A New Adaptive Filter Approach for Acoustic Echo Canceller in Teleconference Systems

Transcription

1 European Scentfc Journal September 28 edton Vol4 No27 ISSN: (rnt) e - ISSN A New Adaptve Flter Approach for Acoustc Echo Canceller n eleconference Systems Hamze Hadar Alaeddne Al Beydoun HS Laboratory Electroncs and hyscs Dept Faculty of Scences I Lebanese Unversty Lebanon Do: 944/es28v4n27p42 URL: Abstract A fleble Frequency doman Bloc Recursve Least Squares (FBRLS) algorthm usng the ult-delay Flter (DF) s presented throughout ths paper In term of performances the DF-FBRLS adaptve flter ntroduces smaller bloc delay and s usually faster and sutable for deal tme-varyng system such as an acoustc echo n a teleconference room he mplementaton of the FBRLS algorthm usng DF adaptve flter allows reducng the FF sze and consequently optmzng the hardware mplementaton that could be performed usng standard DS chps hese good performances are acheved by usng smaller bloc sze and updatng frequently the weght vectors whch wll reduce the total eecuton tme of the adaptve process Smulaton results show that the DF-FBRLS algorthm s better than the FBRLS algorthm n terms of the total eecuton tme and the effcency of the computatonal complety eywords: Adaptve flter Bloc RLS DF Introducton Adaptve dgtal flters have become ncreasngly popular due to ther ntellgent nature of processng sgnals on one hand and the emergence of a famly of powerful dgtal sgnal processors has enhanced ther tass on the other hand (Farhang 998 ; Benesty 2) here are many adaptve algorthms avalable; each has ts own merts and specal applcatons However for applcatons such as an acoustc echo canceller n teleconference systems whch requres flter lengths of several hundreds or thousands of coeffcents the frequency doman bloc adaptve flter based on the Recursve Least Squares (FRLS) algorthm s consdered to be most sutable (Stancu 23 ; Clar 98) hs s because the FRLS adaptve flter mplements the bloc RLS (BRLS) algorthm effcently by usng the Fast 42

2 European Scentfc Journal September 28 edton Vol4 No27 ISSN: (rnt) e - ISSN Fourer ransform (FF) (Clar 98 ; Alaeddne 22 ; Alaeddne 27) In so dong a sgnfcant reducton n computatonal load for the same adaptaton performance s acheved However a few practcal mplementaton problems of the FBRLS adaptve flter have hndered ts applcatons here are as follows: Ineffcent Use of Hardware: ost of the avalable FF or DS chps are desgned and optmzed for small FF sze typcally 256 ponts o mplement an acoustc echo canceller for a few thousands taps several FF chps are cascaded together wth eternal memory to form a larger FF confguraton whch s neffcent and epensve Long Bloc Delay: Snce the FBRLS algorthm mplements bloc processng for eample for the weght sze =24 the frst output of the adaptve flter needs to wat 28 ms for an 8 Hz samplng rate after that the last output of the same bloc s processed Such a long delay would mae the echo more annoyng Large Quantzaton Error n FF: As the sze of an FF becomes larger the number of multplcatons and scalng ncreases hs causes etra quantzaton error Wth these lmtatons n mnd we present a more fleble frequency doman (DF-FBRLS) algorthm he performance of ths algorthm s compared to the estng frequency doman FBRLS It s found that by usng a small FF sze and updatng the weghts more often the DF-FBRLS algorthm has a shorter bloc delay and ts computatonal complety proved to be more effcent wth smaller memory requrements he rest of the paper s organzed as follows In second secton we wll ntroduce the general dagram of the DF adaptve flter hrd Secton presents the proposed DF-FBRLS algorthm hen smulaton results and computatonal complety estmaton of the new algorthm are presented n secton four and compared to those obtaned wth the FBRLS algorthm he DF adaptve flter he DF adaptve flter s ntally developed to mplement the FBLS algorthm (Soo 99) he DF algorthm s bascally a bloc frequency doman adaptve flterng procedure whch conssts of segmentng the flter s mpulse response ŵ of length L n ( N) short successve 43

3 European Scentfc Journal September 28 edton Vol4 No27 ISSN: (rnt) e - ISSN segments L ( L L ) We defne then temporarly subvectors ˆ w of length ˆ w of sze as: wˆ wˆ () ˆ w he segmentaton of the mpulse response s shows n Fgure () Fgure Decomposton of the mpulse response th he segment followng epresson: ŵ nto ˆ w of the mpulse response L wˆ L wˆ vectors ˆ w ŵ s gven by the wˆ wˆ L (2) he frst step of ths algorthm s to convert the most recent overlapped nput samples to the frequency doman va FF as (Clar 98 ; Soo 99 ; Buchner 26): X FF N L X FF (3) 44

4 European Scentfc Journal September 28 edton Vol4 No27 ISSN: (rnt) e - ISSN he output N L L N L N y and the error vector can be epressed as: y last N terms of FF X W (4) d y E FF N (5) Where the operator denotes the term by term multplcaton W s the weght vector and d s the desred vector he updated weght equatons based on the DF-FBLS algorthm are gven by: wˆ th θ (6) wˆ B last L terms of FF X E θ (7) Where B s the bloc step sze and X s defned by: X FF N L (8) N L N N L L (9) Note that the nput/output operatons of the DF adaptve flter s dentcal to the FBLS ecept now the FF s -ponts long he FBLS adaptve flter can n fact be regarded as the specal case of DF wth Fgure (2) llustrates the bloc dagram of the DF-FBLS mplementaton showng the dfferent steps of the weght update usng a typcal eample It s mportant to note that the calculaton s performed n parallel usng sub-vectors whch reduce the FF sze and consequently the eecuton tme 45

5 European Scentfc Journal September 28 edton Vol4 No27 ISSN: (rnt) e - ISSN Fgure 2 rocedure mplementaton of DF-FBLS adaptve flter for N 5 L 4 2 and 5 B 46

6 European Scentfc Journal September 28 edton Vol4 No27 ISSN: (rnt) e - ISSN A mult-delay FBRLS algorthm he weght vector ŵ of FBRLS algorthm s gven by (Alaeddne 22; Alaeddne 27): w wˆ w ˆ ˆ * wˆ q q * () * Where s the forgettng factor and s the nverse correlaton matr of sze ( ): G () G represents the alman gan he fast convoluton denoted by between the vectors and can be calculated n the frequency doman by: * (2) last L terms of FF X E he error vector s smlarly obtaned as the DF-FBLS algorthm (Eq 4 and 5) he frst step of the DF-FBRLS algorthm (Alaeddne 28) conssts of dvdng the vector * nto sub-vectors of smallest sze not as prevously processed hen the man dea of the proposed algorthm s to decompose the two sequences and wthout overlappng unle the prevous DF (Alaeddne 27) accordng to the followng relaton: Where defned by: and [ ] [ ] are two vectors of length ( / ) < [ ] 2 47

7 European Scentfc Journal September 28 edton Vol4 No27 ISSN: (rnt) e - ISSN [ e e e ] he proposed decomposton procedure wthout overlappng s shown n Fgure (3) for 8 N 5 and L 4 Fgure 3 Decomposton of two vectors and nto 4 sub-vectors for 8 N 5 and L 4 and he orgnalty beyond ths choce resdes n the problem presented by the matr multplcaton between both coeffcents and * Actually the calculaton of the FF of both sequences and of length and respectvely based on the BLS and DF-FBLS algorthms shows a result wth common parts of samples Consequently the convoluton of θ * multpled by the bloc step sze B gves a smlar result of that done based on FBLS algorthm On the other hand the bloc step sze B n the FBRLS algorthm s replaced by coeffcent of sze ( ) hs matr creates a problem of calculaton durng the updatng of the flter coeffcents by the DF- FBRLS algorthm Actually the dfference between the FF of both sequences and s N- samples Consequently the result of multplcaton between the two coeffcents and FBRLS algorthm * frequency doman va FF as: hen the convoluton s not the same as obtaned by the can be calculated n the 48

8 European Scentfc Journal September 28 edton Vol4 No27 ISSN: (rnt) e - ISSN ψ X E (3) he FF and ts nverse (IFF) of a sequence of length can be calculated by fndng are proposed by the followng equatons: FF each of length m n X e (4) n 2 m n / m m* m (5) 2 mn/ ψ m e n where m he vector E can be calculated usng the same equaton (4) he orgnalty beyond ths proposal resdes n the segmentaton of the matr nto temporarly matrces of sze : (6) We propose to dvde each matr nto matrces each of sze : herefore the matr matrces of sze : (7) must be dvded also nto temporarly 49

9 European Scentfc Journal September 28 edton Vol4 No27 ISSN: (rnt) e - ISSN (8) Each matr s composed of matrces p of sze : p (9) From the above matr decompostons we defne the calculaton of the scalar q accordng to ths relaton: q (2) As the vector we propose to dvde the vector nto subvectors Each sub-vector s defned by: p (2) where [ ] Consequently the scalar q and the matr can be wrtten n the followng equatons: q (22)

10 European Scentfc Journal September 28 edton Vol4 No27 ISSN: (rnt) e - ISSN q (23) ang nto account the prevous equatons the weght update equaton of L -ponts DF-FBRLS algorthm s proposed by: ˆ ˆ ˆ w w w (24) he L L samples of the weght ˆ w ests n the last L n products n hat s why the result of each product of sze must be dvded nto L n order to have vectors of length L hs technque reduces the computatonal complety of the DF-FBRLS algorthm because the frst L products of L must be ecluded therefore: n q (25) Consequently the weght vector ŵ of DF-FBRLS algorthm taes the followng concludng form: ˆ ˆ ˆ u w w w (26) wth n L L H u (27) H (28) he update of the nverse correlaton matr (Eq ) must have the same decomposton technque proposed n the prevous equatons:

11 European Scentfc Journal September 28 edton Vol4 No27 ISSN: (rnt) e - ISSN (29) Each matr of sze s defned as follow: p (3) ang nto account the matr we defne the vector as follow: (3) Where (32) he proposed algorthm DF-FBRLS allows: he segmentaton of each vectors of length wthout beng overlappng unle the prevous one nto sub-vectors of smaller length than DF ) / ( < he segmentaton of each matr of sze nto matrces of smaller sze he parallel computng of the sub-vectors and matrces whch furthermore reduces the eecuton tme of the proposed algorthm

12 European Scentfc Journal September 28 edton Vol4 No27 ISSN: (rnt) e - ISSN Smulaton results Numercal smulatons have been conducted to evaluate the performance of the proposed DF-FBRLS algorthm In these tests the DF- FBRLS algorthm s compared to the FBRLS algorthm through atlab software he crtera used to evaluate the performance of both FF mplemented FBRLS and DF-FBRLS algorthms are compared as follows: he Echo Return Loss Enhancement (ERLEC) of the compensator wˆ N 2 d n n N ERLEC log 2 N d n yˆ n n N he mpulse response of the echo path compared to the adaptve flter s coeffcents he eecuton tme for the both algorthms to compute FF he computatonal complety he two algorthms are nvestgated n sngle-tal stuaton where emprcal values for the parameters are chosen as N L 4 and 8 he dmenson of the mpulse response s L 28 whch corresponds a delay of 6 ms for a samplng rate of 8 Hz In sngle-tal stuaton the acoustc echo cancellaton system must provde an echo reducton of about 24 db for delays lower than 25 ms and of about 4 db for delay eceedng 25 ms he performance of the DF-FBRLS algorthm s measured usng the ERLEC equaton and seen n Fgure (4) 53

13 European Scentfc Journal September 28 edton Vol4 No27 ISSN: (rnt) e - ISSN Fgure 4 (a) he Echo Return Loss Enhancement (ERLEC) of the compensator w ˆ (b) Dfference of both algorthm n term of ERLEC It can be notced that both algorthms do not reveal any sgnfcant 2 dfference n terms of ERLEC (error dfference s around db) In our case both algorthms provde an echo reducton of about 48 db for a delay of 6 ms he mpulse response of the echo path compared to the adaptve flter s coeffcents s seen n Fgure (5) Fgure 5 (a) Impulse response of the echo path (b) Dfference between the echo path and the DF-FBRLS s flter coeffcents 54

14 European Scentfc Journal September 28 edton Vol4 No27 ISSN: (rnt) e - ISSN he result obtaned n Fgure (5) presents a perfect constructon of echo s path by usng the DF-FBRLS algorthm Whch means that the resdual echo s unheard at the output of the echo cancellaton system Based on the obtaned values seen n table () and n fgure (6) the dfferences between both algorthms resde manly n two ponts whch are the eecuton tme and the computatonal complety of the flter As seen n the table wth the ncrease of the length ( L L / ) of DF-FBRLS flter decreases along wth the eecuton tme of FF At the DF-FBRLS algorthm behaves as the FBRLS one and thus t taes the hghest tme to eecute the FF he FF of length requres log 2 butterfles and each 2 butterfly need two comple addtons and one comple multplcaton he computatonal complety of both algorthms wth L and L 256 s shown n Fgure (6) It can be notced that wth the decrease of L the computatonal complety of DF-FBRLS algorthm decrease unle the one of FBRLS algorthm able Eecuton tme for DF-FBRLS algorthm to compute the FF Fgure 6 Operatons number of both algorthms FBRLS and DF-FBRLS 55

15 European Scentfc Journal September 28 edton Vol4 No27 ISSN: (rnt) e - ISSN Concluson hroughout ths paper a new algorthm to reduce enormously the tme of FF eecuton and the computatonal complety has been presented and smulated he obtaned algorthm fnds many applcatons n several felds nclude radar system echo cancelaton n teleconference room and n headset Our suggeston can be developed furthermore to handle the double tal stuaton and many other ssues References: B Farhang-Boroueny (998) Adaptve Flters heory and Applcatons Wley & Sons ISBN J Benesty GanslerD organ Sondh and SL Gay (2) Advances n Networ and Acoustc Echo Cancellaton Sprnger- Verlag 3 C Stancu J Benesty J aleologu Gansler and S Cochna (23) A wdely lnear model for stereophonc acoustc echo cancellaton Sgnal rocessng vol 93 pp GA Clar S tra and SR arer (98) Bloc mplementaton of adaptve dgtal flters IEEE rans on Crcuts and Systems vol CAS-28 pp H H Alaeddne O Bazz A Alaeddne and G Burel (22) Fast convoluton usng generalzed sldng Fermat number transform wth applcaton to dgtal flterng IEICE Journal E95-A (6) pp7-7 6 H H Alaeddne A Ghath Al-Sahl and Fadlallah (27) New Approach of erformance Analyss of RLS adaptve Flter Usng a Bloc-Wse rocessng EAR Journal vol V pp J S Soo and ang (99) ultdelay bloc frequency doman adaptve flter IEEE rans Acoust Speech Sgnal rocess vol 38 pp H BuchnerJ Benesty Gansler and W ellermann (26) Robust Etended ultdelay Flter and Double-al Detector for Acoustc Echo Cancellaton IEEE rans on Audo Speech and Language rocessng vol 4 pp H H Alaeddne Houssn El H Baghous and G Burel (28) New approach for the treatment of FBRLS algorthm wth long mpulse response IEEE ownet (pp-6) 56