Investigation of the Performance of the Wavelet Packet Based Multi-Carrier CDMA Communications in Rayleigh Fading Channel

Transcription

1 Investgaton of the Performane of the Wavelet Paket Based Mult-Carrer CDMA Communatons n Raylegh Fadng Channel Mohamed N. El-Eandran, Ehab F. Badran and Darwsh A. Mohamed Arab Aademy for Sene and Tehnology and Martme Transport, Alexandra ebadran@aast.edu, darwshm@eng.aast.edu ABSTRACT In ths paper, an nvestgaton of the performane of the wavelet transform and wavelet paket based multarrer CDMA ommunatons n Raylegh fadng hannel s presented for dfferent wavelet famles. Replang the Fourer based omplex exponental arrers of MC-CDMA wth orthonormal wavelets pakets n the applaton of dsrete wavelet paket transform (DWPT) based MC-CDMA s an effent method to avod addng the guard band or yl prefx and to mprove the performane of the system. The bt error rate performane of the wavelet transform and wavelet paket based mult-arrer CDMA Communatons n Raylegh fadng hannel and addtve whte Gaussan nose (AWGN) Channels are ompared wth eah other. Also, the results are ompared wth the performane of FFT based MC-CDMA n Raylegh fadng hannel. Wavelet paket multarrer modulaton performs well for the fadng hannel than onventonal MC-CDMA. Key Words: MC-CDMA, DWPT, DWT, Fadng Channels. 1. Introduton Code Dvson Multple Aess (CDMA) s a multplexng tehnque [1], where a number of users smultaneously and asynhronously aess a hannel by modulatng and spread ther nformaton-bearng sgnals wth pre-assgned sgnature sequenes, t has been onsdered to be a anddate to support multmeda serves n moble rado ommunatons, beause t has ts own apabltes to ope wth asynhronous nature of multmeda data traff, to provde hgher apaty over onventonal aess tehnques suh as tmedvson multple aess (TDMA) and frequenydvson multple aess (FDMA), and to ombat the hostle hannel frequeny seletvty. On the other hand, the multarrer modulaton sheme, often alled orthogonal frequeny-dvson multplexng (OFDM), has drawn a lot of attenton n the feld of rado ommunatons. Ths s manly beause of the need to transmt hgh data rate n a moble envronment whh makes a hghly hostle rado hannel. OFDM systems have advantages suh as robustness aganst multpath and mpulse nose. However, the problem of frequeny offset [2], [3] s onsdered one of the man drawbaks of MC- CDMA systems, resultng from Doppler s shft whh ntrodued sgnal dstorton and power loss. Multarrer CDMA shemes are ategorzed manly nto two groups. One spreads the orgnal data stream usng a gven spreadng ode, and then modulates a dfferent subarrer wth eah hp (n a sense, the spreadng operaton n the frequeny doman) (e.g. MC-CDMA), and other spreads the seral-to-parallel (S/P) onverted data streams usng a gven spreadng ode, and then modulates a dfferent subarrer wth eah of the data stream (the spreadng operaton n the tme doman), smlar to a normal DS-CDMA sheme[4],[5]. Due to the relatonshp between rular and lnear onvolutons n dsrete Fourer transform (DFT), multarrer s one of the modulaton tehnques whh an to ope frequeny seletve fadng for ts advantage n frequeny dversty, MC-CDMA wth ts frequeny dversty s an attratve modulaton sheme for mult-user hgh data rate wreless ommunaton system. In OFDM and MC-CDMA ommunatons, subhannel deomposton annot be aheved wthout addng guard band or yl prefx, where a opy of the end part of the data symbol blok s transmtted. Ths method needs transmttng extra guard nterval sgnals that ntrodues overhead and thus leads to spetral neffeny and performane degradaton. Replang the Fourer based omplex exponental arrers of MC-CDMA wth orthonormal wavelets pakets n the applaton of dsrete wavelet paket transform (DWPT) based MC-CDMA s an effent method to avod addng the guard band or yl prefx and to mprove the performane of the system. In ths paper, the performane analyss of wavelet paket modulaton (WPM) based MC-CDMA n the Raylegh fadng hannel s presented and ompared wth the same model n the AWGN hannel. 2. MC-DS-CDMA The MC-DS-CDMA transmtter spreads the orgnal data stream over dfferent sub-arrers

2 usng a gven spreadng ode n the tme doman. Input seral data stream d s dvded to parallel bloks, whh length equals number of sub-arrers N. In eah sub-arrer DS-CDMA s appled wth the user spef spreadng ode k wth spreadng fator (SF), whh hasn t to be equal to number of sub-arrers (N). A matrx S k s formed as S k =d k k, (1) where d k s olumn vetor wth length N and C k s row vetor wth length SF. Eah olumn vetor from the matrx S k s fed to IDFT. MC-DS-CDMA reever omprses nverse OFDM (wth DFT) and sngle-user or mult-user detetor [5]. 3. MC-CDMA Modulaton The MC-CDMA transmtter spreads the orgnal data stream over dfferent subarrers usng a gven spreadng ode n the frequeny doman [6]. In other words, a fraton of the symbol orrespondng to a hp of the spreadng ode s transmtted through a dfferent subarrer. In a downlnk moble rado ommunaton hannel, we an use the Hadamard Walsh odes as an optmum orthogonal set, beause we do not have to pay attenton to the auto-orrelaton haraterst of the spreadng odes. MC-CDMA employs DFT to dvde the bandwdth nto orthogonal and overlappng subarrers. The n th data symbol for user k, b k (n) s spread by user orrespondng spreadng ode vetor C k eah of the N sub-arrers s modulated by a sngle hp. All the modulated sub-arrers are added to form the base band sgnal as: N 1 = dk ( n) k ( m)exp( jωmt) ( n 1) T t nt k N 1 = dk ( n) k ( m)exp( jωmt) k 1 ( n 1) T t nt (2) The hp duraton equals to the symbol duraton, Where T = T s. The ombned sgnal for all k users, n the synhronzed downlnk dreton s: (3) analyss s smply the proess of deomposng a sgnal nto shfted and saled versons of a partular wavelet. An mportant property of wavelet analyss s the perfet reonstruton, whh s the proess of rebuldng a deomposed sgnal nto ts orgnal transmtted form wthout deteroraton. The dsrete wavelet paket deomposton s omputed by suessve low pass and hgh pass flterng of the dsrete tme doman sgnal as shown n fg. 1. It s alled the mallat-tree deomposton. Its sgnfane s n the manner t onnets the ontnuous-tme mult-resoluton to dsrete tme flters. X(n) s the nput sgnal, where n s nteger. The low pass flter and hgh pass flter are denoted by G and H respetvely. When dsrete wavelet transform s used [7] at eah level, the hgh pass flter produes detal nformaton, whle the low pass flter assoated wth salng funton produes oarse approxmaton. At eah deomposton level, the half band flters produe sgnals spannng only half the frequeny band. Ths doubles the frequeny resoluton as the unertanty n frequeny s redued by half. The dematon by 2 halves the tme resoluton as the entre sgnal s now represented by only half the number of samples. Thus, whle the half band low pass flterng removes half of the frequenes and thus halves the resoluton, the dematon by 2 doubles the sale. The flterng and dematon proess s ontnued untl the desred level s reahed. In ase of dsrete wavelet paket transform (DWPT), at eah deomposton level the whole band flters produes sgnals spannng the entre frequeny band. The DWPT of the orgnal sgnal s then obtaned by onatenatng all the oeffents, startng from the last level of deomposton. Therefore, by arefully olletng preferred nodes and puttng them together, we an obtan a seres of orthogonal "wavelet-paket" arrers, so that those multband wavelet paket subarrers an offer us desrable frequeny dversty mehansm to mtgate mult path fadng and mnmze multple aess nterferene and ntersymbol nterferene. The wavelet Paket reonstruton tree s shown n fg. 2. MC-CDMA based on wavelet paket modulaton (WPM) an be desgned to aheve both frequeny and tme doman dversty, thus redue the dstorton n the reonstruted sgnal whle retanng all the sgnfant features present n the sgnal and the performane of ommunaton systems an be mproved. 4. Wavelet paket waveform [9,1] The data stream s frstly spread by spreadng ode, and then the same hp modulates eah wavelet paket waveform at the same tme, wavelet Fgure 1: Three levels of wavelet Paket deomposton tree.

3 P 1 (t) d k, 1 (t) Enoder d k (t) S/P d k, 2 (t) P 2 (t) s k (t) os ω t d k, M (t) P M (t) Fgure 3: Transmtter Model. Fgure 2: Three levels of wavelet Paket reonstruton tree. 5. Raylegh fadng dstrbuton In moble rado hannels, the Raylegh dstrbuton s ommonly used to desrbe the statstal tme varyng nature of the reeved envelope of a flat fadng sgnal, or the envelope of an ndvdual multpath omponent. It s well known that the envelope of the sum of two quadrature Gaussan nose sgnals obeys a Raylegh dstrbuton. The Raylegh dstrbuton has a probablty densty funton (pdf) gven by r 2 r 2 p( r) = e 2σ, r 2 σ (4) 6. Wavelet Paket Based MC- CDMA Modulaton Tehnque [8] The onventonal DFT-MC-CDMA s a very low ost and omplexty. Due to the onvoluton property of the DFT, the effet of the multpath hannel s onverted nto a sngle omplex hannel oeffent n eah sub-arrer. Therefore smpler frequeny ombnng methods an be used to replae usually omputatonally omplex tme doman equalzaton algorthms. Although the use of yl prefx (CP) n Guard nterval s an easy method to mtgate ISI, t leads to spetral neffeny as well as loss of data throughput. Ths leads us to the ntroduton of other mult-arrer modulaton tehnques suh as fltered multtone (FMT) that do not need the use of the CP. Wavelet based DMT s a form of fltered multtone modulaton [6] [7]. Hybrd mult-arrer CDMA tehnques try to ombne CDMA and OFDM n order to reap the benefts of both tehnques. As wavelets promse to provde better tme and frequeny loalzaton, thus elmnatng the need to append CP, we suggest the use of wavelet paket based MC-CDMA, the transmtter s shown n fg.3 The oded bt stream d k (t) of user k s seral to parallel onverted nto M parallel branhes alled sub-hannels and spread by PN ode k (t) wth hp nterval T,. The resultant hp sequenes are then used to modulate M wavelet paket funtons p (t), =l,..., M. Let R be the nformaton rate and R C be the error ontrol ode rate, then the symbol nterval on eah sub hannel s T=R C /R. Assumng modulaton, the transmtted sgnal of user k s N 1 = 2Ε dk, m( t) k Pm os( ω t) (5) 1 Where E s the energy of the transmtted sgnal over a hp, d k,m (t) represents the oded data bts on sub-hannel m of user k, d t) = d g ( t T ) k, m ( k, m T (6) N 1 k k = C = g T ( t T ) (7) p = ω ( t T ) (8) m m g s (t) stands for retangular pulse of duraton s. N s the perod of PN ode. On the reever sde, reeved sgnal s reonstruted usng flter-banks and eah user s data an be retreved by multplyng the reeved sgnal by user-spef spreadng ode, The reever s shown n fgure 4. r(t) os ω t LPF C k (t) P M (t) Fgure 4: Reever Model. P 1 (t) P 2 (t) P/S Deoder

4 7. Performane Evaluaton of Wavelet transform and wavelet Paket Based MC-CDMA Transever The Wavelet transform Based MC-CDMA Transever system s smulated usng the smulnk of matlab 7. The desgn assumes perfet synhronzaton between the transmtter and the reever. Ths sheme makes use of modulaton as shown n fgure 5. For two users (M = 2); fgure 6 shows the bt error rate performane of the wavelet transform based hybrd modulaton tehnque n AWGN hannel usng the wavelet famles Haar, daubehes1, borthogonal-1 and borthogonal-1/3 orthonormal quadrature mrror flter banks (QMF) and as t an be seen Haar wavelet famly has the better performane, Fgure 7 shows the same system wth Raylegh fadng hannel, the performane n Raylegh fadng hannel s worse than the AWGN hannel that s due to the hannel mpulse response has a multpath delay spread whh s greater than the bandwdth of the transmtted message waveform. When ths ours, the reeved sgnal nludes multple versons of the transmtted waveform whh are attenuated (faded) and delayed n tme, and hene the reeved sgnal s dstorted, but t s better than the onventonal DFT based MC-CDMA n Raylegh fadng hannel. Fgure 8 shows the effet of wavelet order on the performane of MC-CDMA based DWPT n AWGN hannel. Fgure 9 shows the same performane n the DWPT based MC-CDMA n Raylegh fadng hannel, from the fgure t s obvous that daubehes-2 wavelet famly has the better performane. Also, t an be easly seen that even n a fadng hannel DWPT based MC- CDMA s performng better than DFT based MC- CDMA n an AWGN hannel whh s the upper urve n fgure 7. Fadng Channel D W P T Code C 1 Integrate & dump Code C2 Demodulaton 1 (b) Fgure 5: Smulated DWPT Based MC-CDMA Transever. [(a) Transmtter and (b) Reever]. HAAR Bothogonal1 Bothogonal1/3 Fgure 6: The vs. E b /N o performane of MC-CDMA BASED DWT n the AWGN hannel. User 1 User 2 1 Modulaton Modulaton C Code 1 Code C 2 + I D W P T Fadng Channel DFT HAAR Bothogonal 1/1 Bothogonal 1/3 Integrate & dump (a) Demodulaton Fgure 7: vs. E b /N o performane of MC-CDMA Based DWT n the Raylegh Faddng hannel.

5 1 The effet of wavelet order on the performane of MC CDMA DFT DWPT[] DWT[] DWPT[daub2] DWPT[daub4] DWPT[of4] DWPT[borth(1/5)] Referenes [1] S. S. Hara, R. Prasad, Overvew of Multarrer CDMA, IEEE Communaton Magazne, vol.35, no. 12, Deember M=2 N=32 Fgure 8. vs. of DWPT Based MC-CDMA n the AWGN Channel [8] [2] J. Jang and K. B. Lee, Effets of frequeny offsets on MC/CDMA system performane, IEEE Communatons Letters, vol.3, No.7, pp , July [3] J. G. Andrews, and T. H. Meng, "Performane of multarrer CDMA wth suessve nterferene anellaton n a multpath fadng hannel, IEEE Trans. on Communatons, vol. 52, no.5, pp , May daub2 daub4 meyer Bothogonal 1/5 [4] H. Zhang, H. Fan, and A. Lndsey "Wavelet Paket Waveforms For Multarrer CDMA Communatons", Proeedngs of IEEE ICASSP 22, Florda, USA, Vol. 3, pp , 22 [5] K. Fazel, S. Kaser, "Mult-Carrer and Spread Spetrum Systems", Wley, West Sussex England 23. [6] N.Yee, J.P. Lnnartz, and G. Fettwes, Multarrer CDMA n ndoor wreless rado networks, Pro.IEEE Pmr 93, pp , September Fgure 9. Vs. Of DWPT n the Reylegh Fadng Channel 8. Conlusons Haar, daubehes and other wavelets are used to smulate the performane for DWT and DWPT based MC-CDMA n Raylegh fadng and AWGN hannel. DWT and DWPT based MC- CDMA perform better than DFT based MC-CDMA n the Raylegh fadng hannel. Even, when omparng the performane of DWPT based MC- CDMA n Raylegh fadng hannel wth the performane of DFT based MC-CDMA n AWGN hannel, the DWPT performs better. Ideal spetral effeny an be aheved wth the DWPT-MC- CDMA, beause no guard band s requred. [7] S. Bag, N.D. Gohar, Fazal-ur-rehman, An effent wavelet based MC-CDMA transever for wreless ommunatons, IBCAST 25. [8] R. Wan, S. Cheng and J. We, Wavelet Paket Funtons Based Coded MC-CDMA System and Its Performane, Natonal Moble Communaton Researh Lab., Southeast Unversty Nanjng, Chna,2. [9] Saber I. Hassouna, Ehab F. Badran, Darwsh A. Mohamed and Shawk Shaaban, Wavelet Paket Modulaton for Mult-arrer CDMA Communatons, Proeedngs of the 24 th Natonal Rado Sene Conferene (NRSC 27), Caro, Egypt, 13 th -15 th Marh 27. [1] M. Akho-Zaheh, Desgn and Analyss of Multarrer Multode Wavelet Pakets Based CDMA Communaton Systems wth Multuser Deteton", Thess, Graduate Faulty of the Unversty of Akron, August 26.