Proportionate Sign Subband Adpative Filtering Algorithm for Network Echo Cancellers

Transcription

1 Journal of Advances n Computer Networks, Vol. 3, No. 2, June 2015 Proportonate Sgn Subband Adpatve Flterng Algorthm for Network Echo Cancellers J-Hye Seo, Sang Mok Jung, and Poo Gyeon Park are chosen as standard for the NEC. Wth long mpulse response, however, most of the coeffcents are close to zero; t means the typcal network mpulse response s sparse. Second, the exctaton sgnals used for NEC are speech sgnals whch are hghly correlated and non-gaussan process, so many adaptve flterng algorthms suffer from reduced convergence rate. In addton, the background nose can also be hghly non-statonary or strong nterferences. he thrd aspect to be consdered n NEC s double-talk scenaro whch means that far-end and near-end speech are actve smultaneously. In ths case, a near-end speech acts lke a large dsturbance of the flter, so t may causes extremely slow convergence or dvergence. When developng adaptve flterng algorthms used for NEC, these challengng problems should be consdered. An deal algorthm not only should have fast convergence rate and good trackng performance but also acheves small steady-state estmaton error even for long-length echo path. hese problems should be mantaned n the case of non-statonary exctaton sgnal. Furthermore, the algorthm should be robust aganst varaton of the mcrophone sgnal (background nose varatons and double-talk stuaton). he conventonal normalzed least mean squares (NLMS) algorthm s the most wdely used adaptve flterng algorthm due to ts smplcty and robustness [1], [2]. However, for NEC, the NLMS algorthm suffers from reduced convergence rate due to long length of the flter. It s possble to consder the recursve least squares (RLS) algorthm and the affne projecton algorthm (APA) [3] for obtanng fast convergence rate, but they are not approprate for NEC applcaton n practce because of ther heavy computatonal complexty. hus, there are requrements for adaptve flterng algorthms wth fast convergence rate and low computatonal complexty to replace the NLMS algorthm. he network echo path mpulse response s known as sparse n nature. hat s, only a small porton of the coeffcents s actve and other coeffcents are zero or unnotceably small values (nactve). Many adaptve flterng algorthm take advantage of sparseness the echo path and propose some methods to mprove the convergence rate and robustness or lower computatonal complexty. he proportonate NLMS (PNLMS) [4] has been developed to acheve fast ntal convergence rate. It updates coeffcents of the weght vector by assgnng dfferent step szes to dfferent coeffcents based on ther magntude of current estmates. For a large coeffcent, a large value of step sze s assgned n the update process, so ths method allows to obtan fast ntal convergence rate for sparse mpulse responses relatvely ndependent of ther length for sparse mpulse responses. However, the PNLMS algorthm slows down after ts fast Abstract hs paper proposes a proportonate sgn subband adaptve flterng (PSSAF) and an mproved PSSAF (IPSSAF) algorthm for network echo cancellers that deal wth mpulsve nterferences and sparse echo paths. Based on a sgn subband adaptve flterng (SSAF) algorthm that s robust aganst mpulsve nterferences, the proposed algorthm mnmzes L1-norm of the subband a posteror error vector subject to a weghted constrant on the flter coeffcents. A postve defnte weghtng matrx s used for the constrant. In ths paper, we adopt a dagonal proportonate matrx for the constrant to acheve fast ntal convergence rate when the mpulse response s sparse. he components of t s roughly proportonal to the absolute value of current estmate of the flter, so the resultng algorthm s called PSSAF algorthm. o acheve fast ntal convergence rate even for rather non-sparse mpulse responses, an mproved proportonate matrx s also used for the constrant, and the resultng algorthm s named as IPSSAF algorthm. Expermental results show that the proposed algorthms are more robust aganst hghly correlated nput sgnals, mpulsve nterferences, and double-talk than the orgnal normalzed subband adaptve flterng algorthm and the class of proportonate subband adaptve flterng algorthms. Index erms Adaptve flters, proportonate, sgn algorthm, subband adaptve flterng algorthm, weghted constrant, weghtng matrx. I. INROUCION A network echo cancellers (NEC) s an adaptve flter that s one of the best solutons to control acoustc echos of the voce communcaton networks. An adaptve flter estmates the echo path of the network and generates a replca of the room mpulse response, and then the output of the flter s subtracted from the near-end sgnal to obtan clean sgnals. he scheme of the NEC s the same as a classcal system dentfcaton, but there are several challengng problems for modern voce transmsson over telephone networks. he frst one s about the characterstcs of the echo path. he length of the echo path for NEC s extremely long due to long delays caused by large scale network. hus, the adaptve flter usually requres large number of taps, and 512 or 1024 taps Manuscrpt receved September 2, 2014; revsed March 23, hs research was supported by the MSIP (Mnstry of Scence, IC and Future Plannng), Korea, under the I Conslence Creatve Program (NIPA-2014-H ) supervsed by the NIPA (Natonal I Industry Promoton Agency). J-Hye Seo s wth the vson of I Convergence Engneerng, Pohang Unversty of Scence and echnology, Pohang, Gyeongbuk, Korea (e-mal: bmclubhs@postech.ac.kr). Sang Mok Jung and Poo Gyeon Park are wth the epartment of Electrcal Engneerng, Pohang Unversty of Scence and echnology, Pohang, Gyeongbuk, Korea (e-mal: llus2@postech.ac.kr, ppg@postech.ac.kr). OI: /JACN.2015.V

2 Journal of Advances n Computer Networks, Vol. 3, No. 2, June 2015 ntal convergence, and t has slower convergence rate than NLMS when the network mpulse response s not sparse enough. hs problem has been addressed n several papers, and modfcatons to PNLMS algorthm s studed to mprove the performance. he mproved PNLMS (IPNLMS) [5] s proposed to avod degradaton of the performance for the non-sparse mpulse response. It gves more optmal step szes for gven sparseness by usng a control factor, so mantans ts fast convergence rate even n the case of non-sparse mpulse responses. o keep the fast convergence rate durng the whold adaptaton process, the µ-law PNLMS (MPNLMS) s proposed n [6]. Also, the mproved IPNLMS (IIPNLMS) [7] s proposed where the step szes assgned for dfferent coeffcents are determned by two dfferent relatonshps dependng on whether the coeffcent s consdered as actve or nactve. hese concept of proportonate-type algorthms are extended to a normalzed subband adaptve flterng (NSAF) algorthm [8] n [9]. he NSAF algorthm decomposes the nput sgnals nto multple subbands n order to whten the nput sgnals n each subband, so the algorthm s sutable to acheve faster convergence rate than the NLMS algorthm. he computatonal complexty of the NSAF algorthm s not heavy comparng to the RLS or APA, and thus, the proportonate-type subband adaptve flterng algorthms are proper to use n NEC applcatons. In addton to fast convergence rate and low complexty, a robustness can be an consderable ssue for adaptve flterng algorthms. In partcular, double-talk s a bg challengng problem for NEC. o deal wth double-talk stuaton, a double-talk detector () can be used typcally. However, t s not desrable to rely only on because the NEC has tght requrements for detectng double-talk. hus, several adaptve flterng algorthms are developed focusng on the robustness to double-talk [10]-[14]. One of the method s usng L 1 -norm mnmzaton of error because L 1 -norm algorthms are especally robust aganst mpulsve nose such as speech. he basc algorthm usng L 1 -norm s the normalzed sgn algorthm (NSA). he NSA provdes robustness aganst mpulsve nose, but the convergence rate of t becomes slower than the NLMS algorthm. Recently, a sgn subband adaptve flterng (SSAF) algorthm s suggested n [15] whch extends a concept of L 1 -norm error mnmzaton to the NSAF. he SSAF algorthm has good robustness comparng to NSAF algorthm, and acheves rather faster convergence rate than the NSA. In ths paper, we adopt the proportonate approach wth the SSAF to obtan faster convergence for sparse network mpulse responses. Based on the weghted constrant to the weght error vector, we obtaned a weght update equaton for the proposed algorthm mathematcal dervaton. wo types of proportonate matrx based on the PNLMS [4] and IPNLMS [5] are used as a weghtng matrx, and the resultng algorthms are called proportonate sgn subband adaptve flterng (PSSAF) algorthm and mproved PSSAF (IPSSAF) algorthm, respectvely. he PSSAF and IPSSAF algorthm show fast convergence rate for sparse mpulse response, and they also show the robustness aganst hghly correlated nput sgnal, nterferences, and double-talk. Especally, the IPSSAF algorthm also acheves fast convergence rate even for the non-sparse mpulse response. he computatonal complexty of the proposed algorthms are slghtly hgher than the SSAF algorthm, but lower than the NSAF and the famly or proportonate-type NSAF algorthms. Fg. 1. Structure of a network echo canceller (NEC). II. BACKGROUNS A. Network Echo Cancellers Consder a NEC scheme shown n Fg. 1. In Fg. 1, u( n ) denotes the far-end sgnal, and η ( n)= z( n) + v( n) s a near-end sgnal where z( n ) and v( n ) are the near-end speech and background nose sgnal, respectvely. he true echo path s denoted as w wth length M, and the estmaton of t can be o obtaned by mnmzng the dfference between the desred output d( n ) and the estmated flter output y( n ) such that e( n)= d( n) y( n). he desred output that contans the echo, the near-end sgnal can be represented as d( n) = u ( n) w +η( n), and the flter output, the replca of the o echo, can be expressed as y( n) = u ( n) w ( n), respectvely, where u( n) =[ u( n), u( n 1),, u( n M + 1)] s the far-end sgnal vector and w( n) =[ w ( n), w ( n),, w ( n)] s the 0 1 M 1 estmaton of the mpulse response at tme ndex n. B. Sgn Subband Adaptve Flterng Algorthm Fg. 2 shows the conventonal subband adaptve flterng structure. he sgnals u( n) and d( n ) are decomposed nto u ( n ) and d ( n ) by analyss flters H( z ) = 0,1,, N 1. he subband nput sgnals u ( n ) are fltered by the adaptve flter W( z ) and the flter outputs y ( n), = 0,1,, N 1 are obtaned. By decmatng d ( n ) and y ( n ), d ( k ) and, y ( k ) are generated, and t s easy to note that, y ( k) = u ( k) w ( k), where w ( k) s the tap weght vector of, W( z) and u ( k) =[ u ( kn), u ( kn 1),, u ( kn M + 1)]. We use n and k to ndex the orgnal and decmated sgnal, respectvely. efne the subband output error vector e ( ) and subband a posteror error vector e ( k ) as p k e ( k) = d ( k) U ( k) w ( k) (1) e ( k) = d ( k) U ( k) w ( k + 1) (2) p where 0, 1, N 1, d ( k) = [ d ( k), d ( k),, d ( k)] and U( k) = [ u ( k), u ( k),, u ( k)]. 0 1 N 1 100

3 Journal of Advances n Computer Networks, Vol. 3, No. 2, June 2015 Fg. 2. Structure of NSAF algorthm. he sgn subband adaptve flterng (SSAF) algorthm [15] can be obtaned by mnmzng the L 1 -norm of the a posteror error vector wth a constrant on the flter coeffcents, Mnmzng Subject to 2 2 w( k + 1) w ( k ) µ (6) Σ( k) Subject to d ( k ) U ( k ) w ( k + 1) 1 ( k 1) ( k ) 2 µ 2 2 w + w (3) Usng the method of Lagrange multplers, the cost functon can be obtaned as J( w( k + 1))= d ( k) U ( k) w ( k + 1) 1 + γ [ w( k + 1) w ( k) µ ] (7) 2 2 Σ( k) where µ s a postve step sze that does not change dramatcally. Usng Lagrange multplers to solve ths constraned optmzaton problem and replacng e ( k ) to p e ( ) k, the weght update equaton of the SSAF can be obtaned as follows: w( k + 1)= w( k) + µ U( k) sgn( e ( k)) (4) sgn( e ( k)) U ( k) U( k) sgn( e ( k)) Usng the dagonal assumpton, that s, U ( k ) U ( k) = dag[ u ( k) u ( k), u ( k) u ( k),, u ( k) u ], we can wrte (4) as N 1 N 1 w( k + 1)= w( k) + µ U( k) sgn( e ( k)) N 1 u =0 where δ s a regularzaton parameter. ( k) u ( k) + δ III. PROPORIONAE SIGN SUBBAN AAPIVE FILERING ALGORIHM Instead of usng L 2 -norm to the constrant on the flter coeffcents n (3), we can use a weghted norm wth a postve defnte weghtng matrx Σ ( k) as Mnmzng d ( k ) U ( k ) w ( k + 1) 1 (5) where γ s a Lagrange multpler. Settng the dervatve of (7) wth respect to the w ( k + 1) equal to zero, we get 1 1 w( k + 1) = w( k) + Σ ( k) U( k) sgn( e ( k)). (8) p 2γ Snce a posteror error vector e ( ) s not accessble before the update, we need to approxmate t to a pror error vector e ( k ). hen, (8) can be replaced wth p k 1 1 w( k + 1) = w( k) + Σ ( k) U( k) sgn( e ( k)). (9) 2γ Substtutng (9) to the constrant n (7), we obtan 1 = γ 1 2 ( sgn e ( k)) U ( k) Σ ( k) U( k) sgn( e ( k)) µ (10) Substtutng (10) nto (9), the update equaton of the flter coeffcents can be expressed as + µ w( k + 1) = w ( k) ( k) ( k) sgn( ( k)) 1 Σ U e sgn k k k k sgn k 1 ( e ( )) U ( ) Σ ( ) U( ) ( e ( )) (11) We can choose the matrx Σ ( k) dependng on the 1 envronment. hus, we choose Σ( k) = G ( k) = dag[1/ g ( k)] M l 1 l=0 as a weghtng matrx, and then (11) can 101

4 Journal of Advances n Computer Networks, Vol. 3, No. 2, June 2015 process and a Gaussan process,.e., z ( k ) = w( k ) n ( k ), be expressed wth the matrx G (k ) as where n ( k ) s a whte Gaussan random sequence wth zero w ( k + 1) = w ( k ) mean and varance σ n2, and w(k ) s a Bernoull process wth G ( k ) U( k ) sgn(e ( k )) +µ the probablty mass functon gven as P( w) = 1 Pr for (12) sgn(e ( k ))U ( k )G ( k ) U( k ) sgn(e ( k )) w = 0, and P ( w) = Pr for w=1. he average power of a BG process s Pr σn2. Keepng the average power constant, a he components of G ( k ) can be determned accordng to [4] and [5] as gl (k ) = γ l (k ) BG process s spker when Pr s smaller. It reduces to a Gaussan process when Pr = 1. he MS,.e., E w o w ( k ) 2, s an ndcator of the performance of the (13) M 1 algorthms, and t s obtaned by ensemble averagng over 20 ndependent trals. In addton, the regularzaton factors are set to δ = σ u2 for the NSAF, PSAF, SSAF, and PSSAF γ (k ) / M l l =0 algorthms, and δ IP = (1 α ) / 2δ where for the IPSAF and IPSSAF algorthms where σ s a varance of nput sgnal. 2 u γ l (k ) = max( ρ max(q, w0 (k ),, wm 1 (k ) ), wl (k ) ) (14) Fg. 4 shows the MS curves for our proposed algorthms and several other algorthms under consderaton for comparson. AR(1) process generated usng G1 was used as or gl (k ) = 1 α 2 + (1 + α ) wl (k ) (2 w ( k ) 1 +ε ) / M. an nput sgnal, and SNR was set to 30dB. Consderng the strong nterference wth Pr = 0.01, the proposed PSSAF and IPSSAF algorthms show faster convergence rate than the SSAF algorthm, whle the NSAF, PSAF, and IPSAF algorthm dverges because of ther L2-norm mnmzaton of the error vector. (15) he resultng algorthms dependng on the component g l ( k ) n two ways are called proportonate sgn subband adaptve flterng (PSSAF) and mproved PSSAF(IPSSAF) algorthms, repectvely. In (14), the parameter ρ prevents wl (k ) from stallng when t s much smaller than the largest coeffcent and q regularzes the updatng when all coeffcents are zero for the PSSAF algorthm. In (15), the parameter α controls the behavor of the IPSSAF algorthm. When α = -1, the IPSSAF and SSAF are dentcal, and the IPSSAF behaves lke the PSSAF when α gets closer to 1. IV. SIMULAION RESULS A. Performance Comparson In ths secton, we dd several smulatons to verfy the performance of our proposed algorthm. he echo paths used for smulatons have 512 coeffcents and two typcal mpulse responses are depcted n Fg. 3. wo nput sgnals are used n the smulatons: the frst one s obtaned by flterng a whte zero-mean Gaussan random sequence through the G1 ( z ) = 1 / (1 0.9 z 1 ), and the second one s a speech sgnal. Fg. 3. Room mpulse response of the echo path for NEC. (a) Sparse mpulse response. (b) spersve mpulse response. he measurement nose, v(k ), s added to c ( k ) wth a sgnal-to-nose rato (SNR) defned by E[c 2 (k )] 2 E[v (k )] SNR = 10 log10 where c( k ) = u ( k ) w o. he near-end sgnal, z ( k ), s a strong mpulsve nterference wth a sgnal-to-nterference rato (SIR) of -30dB and Bernoull-Gaussan (BG) dstrbuton s used for modelng the nterference sgnal. he BG dstrbuton s generated as the product of a Bernoull Fg. 4. MS curves for the NSAF, PSAF, IPSAF, SSAF, and proposed PSSAF and IPSSAF algorthm wth nterference for sparse mpulse response. Input sgnal s AR(1), and SNR = 30dB. 102

5 Journal of Advances n Computer Networks, Vol. 3, No. 2, June to make the IPSSAF algorthm perform robust to sparseness of the network mpulse responses. Fg. 5. MS curves for the SSAF, PSSAF and IPSSAF algorthm wth nterference for sparse mpulse response. Input sgnal s AR(1), and SNR = 30dB. Echo path s changed abruptly at k = B. rackng Another possble scenaro n NEC s the change of the echo path. he result for ths scenaro s depcted n Fg. 6, where the sparse echo path (Fg. 3(a)) was abruptly changed at k = to the dspersve mpulse response (Fg. 3(b)). Envronment for ths smulaton s the same as n Fg. 4, and the step szes for the SSAF, PSSAF, and IPSSAF were set to make them acheve the same steady-state MS. In Fg. 5, the IPSSAF algorthm acheves the fastest trackng performance among the comparng algorthms, and the PSSAF algorthm acheves better trackng performance than the SSAF algorthm, where the other algorthms track the changed echo path slowly. Fg. 6. MS curves for the PSSAF algorthm for dfferent ρ for µ =0.01. he smulaton envronment s the same as n Fg. 5. Impulse responses n Fg. 3 were used as the (a) sparse and (b) dspersve mpulse responses, respectvely. C. Parameters o verfy the effects of the proportonate matrx for sparse and dspersve echo paths, we dd addtonal smulatons by varyng parameters used for proportonate matrx. Fg. 6, Fg. 7 depct the results of the smulaton for the PSSAF and IPSSAF algorthms, respectvely. AR(1) nput and BG nterference was used n the smulatons for mpulse responses shown n Fg. 3, and the step sze was set to µ = In Fg. 6(a), the PSSAF algorthm wth small ρ(ρ = 0.01) leads to fast convergence rate for sparse mpulse response because more proportonalty for the flter PSSAF algorthm wth larger value of ρ acheves better performance for dspersve mpulse response because larger ρ makes lttle proportonalty, and the algorthm updates the flter coeffcents wth a smlar rate. We verfed that the value of ρ consderably affects the performance of the PSSAF algorthm dependng on the sparseness of the network mpulse responses. We also dd experment about the effect of α for the IPSSAF algorthm n Fg. 7. In Fg. 7(a), as the value of α get closer to -1, the convergence rate of the IPSSAF algorthm get slower for sparse mpulse response. he convergence behavor of the IPSSAF for dspersve mpulse response s shown n Fg. 7(b), and we can notce that the algorthm shows smlar ntal convergence rate regardless of the value of α. As the value of α ncreases, the convergence rate of the IPSSAF algorthm get slower after ntal convergence, but the steady-state estmaton error of the algorthm wth dfferent α s not much dfferent for dspersve mpulse response. he effect of α s less senstve than the effect ρ of the PSSAF algorthm, and t s good to choose α = 0 or α = Fg. 7. MS curves for the IPSSAF algorthm for dfferent α for µ =0.01. he smulaton envronment s the same as n Fg. 5. Impulse responses n Fg. 3 were used as the (a) sparse and (b) dspersve mpulse responses, respectvely.. ouble-alk Scenaro In ths subsecton, we show the performance of the proposed and competng algorthms n the double-talk stuaton. Expermental envronment s the same as Fg. 4 except exctaton sgnal, and mpulse response n Fg. 3(a) s used as the network echo path. Speech sgnals used for double-talk scenaro are depcted n Fg. 8; far-end and near-end speech, respectvely. ouble-talk happen n the perod wth sample [2.0, 4.0] 104. As shown n Fg. 9 and Fg. 103

6 Journal of Advances n Computer Networks, Vol. 3, No. 2, June 2015 (IPSSAF) algorthm. he resultng PSSAF and IPSSAF algorthm showed faster convergence rate than the conventonal L1 algorthm for sparse network mpulse response. Moreover, they acheved more robust performance aganst mpulsve nterferences and double-talk than the exstng algorthms. 10, the NSAF, PSAF, and IPSAF show non-robust performance aganst double-talk dsturbance wthout and wth nterferences. In contrast, the NSA, SSAF, PSSAF and IPSSAF algorthm, a famly of sgn algorthms, show somewhat robust performance aganst both mpulsve nterferences and double-talk dsturbance. Among these famly of sgn algorthms, the proposed PSSAF and IPSSAF acheves faster convergence rate and smaller steady-state estmaton error than the NSA and SSAF algorthm. Wthout any double-talk detector, the proposed PSSAF and IPSSAF show better robustness to double-talk. ACKNOWLEGMEN hs research was supported by the MSIP (Mnstry of Scence, IC and Future Plannng), Korea, under the I Conslence Creatve Program (NIPA-2014-H ) supervsed by the NIPA (Natonal I Industry Promoton Agency). REFERENCES [1] [2] [3] [4] Fg. 8. Speech sgnals used n the double-talk scenaro. (a) Far-end speech (b) Near-end speech. [5] [6] [7] [8] [9] [10] Fg. 9. MS curves for the NSAF, PSAF, IPSAF, NSA, SSAF, and proposed PSSAF and IPSSAF algorthm for double-talk scenaro wthout mpulsve nterferences. [11] [12] [13] [14] Fg. 10. MS curves for the NSAF, PSAF, IPSAF, NSA, SSAF, and proposed PSSAF and IPSSAF algorthm for double-talk scenaro wth mpulsve nterferences. [15] S. Haykn, Adaptve Flter heory, 1st ed. Upper Saddle Rver, NJ: Prentce-Hall, A. H. Sayed, Fundamentals of Adaptve Flterng, New York: Wley, K. Ozek and. Umeda, An adaptve flterng algorthm usng an orthogonal projecton to an affne subspace and ts propertes, Electroncs and Communcatons n Japan, vol. 67-A, no. 5, pp , L. uttweler, Proportonate normalzed least-mean-squares adaptaton n echo cancelers, IEEE rans. on Speech and Audo Processng, vol. 8, no. 5, pp , September J. Benesty and S. L. Gay, An mproved PNLMS algorthm, n Proc. IEEE Internatonal Conference on Acoustcs, Speech, and Sgnal Process, vol. 2, pp , May H. eng and M. oroslovack, Proportonate adaptve algorthms for network echo cancellaton, IEEE rans. on Sgnal Processng, vol. 54, pp , May P. A. Naylor, J. Cu, and M. Brookes, Adaptve algorthms for sparse echo cancellaton, Sgnal Processng, vol. 86, pp , K. A. Lee, W. S. Gan, and S. M. Kuo, Subband Adaptve Flterng: heory and Implementaton, Wley, M. S. E. Abad, Proportonate normalzed subband adaptve flter algorthms for sparse system dentfcaton, Sgnal Processng, vol. 87, no. 7, pp , July J. Benesty, H. Rey, L. R. Vega, and S. ressens, A nonparametrc VSS NLMS algorthm, IEEE Sgnal Processng Letters, vol. 13, no. 10, pp , October Gansler, S. L. Gay, M. M. Sondh, and J. Benesty, ouble-talk robust fast convergng algorthms for network echo cancellaton, IEEE rans. on Speech and Audo Processng, vol. 8, no. 6, pp , November Waterschoot, G. Rombouts, P. Verhoeve, and M. Moonen, ouble-talk-robust predcton error dentfcaton algorthms for acoustc echo cancellaton, IEEE rans. on Sgnal Processng, vol. 55, no. 3, pp , March C. Paleologu, J. Benesty, and S. Cochna, A varable step-sze affne projecton algorthm desgned for acoustc echo cancellaton, IEEE rans. on Audo, Speech, and Language Processng, vol. 16, no. 8, pp , November Z. Yang et al., Proportonate affne projecton sgn algorthms for network echo cancellaton, IEEE rans. on Audo, Speech, and Language Processng, vol. 19, no. 8, pp , November J. N and F. L, Varable regularsaton parameter sgn subband adaptve flter, Electroncs Letters, vol. 46, no. 24, pp , November J-Hye Seo receved the B.Sc. degree n electrcal engneerng from Pohang Unversty of Scence and echnology (POSECH), Pohang, Korea, n 2010, and the M.Sc. degree from the vson of I Convergence Engneerng from POSECH. Currently, she s a Ph.. canddate n the vson of I Convergence Engneerng, POSECH, n Her man research nterests nclude sgnal processng, adaptve flterng algorthm, and mage V. CONCLUSION In ths paper, we proposed proportonate-type sgn subband adaptve flterng algorthms for network echo cancellaton. he proposed algorthm mnmzes L1-norm of the subband a posteror error vector subject to a weghted constrant. Applyng proper postve-defnte weghtng matrx to the weghted constrant, we obtaned proportonate sng subband adaptve flterng (PSSAF) algorthm and mproved PSSAF processng. 104

7 Journal of Advances n Computer Networks, Vol. 3, No. 2, June 2015 mplementatons. Sang Mok Jung receved the B.Sc. and M.Sc. degrees n electrcal engneerng from Pohang Unversty of Scence and echnology (POSECH), Pohang, Korea, n 2010 and 2012, respectvely. Currently, he s a Ph.. degree canddate n the vson of Electrcal Engneerng, POSECH. Hs man research nterests nclude sgnal processng, adaptve flterng algorthm, mage nspectons, network programmng, and ther Poo Gyeon Park receved the B.S. degree and M.S. degree n control and nstrumentaton engneerng from Seoul Natonal Unversty, Korea, n 1988 and 1990, respectvely, and the Ph.. degree n electrcal engneerng from Stanford Unversty, Stanford, CA, n Snce 1996, he has been afflated wth the vson of Electrcal Engneerng, Pohang Unversty of Scence and echnology, where he s currently a professor. Hs current research nterests nclude robust, LPV, and network-related control theores, delayed systems, fuzzy systems, sgnal processng, and wreless communcatons for personal area network (PAN). 105