Instantaneous Gradient Based Dual Mode Feed-Forward Neural Network Blind Equalization Algorithm

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1 esearch Joural of Applied Scieces, Egieerig ad Techology 5(: , 03 ISSN: ; E-ISSN: Mawell Scietific Orgaizatio, 03 Submitted: May 30, 0 Accepted: Jue 3, 0 Published: Jauary, 03 Istataeous Gradiet Based Dual Mode Feed-Forward Neural Network Blid Equalizatio Algorithm Yig Xiao Departmet of Iformatio ad Commuicatio Egieerig, Dalia Natioality Uiversity, Dalia, 6600, Chia Faculty of Electroic Iformatio ad Electrical Egieerig, Dalia Uiversity of Techology, Dalia 604, Chia Abstract: To further improve the performace of feed-forward eural etwork blid equalizatio based o Costat Modulus Algorithm (CMA cost fuctio, a istataeous gradiet based dual mode betwee Modified Costat Modulus Algorithm (MCMA ad Decisio Directed (DD algorithm was proposed. The eural etwork weights chage quatity of the adacet iterative process is defied as istataeous gradiet. After the etwork coverges, the weights of eural etwork to achieve a stable eergy state ad the istataeous gradiet would be zero. Therefore dual mode algorithm ca be realized by criterio which set accordig to the istataeous gradiet. Computer simulatio results show that the dual mode feed-forward eural etwork blid equalizatio algorithm proposed i this study improves the covergece rate ad covergece precisio effectively, at the same time, has good restart ad trackig ability uder chael burst iterferece coditio. Keywords: Blid equalizatio, costat modulus algorithm, dual mode algorithm, feed-forward eural etwork, istataeous gradiet INTODUCTION I the digital commuicatio systems, fiite badwidth ad multi-path propagatio characteristics of the commuicatio chaels ca cause severe Iter- Symbol Iterferece (ISI i high data rate commuicatio systems (Yi-Big et al., 00, which may lead to high error rates i symbol detectio. Adaptive equalizatio techology is a effective meas of elimiatig iter-symbol iterferece. Compare with traditioal adaptive equalizatio, blid equalizatio techique does ot require ay traiig sequece to implemet compesatig ad trackig of the chael, which ca improve the quality of the commuicatio, at the same time, save the commuicatio badwidth (Xiao ad Yu-Hua, 009. For iterceptio of military iformatio ad multi-user broadcast commuicatios, there is o traiig sequece ca be eploited, uder these coditios, blid equalizatio has importat practical value. I all kids of the blid equalizatio algorithms, eural etwork blid equalizatio is oe of the oliear equalizatio algorithms, which ca ot oly apply to the miimum phase chael, also applies to the maimum phase chael, icludig the oliear chael (Xiao et al., 009. The chael is more or less has oliear characteristics i the actual commuicatio system, so eural etwork blid equalizatio has importat sigificace i the practical egieerig. The feed-forward eural etwork has mathematical theory ad simple realizatio process, so it is most widely used. Blid equalizatio by feedforward eural etwork usually adopts the cost fuctio of Costat Modulus Algorithm (CMA (Yag et al., 0, the the covergece rate is very slow ad the steady state error is big. I cotrast, Decisio Directed (DD algorithm has faster covergece rate ad better covergece precisio, but if the eye diagram of the received sigal is ot ope, DD algorithm ofte divergece or covergece error. The basic idea of dual mode blid equalizatio is derived from the features of CMA ad DD algorithm, set a reasoable threshold allows the algorithm to betwee two algorithms are timely switch, which a combiatio of two algorithms to their respective advatages ad further improves the blid equalizatio performace. Accordig to the threshold settig differece, differet dual mode algorithm ca be obtaied. I this study, we use the istataeous gradiet chage rate to set threshold ad a ew dual mode eural etwork blid equalizatio algorithm was proposed, at last by usig computer simulatios proved the validity of the algorithm compared with decisio circle based dual mode algorithm ad sig error based dual mode algorithm, meawhile, the performace for restart ad trackig Ability uder the chael has burst iterferece was doe to prove the practical egieerig value. 67

2 es. J. Appl. Sci. Eg. Techol., 5(: , 0 ( Ukow Chael h( + y ( Neural ( Decisio ˆ ( etwork device Blid equalizatio algorithm Fig. : Block diagram of eural etwork blid equalizatio DUAL MODE NEUAL NETWOK BLIND EQUALIZATION Feed-forward eural etwork blid equalizatio: The priciple of eural etwork blid equalizatio ca be show as Fig. (LU, 003. Neural etwork blid equalizatio use eural etwork to act as blid equalizer ad the priciple is same to trasversal equalizer. I Fig., is the iput sequece of ukow chael, h( is the chael impulse respose sequece, the output sequece of chael is s(, ( is a gauss white oise at to s(, the y( as the eural etwork equalizer iput sequece is received, the output sequece of equalizer ( ca be decided to obtai the recovery sequece (. Accordig to the trasmissio theory of commuicatio system ca kow: s( = h( ( y ( = s( + ( ( If we take w( as equivalet covolutio weight coefficiet of eural etwork filter: = w( y( (3 The purpose of blid equalizatio is to recover the sedig sequece, ( ca be obtaied directly by observed sequece y( ad satisfy: ( = DDee (4 where, D : Costat delay φφ : Costat phase shift The sedig sequece recovery quality is ot affected by D, phase shift φφ ca be get rid of by decisio set. Combiig ( ad (3 ad igorig covolutio oise, ( ca be show as: 67 = h( w( (5 It ca be see that the coditio of availability of (4 is that associate impulse respose of chael ad equalizer must satisfy (6: φ h ( w( = [0,,0, e,0,0] (6 The realizatio of feed-forward eural etwork blid equalizatio ca establish etwork learig obective fuctio by use of observed sequece. The weight coefficiet of eural etwork is updated via special algorithm, which ca make obective fuctio achieve miimum, that is, associate impulse respose of equivalet covolutio weight w( ad chael satisfies (6. Accordig to SW theorem, the iput ad output sigal have the same variace ad the absolute value of kurtosis are equal, which is the ecessary ad sufficiet coditios to equalizatio. It idicates that the implemet of blid equalizatio relies o sigal statistical property. Feed-forward eural etwork blid equalizatio takes cost fuctio of CMA algorithm as obective fuctio to trai etwork, while the cost fuctio of CMA ust make use of sigal high-order statistical property idirectly. Blid equalizatio by FNN has slow covergece rate because of adoptig error Back Propagatio (BP algorithms (Godard, 980 ad it is easy to fall ito locally miimum poit due to o-coveity of cost fuctio. Cybeco has proved that trilevel feed-forward eural etwork ca approimate ay cotiuous fuctio with ay precisio. The topological structure of trilevel feed-forward eural etwork ca be show as Fig., where, w i ( (i =,...m, =,... is weight coefficiet from iput layer to hidde layer. W ( ( =,... is weight coefficiet from hidde layer to output layer, u (, v ( ad I( is iput sequece of hidde layer, output sequece of hidde layer ad iput sequece of iput layer respectively. The the state equatios ca be show as: T

3 y( w i es. J. Appl. Sci. Eg. Techol., 5(: , 0 ( ( ( J D = { ( } CM (5 w w y( y( m + y ( m Fig. : Trilevel FNN structure w ( for output layer: = f [ I( ] v ( w ( (6 from (4,(5 ad (6, iterative formula is: w ( = w ( + H ( v ( + (7 µ where, μ is step-size: u ( = w ( i i= i [ ] ( f u ( v = (8 I ( = w ( v ( = ( f [ I( ] = (7 (9 (0 ( = ( [ ] f I( ( H CM (8 for hidde layer: I [ ( ] ( = f I w ( w ( (9 i I w ( ( i = w i [ ] y( i ( f u ( (0 where, f(. is the trasfer fuctio of eural etwork ad the trasfer fuctio ca be chose as: f ( e e = λ ( e + e For traiig etwork, the mootoicity of trasfer fuctio must be esured, so its derived fuctio must be greater tha zero. This requires adustmet parameters λ be greater tha zero. The value of λ is determied by the amplitude of sigal, that is, λ should be greater if amplitude of sigal is greater, vice versa. Combied with CMA cost fuctio, the obective fuctio of blid equalizatio by eural etwork is: J [ ] = ( D CM ( 4 k k E CM = (3 E ( Usig BP algorithm, the iterative formula is show as: J D w( + = w( µ (4 w ( from (9 ad (0, (4 becomes: w where, H i ( + = w ( + µ H ( y( i i ( ( = f u ( [ ] w ( H ( Dual mode blid equalizatio algorithm: CMA is a special case of Godard algorithm, also is the most widely used blid equalizatio algorithm belogig to Bussgag for it is simple computatio ad stable performace. But CMA blid equalizatio covergece rate is slow ad has big state steady error after covergece; also it is less sesitive to the phase of iput sigal, the a med CMA (MCMA (Ye-Cai et al., 0 was proposed based o CMA, MCMA ca effectively correct the phase deflectio. The cost fuctio of MCMA is: J D [ ( ] [ ( ] + I I = ( where, ( ad II ( deote the real part ad Imagiary part of ( respectively, ad I is defied as: 673

4 es. J. Appl. Sci. Eg. Techol., 5(: , 0 ( 4 4 E ( = E( ( diagoal elemets of weights betwee iput ad hidde I I = E( ( (4 layer ad the ceter elemets of weights betwee I ( hidde ad output layer iitialize to, the other weights set to 0. Step size μ = The compariso is i terms The cost fuctio of DD is: of mea square error (MSE (Li-Ju ad Ze-Mi, 00, which is defied as: J [ ( ˆ( ] DD = (5 MSE( = ( k ˆ( k (30 I this study, dual mode algorithm is set accordig to MCMA ad DD algorithm. Defie the istataeous gradiet chage rate as: g( = w ( w w ( w i i i ( i ( (6 Accordig to the limit theorem ad L' Hospital ule, if the algorithm stability covergece, the lim g( =. The istataeous gradiet chage rate reflects the etwork steady state ad it ca be used as the threshold for dual mode algorithm switchig criterio. From the iterative process of eural etwork blid equalizatio algorithm, dual mode blid equalizatio eural etwork algorithm implemet ca oly chage H ( i the iterative formula. Accordig to MCMA: { ( = ( ( I ( I I ( } ( ( H + f I ad accordig to DD algorithm: ( = [ ˆ( ] f ( I( (7 H (8 cv Hidde layer weights of eural etwork are updated accordig to the error back propagatio algorithm without modificatio. Here accordig to the istataeous gradiet chage rate is give the dual mode eural etwork weights updatig formula whe g ( large or less tha δ: ( + = ( + µ ( ( ( + = ( + µ ( ( w w H v w w H v COMPUTE SIMULATIONS (9 I the simulatios, equivalet probability biary sequece is adopted to act as sedig sigal ad QPSK modulatio is utilized. Addig oise is bad-limited gauss white oise with zero mea. The structure of wavelet eural etwork equalizer set to 5 0. The 674 k = The simulatio commuicatio chael adopt miphase chael which the impulse respose is h = [0.33, , ad 0.343]. The threshold of dual mode sets δ = I order to verify the performace of the dual mode eural etwork blid equalizatio (DUAL-IGC proposed i this study, dual mode based decisio circle blid equalizatio (DUAL-DC (Ye-Cai ad Ya-Pig, 007 ad dual mode based sig error blid equalizatio (DUAL-SE (Jia-Qi ad Nig, 009 is doe i the simulatio for compariso. Figure 3 shows the covergece curve with SN = 8.6 db after 500 times Mote Carlo simulatio. From Fig. 3 ca see that DUAL-IGC has faster covergece rate ad lowest MSE. MSE/dB Iteratio times ( Fig. 3: MSE covergece curve MSE/dB Fig. 4: MSE covergece curve MCMA DUAL-DC DUAL-SE DUAL-lGC Iteratio times (

5 es. J. Appl. Sci. Eg. Techol., 5(: , 0 To further verify the performace of DUAL-IGC algorithm for chael burst iterferece, whe the iterative times = 5000, let the refractio way phase reversal that is h = [0.33, , , ] at that time to simulatio chael burst iterferece, the result of 500 times Mote Carlo simulatio is show as Fig. 4. From Fig. 4 ca see that the dual mode method proposed i this study has good restart ad trackig ability uder chael burst iterferece coditio. CONCLUSION I this study a ew dual mode eural etwork blid equalizatio algorithm based o the istataeous gradiet chage rate was proposed, the theory aalysis shows that the istataeous gradiet chage rate reflects the stability of the etwork ad the threshold ca set accordig to it. Simulatio results prove that the proposed algorithm has good equalizatio performace ad has good restart ad trackig ability uder chael burst iterferece coditio, therefore this study has a certai practical value. ACKNOWLEDGMENT This study was supported i part by Fudametal esearch Fuds For the Cetral Uiversities No. DC008 ad Scietific ad Techological esearch Proect for Educatio Departmet of Liaoig Provice No EFEENCES Godard, D.N., 980. Self-recoverig eqlualizatio ad carrier trackig i two-dimesioal data commuicatio systems. IEEE Tras. Comm., 8(: Jia-Qi Z. ad G. Nig, 009. Joit CMA+DDLMS blid equalizatio algorithm. J. Tsighua U. Sci. Tech., 49(0: Li-Ju, P. ad L. Ze-Mi, 00. A dual-mode blid equalizatio. J. Beiig U. Posts Telecommu., 8(3: Lu,., 003. Study o the equalizatio algorithm based o the eural etwork. MA Thesis, i Taiyua Uiversity of Techology, Taiyua. Xiao, Y. ad D. Yu-Hua, 009. A blid equalizatio by cascaded hybrid wavelet eural etwork. If. Co., 8(4: Xiao, Y., L. Zhe-Xig ad D. Yu-Hua, 009. Blid equalizatio based o FNN usig dyamic obect fuctio. J. Syst. Simulat., (4: Yag, L., H.E. Xiao-Xiag ad Y. Gag, 0. A ovel blid equalizatio method for recombiatio of sigals. JDCTA, 5(8: Ye-Cai, G. ad Z. Ya-Pig, 007. Decisio circle based dual mode costat modulus blid equalizatio algorithm. J. Data Acquisit. Proc., (3: Ye-Cai, G., H. Lig-Lig ad. Dig, 0. Orthogoal wavelet trasform weighted multimodulus blid equalizatio algorithm based o quatum particle swarm optimizatio. Acta Phys. Si., 6(5: -6. Yi-Big, Z., Z. Ju-Wei, G. Ye-Cai ad L. Ji-Mig, 00. A costat modulus algorithm for blid equalizatio i α-stable oise. Appl. Acoust., 7(7: