A new training strategy for DFE-MLP using Modified BP algorithm and application to channel equalization

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1 WSEAS RANSACIONS o SIGNAL PROCESSING Samr Sada, Abd Elkrm Moussaou, Mohamed Ghadjat A ew trag strategy for DFEMLP usg Modfed algorthm ad applcato to chael equalzato SAMIR SAIDANI, ABD ELKRIM MOUSSAOUI, MOHAMED GHADJAI Departmet of Electrcal ad Automatc Egeerg Departmet of Electrocs ad elecommucatos Uersty 8 ma 945 Guelma 4, 4 Guelma ALGERIA sada.samr@uguelma.dz & samrtlc@gmal.com Abstract: I ths work, a ew trag strategy usg a ew modfed backpropagato () algorthm for a multlayer perceptro (MLP) based upo the preously troduced [8], [9] s proposed. Its performace s estgated ad compared to those of MLPDFE based o the stadard algorthm ad the preously troduced [8], [9]. he results show mproed performace obtaed by the ew structure olear chaels. KeyWords: Mult layer perceptro (MLP), Decso feedback equalzer (DFE)ackpropagato (), Chael Equalzato, Dgtal Commucato. Itroducto Adapte chael equalzer plays a mportat role dgtal commucato systems. It s used to reduce the effects of chael dstorto such as ose, tersymbol terferece (ISI), o lear dstortos, etc. Nolear equalzers are superor to lear oes applcatos where the chael dstorto s too seere for a lear equalzer to hadle [], [], [3]. A decso feedback equalzer (DFE) s a olear equalzer that s wdely used stuatos where the ISI s ery large [], [3]. More recetly, artfcal eural etworks hae bee used the feld of chael equalzato. Neural etworksbased equalzers hae bee proposed as alterates to classcal equalzers ad proded sgfcat performace mproemet a arety of commucato chaels because of ther capable performace hadlg olear problems [4], [5]. hese equalzers are employg arous eural etwork structures, such as multlayer perceptro (MLP) whch s oe of the most popular eural etwork used dgtal commucatos [6], ad t has bee corporated to the DFE (Decso Feedback Equalzer) to ehace ts performace. It s show that the MLPbased DFE traed wth the backpropagato algorthm () ge a sgfcatly mproed performace oer the smple DFE []. Backpropagato () algorthm s the best kow ad oe of the most commo learg algorthms used eural etworks [4], [7]. For a stadard algorthm, the error sgal whch s obtaed by comparg the output of the ode the output layer wth the desred respose [4], s propagated layer by layer from the output layer to the put layer to adaptely adjust all weghts the MLP (hece the ame back propagato algorthm for ths trag process). herefore all parameters of the MLP are obtaed by a sgle algorthm [8]. A ew learg scheme amed Modfed backpropagato algorthm appled to decsofeedback equalzato has bee proposed for mproe the performace of the stadard algorthm [8], [9]. he Modfed backpropagato algorthm (H) proposed by [8], [9] Based o the herarchcal approach, from the put layer to the output layer of the MLP, eery two layers of eural odes (wth oe hdde layer) wll be traed wth a ddual algorthm. Where each algorthm operates a twolayer submlp. hese submlp s are arraged from the put layer to the output layer of the MLP. I ths paper, the MLP s adjusted by two algorthms depedetly, wth a ew scheme herarchcal (NH) algorthm. he MLP ca be dded to two submlps, ad each submlp s optmsed by ts ow algorthm whch oe of the operates the frst layer ad the other oe operates all the other layers (secod layer to output layer). he performace of the ew scheme herarchcal (NH) algorthm s ealuated ad t s show that a great mproemet performace s obtaed through the use of ths techque oer both the proposed by [8], [9] ad the MLPDFE based o the stadard algorthm. EISSN: Volume 3, 7

2 WSEAS RANSACIONS o SIGNAL PROCESSING Samr Sada, Abd Elkrm Moussaou, Mohamed Ghadjat hs paper s orgazed as follows. Secto brefly troduces the decso feedback equalzer. he multlayer perceptro based decso feedback equalzer s cosdered secto 3. Secto 4 ges the derato of the algorthm alog wth the proposed Archtecture. Subsequetly, Secto 5 prodes the smulato results. Fally, our cocluso s preseted Secto 6. Decso Feedback Equalzer (DFE) A decso feedback equalzer (DFE) s a olear equalzer that s broadly used for chaels wth seere ampltude dstorto []. Fg. shows such a decso feedback equalzer (DFE). w x() Feedforward flter Feedback flter z z z z z u() w w w3 w4 w5 w6 he feedforward ad feedback flter weght ectors are wrtte a jot ector as: W w, w,..., w k k (4) k ad k represet the feedforward ad feedback flter tap legths respectely. o further mproe the capactes of the DFE, eural etworks hae bee tegrated to ts fudametal structure. 3 MLP Based DFE A MLPbased DFE wth two hdde layers, as show Fg., cossts of a feedforward ad feedback secto. he put to the feedforward flter s the sequece of osy receed sgal samples. he put to the feedback flter s the output symbol decso sequece from a olear symbol detector. e() y() Decso Dece z Feedforward secto Feedback secto Fg. Decso Feedback Equalzer Hdde Layer N N he structure of the decso feedback equalzer cossts of two flters a feedforward flter (FFF) ad a feedback flter (FBF). he put to the FFF s the sequece of the receed symbols whle the FBF has, as put, the output of the decso dece (the hard symbol estmates). he basc dea s that f the alue of the symbols preously foud are kow, the the ISI cotrbuted by these symbols ca be cacelled exactly, by remog past symbols alues wth sutable weghtg from the equalzer output []. Cosder that the DFE s updated wth a recurse algorthm the feedforward flter weghts ad feedback flter weghts ca be jotly adapted by the LMS algorthm o a commo error sgal e() as show (). W W e V () Where eu y () ad Vx, x,.., xk, uk,.., u (3) Hdde Layer Fg. hreelayer MLP based DFE structure. he basc elemet of the multlayer perceptro s the euro. Each euro the layer has prmary local coectos ad s characterzed by a set of real weghts [w j, w j,. w Nj ] appled to the preous layer to whch t s coected ad a real threshold leel I j. he jth euro the pth layer accepts real puts p, from the (p)th layer ad h produces a output p, expressed the followg j way: N p p p p p s j whj h I j (5) h p p j f s N Output Layer 3 3 t ˆ d (6) hs output alue p seres also as put to the j (p)th layer to whch the euro s coected. I N EISSN: Volume 3, 7

3 WSEAS RANSACIONS o SIGNAL PROCESSING Samr Sada, Abd Elkrm Moussaou, Mohamed Ghadjat the aboe expressos, f(.) represets the actato fucto. I ths paper we are gog to use the hyperbolc taget fucto (f(x) =tah(x)) the hdde layer ad the lear fucto the output layer. 4 Backpropagato algorthm wth the ew scheme herarchcal (NH) he MLPbased DFE wth two hdde layers traed wth, modfed backpropagato (H) algorthm ad ew scheme herarchcal algorthm (NH) are show Fgs. 3, 4 ad 5, respectely. he backpropagato algorthm has become the stadard algorthm used for trag multlayer perceptro. It s a geeralzed LMS algorthm that mmzes the measquared error betwee the desred ad actual outputs of the etwork []. I the algorthm, the output alue s compared wth the desred output, resultg a error sgal []. hs error sgal s fed back through the etwork whose weghts are adjusted to mmze a cost fucto (Fg.3). z Feedforward secto Feedback secto N e Output Layer t(d) Fg.3 hreelayer MLPDFE traed wth the stadard algorthm. he Modfed backpropagato algorthm H proposed by [8], [9] Based o the herarchcal approach, from the put layer to the output layer of the MLP, eery two layers of eural odes (wth oe hdde layer) wll be traed wth a ddual algorthm. Where each algorthm operates a twolayer submlp. hese submlp s are arraged from the put layer to the output layer of the MLP. Accordg to fgure 4, he algorthm operates a twolayer perceptro structure, ad the N N 3 3 t ˆ d algorthm operates a oelayer perceptro structure. Feedforward secto z e e N e t(d) Feedback secto N N 3 3 t ˆ d Fg.4 hreelayer MLPDFE traed wth the H algorthm. Howeer, the ew scheme herarchcal NH algorthm cossts of two algorthms. he frst algorthm () operates the frst layer ad the secod algorthm () operates all the other layers (secod layer to output layer). he MLPbased DFE wth two hdde layers traed wth ew scheme herarchcal algorthm (NH) as show Fg. 5. he algorthm operates a oelayer perceptro structure, ad the algorthm operates a twolayer perceptro structure. Feedforward secto z e N e t(d) Fg.5 hreelayer MLPDFE traed wth the NH algorthm. Feedback secto N N e N en e 3 3 t ˆ d N t(d) EISSN: Volume 3, 7

4 WSEAS RANSACIONS o SIGNAL PROCESSING Samr Sada, Abd Elkrm Moussaou, Mohamed Ghadjat I order to dere the NH algorthm, we defe the error cost fucto relate to the th ode of the pth layer as : p p e (6) where p p e t d (7) he algorthm performs a gradet descet o ths fucto the adjustmets of the weght p w j ad threshold leel p I each algorthm ca be dered as : p p p p w j. p w w j j p. p. p p j wj (8) p p p p p I B. p. I B (9) Where x. s the gradet of p wth respect to x. p ad B p are the leargrate parameters of the weghts ad threshold leels, respectely. he delta fucto p (8) ad (9) ca be defed as : p p p p. p e s () Furthermore, the formula for the (p)th layer ca be obtaed recursely as N p p p p. ' p j wj j ' Where p s the derate of p. () p p p p p w.. j j w j () (3) p p p I B. he formula of NH algorthm Fg. 5 ca be dered as follows. For the frst algorthm (): he adjustmets of the weghts w j ad the thresholdleel I ca be wrtte as: wj. wj wj s.. w s j wj.. j wj (4) I B. I s B.. s I B. (5) Where the delta fucto ca be ealuated as. e s (6) For the secod algorthm (): he adjustmets of the weghts 3 w j ad the thresholdleel 3 I ca be wrtte as : w j. 3 wj w j s wj s wj j wj (7) I B. 3 I s B. 3. s 3 I 3 3 B. (8) he delta fucto 3 ca be ealuated as : s e (9) he adjustmets of the weghts w j ad the thresholdleel I ca be wrtte as : 3 w.. j j wj () ad 3 I B. () Where the delta fucto ca be ealuated as: 3 3 ' w. () Where respect to ' s the derate of the wth s. he smulato results wll demostrate that the NH algorthm ca mproe the performace of the H ad the stadard algorthm. EISSN: Volume 3, 7

5 WSEAS RANSACIONS o SIGNAL PROCESSING Samr Sada, Abd Elkrm Moussaou, Mohamed Ghadjat 5 Smulato results he performace of ew scheme herarchcal (NH) algorthm s ow examed ad compared wth classcal ad H proposed [8, 9]. he MLPDFE structure uses fe samples the put layer, four samples the feedforward secto ad oe sample the feedback secto, the umber of euros the frst ad secod hdde layer ad the output layer s 9, 3, ad, respectely {(4,)DFE wth (9,3,)MLP Structure} [8]. he dgtal message appled to the chael s made of uformly dstrbuted bpolar radom umbers {, }. he chael ose s take to be addte whte Gaussa ose wth a sgal to ose rato (SNR) of 5dB. he learg parameters =.7 =.5 are used for the algorthm, ad the learg parameters =.7 =.5 ad 3 3 =.7 =.5 are used for the NH ad H algorthm. Sce the three algorthms aboe are used the same MLP structure. wo chael models are used the smulato ad are descrbed by ther trasfer fuctos: H z z.348z, (3) ad H z z z. (4) he egealue spreads for frst ad secod chael are 5 ad 8, respectely. hese chaels are wdely used lterature to ealuate the performace of equalzers [], [3], [4], [8]. he mea squared error (MSE) s oe of the most useful measures for the performace of a equalzer. Here, the MSE performace s determed by takg a aerage of 6 ddual rus, each of whch oles a dfferet radom sequece ad has a legth of 3 symbols. All the symbols are used for trag the ealuato of the MSE. Durg ths part of the smulatos, the performace measure s obtaed through the use of learg cures, ad BER cures. We cosder a olear chael composed of a lear chael followed by a memory less olearty defed by: 3..5 z y y y (5) Where y() s output of the lear part of the chael, z() s the olear chael output ad () s the addte Gaussa ose. MSE (db) Samples Fg.6 Learg cures for the dfferet algorthms wth chael H z MSE (db) Fg.7 Learg cures for the dfferet algorthms wth chael H z. Fg.6 shows the coergece cures of the three algorthms for the frst chael, these cures shows a clear mproemet both the coergece tme ad the steady state MSE whe usg the proposed herarchcal. It s also clearly show that NH algorthm performs better tha H algorthm. As show Fg.7, a smlar mproemet s also obtaed for the secod chael despte ts larger egealue spreads. Fg.8 ad Fg.9 shows the BER performace wth arous algorthms for the chael (3) ad chael (4), respectely. he BER performace s determed by takg a aerage of ddual rus, each of whch oles a dfferet radom sequece ad has a legth of symbols. he frst symbols are used for trag ad the rest are used for testg. he results dcate that the proposed NH algorthm yelds a much lower BER tha the stadard ad the H algorthm. H NH H NH Samples EISSN: Volume 3, 7

6 WSEAS RANSACIONS o SIGNAL PROCESSING Samr Sada, Abd Elkrm Moussaou, Mohamed Ghadjat.5 H NH to the output layer). he smulato has demostrated the effecteess of the proposed scheme terms of the steady state mea square error (MSE) attaable ad BER cures for olear chaels. log(ber) SNR (db) Fg.8 BER cures for the three algorthms wth chael z log(ber) H SNR (db) Fg.9 BER cures for the three algorthms wth chael z H H NH 6 Cocluso I ths paper, we hae used a ew scheme herarchcal (NH) algorthm to update the multlayer perceptro based decso feedback equalzer (MLPDFE). he performace of the ew herarchcal (NH) algorthm s compared to that of the MLPDFE based o the stadard algorthm, ad the preously troduced [8], [9]. he dfferece betwee the algorthm proposed ths paper ad the algorthm proposed [8], [9] s that ths latter, the MLP s dded to seeral submlps. hese submlps are arraged from the put layer to the output layer of the MLP ad each oe cotas two layers of eural. Eery two layers of eural wll be traed wth a ddual algorthm. Whereas, the proposed algorthm (NH), the MLP s adjusted by two algorthms depedetly whch oe of the operates the frst layer of the MLP ad the other oe operates all the other layers of the MLP (from the secod layer Refereces: [] M. N. ehra, M. Shakhs, H. Khoshb, Kerel Recurse Least Squaresype Neuro for Nolear Equalzato, IEEE st Coferece o Electrcal Egeerg, Mashhad, Ira, May 46, 3. [] K. Mahmood, A. Zdour, A. Zergue, Performace aalyss of a RLSbased MLP DFE tmearat ad tmearyg chaels, Dgtal Sgal Processg, Vol.8, No.3, 8, pp [3] A. Zergue, A. Shaf, M. Bettayeb, Multlayer perceptro based DFE wth lattce structure, IEEE rasacto o Neural Network, Vol., No.3, 8, pp [4] P. Sakumar, L. Arth, Ehacemet of New Chael Equalzer Usg Adapte Neuro Fuzzy Iferece System, IOSR Joural of Electrocs ad Commucato Egeerg (IOSRJECE), Vol.6, No., 3, pp [5] S. Pada, P.K. Mohapatra, S.P. Pagrah, A ew trag scheme for eural etworks ad applcato olear chael equalzato, Appled Soft Computg, Vol.7, 5,pp [6] M. Ibkahla, Applcatos of eural etworks to dgtal commucatoasuey, Sgal Processg, Vol.8, No.7,, pp [7] S. Pada, A. Sarag, S. P. Pagrah, A ew trag strategy for eural etwork usg shuffled frogleapg algorthm ad applcato to chael equalzato, AEU Iteratoal Joural of Electrocs ad Commucatos, Vol.68, No., 4, pp [8] C. M. Lee, S. S. Yag, C.L. Ho, Modfed backpropagato algorthm appled to decsofeedback equalsato, Image Sgal Process, Vol.53, No.6, 6, pp [9] S.S. Yag, C.L. Ho, C.M. Lee, H: Improemet Algorthm for a Adapte MLP Decso Feedback Equalzer, IEEE rasactos O Crcuts Ad Systems, Vol.53, No.3, 6, pp [] S. Quresh, Adapte equalzato, Proceedg of IEEE, Vol.73, No.9, 985, pp [] R. S. Scalero, N. epedeleloglu, A fast ew algorthm for trag feedforward eural etworks, IEEE rasactos o Sgal Processg, Vol.4, No., 99, pp.. EISSN: Volume 3, 7