: )) norm y T L + T y L > (c). If norm( y ( T L : T) y (: L)) + + y = y end; end; 4. If + B Go back to step. end; In ths new method, BSS( x ) n Step means to separate mxng sgnals usng BSS algorthms. In ths paper, we choose the fast fxed-pont algorthms for complex-valued sgnals based on negentropc contrast crteron n [], whch s used n [8]. Ths s convenent to compare the performance of our new method wth the Permutaton Method n [8]. The correlaton matrx of overlappng sgnals Φ n Step s L L, whch results from the wdely accepted concept that the expectaton value of random varable can be approxmately represented by the mean value of all samples for one realzaton n tme doman when the varable s statonary. Therefore, accordng to the assumptons A and A, E-ISS: Volume,

4 We Zhao, Yuehong Shen, Pengcheng Xu, Zhgang Yuan, Ymn We, We Jan we have followng approxmate estmaton. g s = Δ g s Φ= E = g s gs g s = = = gs = + + gs ( g s) gs ( g s) = = = = = E + + s ( g s ) gs ( g s ) g = = = = (6) In Step 3, [ temp, mark] = max( abs( Φ (,:))) n (a) s the MATLAB functon that s used to fnd the maxmzaton value of each row n abs( Φ (,:)) and return the value and correspondng column ndex, n whch abs means the absolute value or norm value when t corresponds to complex-valued varable. The purpose of (a) s to search for the dependent component n the next block, whch s based on the fact that E{ ss } =, and Ess { } =, =. (b) ams to elmnate the permutaton ndetermnacy. When there doesn t exst permutaton ndetermnacy, Φ can be smplfed as + g( g ) s Δ + g( g ) s Φ= E + g ( g ) s + g( g ) + g( g ) = + g( g ) (7) (c) ams to elmnate the phase ndetermnacy. ote that we ust consder to change the phase by π, whch can be seen clearly n (c). More precsely, we only consder the case g ( g + ) =±, whch may not satsfy the practcal needs absolutely. owever, note that t s well acceptable and sutable n the case that our system model and assumptons are consdered n ths paper. As for the case g ( g + ) ±, we postpone t to our future work. When there aren t permutaton and scalng ndetermnaces, the correlaton matrx Φ can be smplfed to be dentty matrx,.e., Φ =I. 4 Smulaton and Experment Results 4. Computer smulatons 4.. Smulaton In ths secton, we choose the sne sgnal, square sgnal and random sgnal as sources. The number of mxng sgnal block B s, n whch sources are randomly mxed. The number of samples of each mxng sgnal block T s and the number sze of correspondng overlappng sgnals L s set. The classcal algorthm n [] s chosen as the separaton method, whch s smlar to that n [8]. The smulaton results are shown n Fg Source Source Source umber of samples wth fve blocks Separaton wthout usng our method Separaton wthout usng our method Separaton 3 wthout usng our method umber of samples wth fve blocks Separaton wth usng our method Separaton wth usng our method Separaton 3 wth usng our method umber of samples wth fve blocks Fg. 4. Smulaton results wth the sne sgnal, square sgnal and random sgnal. The frst column s source sgnal, the second column s the separaton sgnal concatenated wthout usng our method and the thrd column s the separaton sgnal concatenated wth usng our method. As shown n Fg. 4, t can be seen clearly that the connected separaton sgnals n each adacent sgnal block n the second column are dfferent from correspondng source sgnals. Ths means that the source sgnals are not recovered successfully, whch s caused by the ndetermnaces n BSS. owever, n the thrd column, t can be observed obvously that the separated components between adacent sgnal blocks are concatenated successfully by usng our proposed method. Therefore, our new approach s very effcent n terms of solvng the permutaton and scalng ndetermnaces n BSS when the mxng sgnals are processed block by block. 4.. Smulaton In ths secton, we choose three speech sgnals as sources because speech sgnals are usually not contnuous n tme doman. Gven the fact that our new method utlzes the dependent correlaton between the overlappng sgnals n tme doman, we consder to perform smulatons to valdate the performance of our approach wth speech sgnals. Moreover, the speech sgnals are wdely used n the E-ISS: Volume,

5 We Zhao, Yuehong Shen, Pengcheng Xu, Zhgang Yuan, Ymn We, We Jan realstc applcaton, especally n the wreless and moble communcaton. The number of mxng sgnal block B s, n whch sources are randomly mxed. The number of samples of each mxng sgnal block T s and the number sze of correspondng overlappng sgnals L s set. The classcal algorthm n [] s chosen as the separaton method, whch s smlar to that n [8]. The smulaton results are shown n Fg.. Source -... x 4 Source -... x 4 Source umber of samples wth fve blocks4 x Separaton wthout usng our method -... x 4 Separaton wthout usng our method -... x 4 Separaton 3 wthout usng our method -... umber of samples wth fve blocks4 x Separaton wth usng our method -... x 4 Separaton wth usng our method -... x 4 Separaton 3 wth usng our method umber of samples wth fve blocks x Fg.. Smulaton results wth speech sgnals. The frst column s source sgnal, the second column s the separaton sgnal concatenated wthout usng our method and the thrd column s the separaton sgnal concatenated wth usng our method. Compared the concatenated separaton sgnals n the second column wth the source sgnals n the frst column, t can be observed clearly that the separated sgnals n each adacent block are not connected correctly. When our proposed method s used, the concatenated separaton sgnals n the thrd column are almost the same wth the sources. Ths means that our method succeeds n elmnatng the permutaton and scalng ndetermnaces n the case that mxng sgnals are splt n block and processed block by block Smulaton 3 In ths secton, we perform smulatons to analyze the performance of our ndetermnacy elmnaton method, whch s manly compared wth that n [8]. We choose the sgnals n Smulaton secton as sources. In order to mprove the tme effcency of our method, we set the number of samples of each block T=4 and the number of blocks B vares from to. The length of overlappng sgnals changes from to 4,.e., L=, 4,, 4. For convenence and smplcty, we choose α = T L wth α =,, 4, and as the donaton. The classcal algorthm n [] s chosen as the separaton method. The mean value of mean square error (MSE) between concatenated separaton sgnals and sources s chosen as the measure crteron for separaton qualty. And the executon tme of concatenatng all separated sgnal blocks s chosen as the measurement of effcency n terms of computatonal speed, for whch the computer s Intel (R) Core Duo CPU, 3.Gz,.99Gz, 3. GB RAM. To ensure the valdty and relablty of smulaton data, Monte-Carlo runs are performed ndependently. The smulaton results are llustrated n Fg. 6 and Fg. 7. Average MSE Average executon tme (s) 6 x Permutaton method Our proposed method wth α= Our proposed method wth α= Our proposed method wth α=4 Our proposed method wth α= Our proposed method wth α= x umber of blocks Fg. 6. MSE between sources and connected separatons for Permutaton Method n [8] and our proposed method wth α =,, 4, and averaged over Monte-Carlo runs Permutaton method Our proposed method wth α= Our proposed method wth α= Our proposed method wth α=4 Our proposed method wth α= Our proposed method wth α= umber of blocks Fg. 7. Executon tme of concatenatng the separated sources n dfferent number of blocks for Permutaton Method and our proposed method wth α =,, 4, and averaged over Monte- Carlo runs. As shown n Fg. 6, t can be observed clearly that the MSE value of Permutaton Method and our proposed method decreases wth the number of blocks ncreasng. When the block sze s fxed, the MSE of our approach dffers wth the length of overlappng sgnals changng. More precsely, when B vares from to, our proposed method outperforms Permutaton Method wth α =,, 4,, and the performance of our approach becomes slghtly better and better wth α decreasng. owever, when α =, our method performs worse than Permutaton Method, whch s caused by the fact that the number of samples of the overlappng sgnals s not many enough. ence, t can be E-ISS: Volume,

6 We Zhao, Yuehong Shen, Pengcheng Xu, Zhgang Yuan, Ymn We, We Jan predcted that, n the same condton, the performance of our method wll be worse and worse when α s larger than. Snce the choce of α relates to the length of sgnal blocks, t s dffcult to determne the exact α such that our approach performs better or worse than Permutaton Method. From Fg. 7, we can see obvously that the executon tme of our proposed approach wth α =,, 4,, s less than that of Permutaton Method. The advantage of our method becomes more and more apparent when the number of blocks ncreases and the length of overlappng sgnals decreasng. For nstance, when B=3, the executon tme of Permutaton Method s about 77s, whle our method needs about 74s, 7s, 67s, 6s, 63s, respectvely, for α =,, 4,,. Furthermore, when B=4, the tme of the former s about s, whle the latter needs about 97s, 9s, 9s, 86, 84s. And t can be predcted that, when α ncreases, the tme of our method wll be less, whch s not llustrated n Fg. 7. Combned Fg. 6 and Fg. 7, we can draw the concluson that, when the block sze and correspondng length of overlappng sgnals are chosen approprately, our proposed method s more effcent than Permutaton Method n terms of separaton qualty and computatonal speed. For example, when B= and α =, the performance of our approach s not only better than Permutaton Method but also only needs much less tme of the latter. owever, when B= and α =, our approach needs much less tme than Permutaton Method but the performance of t s worse than the latter. Therefore, the performance of our proposed method wth respect to separaton qualty and computatonal speed can be adusted accordng to the choce of block sze and correspondng length of overlappng sgnals. More analyss about the exact relatonshp between them n detal wll be ncluded n our latter work. In general, when the number of samples of sgnal blocks s about, α = to 4 s recommended. 4. Realstc experments 4.. Realstc wreless communcaton model In ths secton, a wreless communcaton system wth two transmttng and recevng antennas s constructed n ths paper, whch s shown n Fg. 8. For smplcty, we assume the carrer and local frequences are the same,.e., ω = ω = ω3 = ω4 = ω = 3Mz. And the synchronous and carrer frequency offset problems are not consdered n ths paper. I Q I Q cos( ωt ) sn(ω t) cos( ωt) sn( ωt) cos( ω3t) sn(ω t) 3 cos(ω t) 4 sn( ω4t) I Q I Q Fg. 8. Wreless communcaton system model The transmtted source sgnals are complexvalued, denoted by s s I+ Q = = s I + Q (8) As shown n Fg. 8, the sources are modulated on carrer frequences, whch s send out through transmttng antennas. At the recever, the receved sgnals are demodulatng through local frequences. After low flterng, the mxng sgnals can be approxmately seen as the mxture of sources, whch are represented as x I + Q a a s x = = = x I + Q a a s (9) x= As where A denotes the wreless channel, whch s unknown. The separatng operator s gven as y w w x y = = y w w x () y = W x In order to satsfy the assumptons A and A, we use two E4438C [3] as the transmtters, whch can send rado sgnals n the form of sngle, AM, BPSK, speech and so on. At the recever, we use the USRP wth GU Rado [4] devce to receve the RF sgnals. To satsfy A, we set the dstance of two transmtters about meters away and make sure that they transmt sgnals ndependently. In ths way, the source sgnals are statstcally ndependent, even though they are not absolutely ndependent. owever, the approxmate ndependence between sources s accepted, whch s verfed by our expermental results n the followng. To satsfy A, we set the dstance between transmtters and recevers about meters away, whch ensures that the wreless channel s as approxmately lnear and nstantaneous as possble. Although the mxng system s not absolutely lnear E-ISS: Volume,

7 We Zhao, Yuehong Shen, Pengcheng Xu, Zhgang Yuan, Ymn We, We Jan and nstantaneous, t s so approxmate that the expermental results prove that t works well. 4.. Experment In ths secton, we choose two sngle sgnals as sources. When the sample rate s fxed, we set the number of samples of each block T= and the number of blocks B=. ere we set the length of the overlappng sgnals L=T/=. The transmtted power s dbm and the classcal algorthm n [] s chosen as the separaton method. The expermental results are shown n Fg. 9, Fg. and Fg x 4 Mxture - 3 umber of samples.. x 7 Mxture Mxture - 3 umber of samples. x 6.. Mxture Fg. 9. Mxng sgnals wth fve blocks n tme and frequency doman Separaton wthout concantenatng -. 3 umber of samples Separaton wthout concantenatng Separaton wthout concantenatng -. 3 umber of samples Separaton wthout concantenatng Fg.. Separatng sgnals wthout usng our proposed approach n tme and frequency doman Separaton wth concatenatng -. 3 umber of samples Separaton wth concatenatng Separaton wth concatenatng -. 3 umber of samples Separaton wth concatenatng Fg.. Separatng sgnals usng our proposed approach n tme and frequency doman As shown n Fg., the concatenated sgnals after separatng don t recover the orgnal sources correctly, whch s more obvous n the frequency doman. Compared the frequency doman of Fg. 9 and Fg., we can see that the permutaton and scalng ndetermnaces affect the separaton qualty serously when tyng each separated adacent block together. owever, note that the sgnals n Fg. usng our new approach successfully recover the orgnal source waveform. It can be observed clearly n the frequency doman that two sngle sgnals are totally separated. Compared the tme doman sgnals n Fg. and Fg., we can see that the connecton ambguty caused by permutaton and scalng ndetermnaces are elmnated by usng our new method. In order to verfy the performance of our method further, we analyze the correlaton matrces of the overlappng sgnals brefly as follows Φ = Φ = Φ = Φ = As for Φ, when =, [ temp, mark ] = [.3,], whch means that frst separated sgnal n the -th block corresponds to the second separated component n the (+)-th block. Then the second sgnal n the -th block corresponds to the frst n the (+)-th block, whch can be drawn from [ temp, mark ] = [.7,] wth = Experment In ths secton, we nvestgate the effect of the transmtted power of sources on the separaton qualty of our proposed method and Permutaton Method n [8]. We choose the number of blocks B=, for whch the number of samples of each block T=. The length of overlappng sgnals changes from to 4,.e., L=, 4,, 4. For convenence and smplcty, we choose α = T L wth α =,, 4, and as the donaton. The transmtted power ranges from - dbm to dbm, and the classcal algorthm n [] s chosen as the separaton method. The expermental results are shown n Fg.. E-ISS: Volume,

8 We Zhao, Yuehong Shen, Pengcheng Xu, Zhgang Yuan, Ymn We, We Jan Average MSE Permutaton method Our proposed method wth α= Our proposed method wth α= Our proposed method wth α=4 Our proposed method wth α= Our proposed method wth α= x The transmtted power of sources (dbm) Fg.. MSE between sources and connected separatons for Permutaton Method n [8] and our proposed method wth α =,, 4, and when the transmtted power ranges from - dbm to dbm averaged over Monte-Carlo runs. From Fg., we can see clearly that the performance of our method and Permutaton Method changes wth the transmtted power ncreasng, whch s dfferent from the computer smulatons. In fact, when the transmtted power ncreases, the performance of two methods doesn t become better and better monotonously. Ths s a specal and nterestng phenomenon for practcal applcaton. More precsely, when the transmtted power s low such as - dbm, the nose and nterference domnate n the receved sgnals so that the source sgnals can t be dstngushed obvously. owever, when the transmtted power s too hgh such as dbm, the transmtters produce many other nonlnear frequency components,.e., harmonc wave, whch s caused by the nonlnear dstorton of amplfers n the transmtted devces. owever, when the transmtted power s controlled approprately such as dbm, our method provdes good performance. Most mportantly, our method shows better performance n terms of separaton qualty than Permutaton Method when the transmtted power changes, whch can be seen clearly n Fg.. Although these experments are easy and smple, we beleve the expermental results are very sgnfcant, especally for future correspondng practcal applcatons. Concluson Ths paper deals wth the permutaton and scalng ndetermnaces problem of BSS n the case where the contnuously mxng sgnals are splt n tme and processed block by block. Due to the nherent ndetermnaces of BSS, tyng the separated sgnals n each adacent tme block can t recover the orgnal sources correctly. Ths paper proposes a novel approach to elmnate the permutaton and scalng ndetermnaces by overlappng adacent sgnal blocks. Smulatons and realstc experments are performed to valdate the performance of our new approach. Future work ncludes the extenson of mxture channel to convoluton and nonlnear, for whch more complcated realstc experments wll be performed. Acknowledgment Ths work s supported by the atonal atural Scence Foundaton of Chna under Grant o References: [] A. Yeredor, Performance Analyss of the Strong Uncorrelatng Transformaton n Blnd Separaton of Complex-valued Sources, IEEE Transactons on Sgnal Processng, Vol. 6, o.,, pp [] M. S. Alreza and D. R. Bhaskar, An ICA- SCT-PD Flter Approach for Trackng and Separaton of Unknown Tme-varyng umber of Sources, IEEE Transactons on Audo, Speech, and Language Processng, Vol., o. 4,, pp [3] F. Yn, T. Me and J. Wang, Blnd Source Separaton based on Decorrelaton and onstatonarty, IEEE Transactons on Crcuts and Systems I, Vol. 4, o., 7, pp [4] M. Z. Ikram and D. R. Morgan, A Beamformng Approach to Permutaton Algnment for Multchannel Frequency- Doman Blnd Speech Separaton, n Proceedngs of the ICASSP, Florda,, pp [] J. Anem uller and B. Kollmeer, Modulaton Decorrelaton for Convolutve Blnd Source Separaton, n Proceedngs of the ICA, ong Kong,, pp. -. [6]. Murata, S. Ikeda and A. Zehe, An Approach to Blnd Source Separaton based on Temporal Structure of Speech Sgnals, eurocomputng, Vol. 4, o. -4,, pp. -4. [7] M. Z. Ikram D. R. and Morgan, Permutaton Inconsstency n Blnd Speech Separaton: Investgaton and Solutons, IEEE Transactons on Speech and Audo Processng, Vol. 3, o.,, pp. -3. [8] T. Amshma, A. Okamura, S. Morta and T. Krmoto, Permutaton Method for ICA Separated Source Sgnal Blocks n Tme Doman, IEEE Transacton on Aerospace and Electronc Systems, Vol. 46, o.,, pp E-ISS: Volume,

9 We Zhao, Yuehong Shen, Pengcheng Xu, Zhgang Yuan, Ymn We, We Jan [9]. Saruwatar, T. Takatan,. Yamao, T. shkawa and K. Shkano, Blnd Separaton and Deconvoluton for Real Convolutve Mxture of Temporally Correlated Acoustc Sgnals usng SIMO Model-based ICA, Proceedngs of the 4th Internatonal Symposum on Independent Component Analyss and Blnd Sgnal Separaton, 3, pp []. Sawada, R. Muka, S. Arak and S. Makno, A Robust and Precse Method for Solvng the Permutaton Problem of Frequency-doman Blnd Source Separaton, Proceedngs of the 4th Internatonal Symposum on Independent Component Analyss and Blnd Sgnal Separaton, 3, pp. -. [] V. Zarzoso, P. Comon and R. Phlypo, A Contrast Functon for Independent Component Analyss wthout Permutaton Ambguty, IEEE Transacton on eural etworks, Vol., o.,, pp [] E. Bngham and A. yvarnen, A Fast Fxed- Pont Algorthm for Independent Component Analyss for Complex Valued Sgnals, Internatonal Journal of eural System, Vol., o.,, pp. -8. [3] [4] wk/usrp E-ISS: Volume,