EFFICIENT LOW DELAY FILTERING FOR RESIDUAL ECHO SUPPRESSION

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1 EFFICIENT LOW DELAY FILTERING FOR RESIDUAL ECHO SUPPRESSION Chrstelle Yemdj, Moctar Moss Idrssa and Ncholas W. D. Evans EURECOM Insttute 656 Sopha-Antpols, France {yemdj, moss, web: Chrstophe Beaugeant Infneon Technologes 656 Sopha-Antpols, France web: ABSTRACT In telecommuncatons termnals speech qualty s often degraded by acoustc echo. Varous approaches to echo cancellaton have been proposed and generally nvolve two separate stages, namely those of adaptve echo cancellaton and, as s the focus here, resdual echo suppresson. Whlst computatonally effcent, resdual echo suppresson approaches based on gan loss control have poor double talk performance. Sub-band approaches gve better performance but generally ntroduce a sgnfcant sgnal delay. Ths paper reports new expermental work whch assesses the performance of three low delay approaches to suppress resdual echo through tme doman convoluton. Results show that a new approach, based on the nverse dscrete Fourer transform, performs as well as the exstng approaches for both lnear and non-lnear echo whlst mantanng computatonal effcency and low sgnal delay. Index Terms echo cancellaton, echo postflterng, lnear echo, non-lnear echo, sub-band flterng, FIR flter. 1. INTRODUCTION An acceptable level of speech qualty s an mportant requrement for any telecommuncatons termnal. Wth moble devces, however, speech qualty s often degraded by varyng levels of ambent nose and acoustc echo. In nosy envronments, the mcrophone s senstve to near-end speech and ambent nose whch are both transmtted to the far-end speaker. Acoustc echo results from the couplng between the loudspeaker and the mcrophone and, as a result, the far-end speaker can sometmes hear a delayed verson of ther own voce, where the delay s ntroduced by the communcatons lnk. Acoustc echo cancellaton (AEC) and nose compensaton are used to tackle these problems [1]. Ths paper s concerned solely wth the problem of AEC. Most approaches to AEC are based on adaptve flters [1]. As llustrated n Fgure 1, an adaptve flter s used to generate an estmate of the echo sgnal whch s then subtracted from the mcrophone sgnal. However, because of the lmted flter order, changes n the acoustc path and non-lneartes, the resultng sgnal generally contans some resdual echo. s are commonly used to obtan further echo attenuaton [1]. A smple and popular approach to resdual echo suppresson s that of gan loss control (GLC) [1, 2]. GLC algorthms smply consst n applyng an attenuaton to the uplnk sgnal. Although ths gan s generally calculated as a functon of the loudspeaker power [2] t mpacts on near-end speech durng double talk perods because t s appled ndependently to the presence, or not, of near-end speech. To overcome the poor double talk performance of GLC sub-band echo postflters [3] are often used and are the focus of the work presented here. Sub-band postflters are preferred to GLC because they consst of sub-band gans and can therefore specfcally target frequences where resdual echo s audble. Such resdual echo suppresson flters can be appled to the uplnk sgnal n the spectral doman. Even though sub-band flterng () s advantageous because of ts low computatonal complexty t, however, ntroduces sgnfcant delay n the output sgnal. Ths delay can be reduced by performng the flterng n the tme doman through a convoluton. In ths case, the sub-band spectral gans are used to determne a broadband fnte mpulse response (FIR) flter. Popular approaches nclude the Flter Bank Equalzer () or the Low Delay Flter (), presented n [4]. The approach was used n [5] for jont nose reducton and resdual echo suppresson and n [6] for jont reverberaton and nose suppresson. Another alternatve, reported by Hänsler n [7], nvolves the use of the nverse dscrete Fourer transform () of the spectral gans to suppress resdual echo. The sde by sde performance comparson of these approaches has, to our knowledge, not been prevously reported. Ths paper presents the frst comprehensve comparatve assessment of the,, and approaches to sub-band resdual echo processng. The remander of ths paper s organzed as follows. In the next secton we present the algorthm used for the calculaton of the spectral gans and dfferent flterng scheme that can be used for processng resdual echo. In Secton 3, we compare the computatonal complexty of the dfferent approaches. Secton 4 presents our expermental setup used for smulatons. Performances of the dfferent approaches are presented n Secton 5 and conclusons are presented n Secton ECHO POSTFILTERING Fgure 1 llustrates the echo cancellng scheme used n our nvestgatons: AEC followed by a postflter to process the resdual echo. The mcrophone sgnal y(n) s composed of the near-end speech sgnal s(n) and of the echo sgnal d(n). The adaptve flter s used to generate an estmate of the echo sgnal d(n) ˆ whch s subtracted from the mcrophone sgnal. The error sgnal e(n) s composed of the resdual echo e r (n) and of near-end speech s(n). The postflter ams to suppress the resdual echo. In the followng, we descrbe the postflter nvestgated. Secton 2.1 detals the common sub-band analyss used n our smulatons. In Secton 2.2, we present the algorthm used to calculate the spectral gans. Lastly, Secton 2.3 presents the nvestgated flterng approaches. 2.1 Sub-band analyss As shown n Fgure 2, the error sgnal e(n) and the loudspeaker sgnal x(n) are splt nto sub-band sgnals e (n) and x (n) respectvely, where denotes the sub-band ndex and ranges from to M 1. In our case, sub-band analyss and synthess are performed through a dscrete Fourer transform-modulated. One property of such s s that each bandpass flter corresponds to a frequency shfted duplcate of a lowpass flter h(n). In the lterature h(n) s referred to as a prototype flter [8]. Moreover, sub-band sgnals e (n) and x (n) have a reduced bandwdth compared to the orgnal nput sgnals e(n) and x(n). Therefore, the bt rate of the sub-band sgnals can be downsampled by a factor r, wth the constrant that r M to avod frequency do-

2 x(n) AEC downlnk path x(n) d(n) s(n) Adaptve flter ˆd(n) Uplnk path y(n) + e(n) ŝ(n) Fgure 1: Echo cancellng scheme llustratng AEC followed by a sub-band echo postflter wth flterng n the sub-band doman. man alasng [8]. The beneft of downsamplng s that the resdual echo suppresson flter update s performed at a samplng rate that s lower than that of the nput samplng rate. In our smulatons, the above s mplemented through a polyphase network (PPN) [7]. Wth the PPN mplementaton, the sub-band analyss stage requres one convoluton and one Fourer transform nstead of M convolutons. 2.2 Spectral gans For each sub-band, the gan of the echo postflter s updated usng a Wener flterng rule [3]: G (n) = ξ (n) 1+ξ (n), (1) where ξ (n) s the sgnal (near-end speech) to echo rato (SER). In practce, the SER s unknown and, consequently, t needs to be estmated. In our mplementaton, the SER s estmated through the Ephram and Malah approach [9]: ξ (n) = β ŝ 2 (n 1) (n 1) +(1 β) max(ξ post (n),) (2) where the smoothng constant β les n the nterval ],1[, ŝ (n 1) s the th sub-band near-end speech sgnal estmate, (n) s the resdual echo spectral densty and ξ post (n) s the a posteror SER. The resdual echo spectral densty n Equaton 2, (n), s estmated accordng to [3]: (n) = γxe (n) γ xx (n), (3) where γ xe (n) s the crosspower spectral densty between x(n) and e(n) and γ xx (n) s the loudspeaker power spectral densty. The a posteror SER n Equaton 2, ξ post (n), s calculated accordng to: ξ post (n) = e2 (n) 1. (4) (n) In all cases, the spectral denstes γ xx (n) and γ xe (n) are estmated through autoregressve smoothng as n [3]. 2.3 ng Usng the postflter presented above echo can be processed ether n the sub-band doman as descrbed n Secton (see Fgure 2(a)) or n the tme doman as descrbed n Secton (see Fgure 2(b)) Sub-band flterng Sub-band flterng () s llustrated n Fgure 2(a) and conssts of applyng the th sub-band gan G (n) on the th sub-band mcrophone sgnal e (n) as a multplcatve factor ŝ (n) = G (n) e (n). (5) e(n) e (n) x (n) Gan update G (n) Subband flterng ŝ(n) Synthess (a) Echo flterng n the sub-band doman. e(n) e(n) Gan update x (n) G(n) FIR flter calculaton Convoluton (b) Echo flterng wth an FIR flter. ŝ(n) x(n) ŝ(n) Fgure 2: sub-band echo postflter detaled scheme. The full-band mcrophone sgnal ŝ(n) s recovered by processng the sub-band sgnals ŝ (n) through the approprate synthess flter bank. Spectral gans are postve real numbers (zero phase), therefore the nput sgnal phase s not modfed. Moreover, for the analyss and synthess stages, we restrct ourselves to lnear phase prototype flters. The overall system (sub-band analyss and synthess) ntroduces a sgnal delay of L 1 samples, where L s the length of the prototype flter Tme doman flterng Fgure 2(b) shows the sub-band echo postflterng scheme wth a fnte mpulse response (FIR) flter. The sub-band sgnals x (n) and e (n) are used to calculate the sub-band gans G (n) accordng to the equatons n Secton 2.2. The sub-band gans G (n) are used to determne an FIR flter. Ths FIR flter s calculated accordng to the, or flter rule. The echo suppresson s therefore done through convoluton of the nput sgnal e(n) wth any of the FIR flters. To avod phase dstortons and to ensure a constant sgnal delay, we ensure that these flters are lnear phase flters [8]. We now present the three dfferent FIR flters consdered. Flter bank equalzer (): The was ntroduced n [4] and s the mathematcal tme doman equvalent of the approach. The s expressed as follows: g f be (n) = h(n) g(n), (6) where h(n) s the prototype flter of the sub-band analyss stage and g(n) s the of the spectral gans G (n). As the spectral gans are postve (zero-phase), the lnear phase property s assured f h(n) has lnear phase. Ths condton s fulflled, for example, f h(n) s symmetrc. The process ntroduces a sgnal delay of (L 1)/2 samples, that s half the delay ntroduced by the method. Low delay flter (): Although the has lower sgnal delay than the correspondng, smaller sgnal delays can be acheved by approxmatng the by a lower degree flter [4, 6]. The s obtaned by truncatng the wth a wndow of length P wth P < L. The wndow can chosen arbtrarly or chosen so as to mantan lnear phase. As the has lnear phase, one

3 can use a wndow whch s symmetrc along L/2. We used the Hammng wndow n our smulatons. Experments wth dfferent values of P showed that for an of length L, an of L/2 taps s a good match no matter what the number of sub-bands. Inverse Dscrete Fourer Transform () flter: A more ntutve approach mght be to obtan the FIR flter smply by applyng the to the updated spectral gan factors [7]. The of the gans corresponds to a non-causal zero phase flter. A causal flter s obtaned by applyng a temporal shft of (M 1)/2. In the frequency doman, the temporal shft corresponds to a phase modfcaton: the zero-phase flter then becomes a lnear phase flter. 3. COMPUTATIONAL COMPLEXITY Our study of tme doman flters for sub-band adaptve flterng s manly motvated by the reducton of sgnal delay. However, computatonal complexty s an aspect whch s of crucal mportance to real tme mplementatons. Table 1 shows the algorthmc complexty, memory requrements and sgnal delay characterstcs of each dfferent flterng approach (,, and ). The number of multplcatons and addton operatons presented n columns 2 and 3 of Table 1 do not nclude the number of operatons needed for the calculaton of spectral gans nor the Fourer transform requrements snce these are the same for all approaches. The and are mathematcally equvalent flterng schemes. However, from Table 1, we can see that, although the has lower sgnal delay than the correspondent, t s more computatonally demandng (more multplcatons). The s a more computatonnally effcent alternatve to, has a lower sgnal delay and s therefore a better trade-off between the and the n terms of algorthmc complexty and memory requrements. If the and flters have the same length (P = M), the delay and memory requrements are the same for each approach but the method requres even fewer operatons than the. Multplcatons Addtons Memory Sgnal delay 2.L+M r L M r +(L 1) 2.L L 1 2.L r + L L M r +(L 1) 2.L L L+P r + P L M r +(P 1) L+P P 1 2 L L M M 1 r + M r +(M 1) L+M 2 Table 1: Number of operatons requred per sample for each approach to sub-band flterng. The analyss and synthess stages are mplemented through a polyphase network. 4. EXPERIMENTAL SETUP The dfferent flterng methods presented above are compared through smulatons as descrbed below. In Secton 4.1, we descrbe our system setup. Secton 4.2 presents the method used to generate our test sgnals. Our approach to assessment s descrbed n Secton System setup In each case, the sub-band sgnals are extracted usng a DFTmodulated where the prototype flter h(n) of length L s defned as: h(n) = 1 [ ( 2π M snc n L )] w L (n), (7) M 2 where w L s a Hammng wndow also of length L. For all experments reported here, L s equal to 128. The length of the flter P s set to L/2 = 64. The number of sub-bands M s equal to 64 and was chosen to gve a satsfactory compromse between acceptable frequency resoluton and realstc computatonal complexty of the Fourer transform. When usng fewer sub-bands,.e. reduced frequency resoluton, there s a notceable degradaton n performance whereas the use of more sub-bands leads to excessve computaton. Fnally, we use a downsamplng factor of r = M/2 = Speech sgnals All speech sgnals used n our smulatons are sampled at 8 khz. Mcrophone sgnals contan an echo-only perod followed by a double talk perod. The echo-only perod s of nterest to evaluate echo suppresson whereas the double talk perod s of nterest to assess near-end speech qualty. The echo sgnal s obtaned by convolvng a lnear or non-lnear loudspeaker sgnal wth an acoustc path response. The resultng echo sgnal s then added artfcally to a near-end speech sgnal to synthesze the mcrophone sgnal. The SER of resultng sgnals ranges from -5dB to 1dB wth the near-end speech actve level beng set at -26dB. The near speech and echo level are set usng the ITU-T speech voltmeter [1]. The acoustc path responses used to generate the echo were measured usng real moble termnals n an offce envronment and are dentcal to those used n [11]. Loudspeaker non-lneartes are smulated accordng to a Volterra model [12] as used n [11]: x nl (n) = x(n)+a x 2 (n)+b x 3 (n) (8) where x nl (n) s the non-lnear loudspeaker sgnal, x(n) s the lnear loudspeaker sgnal and (a, b) are weghtng components rangng between and 1. For the experments reported n ths paper, we used a = 1 and b = 1. Other expermental work conducted by the authors of [11] shows that ths confguraton typfes the case when a moble termnal s used n handsfree mode. We used a database of 16 speech sgnals and results presented n ths paper correspond to typcal observatons. 4.3 Assessment Each flterng method s assessed stand-alone (.e. wthout the AEC module) and n combnaton wth AEC (.e. for resdual echo suppresson). It s of nterest to study the postflter performance wthout AEC snce t can be used alone n case of reduced computatonal load. Moreover such a confguraton characterses performance when the postflter s used for resdual echo suppresson whle the AEC module has not yet converged. When the postflter s used wth AEC, we effectvely evaluate ts performance when used solely for resdual echo suppresson. In ths case, we focus on perods where the AEC module has converged. The AEC algorthm used for all nvestgatons reported here s the sub-band normalzed least mean square method as descrbed, n [2]. Performance s assessed n terms of echo return loss enhancement (ERLE) measurements and nformal lstenng tests. The ERLE measures the amount of echo suppresson and s defned as the energy rato between the echo before the postflter and that at the output. In our mplementaton, the ERLE s measured over wndows of N samples: ( N φ 2 ) (N) ERLE(m) = 1 log 1 N ŝ 2 (N) where N spans over 256 samples and φ(n) s the mcrophone sgnal y(n) when the postflter s used alone and s the resdual echo sgnal e(n) when t s used for resdual echo suppresson. Informal lstenng tests are necessary to complete the assessment of processed speech sgnal wth subjectve qualty percepton. (9)

4 (a) ERLE aganst tme for the dfferent s used for echo cancellaton (b) ERLE aganst tme for the dfferent s used for resdual echo suppresson (a) ERLE aganst tme for the dfferent s used for echo cancellng (b) ERLE aganst tme for the dfferent s used for resdual echo suppresson SER n db (c) Average ERLE aganst SER for the dfferent methods when the postflter s used for resdual echo suppresson. SERs are measured at the nput of the AEC module SER n db (c) Average ERLE aganst SER for the dfferent methods when the postflter s used for resdual echo suppresson. SERs are measured at the nput of the AEC module. Fgure 3: ERLE measurements n lnear echo case. 5. RESULTS In ths secton we present an assessment of the four dfferent approaches to echo postflterng presented n Secton 2.3. Secton 5.1 presents an assessment n the case of lnear echo whereas results wth loudspeaker non-lneartes are presented n Secton Smulaton results wth lnear echo Results where the postflter s used stand alone and where the postflter s used n combnaton wth AEC are both reported here. wthout AEC: Fgure 3(a) llustrates a typcal ERLE profle aganst tme durng an echo-only perod for each flterng method. Here, the postflter s used wthout the AEC module. Fgure 3(a) shows that all the flterng methods have approxmately the same behavor; the curves are almost dentcal. Nevertheless, we can see that the flter sometmes acheves less echo suppresson than do the other flterng methods. For example, at tme t = 1s, the method acheves about 1dB less ERLE than the other methods. Perods where the method acheves less echo suppresson correspond to ntervals where the SER s locally low. We note that echo remans slghtly audble n processed sgnals, especally durng double talk. Informal lstenng tests show that echo-only and double talk perods processed through the method are perceved as muscal nose (random spectral peaks of short duraton). In contrast, echo-only and double talk perods processed by FIR flters contan cracklng nose; sgnals processed by FIR flters have a much smoother spectrogram than those processed by the method. Ths dfference can be explaned by the fact that the effectve frequency response of the FIR flters s smoother compared to the orgnal spectral gans. The cracklng s slghtly more perceptble n sgnals processed by the method: ths can be explaned by the fact that the effectve frequency response of the flter has large varatons between consecutve dscrete frequency bns (here the dscrete frequency bns are those where the Fgure 4: ERLE measurements n non lnear echo case. spectral gans are calculated) where dfferences n gan are greater than 1dB. We can therefore assume that the use of a prototype flter n the defnton of the (and addtonal wndowng for the compared to the ) somehow results n a smoothng n the frequency doman because the effectve frequency responses of the and do not have the large varatons observed on the flter frequency responses. Nevertheless, for values of SER greater than 5dB, performance durng echo-only and double talk perods s good. But, as the SER falls, the artfacts ntroduced durng double talk (muscal nose for method and cracklng nose for FIR flters) become very annoyng. wth AEC: Fgure 3(b) shows the ERLE profles for each flterng method durng an echo-only perod for the sub-band echo postflter when used for resdual echo suppresson (.e. wth combned AEC). Agan, all the flterng methods have the same behavor, wth a reduced gap between the method and the others. Improvements obtaned wth the method s due to the fact that the AEC mproves the SER at the nput of the postflter. Fgure 3(c) shows mean ERLE aganst SER at the nput of the AEC. The mean ERLE s calculated durng echo-only perods after the AEC module has converged. The AEC acheves echo suppresson of about 24dB. In Fgure 3(c), we see that the and methods are equvalent; they have the same ERLE. The approach gves slghtly better performances than or methods n terms of ERLE whereas the method acheves an ERLE of between 1 and 3dB less than the and methods. The overall system (AEC + postflter) acheves an average ERLE of about 4dB when usng any of the, or approaches. Once the AEC module has converged, the dfferences between the four flterng methods s no longer perceptble durng echo-only perods as echo s naudble. Durng double talk perods, dfferences between the flterng methods are audble but not annoyng. As s the case when the postflter s used alone, we note the

5 presence of small cracklng between syllables (durng the double talk) n sgnals processed by the FIR flter and the presence of muscal nose n sgnals processed n the spectral doman. 5.2 Smulaton results wth non lnear echo Once agan, we present results where the postflter s used stand alone and where the postflter s used for resdual echo suppresson. wthout AEC: Fgure 4(a) shows the ERLE for each flterng method durng an echo-only perod. Here, the postflter s used wthout the AEC module. Once agan, all the flterng methods have the same behavor but n general, the flter acheves less echo suppresson than do the others and, just as for the lnear echo case, these ntervals correspond to where the SER s locally low. As for the lnear case, we note the presence of cracklng nose n FIR-processed sgnals. Sgnals processed by the and methods sound the same but dfferences between the method and the or methods are notceable durng echo-only and double talk perods. Sgnals processed by the method contan more echo and the cracklng nose s also more audble whch, n ths case, s always perceved as annoyng. The poor performance of the approach can once agan be explaned by the fact that the has dffcultes to follow large gan varatons. Cracklng present n sgnals processed by or methods can be perceved as annoyng for low SER (typcally SER db). For speech sgnals processed n the sub-band doman, we note the presence of muscal nose durng both echo-only and double talk perods. The muscal nose s perceved as annoyng for SERs lower than db. wth AEC: Fgure 4(b) shows the mean ERLE of each flterng method durng an echo-only perod for the sub-band echo postflter when used for resdual echo suppresson. Here we take nto account only the amount of echo suppressed by the postflter. Once agan, all the flterng methods have the same behavor and, as for the lnear case, there are less dspartes between the method and the others. Fgure 4(c) shows mean ERLE aganst SER at the nput of the AEC. The mean ERLE s calculated on an echo-only perod where the AEC module has converged to ts optmal response. Here, we can see that the method acheves the best results. The AEC module mproves the SER at the postflter nput, whch s stll hgher than n the lnear case snce the AEC acheves less echo reducton. As for the lnear case (Fgure 3(c)), the acheves more echo reducton than the other methods at low SERs. Fgure 4(c) also shows that the and methods are stll equvalent whereas the method acheves about 1 to 2dB less ERLE than does the method. In the presence of non-lneartes, the AEC acheves about 13dB of echo suppresson whch s approxmately 1dB less than n the lnear case. The overall system (AEC + postflter) acheves an average ERLE of about 32dB when usng the, or approaches: that s about 6dB less than for the lnear case. Informal lstenng tests reveal that the AEC output contans mostly non-lnear echo. Therefore, the dffculty when analyzng sgnals processed by the postflter s to dstngush artfacts due to non-lneartes from those ntroduced by the postflter. Although most of ths resdual echo s suppressed by the postflter, echo s stll slghtly audble durng echo-only perods. As for the lnear case, we note the presence of cracklng n sgnals processed by FIR flters and the presence of muscal nose n sgnals processed n the sub-band doman. The cracklng s slghtly more audble for -processed sgnals and s annoyng for SERs lower than db. Compared to the case where the postflter s used stand alone, near-end speech qualty durng double talk s mproved. Ths s explaned by the fact the AEC module mproves the SER at the postflter nput. 6. CONCLUSION Ths paper presents the frst comparson of four dfferent flterng approaches that can be used wthn a sub-band echo postflter. Our postflter s assessed as a stand alone soluton to echo cancellaton and n combnaton wth an adaptve approach to acoustc echo cancellaton. Both lnear and non-lnear echo s consdered. Results show that, for hgh SERs, all the flterng methods lead to effcent echo cancellaton and, when used for resdual echo suppresson wth lnear echo, they all produce speech of equvalent qualty. For non-lnear echo the method gves equvalent performance to the other approaches at hgh SERs, whereas the, and approaches gve better performance at lower SERs. In the presence of hgh non-lneartes, the method gves a good compromse between effectve echo suppresson, computonal complexty and sgnal delay. It s shown that the method leads to small sgnal delays and s the most computatonally effcent. For lnear echo and moderate level of non-lneartes, the method gves good results n terms of ERLE and speech qualty. The expermental work presented n ths paper thus shows that the method s an appealng alternatve to, or methods. REFERENCES [1] E. Hänsler and G. Schmdt, Acoustc Echo and Nose Control: A Practcal Approach. Wley-Interscence, 4. [2] P. Degry and C. 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