Neuro-Fuzzy Network for Adaptive Channel Equalization

Transcription

1 Neuro-Fuzzy Network for Adaptve Channe Equazaton Rahb H.Abyev 1, Tayseer A-shanabeh 1 Near East Unversty, Department of Computer Engneerng, P.O. Box 670, Lefkosa, TRNC, Mersn-10, Turkey rahb@neu.edu.tr Near East Unversty, Department of Eectrca and Eectronc Engneerng, P.O. Box 670, Lefkosa, TRNC, Mersn-10, Turkey shanabeh@neu.edu.tr Abstract Ths paper presents the equazaton of channe dstorton by usng neuro-fuzzy network. The structure and earnng agorthm of neuro-fuzzy network have been descrbed. Usng earnng agorthm of neuro-fuzzy network an adaptve equazer have been deveoped. The deveoped equazer recovers transmtted sgna effcenty. The use of neuro-fuzzy equazer n dgta sgna transmsson aows to decrease tranng tme of parameters and the compexty of network. The resut obtaned from the smuaton s compared wth the smuaton resut of neura equazer, and t s shown that neuro-fuzzy equazer has better performance than other one. 1. Introducton In today s communcaton envronment, the channes are affected by both near and nonnear dstorton. To equaze channe dstortons, such as ntersymbo nterferences, channe noses the varous equazers have been apped [1]. Cassca equazers do not perform we n rapdy fadng channes. When channe has tme-varyng characterstcs and channe mode s not precsey known adaptve equazaton s apped. Adaptve equazaton can be dvded nto two types sequence estmaton and symbo detecton []. Sequence estmaton needs channe estmaton, and s computatonay compex. In ths paper, adaptve channe equazaton that reazes symbo detecton technque s consdered. Ths s a cassfcaton probem n whch nput baseband sgna s mapped onto a feature space determned by the drect nterpretaton of known tranng sequence. Here, the am s to separate the symbos n the output sgna space whose optma decson regons boundares are nonnear. Recenty, dfferent approaches have been proposed for channe equazaton. Cassca approaches for adaptve equazer desgn are based on knowedge of the parametrc channe mode [3]. These are mpemented by dentfyng the dynamc of channe and then constructng an equazer usng the dentfed channe mode. These processes requre certan tme to gather statstca data about the channe and are tme consumng. Another type of adaptve equazer s decson feedback equazer that can be used to mprove the performance of equazer. Next approach to equazer desgn s based on ncreasng the number of equazer taps and choosng the coeffcents from dfferent ranges of vaues accordng to the amptude of dstorted sgnas [4]. In ths approach a arge number of coeffcents and swtchng threshods are requred. Nowadays neura networks are wdey used for channe equazaton [5-11]. One cass of nonnear adaptve equazer s based on mutpayer perceptons (MLP and rada bass functons (RBF [3-5,7,9,10]. Dfferent MLP structures have been ntroduced for channe equazaton [8,9]. The MLP equazers requre ong tranng and are senstve to the nta choce of Proceedngs of the Ffth Mexcan Internatona Conference on Artfca Integence (MICAI'06

2 network parameters. The RBF equazers are smpe and requre ess tme for tranng, but usuay requre a arge number of centers, whch ncrease the compexty of computaton. The appcaton of neura networks for adaptve equazaton of nonnear channe s gven n [11,1,13]. In [11] the equazer s traned by mnmum error entropy crteron. Usng 16 QAM scheme the smuaton of equazaton of communcaton systems s carred out. In [1,13] recurrent neura network s apped for equazaton of nonnear communcaton channes. Decson feedback neura equazer s deveoped [13] by usng Kaman fter. Smuaton s performed for dfferent nonnear channe modes. One of the effectve ways for deveopment of adaptve equazers for nonnear channes s the use of fuzzy technoogy n ther deveopment. Ths type of adaptve equazer can process numerca data and ngustc nformaton n natura form [14]. Fuzzy equazer that ncudes fuzzy IF-THEN rues was proposed for nonnear channe equazaton n [14]. Human experts determne the fuzzy rues usng nput-output data pars of the channe. These rues are used to construct the fter for nonnear channe. The recursve east squares and east mean squares agorthms are apped to change parameters of the membershp functons of rues. The ncorporaton of ngustc and numerca nformaton mproves the adaptaton speed and the bt error rate (BER. In [15], t was ndcated that a near transversa fter requres a much arger tranng set to acheve the same error rate as t was acheved by fuzzy ogc equazer. The fuzzy ogc equazers are aso proposed for quadrature amptude moduaton (QAM consteaton channe equazaton [16], and for mpementaton a Bayesan equazer to emnate cochanne nterference [17,18]. TSK-based decson feedback fuzzy equazer s deveoped by usng evoutonary agorthm and apped QAM communcaton system [19]. In some cases the constructon of proper fuzzy rues for equazers s dffcut. In that case one of the effectve technooges for constructon of equazer s knowedge base s the use of neura network. In ths paper, the adaptve channe equazaton by usng recurrent neurofuzzy network s consdered. Recurrent neuro-fuzzy technoogy aows the use of sma number of parameters and fast and easy tranng of the equazer. The equazer based on neura networks does not need approprate knowedge about channe dynamcs. These equazers gve better bt error rate (BER resuts, at the cost of computatona strength.. Neuro-Fuzzy Inference System for Channe Equazaton Structure of neuro-fuzzy nference system used for channe equazaton s gven n Fgure 1. Because of feedback connecton we ca such structure recurrent structure. Network nput sgnas are the externa nput sgnas apped to the network at tme k, x (k (=1..N and tmedeay of the output sgna of the network u(k-d. N s number of neurons n the nput ayer. d s deay (d=1..d. In frst ayer the number of nodes are equa to the sum of externa nputs and one-, two-,, D-step deayed output sgnas. In second ayer each node corresponds to one ngustc term. For each nput sgna enterng the system the membershp degree to whch nput vaue beongs to a fuzzy set s cacuated. To descrbe ngustc terms a Gaussan membershp functon s used. ( x c1 σ 1 µ 1 ( x = e, =1..n, =1..J (1 ( u c1 + n, σ1 + n, µ 1 ( u = e, =1..D, =J+1..J+P ( Proceedngs of the Ffth Mexcan Internatona Conference on Artfca Integence (MICAI'06

3 x 1 x n u(k-d u(k-1 c1 11 c1 1 c u1 R 1 R R L c L c 1 u u z -1 z -D Fgure 1. Structure of recurrent neuro-fuzzy nference system Here u =u(-. c1 and σ1 are the center and wdth of the Gaussan membershp functon of the th term of th nput varabe, respectvey. n s number of externa nput sgnas. J s number of ngustc terms assgned for externa nput sgnas x, P s number of ngustc terms assgned for one-, two-,, D- deayed output sgna of network. In the thrd ayer the number of nodes corresponds to the number of rues. Each node represents one fuzzy ogc rue. Here to cacuate the vaues of output sgnas of the ayer AND (mn operaton s used. µ = µ1 ( r, =1..L, =1..J+P (3 Here r = {x1,, x n, u1,, u D}, = 1,,n + D. Π s mn operaton. These µ sgnas are nput sgnas for the next ast ayer. Ths ayer s a consequent ayer. In ths ayer the output sgnas of prevous ayer are mutped to the weght coeffcents of network and sum of these products s cacuated. Weght coeffcents of recurrent neuro-fuzzy system are represented by fuzzy set of output varabes. They are descrbed by Gaussan functon. If as a defuzzfcaton operaton we use oca mean of maxmum then ony the center of Gaussan functon s used n the next ayer for defuzzfcaton. In ths case durng deveopment of contro system the wdth of Gaussan functon s not used. In formua (4 the parameters c w represent the center of fuzzy coeffcents. Output of ffth ayer s cacuated as u L = 1 = L µ * c After cacuatng output sgna of NNFN the tranng of network starts. = 1 µ (4 Proceedngs of the Ffth Mexcan Internatona Conference on Artfca Integence (MICAI'06

4 Tranng ncudes the adustng of the parameters vaues of membershp functon c and σ (=1,..,m, =1,..,n n second ayer and parameters vaues c ((=1,..,L n forth ayer (consequent part. In the paper supervsed earnng agorthm s used for tranng the parameters of neuro-fuzzy system. At frst step, on the output of network the vaue of error s cacuated. O d E = 1 ( u u (5 = 1 d Here O s number of output sgnas of network (n gven case O=1, u and u are desred and current output vaues of network, correspondngy. To defne the accurate vaues of unknown parameters c supervsed earnng agorthm s used c ( t + 1 = c ( t + γ c (6 here γ s earnng rate. E d = = ( u( t u ( t (7 c c The adustment of the membershp functons of nput ayer s carred out by correcton unknown parameters c1 and σ. The foowng formuas can be used for earnng these parameters. c1 ( t = c1 1 ( t + γ c1, where c1 = c1 (8 σ 1 ( t = σ1 ( t + γ σ1, where σ1 = σ1 (9 Here = u( t u d ( t, c u = L µ = 1 (0 ( x c µ ( x = 0, ( x c σ f s connected otherwse node to rue node (11 Proceedngs of the Ffth Mexcan Internatona Conference on Artfca Integence (MICAI'06

5 ( x c µ ( x f node 3 σ ( x = s connected to rue node σ 0, otherwse Usng (6, (8 and (9 the earnng of the parameters of recurrent neuro-fuzzy system s carred out. 3. Smuaton Structure of equazaton system s shown n Fgure. The random bnary nput sgnas s(k are transmtted through the communcaton channe. Channe medum ncudes the effects of transmtter fter, transmsson medum, recever fter and other components. Input sgnas can be dstorted by noses, ntersymbo nterferences. Intersymbo nterference s many responsbe for near dstortons, nonnear dstortons are ntroduced through converters, propagaton envronment, etc. Channe output sgnas are ftered and entered to the equazer, for equazaton of dstortons. Durng equazer desgn, on the output of equazer current sgnas are compared wth nput sgnas transmtted through the channe. In case of presence of error the earnng of neuro-fuzzy equazer start. Learnng ncudes the adustng of the parameters vaues of the equazer by usng formuas (6, (8 and (9. Learnng s contnued unt, for a nput-output pars, the vaue of error woud be mnmum acceptabe vaue. (1 Channe medum n(k s(k x(k Channe Σ z -1 z -... z -m deay e(k Σ x(k x(k-1 x(k- x(k-m Equazer s(k Fgure. The structure of equazaton system Durng smuaton the transmtted sgnas s(k are nput known sampes wth an equa probabty of beng 1 and 1. These sgnas are corrupted by addtve nose n(k. The corrupted sgnas are nputs for equazer. In channe equazaton, the probem s the cassfcaton of comng nput sgna of equazer onto feature space whch s dvded nto two decson regons. A correct decson of equazer occurs f s ( k = s( k. Here s(k s transmtted sgna,.e. channe nput, s (k s the decson output of equazer. Based on the vaues of transmt- Proceedngs of the Ffth Mexcan Internatona Conference on Artfca Integence (MICAI'06

6 ted sgna s(k (.e. ±1 the channe state can be parttoned nto two casses R + and R -. Here R + ={x(k s(k=1} and R - ={x(k s(k=-1} [5, 6]. In ths paper the recurrent neuro-fuzzy network structure and ts tranng agorthm are used to desgn equazer for equazaton of channe dstorton. Durng smuaton we use the foowng channe mode. x(k = 0.348s(k s(k s(k - + n( k (13 Durng equazer desgn the sequence of transmtted sgnas are gven to the channe nput. The transmtted data sequence s(k conssts of 500 symbos. They are assumed to be an ndependent sequence takng vaues from {-1,1} wth equa probabty. The addtve Gaussan nose n(k s added to the transmtted sgna. In the equazer-usng target transmtted sgna the devaton from the current network output s determned. Ths error s used to adust equazer parameter. Tranng s contnued unt the vaue of error for a tranng sequence of sgnas woud be acceptaby mnmum vaue. Durng smuaton the nput sgnas for equazer are outputs of channe x(k, x(k-1, x(k-, x(k-3. The three ayer recurrent neuro-fuzzy network structure s taken. In the hdden ayer number of neurons are 16. The tranng of recurrent neuro-fuzzy network equazer (NFNE have been carred out. Fgure 3 ustrates the curve that descrbes the performance (Bt error rate versus sgna-nose rato anayss of recurrent neuro-fuzzy network equazer (NFNE and neura equazer for channe (1. Here sod ne s the performance of NFNE equazer, dashed ne s the performance of neura equazer. The channe states are potted n Fgure 4. Here Fgure 4(a demonstrates nose free channe states, 4(b- channe states wth addtve nose, and 4(c - channe states after equazaton of dstortons. The obtaned resut satsfes the effcency of appcaton of recurrent neuro-fuzzy technoogy n channe equazaton. 4. Concuson Cassc equazers do not performs we for tme-varyng channes. In the paper usng recurrent neuro-fuzzy network structure the deveopment of adaptve equazer s carred out. The operaton prncpe and earnng agorthm of recurrent neuro-fuzzy network are presented. The recurrent NFNE s constructed for the channe n presence of addtve dstorton. The resuts obtaned from the smuaton satsfy the effcency of appcaton of NFNE n adaptve channe equazaton. References [1] Proaks J. Dgta Comuncatons, New York, McGraw-H, [] Quresh, S.U.H. Adaptve equazaton. Proc.IEEE, 73, (9, 1985, pp [3] D.D.Faconer, Adaptve Equazaton of Channe Nonneartes n QAM Data Transmsson Systems, Be System Technca Journa, vo.7, no.7, [4] C.F.N.Cowan, S.Semnan. Tme-varant equazaton usng nove nonnear adaptve structure. Int.J.Adaptve Contr. Sgna Processng, vo.1,no., 1998, pp [5] Chen, S., Gbson, G.J., Cowan, C.F.N., and Grant, P.M. Adaptve equazaton of fnte non-near channes usng mutpayer perceptrons. Sgna Process,0,(, 1990, pp [6] Chen, S., Gbson, G.J., Cowan, C.F.N., and Grant, P.M. Reconstructon of bnary sgnas usng an adaptve rada-bass functon equazer, Sgna Processng,,(1, 1991, pp [7] Chen, S., Mcaughn, S. and Mugrew, B. Compex vaued rada based functon network, Part II appcaton to dgta communcatons channe equazaton, Sgna Processng, 36, 1994, pp [8] M.Peng, C.L.Nkas, J.G.Proaks, Adaptve Equazaton for PAM and QAM Sgnas wth Neura Networks, n Proc. Of 5 th Asomar Conf. On Sgnas, Systems & Computers, vo.1, 1991, pp [9] M.Peng, C.L.Nkas and J.Proaks, Adaptve equazaton wth neura networks new mutpayer perceptron structure and ther evauaton Proc.IEEE Int. Conf.Acoust., Speech, Sgna Proc., vo.ii,(san Francsco,CA, 199, pp Proceedngs of the Ffth Mexcan Internatona Conference on Artfca Integence (MICAI'06

7 [10] J.S.Lee, C.D.Beach and N.Tepedeenogu, Channe equazaton usng rada bass functon neura network Proc.IEEE Int. Conf.Acoust., Speech, Sgna Proc., 1996, vo.iii, (Atanta, GA, 1996, pp [11] Denz Erdogmus, Denz Rende, Jose C. Prncpe, Tan F. Wong. Nonnear channe equazaton usng mutpayer perceptrons wth nformaton-theoretc crteron. In Proc. Of 001 IEEE Sgna Processng Socety Workshop, 001, pp [1] H.R.Jang, K.S.Kwak. On modfed compex recurrent neura network adaptve equazer. J.Crc.Syst.Comput., vo.11,no.1, 00, pp [13] Jongsoo Cho, Martn Bouchard, Tet Hn Yeap. Decson feedback recurrent neura equazaton wth fast convergence rate. IEEE transacton on Neura Networks, Vo.16, No.3, 005 [14] L-Xn Wang, Jerry M. Mende. Fuzzy adaptve fters, wth appcaton to Nonnear Channe Equazaton. IEEE Transacton on Fuzzy Systems, vo.1, No.3, [15] P.Sarwa and M.D.Srnath, A fuzzy ogc system for channe equazaton. IEEE Trans. Fuzzy System, vo.3, 1995, pp [16] K.Y.Lee. Compex fuzzy adaptve fters wth LMS agorthm. IEEE Transacton on Sgna Processng, vo.44, 1996, pp [17] S.K.Patra, B Mugrew. Effcent archtecture for Bayesan equazaton usng fuzzy fters. IEEE Transacton on Crcut and Systems II, vo. 45, 1998, pp [18] S.K.Patra, B Mugrew. Fuzzy mpementaton of Bayesan equazer n the presence of ntersymbo and cochanne nterference. Proc. Inst. Eect. Eng. Commun., vo. 145, pp.1998, pp [19] S.Su, Cha-Lu, Chen-Mn Lee. TSK-based decson feedback equazaton usng an evoutonary agorthm apped to QAM Communcaton Systems. IEEE Transactons on Crcuts and Systems, vo.5, No.9, 005. [0] Rahb Abyev, Fakhreddn Mamedov, Tayseer A-shanabeh. Neuro-fuzzy system for Channe Nose Equazaton. Internatona MutConference n Computer Scence & Computer Engneerng. Internatona Conference on Artfca Integence.IC-AI 04, Las Vegas, Nevada, USA, June 1-4, 004. Fgure 3. Performance of NFNE (sod ne and neura (dashed ne equazers Proceedngs of the Ffth Mexcan Internatona Conference on Artfca Integence (MICAI'06

8 a b c Fgure 4. Channe states a nose free, b wth nose, c after equazaton Proceedngs of the Ffth Mexcan Internatona Conference on Artfca Integence (MICAI'06