OFDM-BPSK Wireless Communication System Performance under Employment of Generalized Receiver

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1 OFDM-BPSK Wireless Commuicatio System Performace uder Employmet of Geeralized Receiver XUEFEI LI, VYACHESLAV TUZLUKOV School of Electroics Egieerig, College of IT Egieerig Kyugpook Natioal Uiversity 7 Sakyuk-dog, Buk-gu, Daegu 7-7 SOUTH KOREA riaa@hotmail.com, tuzlukov@ee.ku.ac.kr Astract: - I this paper, we discuss the performace of the orthogoal frequecy divisio multiplexig (OFDM) wireless commuicatio systems usig the iary phase shift keyig (BPSK) modulatio over Rayleigh fadig chael implemetig the geeralized receiver (GR) costructed i accordace with the geeralized approach to sigal processig i oise. We compare OFDM-BPSK wireless commuicatio systems ased o the Neyma-Pearso receiver ad GR. The relied aalysis ad simulatio results demostrate a superiority of GR implemetatio i OFDM-BPSK wireless commuicatio systems i compariso with the Neyma-Pearso oe. Key-Words: - Geeralized receiver; orthogoal frequecy divisio multiplexig (OFDM); iary phase shift keyig (BPSK); Neyma-Pearso receiver; sigal-to-oise ratio (SNR); proaility of error. Itroductio Orthogoal frequecy divisio multiplexig (OFDM) is a multicarrier modulatio techique. This approach is widely used i wireless commuicatio systems. With growth i the umer of moile users, the requiremets for high data rate i wireless commuicatio systems have ee sharply icreased. Sice OFDM techique esures high data trasmissio rate ad high adwidth efficiecy, it has ecome a potetial research techology. I geeral, there are several data modulatio schemes that are used with OFDM, such as the iary phase shift keyig (BPSK), the quadrature phase shift keyig (QPSK), ad the quadrature amplitude modulatio (QAM). Differet modulatio schemes have differet code rate. Additive white Gaussia oise (AWGN) chael, Rayleigh fadig chael, ad Ricia chael are usually cosidered uder aalysis of wireless commuicatio systems. There are a large umer of joural papers devoted to ivestigatio of OFDM techique i wireless commuicatio systems usig the aove metioed chael models [-]. Owig to high performace, the OFDM wireless commuicatio systems are ivestigated itesively. Various chael estimatio ad diversity techiques are proposed to ehace the performace of OFDM wireless commuicatio systems [-]. The chael estimatio for OFDM systems ased o lock-type pilot arragemet is a very useful ad efficiet method [4]. This techique is ased o the least square (LS) method or miimum mea-square error (MMSE) method. I this paper, we ivestigate the performace of OFDM wireless commuicatio systems applyig the geeralized receiver (GR) desiged ased o the geeralized approach to sigal processig i oise. GR is a liear comiatio of the Neyma-Pearso (NP) receiver that is optimal for detectio of sigals with kow parameters ad the eergy receiver that is optimal for detectio of sigals with ukow parameters [5-7]. This comiatio allows us to make a decisio a yes sigal or a o sigal i the iput process ased o aalysis of the joitly sufficiet statistics of the mea ad variace of the likelihood fuctio. The Neyma-Pearso (NP) receiver is ased o defiitio of sufficiet statistics of the likelihood mea oly. The eergy receiver is ased o defiitio of sufficiet statistics of the likelihood fuctio variace oly. Thus, the GR delivers us more iformatio aout the likelihood fuctio i the form of the joitly sufficiet statistics of the mea ad variace. This paper is orgaized as follows. The asic priciples of OFDM wireless commuicatio system model are discussed i Sectio. We recall riefly ISBN:

2 Fig. OFDM-BPSK trasmitter the mai fuctioig priciple of the GR i Sectio. The performace of the OFDM-BPSK wireless commuicatio system employed GR is ivestigated i the Sectio 4. Simulatio results are discussed i the Sectio 5. Fially, some coclusios are made i Sectio 6. System Model. Trasmitter The trasmitter lock diagram of OFDM-BPSK wireless commuicatio system is show i Fig. [8]. I order to maitai the orthogoality characteristic of the carriers, the iput data should e modulated firstly. Pilot symol isertio is used to estimate the chael. At the trasmitter, the sigal is defied i the frequecy domai. The complemet of iverse discrete Fourier trasform (IDFT) allows us to covert the frequecy domai ito the time domai. The asead BPSK-OFDM trasmitted sigal ca e preseted i the followig form: N ( ) j t / T x t X e t T, () where N deotes the umer of arrowad chaels, T is a pulse duratio, ad X is the BPSK message sigal trasmitted over the th suchael.. Chael Model The asead sigal at the receiver iput i OFDM- BPSK wireless commuicatio system ca e preseted i the followig form: Y HX N, () where X is the asead trasmitted sigal matrix, H is the chael matrix, elemets of which are the chael respose, ad N is the oise matrix, elemets of which are AWGN with zero mea ad the variace. Rayleigh fadig chael model is applicale whe there is o lie of sight commuicatio chael. Owig to Rayleigh fadig, the elemets of the chael matrix H are distriuted i accordace with Rayleigh law. I additio, applyig the cetral limit theorem, each path of Rayleigh fadig ca e modeled as the circularly symmetric complex Gaussia radom variale [9]. I this case, the elemets of chael matrix ca e preseted i the followig form: H x ix re where r ad the chael matrix elemets distriuted; limits of the iterval i m, () are the amplitude ad phase of H, r is Rayleigh m is uiformly distriuted withi the -, ; ad x ad x are the zero mea idepedet ad idetically distriuted (i.i.d.) Gaussia radom variales with variace.. Geeralized Receiver (GR) Accordig to the geeralized approach to sigal processig (GASP) i oise, GR has two iput liear systems that ca e preseted i the form, for example, of the adpass filters, amely, the prelimiary filter (PF) ad the additioal filter (AF). PF is detued with respect to AF y the cetral or resoat frequecy o the value 4~5 times the sigal adwidth. Owig to this coditio, there are additive mixture of sigal ad oise at the PF output ad oly the oise at the AF output. The oise formig at the AF output is called the referece oise. The model sigal geerator (MSG) is used to geerate the referece sigal or model sigal i the GR. The GR flowchart is preseted i the Fig.. At GR iput, there is oly oise w [ ] uder H ad oise ad sigal s[ ] w[ ] uder H. Because the AF ad the PF are the liear systems, we ca oserve the Gaussia oise at the AF ad the PF outputs if the oise is the Gaussia oise at the AF ad the PF iputs. The output oise at the PF ad the AF take the followig form: PF AF N [ ] h [ ] w [ ] PF (4) N [ ] h [ ] w [ ] (5) If the GR iput oise is AWGN with zero mea ad two-sided power spectral desity N /, the oise at the AF ad PF outputs is also Gaussia with zero mea ad variace give y []: N = 8 F, (6) AF ISBN:

Fig. Geeralized Receiver (GR) where is the resoace frequecy, i the case of PF ad AF are the RLC oscillatory circuits with the resoace amplitude-frequecy respose, is equal to / LC, ad F is the adwidth

3 Fig. Geeralized Receiver (GR) where is the resoace frequecy, i the case of PF ad AF are the RLC oscillatory circuits with the resoace amplitude-frequecy respose, is equal to / LC, ad F is the adwidth of PF that ca e preseted i the followig form: R F,. (7) L Chael Estimatio I OFDM wireless commuicatio system, the estimatio of chael matrix is ecessary ecause the radio chael is time-varyig multiple fadig ad selective fadig is preseted i the time domai ad frequecy []. We ca estimate the chael usig pilot symols. This pilot chael estimatio has ee developed uder assumptio aout slow fadig chael i wireless commuicatio system. The chael estimatio for this pilot arragemet ca use the least square (LS) or miimum mea square error (MMSE) techiques to otai the chael estimatio at the pilot locatios. Employmet of MMSE techique to otai the chael iformatio allows us to otai the etter performace i compariso with usig the LS procedure []. Usig the pilot chael estimatio techology ased o MMSE, we ca preset the estimatio of chael gai matrix i the followig from [] H H MMES = R + HH RHH XX H LS, (8) H where R E HH HH is the autocorrelatio matrix of the chael, ad H ˆ LS is the chael estimatio ased o LS method ca e preseted i the followig form []: ˆ LS H H + X N. (9) Accordig to the [], the chael estimatio ca e modeled as the true chael. Thus, it ca e modeled as the adpass statioary complex Gaussia process with zero mea. Hece, the elemets of the estimated chael matrix ca e preseted i the followig form: i Hm x ix4 r e, () where r ad are the amplitude ad phase of the elemets of the estimated chael matrix H, r is Rayleigh distriuted, is uiformly distriuted withi the limits of the iterval -,, ad x ad x4 are the i.i.d. Gaussia radom variales with zero mea ad variace []. As follows from () ad (6), we ca defie the variaces of chael matrix elemets ad the elemets of the estimated chael matrix i the followig form: E H m E x E x, () E Hˆ m E x E x 4. () It is easy to see that E[ xx ] ad E[ xx4]. ad, The cross-correlatios etwee x, x x x 4 ca e preseted i the followig form: * Ex x Exx4 Re E HmH m, () Also, the cross-correlatios etwee x, x4 ad x, x ca e preseted i the followig form: Im * m m E x x4 E xx E H H. (4) Hece, we ca defie the correlatio coefficiets i the followig form []:,. (5) The joit proaility desity fuctio (pdf) of ( x, x, x, x ) ca e preseted i the followig form: 4 p( x, x, x, x4 ) exp ( ) T x x, (6) where vector x ( x, x, x, x4 ), is the crosscorrelatio matrix ca e preseted i the followig form. (7) ISBN:

(9) The error proaility for wireless commuicatio system i AWGN chaels with BPSK modulatio at GR output whe N is give y [4]: E P Q log ( M ), () Q( ) is the Gaussia Q -fuctio ad M.

4 Hece, the joit proaility desity fuctio (pdf) of polar coordiate ( r, r, ) ca e preseted i the followig form: rr p( r, r, ) ( ) where. r exp ( ) r r r cos si (8) 4 Performace Aalyses The average SNR at the GR output ca e determied i the followig form [6]: q. (9) The error proaility for wireless commuicatio system i AWGN chaels with BPSK modulatio at GR output whe N is give y [4]: E P Q log ( M ), () Q( ) is the Gaussia Q -fuctio ad M. Hece, the error proaility at GR output i AWGN chaels with BPSK modulatio ca e rewritte as the form of, r cos P( r ) Q, () I the case of Rayleigh fadig chael, the proaility of error is defied i the followig form [5]: P p( r, r, ) P ( r, ) ddr dr. () Sustitutig the (8) ad () ito (), we ca otai the proaility of error uder employmet of GR i wireless commuicatio systems with Rayleigh fadig chael ad BPSK modulatio i the followig form P GD q q q. () Tale Simulatio Parameters Parameters Sigal Costellatio Chael Model Average SNR (the real part of the correlatio coefficiet etwee chael matrix ad estimated chael matrix) (the imagiary part of the correlatio coefficiet etwee chael matrix ad estimated chael matrix) Specificatios BPSK Rayleigh Fadig chael q db.95. Neyma-Pearso receiver uder the same coditios. The simulatios is ased o IEEE 8.la wireless local area etwork (WLAN) stadard [6]. For simplicity sake, we cosider oly BPSK modulatio. The system parameters used i the simulatio are preseted i Tale. Simulatio results for the case of sigle-carrier arrowad chael are preseted i the Fig.. From Fig., we see that the proaility of error is a fuctio of the correlatio coefficiet. Whe is equal to, the OFDM-BPSK wireless commuicatio system either uder employmet of the Neyma-Pearso receiver or GR presets the est performace. Whe the proaility of error is approximately equal to, the SNR gai i favor of GR employmet is more tha 6 db i compariso with the Neyma-Pearso receiver. With decreasig 5 Simulatio Results I this sectio, we preset simulatio results for the OFDM-BPSK wireless commuicatio system employig the GR ad compare it with the OFDM- BPSK wireless commuicatio system usig the Fig. Performace of OFDM-BPSK system ISBN:

5 from to.95, a superiority of GR employmet i OFDM-BPSK wireless commuicatio system is kept, ut the proaility of error is icreased. For example, at.99, we oserve that the SNR gai i favor of GR i compariso with the Neyma-Pearso receiver is approximately equal to 7dB, ut the proaility of error is equal to. At.95, compared with the Neyma-Pearso receiver, the SNR gai is approximately equal to 5.8 db, ut the proaility of error is equal to oly. Fig.4 presets the error proaility of OFDM- BPSK wireless commuicatio system as a fuctio of average SNR whe is fixed, for example, ad is the variale parameter. With icreasig i, the error proaility decreases. The superiority of GR employmet i OFDM-BPSK wireless commuicatio systems i compariso with the Neyma-Pearso receiver is ovious. At., whe the error proaility is equal to, we oserve that the SNR gai is approximately equal to 6dB i compariso with Neyma-Pearso receiver. The OFDM-BPSK wireless commuicatio system as a fuctio of correlatio coefficiet at the fixed has the same character whe, is the variale. With decreasig i from. to, the proaility of error is icreased. For example, at, we see that the SNR gai i favor of GR employmet i compariso with the Neyma- Pearso receiver is more tha 5 db, ut the.8 proaility of error is equal to. Fig.4 Performace of OFDM-BPSK system = for aout 6 db at the error proaility equal to whe. With decreasig i the correlatio coefficiets ad, we oserve a superiority of GR implemetatio i OFDM-BPSK wireless commuicatio system i compariso with the Neyma-Pearso receiver, ut the proaility of error is icreased. The correlatio coefficiets ad play a very importat role to defie the OFDM-BPSK wireless commuicatio system performace uder implemetatio of oth the GR ad Neyma-Pearso receiver. Ackowledgmet This research was supported y Kyugpook Natioal Uiversity Research Grat, 6 Coclusios I this paper, we study the error proaility performace of OFDM-BPSK wireless commuicatio system employig oth the Neyma-Pearso receiver ad GR. We defie the error proaility of OFDM-BPSK wireless commuicatio system as a fuctio of correlatio coefficiets ad, which are the correlatio coefficiet etwee the elemets of the chael matrix ad estimated chael matrix. Uder employmet of the GR i OFDM-BPSK wireless commuicatio system there is a superiority i compariso with implemetatio of the Neyma- Pearso receiver. SNR gai is for aout 6 db at the error proaility equal to whe, ad Refereces [] L. Wa, V. K. Duey, Bit Error Proaility of OFDM System Over Frequecy Noselective Fast Rayleigh Fadig Chaels, IEEE Electroics Letters, Vol.6, No.5, July, pp.6-7. [] J. Lu, T. Tjhug, F. Adachi ad C. L. Huag, BER Performace of OFDM-MDPSK System i Frequecy Selective Ricia Fadig with Diversity Receptio, IEEE Tras. o Vehicular Techology, Vol.49, No.4, July, pp [] Y. H. Kim, I. Sog, H. G. Kim, T. Chag, ad H. M. Kim, Performace Aalysis of a Coded OFDM System i Time-Varyig Multipath Rayleigh Fadig Chaels, IEEE Trasactios o Vehicular Techology, Vol.48, No.5, Septemer 999, pp ISBN:

6 [4] S. Varade ad K. Kulat, BER Compariso of Rayleigh Fadig, Ricia Fadig ad AWGN Chael usig Chaotic commuicatio ased MIMO-OFDM System, Iteratioal Joural of Soft Computig ad Egieerig (IJSCE), Vol., No.6, Jauary, pp [5] M. K. Mishra ad N. Sood, SER Aalysis of OFDM System over Rayleigh Fadig Chael, Iteratioal Joural of Computer Applicatios, Vol., No.6, May, pp [6] M. Russell ad G. L. Stuer, Iterchael Iterferece Aalysis of OFDM i a Moile Eviromet, IEEE Vehicular Techology Cof, Chicago, IL July 995, Vol., pp [7] R. Craciuescu, S. Haluga ad O. Fratu, Performaces of LMS/NLMS Algorithms For CDMA RAKE Receivers, th Iteratioal Coferece o Telecommuicatio i Moder Satellite Cale ad Broadcastig Services (TELSIKS), 5-8 Oct, Nis, Seria, Vol., pp [8] N. Sood, A. K. Sharma, M. Uddi, BER Performace of OFDM-BPSK ad QPSK over Nakagamim Fadig Chaels, Proc. of d IEEE Iteratioal Advace Computig Coferece, IACC-, Fe., pp [9] A. Katariya, A. Yadav ad N. Jai, Performace Elevatio Criteria for OFDM uder AWGN Fadig Chael usig IEEE 8.a, Iteratioal Joural of Soft Computig ad Egieerig (IJSCE), Vol., No., July, pp. -. [] R. Craciuescu ad S. Haluga, Guard Iterval Effect o OFDM/BPSK Trasmissios over Fadig Chaels, th Telecommuicatios forum TELFOR, [] M. Hsieh ad C. Wei, Chael Estimatio for OFDM Systems Based o Com-Type Pilot Arragemet i Frequecy Selective Fadig Chaels, IEEE Trasactios o Cosumer Electroics, Vol. 44, No., Feruary 998. [] A. K. Sadek, W. Su ad K. J. R. Liu, Diversity Aalysis for Frequecy-Selective MIMO- OFDM Systems with Geeral Spatial ad Temporal Correlatio Model, IEEE Trasactios o Commuicatios, Vol. 54, No. 5, May 6, pp [] Y. Zhao ad A. Huag, A Novel Chael Esti- Matio Method for OFDM Moile Commui- Catios Systems Based o Pilot Sigals ad Trasform Domai Processig, i Proc. IEEE 47 th Vehicular Techology Coferece, Phoeix, USA, May 997, pp [4] Y. Li, Pilot-Symol-Aided Chael Estimatio for OFDM i Wireless Systems, IEEE Trasactios o Vehicular Techology, Vol. 49, No.4, July. [5] V. Tuzlukov, A New Approach to Sigal Dete- Ctio Theory, Digital Sigal Processig, Vol. 8, No., pp , 998. [6] V. Tuzlukov, Sigal Detectio Theory, Spriger - Verlay, New York,. [7] V. Tuzlukov, Sigal Processig Noise, CRC Press, Boca Rato,. [8] A. R. S. Bahai, B. R. Saltzerg, Multicarrier Digital Commuicatios: Theory ad Applicatios of OFDM, Kluwer Academic/ Pleum, 999. [9] M. S. Islam, G. R. Barai ad A. Mahmood, Performace Aalysis of Differet Modulatio Schemes usig OFDM Techiques i Rayleigh Fadig Chael, IJFPS, Vol., No., March, pp. 7. [] V. Tuzlukov, Sigal Processig y Geeralized Receiver i DS-CDMA Wireless Commui-catio Systems with Frequecy- Selective Chaels, Circuits Syst Sigal Process, Vol., No.6,, pp.97. [] S. Coleri, M. Erge, A. Puri ad A. Bahai, Chael Estimatio Techiques Based o Pilot Arragemet i OFDM Systems, IEEE Trasactios O Broadcastig, Vol. 48, No., Septemer, pp. -9 [] M. X. Chag ad Y. T. Su, Performace Aalysis of Equalized OFDM Systems i Rayleigh Fadig, IEEE Trasactios o Wireless Commuicatios, Vol., No.4, Octoer, pp.7-7. [] M. X. Chag ad Y. T. Su, Model-Based Chael Estimatio for OFDM Sigals i Rayleigh Fadig, IEEE trasactios o commuicatios, Vol. 5, No. 4, April, pp [4] V. Tuzlukov, MPAM Sigal Processig y Geeralized Receiver uder Nakagami Fadig, Joural of Commuicatio ad Computer. No.8,, pp [5] M. K. Simo ad M. S. Alouii, Digital Commuicatio over Fadig Chaelsr. Eglewood Cliffs, NJ: Pretice Hall, 995. [6] R. Va Nee, ad R. Prasad, OFDM for Wireless Multimedia Commuicatios,Artech House,. ISBN:

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