MC-CDMA Systems with Uplink and Downlink Receivers over Fading Channels

Transcription

1 MC-CDMA ystes with Uplik ad Dowlik Reeivers over Fadig Chaels MIH HUG LE ad IKO E. MAORAKI hool of Egieerig ad Idustrial Desig Uiversity of Wester ydey eod Aveue Kigswood 747..W. AURALIA Departet of Coputer iee Military Istitutios of Uiversity Eduatio Hellei aval Aadey era Hatzikyriakou 8539 Piraeus GREECE Abstrat: - Bit error rates of uplik ad dowlik Multiarrier Code Divisio Multiple Aess (MC-CDMA syste usig oheret Maxial-Ratio Cobig (MRC ad Equal Gai Cobiig (EGC reeivers are estiated over Rayleigh fadig haels. he aalysis assues that differet subarriers experiee idepedet fadig haels but ot eessary idetially distributed. he aalysis is based o Gaussia approxiatio of the ultiple aess iterferee. Geeralized bit error rate (BER expressios for both uplik ad dowlik with MRC ad EGC reeivers were derived. he aalytial results are supported with oputer siulatio results. he effet of fadig paraeters uber of users ad uber of subarriers were preseted. he BER perforae of the EGC reeiver i the uplik is highly iflueed by the fadig paraeter opared with the MRC reeiver. he EGC reeiver ahieves advatages opared to the MRC reeiver i the dowlik the MRC reeiver obtais sall iproveet opared to the EGC i the uplik. Key-Words: - Multiarrier Code Divisio Multiple Aess Maxial Ratio Cobiig Equal Gai Cobiig Uplik MC-CDMA Reeiver Dowlik MC-CDMA Reeiver. Itrodutio Multiarrier ode divisio ultiple aess has attrated sigifiat attetio as a dowlik ouiatio ethod for fourth geeratio obile ouiatio systes. MC-CDMA ahieves high quality ad high apaity ouiatio i a ultipath fadig eviroet beause frequey doai spreadig sigals geerate frequey diversity without ay error orretig ode. he appliatio of diret-sequee (D spread spetru ( ode-divisio ultiple-aess (CDMA to ellular ouiatios systes has bee aalysed. D-CDMA syste has bee osidered to be a adidate to support ultiedia servies i obile ouiatios beause it has apabilities to ope with asyhroous ature of ultiedia data traffi to provide higher apaity over ovetioal wireless aess shees ad to ope with a hostile ultipath fadig eviroet. However the oputatioal oplexity of Rake reeiver i a CDMA syste ireases expoetially as the data trasissio rates ad badwidths irease. I additio ultipath propagatio auses iterhip-iterferee (ICI i the D-CDMA syste ad severe itersyboliterferee (II i high data rate systes if the hael delay spread exeeds the sybol duratio []. Multiarrier ode divisio ultiple aess has bee proposed to offer high data rate servies i fadig haels sie 993. Basially MC-CDMA is a obiatio of CDMA with orthogoal frequey divisio ultiplexig (OFDM sigallig. It is osidered to be ore suitable to solve the probles assoiated with the D-CDMA shees. I a MC- CDMA syste a sigle data sybol is trasitted over ultiple arrowbad subarriers. he arrowbad sigals o subarriers experiee frequey o-seletive fadig that eliiates the eed for additioal equalizer at the reeiver side. Orthogoality of trasitted subarrier sigals is a ruial fator i aitaiig the spetral effiiey at axiu level. Reet advaes i oputatio power ake the ipleetatio of ultiarrier systes feasible usig e.g. fast Fourier trasfor (FF. ie the MC-CDMA tehique possesses the advatages of both OFDM ad CDMA it has the properties desirable for future high data-rate wireless ultiedia servies suh as isesitivity to frequey-seletive hael with a siple oe-tap

2 frequey doai equalizer frequey diversity ad apability of hadlig diverse ultiedia traffi. he perforae of MC-CDMA i both uplik ad dowlik of a obile ouiatio syste based o differet approxiatio tehiques for Rayleigh fadig haels were ivestigated. uerous papers have bee dediated to the bit error rate aalysis of MC-CDMA. I this paper we preset aifestatio for BER of MC-CDMA with Rayleigh fadig hael usig uerous users various types of reeivers both for uplik ad dowlik []. Multiarrier CDMA ystes MC-CDMA syste odel is exaied. A sigle ell i MC-CDMA syste obtais M siultaeous users eah user has subarriers. Propagatio haels of all users are assued to be uorrelated.. rasitter Model rasitter odel of MC-CDMA syste is siilar to that of OFDM syste used e.g. i the Digital Audio Broadastig (DAB syste. he ai differee is that a MC-CDMA syste trasits the sae sybol i parallel through several subarriers whereas a OFDM syste trasits differet sybols at differet subarriers. Figure illustrates the blok diagra of the trasitter i MC-CDMA syste. Every user has a pseudo rado sigature sequee give by:... [] : (... M where the eleets [] are odelled as idepedet ad idetially distributed (i.i.d. rado variables (r.vs with equal probability Prob( []+ Prob( [] /. he sae sigature sequee hip is used to odulate eah of the arriers of the th user. he axiu uber of users i the syste is M. he iput data sybols of the th user geerate a strea of equal probability data sybols d with ( E[ d ] give by d { d : l } ( with frequey doai spreadig eah data bit is ultiplied by hips of the sigature sequee [3]. rasitted sigal G (t orrespodig to the lth data bit of the th user is defied by: G P ( t [] d l Q. os f t π + Π ( t lb b (3 b where P is the power of data bit. Π b ( t is the retagular pulse defied i the [ b ].. Reeiver Model Reeiver odel with M ative users i the MC- CDMA syste the reeiver sigal a be writte as: M P h( t [] d l Q.os π f + t + ψ Π b b + σ b ( t l ρ ( t (4 where (t is the additive white Gaussia oise (AWG with double-sided power spetral desity of o /. he ea power of the th subarrier sigal is P defied as P E[ ]. Assuig that the ea powers of all subarriers are equal the ea total power of the th user sigal is P P. he operatio of a equalizer is eessary to upgrade the perforae of the syste e.g. ultiplyig eah subarrier by a fator. Hee oly oe tap frequey doai equalizers are osidered here. he blok diagra of the reeiver i MC-CDMA syste is depited i Fig.. With oheret deodulatio the deisio variable w of the lth data bit of the th user is give by: w l ( l+ b l h ( t [] Q. os π f + t + ψ dt (5 b where ψ deotes the reeiver's estiatio of the phase at the th sub arrier of the desired sigal [3]. I straightforward aer it is assued that differet subarriers experiee i.i.d. fadig haels although the assuptio is ot eessary for the aalysis. Walsh-Hadaard odes are eployed as the sigature sequees i this paper. Assuig that the users are tie syhroous after deodulatio ad obiig subarrier sigals the deisio variable is obtaied as: w l G + K + σ (6 he deisio variable osists of three opoets the first ter orrespods to the desired sigal the seod ter orrespods to the ultiple aess iterferee fro other users ad the last ter orrespods to the oise. Assuig perfet phase syhroizatio of users ψ ψ. he desired sigal opoet P G d (7 he ultiple aess iterferee ter is desribed as

3 Fig. rasitter i MC-CDMA syste Fig. Reeiver i MC-CDMA syste P K M d ( [] []. os ψ ψ (8 iilarly the oise ter a be writte as σ b ( l + b [] σ ( t Q. os π f + t + ψ dt (9 b wo obiig ethods of axial-ratio obiig ad equal gai obiig are preseted i this paper. he axial-ratio obiig is based o orretig the phase shift ad weightig the reeived sigal with the hael fadig paraeter. he assiged equalizatio oeffiiets are J ( where J l is the estiated value of b J ad (. * deotes the oplex ougatio. MRC is the optiu diversity obig tehique with respet to the bit error rate. he uorrelated diversity brahes ad o iterferee are assued [4]. he equal gai obiig is also kow as phase equalizatio ad it is based o orretig oly the phase shift itrodued by the hael. Eah subarrier is orretig its phase by seletig: J J ( 3 Uplik ad Dowlik MC-CDMA Reeivers over Fadig Chael 3. Uplik MC-CDMA Reeivers I uplik MC-CDMA reeivers the sigal to iterferee plus oise ratio is abbreviated as R eed to be defied first. For sipliity the oise opoets are approxiated as zero-ea Gaussia distributed rado variables. iilarly it is assued that the spreadig ode hips ad iput data bits are rado ad idepedet. he ultiple aess iterferee (MAI opoets are approxiated to be zero ea Gaussia distributed r.vs. his approxiatio is based o the Cetral Liit heore (CL whih is osidered fairly aurate at least for large uber of users (M>. Geerally speakig the th user oditioal R (Coditioed o a be expressed as: E ( w R ( W w (

4 ... where [ ] the fadig aplitudes vetor of the th user. W is variae. Assue idepedet users ad idepedet subarriers ( P E w (3 4 ad W ( w W ( K + W ( σ (4 where ψ ψ ψ ψ adψ ad are i.i.d r.v. s uiforly distributed i the rage of [π]. he probability desity futio (pdf of a ψ E[os ψ be obtaied with ( ] [ os ( ] E ψ. uh phase distortio will radoize the phase ad osequetly ael the effet of the orthogoality of the spreadig odes at the reeiver [4]. he oditioal variae of the MAI a be expressed as W M P ( K E[ ] (5 8 ad siilarly the oditioal variae of the oise opoets is: ( W σ (6 4 ubstitutig (6 (5 ad (3 ito ( we obtai the followig expressio for the oditioal R (Coditioed o : R 4 M P + E[ ] 4 P 8 (7 For uplik MC-CDMA reeiver with MRC the assiged equalizatio oeffiiet is the oplex ougate of (8 Hee fro (7 the R for uplik MC-CDMA reeiver with MRC a be writte R δ M + δ (9 P Eb where δ is the bit eergy to oise ratio of the th user ad E[ ]. For uplik MC-CDMA reeiver with EGC the weights are set all to uity i.e. ( whih is uh sipler tha MRC as it does ot require hael estiatio. Usig (7 the R for EGC for uplik MC-CDMA reeiver a be writte as [5]: R δ ( M + δ ( 3. Dowlik MC-CDMA Reeivers I dowlik MC-CDMA reeivers the differet users arrive at oe partiular reeiver through the sae hael. hus we assue perfet phase orretio for the iterferee. Cotrary to the uplik the phase distortio is ot preset ad the orthogoality of the subarrier odes is ot destroyed by the hael. ie Walsh odes are eployed as the sigature sequee for all users the MAI ter a be rewritte as: K M. P d ' ( ' ' where the power of all uses is the sae P P P. he exaiatio of dowlik MC-CDMA reeiver with MRC is siilar to that of the uplik ad usig ( ad (8 the oditioal variae of the MAI is writte as: ( ( P W K M 4 (3 ad the orrespodig R is expressed as: R δ + ( M δ (4 he ivestigatio of dowlik MC-CDMA reeiver with EGC is siilar to that of the uplik ad usig ( ad ( the oditioal variae of the MAI is writte as [5]: Γ i + ( ( W K M P (5 4 Γ( i i ad the orrespodig R is expressed as:

5 R ( δ (6 Γ i + + ( M δ Γ( i i 3.3 Uplik ad Dowlik MC-CDMA Reeivers he oditioal probability of bit error for oheret BPK is: δ P ( eδ Γ (7 π he Laplae rasfor ethods are applied to fid the pdf of Rδ f(δ the average BER a be foud by ( e δ f ( δ dδ P ave P (8 he pdf of su of i.i.d. Gaa distributed Rado variable is G. ie the ultiuser systes are exaied i this paper the average BER of the syste is provided by: M BER P ave ( (9 M MC-CDMA syste with EGC reeiver for 8 subarriers ad i for Rayleigh hael is deostrated i Figure 4. Figures 3 ad 4 show the aalytial results ad oputer siulatio for the MRC ad EGC reeivers i a Rayleigh fadig hael (i with differet uber of ative users. he uber of subarriers used i the siulatio syste is 8 ad this eas the ase of 8 ative users orrespods to the fully loaded ase. Fro Figures 3 ad 4 it should be oted that MRC uplik ethod provides better perforae tha EGC uplik tehique. he effet of the uber of ative users is preseted to show the ifluee of the MAI o the BER perforae. It is obvious that the uplik EGC reeiver provides higher BER tha the uplik MRC reeiver. 4 uerial Results he BER perforae of MC-CDMA reeivers are defied i the losed for solutios. he explaatios are geeralized for both up ad dow liks usig two differet equalizatio tehiques aely EGC ad MRC. o alulate the BER it is assued that the ea power of eah iterferee ter is equal to the ea power of the desired sigal. It is assued that the users i uplik are syhroous withi the yli prefix. Flat fadig hael at eah subarrier is used ad i.i.d. fadig aog differet subarriers is assued i the aalysis ad siulatios. he aalytial outoes are preseted to exaie the BER perforae of MC-CDMA reeivers i Rayleigh fadig hael with ultiple users. he effet of the uber of users fadig paraeter i the uber of subarriers ad equalizatio ethod were ivestigated. he uber of subarriers is equal to the legth of the sigature sequee. he aalytial results are arried with oputer siulatio results for Rayleigh fadig as a speial ase. he siulatio syste utilizes Walsh-Hadaard odes as the sigature sequee whih results i zero ross orrelatio providig the sigal sequees are bit syhroized without hael fadig. he uplik MC-CDMA syste with MRC reeiver for 8 subarriers ad i for Rayleigh hael is illustrated i Figure 3. he uplik Fig. 3 Uplik MC-CDMA syste with MRC reeiver for 8 subarriers ad i for Rayleigh hael. Fig. 4 Uplik MC-CDMA syste with EGC reeiver for 8 subarriers ad i for Rayleigh hael. he dowlik MC-CDMA syste with MRC reeiver for 8 subarriers ad i for Rayleigh hael is exeplified i Figure 5. he dowlik MC-CDMA syste with EGC reeiver for 8

6 subarriers ad i for Rayleigh hael is show i Figure 6. Figures 5 ad 6 preset the BER perforae opariso of oputer siulatio ad aalytial results of MRC ad EGC reeivers for dowlik i Rayleigh fadig hael. he effet of the uber of ative users is obvious. Fro Figures 5 ad 6 it should be oted that EGC dowlik ethod offers better perforae tha MRC dowlik tehique. he MRC with its oplexity will ot be affeted sie the auray of the hael estiatio would result ito soe degradatio i the perforae. Fig. 5 Dowlik MC-CDMA syste with MRC reeiver for 8 subarriers ad i for Rayleigh hael. Fig. 6 Dowlik MC-CDMA syste with EGC reeiver for 8 subarriers ad i for Rayleigh hael. Fro Figures 3 ad 5 the BER of MRC reeiver i dowlik is higher tha uplik the MRC reeiver for uplik outperfors the MRC reeiver for dowlik. Coparig Figures 4 ad 6 the BER of EGC reeiver i dowlik is lower tha uplik the EGC reeiver for dowlik outperfors the EGC reeiver for uplik. 5 Colusio Perforae aalysis of BER for MC-CDMA reeivers with ultiple ative users over Rayleigh fadig haels was preseted i this paper. he aalysis was applied to evaluate the perforae of both EGC ad MRC reeivers i uplik ad dowlik. A losed ad geeral forula was derived for the BER that a be applied for EGC ad MRC equalizers for uplik ad dowlik MC-CDMA reeivers. he BER expressio is valid for real fadig paraeters that ake it appliable for other types of fadig hael iludig Riia hael with proper appig betwee fadig paraeter ad Rie fator. he approah i this paper has the advatage of sipliity geerality losed for expressios ad oputatioal effiiey. uerial results were preseted based o the expressios derived ad arried out for Rayleigh fadig hael. he uplik MC-CDMA reeiver with MRC obtais advatage opared with the uplik MC-CDMA reeiver with EGC. However the dowlik MC-CDMA reeiver with EGC has advatage opared with the dowlik MC-CDMA reeiver with MRC. Otherwise the dowlik MC-CDMA reeiver with EGC outperfors the uplik MC-CDMA reeiver with EGC ad the uplik MC-CDMA reeiver with MRC ehaes the dowlik MC-CDMA reeiver with MRC. Referees: []. Beveuto P. Bisaglia M.Fio oftiterferee aellatio for dowlik ad uplik MC-CDMA systes Persoal Idoor ad Mobile Radio Couiatios PIMRC 4 5th IEEE Iteratioal yposiu Vol. 4 pp [] I. Cosovi M. hell A. priger O the perforae of differet hael pre-opesatio tehiques for uplik tie divisio duplex MC- CDMA Vehiular ehology Coferee VC IEEE 58th Vol. 3 pp [3]. Hara R. Prasad Desig ad perforae of ultiarrier CDMA syste i frequey-seletive Rayleigh fadig haels Vehiular ehology IEEE rasatios Vol.48 Issue5 999 pp [4] Z. Wei J. Lider MC-CDMA i the uplik: a trasissio shee whih tolerates frequey offsets ad frequey seletive haels Persoal Idoor ad Mobile Radio Couiatios PIMRC 4 5th IEEE Iteratioal yposiu Vol. 4 pp [5] H. teeda M. Moeelaey he effet of arrier frequey offsets o dowlik ad uplik MC-D-CDMA eleted Areas i Couiatios IEEE Joural Vol.9 Issue pp