Optimization and Implementation for the Modified DFT Filter Bank Multicarrier Modulation System

Transcription

1 Journal of Communatons Vol. 8, No. 0, Otober 203 Optmzaton and Implementaton for the odfed DFT Flter Ban ultarrer odulaton System Guangyu Wang, Wewe Zhang, Ka Shao, and Lng Zhuang Chongqng Key Laboratory of oble Communaton, Chongqng Unversty of Posts and Teleommunatons, Chongqng, , Chna Emal: Abstrat The modfed Dsrete Fourer Transform (DFT flter ban s a Nearly Perfet Reonstruton (NPR system based on pseudo-qf flter ban. In ths paper, we ntrodue an optmzed algorthm to mplement the DFT flter ban based multarrer modulaton system. The system based on ths optmzaton algorthm has the low error rate and system delay. To verfy the desgned system we have ompared the DFT multarrer modulaton system wth the OFD modulaton system. The results show that at hgh speed ommunaton the data error rate n the DFT flter ban multarrer modulaton system s lear mproved n omparson wth OFD systems. Index Terms DFT flter ban, NPR, Error rate, Optmzaton algorthm I. INTRODUCTION Dgtal flter bans have been wdely appled and are partularly useful n subband odng and multple arrer data transmsson []-[6]. Hstorally, there are two lasses of modulated flter bans, namely DFT flter bans and osne flter bans. Beause the DFT flter ban provdes no mehansm to anel adjaent spetrum alasng omponents aused by subsamplng the subband sgnals, ths nd of flter ban s onsdered as nonsutable for subband odng. Ths dsadvantage has been overome by ntrodung a ertan modfaton whh leads to the modfed DFT (DFT flter ban [7]- [2].The modfed dsrete Fourer transformaton s a hgh effent nearly perfet reonstruton system based on pseudo-qf flter ban[8,2]. Fg. shows the polyphase deomposton struture for DFT flter ban based multarrer modulator. It onssts of the analyss and synthess flter bans. The DFT flter ban s a omplex modulated hannel flter ban based on the DFT. There are two steps of dematon. The frst step of dematon s the /2 ( must be even fator. The seond step of dematon s the fator two samplng. After total -dematon, eah hannel wll be dvded nto two parts,.e. real part and magnary part. The tme delay s ntrodued ether anusrpt reeved July 30, 203; revsed Otober 27, 203. Ths wor was supported by Natonal Natural Sene Foundaton of Chna (No and Sno-Fnland Cooperaton Projet (No. 08. Correspondng author emal: zhangwe2267@63.om. do: /jm nto the magnary part or nto the real part. Suh a tme delay ours between real part and magnary part among adjaent hannels nterhangeably. Ths struture s able to anel exatly the adjaent spetrum alasng. The nonadjaent spetrum alasng s suppressed by an approprately low stop band gan of the analyss and synthess flters. II. DFT FILTER BANKS In order to explan the mehansm to anel adjaent spetrum alasng, we frst onsder the hannel DFT flter ban system. The analyss flter ban an be desrbed by where W H ( z H( zw, 0,,2,..., ( e 2 j. The synthess flter ban s G ( z H( zw, 0,,2,.... (2 The synthess flter ban output sgnal, namely X( z an be wrtten as X ( z G ( z H ( zw X ( zw 0 0 l X zw H zw H zw l0 0 ( ( (. Supposng the prototype flter to be band-lmted to 2 /, namely j H( e 0, 2 /, Eq. (3 an be rewrtten as X ( z H ( zw H ( zw X ( zw l l 0 l 0 H ( z X ( zw ], (3 G ( z[ H ( z X ( zw H ( z X ( z (4 where the produt G( z H( z desrbes the transfer funton of the th hannel, G( z H ( z and G ( z H ( z desrbes the adjaent-spetrum alasng. The orrespondng frequeny performane sheme for th hannel s depted n Fg Engneerng and Tehnology Publshng 65

2 Journal of Communatons Vol. 8, No. 0, Otober 203 z 2 2 h(2 h(2 2 h(2 h( xn ˆ( z z z z h ( h ( h ( 2 z z IFFT Re Im Im Re z z FFT h ( h ( 2 h ( z z z z xn ( 2 h(0 2 Im 2 z z 2 Re 2 h(0 2 z (a The transmtter(the synthess flter bans (bthe reever (the analyss flter bans Fgure. Polyphase deomposton struture for the DFT flter ban based multarrer modulator ( a H ( e j H ( e j H ( e j ( j H e ( R 2 X ( z G ( z[ H ( z X ( z H ( z X ( zw 2 H zw X zw H ( zw X ( zw ]. ( ( 2 (7 ( b 2 ( / 2 / 2 ( / j G ( e G ( e j 2 / Fgure 2. Frequeny performane for -th hannel: (a Components of analyss flter ban; and (b Components of synthess flter ban. In Fg., the real subband sgnal an be desrbed as ( R n X ( z [ h( n Re{ x( n W}] n n [ h( n x( n{ W W }] 2 H ( z[ X ( zw X ( zw ] 2 2 H( z[ X ( z X ( zw ]. 2 The th hannel output sgnal n synthess flter ban reads where ( R 2 X ( z G ( z H ( z[ X ( z X ( zw ], (5 (6 2 X zw s the mrror spetrum lyng 2 ( symmetrally wth respet to X( z about the enter frequeny of the th hannel. Supposng that the orgnal j sgnal spetrum Xe ( les between and hannel, and onsderng the th hannel alasng spetrum, the real-part sgnal n th hannel s In the same way, the magnary-part sgnal n -th hannel ( I 2 X ( z G ( z H ( z[ X ( z X ( zw ]. (8 2 Beause the magnary-part subband sgnal has the phase offset of /2n -th hannel, the sgnal must be multpled by fatorw l /2. In other words, t s equal to + f l 0 and equal to - f l. So we obtan the magnary part n the -th hannel as ( I X ( z G( z{ H( z X ( z 2 H z X zw H zw X zw (9 H zw X zw 2 ( ( ( ( 2 ( ( }. Addng (7 and (9 yelds 2 X ( z G ( z[ H ( z X ( z H ( zw X ( zw ]. (0 Furthermore, usng the same way, the output sgnal n ( + -th hannel an be formulated le X +( z G ( z[ H ( z X ( z H zw X zw 2 ( ( ]. ( Addng (0 and (, and usng ( and (2, we get the reonstruton sgnal 2 2 X ( z X ( z[ H ( zw H ( zw ]. (2 203 Engneerng and Tehnology Publshng 652

3 Journal of Communatons Vol. 8, No. 0, Otober 203 For the perfet reonstruton only f H ( zw H ( zw. 2 2 Namely, the prototype flter s approxmately power omplementary. III. OPTIIIZATION AND PROTOTYPE FILTER DESIGN A. Prototype Flter Desgn In the DFT flter ban, the analyss flter ban and the synthess flter ban are derved from the lnear phase FIR prototype flter by unform frequeny shft. So the desgn of DFT flter ban an be restrted to the prototype flter desgn. The followng dstortons should be taen nto aount n the desgnng proess. Alasng dstorton: t s produed by the demator of the analyss flter ban. 2 Ampltude and phase dstorton: the reason s that no all-pass funton exsts n the pass band of analyss and synthess flter ban. In the prate desgn the followng lmtatons should be taen nto aount: a The prototype flter should be lnear phase,.e h(n=h(l--n,where L means the flter length. b The transfer funton should be able to provde hgh stop band attenuaton. The transform funton should be able to realze an approxmaton of the power omplementary property. That means: H ( zw H ( zw. 2 2 d The number of oeffents of the transfer funton should be mnmzed. B. Square Root Rased-Cosne Funton The rased-osne funton 2 j H ( e whh s equal to unty n the pass band ( r and zero n the stop band ( r.where r (0 r s the roll-off fator, s the ut-off frequeny. The rased-osne funton s 2 j H ( e os( ( r. ( r Wth /, 2 / and r, we obtan 2 j( 2 H ( e ( os(. ( If s even 2 j( 2 H ( e ( os( (5 0 0 The adjaent hannel transfer funton s power omplementary. Calulatng square root for (3 and usng 2 os ( x os(2 x, (6 2 2 the square root rased-osne funton s j H( e os( ( r, r r. 4r (7 Fnally, we get the square root rased-osne funton transfer funton as 4 rn ( r n ( r n os sn hn (, 2 4rn n (8 where n. Aordng to the power omplementary ondton, square root rased-osne funton has better performane than rased-osne funton. From (8, we now that the prototype funton has nfnte mpulse response. From the pratal respet of vew we an get the ausal fnte mpulse response by trunatng and tme shftng. However, the trunated fnte mpulse response s no more power omplementary. In other words the ampltude dstorton always exsts. But we ould selet the approprate roll-off fator and the flter length to mnmze t. C. Optmzaton Algorthm Our earler study shows that for the QPSK baseband modulaton the DFT flter ban multarrer modulaton system has the smlar performane wth the OFD system, even though the prototype flter length s nreased. But wth the nrement of prototype flter rolloff fator the system error rate an be dereased. For the 6QA and 64QA, the DFT flter ban multarrer modulaton system has better performane than the OFD system. For the 6QA, the ost s the nrement of prototype flter length. For the 64QA, the DFT flter ban multarrer modulaton system has better performane than the OFD system even though the flter length s unhanged. Otherwse, for the 6QA and 64QA, nreasng the prototype flter roll-off fator also an derease the system error. However, nreasng the length of prototype flter means the nrement of system delay, and nreasng the roll-off fator of prototype flter means the effeny reduton of spetrum utlzaton. In order to get the better system performane, we wll optmze the prototype flter to mnmze the system overall delay and mprove the effeny of spetrum utlzaton. Suppose that the prototype flter length s L=N*, where N s the length fator and means the number of DFT flter ban hannel. The target of optmzaton proess s to fnd the mnmal N to mnmze the overall system delay, whle eepng the system performane. In the optmzaton proess, we have two varables N (the length fator and r (the roll-off fator of the prototype flter.the objetve funton s hn ( ( hn ( s the 203 Engneerng and Tehnology Publshng 653

4 Spetrum of flter ban Frequeny response of RRC RRC (prototype flter Journal of Communatons Vol. 8, No. 0, Otober 203 prototype flter oeffents.the onstran ondton s that the error rate n the DFT flter ban system based modulaton system should be less than the error rate of the OFD system. The optmzaton flow hart s showed n Fg. 3. The optmzaton proess s to fnd the optmzed square root rased-osne funton n respet wth varables N and r, wth the DFT based modulaton system has mnmal system delay. Begnnng Desgn varables r and N Obtanng the prototype flter oeffents h(n n Fgure 4. Tme-doman haraterst of square root rased-osne funton (L=28, r=0.5 0 DFT flter ban modulaton -20 Implementaton OFD system Calulaton DFT system errorrate (DFT_SER Calulaton OFD system errorrate (OFD_SER DFT_SER<OFD_SER? no -80 yes -00 Obtanng the optmum values r and N -20 Endng Fgure 3. Optmzaton flow hart for DFT flter ban multarrer modulaton system. Aordng to the above, desgn of the prototype flter ome down to the follow optmzaton problem: mn{ hn ( } Nr, s. t, DFT _ SER OFD _ SER 0 Durng the optmzaton proess we tae the dfferene of error rate between DFT multarrer modulaton system and OFD system as rteron ( DFT _ SER OFD _ SER. Wth the nreasng SNR, the dfferene of error rate between the two systems wll gradually derease. The error rate of two systems wll tend to be equal when the SNR nreases to a ertan degree. So, n our optmzaton proess we frstly searh the poston n the SNR-oordnate, where the error rate of two systems s equal. Then, tang ths SNR-pont as referene we loo at the error rate values at the SNRpont before the referene pont, and he f the error rate of the DFT based modulaton system s larger than the error rate of OFD system at ths SNR-pont. If the ondton s not met, we nrease the N and r values and alulate agan the error rate for both modulaton systems and ompare them agan, untl the ondton s satsfed. At last we get the values of varable N and r, wth them we get the prototype flter Fgure 5. Frequeny haraterst of square root rased-osne funton (L=28, r= Fgure Power omplementary for square root rased-osne funton Here, we want to pont out that the ntalzaton values of N and r have lear nfluene on the results. Based on our extensve experments we found that N=6 and r=0.5 are reasonable ntalzaton values. Fg. 4 and Fg. 5 show the square root rased-osne funton obtaned by the ntalzaton values N and r n the tme-doman and the frequeny-doman, respetvely. Its hghest stop band attenuaton s -40dB. The frequeny response of an 8- hannel DFT flter ban based on ths prototype funton s showed n Fg. 6, where the power 203 Engneerng and Tehnology Publshng 654

5 Journal of Communatons Vol. 8, No. 0, Otober 203 omplementary property of square root rased-osne funton s depted. Baseband modulaton X( n pont data frames DFT Synthess flter ban Data synthess xn ( Add prefx The transmtter The reever hannel sn ( Baseband demodulaton X( n Data synthess DFT Analyss flter ban xn ( pont IFFT Frequenydoman equalzaton pont FFT ove prefx Fgure 7. Implementaton struture of DFT flter ban multarrer modulaton system. IV. DFT FILTER BANK ULTICARRIER ODULATION SYSTE A. DFT odulator The polyphase deomposton struture for DFT flter ban multarrer modulator s showed n Fg.. The transmtter s omposed of synthess flter ban, and the IFFT algorthm s used to mplement IDFT. The purpose of transmtter s to modulate eah subarrer wth nput sgnal usng synthess flter ban (IFFT. The reevng termnal s omposed of analyss flter ban, where we use the FFT algorthm to mplement t, beause the purpose of the reever s to reonstrut the nput sgnal. Wth polyphase struture we have possblty to use FFT algorthm to mplement the DFT flter ban multarrer modulaton system. In order to omplete the polyphase deomposton, the baseband modulated sgnal xn ( wll be shfted and then demated by samplng fator /2 (/2 s used to produe the fator (. The resulted polyphase deomposton sgnal wll be IFFT transformed, then dvded nto real part and magnary part, whh s a ey step to anel adjaent spetrum alasng. In the reever, the nversed operatons wll be arred. In ths system mplementaton proess, the most mportant pont s to buffer the nputted and outputted sgnal when mplementng the system beause of nherent delay n the system. B. DFT Flter Ban ultarrer odulaton System Fg. 7 shows the DFT flter ban multarrer modulaton system struture. Frstly, the nput sgnal wll be baseband modulated to map the nput sgnals nto the omplex samples. In the smulaton we use QPSK, 6QA and 64QA as baseband modulaton. Seondly, baseband modulated samples wll be proessed by the flter ban modulator to get the multarrer modulated sgnal that wll be added wth yle prefx before transmtted to hannel. The yle prefx s the opy verson of the last part of the urrent output data frame and for the hannel equalzaton. In ths paper, the length of yle prefx s the last twenty samples and the resulted samples stream wth CP wll be transmt nto hannel. The hannel seleted here s based on 3GPP TS and added wth AWGN n order to smulate the pratal ommunaton envronment. At the reever, the reverse proessng wll be done to reonstrut the nput sgnal streams. Our earler study shows that for the QPSK baseband modulaton the DFT flter ban multarrer modulaton system has the smlar performane wth the OFD system, even though the prototype flter length s nreased. But wth the nrement of prototype flter rolloff fator the system error rate an be dereased. For the 6QA and 64QA, the DFT flter ban multarrer modulaton system has better performane than the OFD system. For the 6QA, the ost s the nrement of prototype flter length. For the 64QA, the DFT flter ban multarrer modulaton system has better performane than the OFD system even though the flter length s unhanged. Otherwse, for the 6QA and 64QA, nreasng the prototype flter roll-off fator also an derease the system error. However, nreasng the length of prototype flter means the nrement of system delay, and nreasng the roll-off fator of prototype flter means the effeny reduton of spetrum utlzaton. In order to get the better system performane, we wll optmze the prototype flter to mnmze the system overall delay and mprove the effeny of spetrum utlzaton. V. SIULATION RESULTS 203 Engneerng and Tehnology Publshng 655

6 Journal of Communatons Vol. 8, No. 0, Otober 203 Under multpath hannel, we use a 32-hannel flter ban. The baseband modulatons are 6QA and 64QA. Detaled smulaton parameters are lsted n Table I. SER (symbol error rate SER (symbol error rate TABLE I. SIULATION PARAENTERS PARAETERS DFT OFD Subarrers Cyl prefx Baseband modulaton 6QA 64QA 6QA 64QA Bandwdth 0 Hz 0Hz Equalzaton Zero-Forng Zero-Forng Prototype Funton SRRC Retangular SER omparson of OFD and FBC-DFT wth QA OFD DFT SNR [db] (sgnal to nose Fgure 8. The optmzed error rate omparson between DFT flter ban system and OFD system for 6QA (N=7, r= SER omparson of OFD and FBC-DFT wth QA6 OFD DFT SNR [db] (sgnal to nose Fgure 9. Error rate omparson between OFD system and DFT system (6QA, N=6, r=0.5 For the 6QA, we get the optmzaton parameters of N=7 and r=0.2. Wth these parameters of N and r we an aheve the mnmal system delay wth a reasonable performane mprovement for the error rate showed n Fg. 8. From ths fgure, we an see that the DFT flter ban multarrer modulaton system s stronger aganst the symbol errors than the OFD system. If we want to further mprove the system performane we an smply nrease the length fator N to 6. In ths ase, as showed n Fg. 9, the error rate of DFT modulaton system s lear better than OFD system. Ths means that the longer are the flter ban oeffents, the better error robustness the DFT flter ban multarrer modulaton system has. Nevertheless, ths osts the system delay. SER (symbol error rate SER omparson of OFD and FBC-DFT wth QA64 OFD DFT SNR [db] (sgnal to nose Fgure 0. Error rate omparson between DFT flter ban system and OFD system (64QA N=4, r=0.5 For the 64QA, we get the optmzed parameter of N=4 and r=0.5. Fg. 0 shows the error rate omparson between the DFT flter ban multarrer modulaton system and the OFD system for 64QA at the optmzed parameters. From fgure 0 we an see that the symbol error rate of the DFT flter ban multarrer modulaton system s muh lower than the OFD system. Comparng Fg. 8 and Fg. 0, t an be seen that the error rate mprovement for 64QA s larger than for 6QA. The system delay for 64QA s also lower. So, we an say that the DFT based modulaton system s more sutable for hgh speed data transmsson, beause 64QA s faster than 6QA. VI. CONCLUSIONS In ths paper we ntrodued an optmzaton algorthm to desgn the prototype funton for the DFT flter ban based multarrer modulaton system. In omparson wth OFD system, the desgned DFT flter ban modulaton system has lear performane mprovement n respet wth system error rate. In partular, for the hgh speed baseband modulaton le 64QA, the desgned DFT flter ban modulaton system s muh better than OFD system. Suh property s qute useful for the desgn of modulaton systems n the next moble ommunaton networ. ACKNOWLEDGENT Ths wor s supported by the Natonal Natural Sene Foundaton of Chna (No and Sno- Fnland Cooperaton Projet (No. 08. REFERENCES [] G. Y. Wang, Analyss of quantzaton errors n subband speeh odng wth modfed DFT flter bans, Sgnal Proessng, vol. 86, no. 2, pp , Feb Engneerng and Tehnology Publshng 656

7 Journal of Communatons Vol. 8, No. 0, Otober 203 [2] G. Y. Wang, K. Shao, and L. Zhuang, Tme-varyng multarrer and sngle-arrer modulaton system,, IET Sgnal Proessng, vol. 7, pp. -2, arh 203. [3] P. N. Heller, T. Karp, and T. Q. Nguyen, A general formulaton of modulated flter bans, IEEE Trans. on Sgnal Proessng, vol. 47, no. 4, pp , 999. [4] N. J. Flege, Computatonal effeny of modfed dft polyphase flter bans, n Pro. 2th Annual Aslomar Conferene, November 993. [5] T. Q. Nguyen and R. D. Kolplla, The theory and desgn of arbtrary-length osne modulated flter bans and wavelets, satsfyng perfet reonstruton, IEEE Trans. on Sgnal Proessng, vol. 44, no. 3, pp , 996. [6] P. P. Vadyanathan, ultrate Systems and Flter Bans, Englewood Clffs, N.J.: Prente- Hall, 993. [7] G. Y. Wang, Z. F. Zhang, and Q. B, Chen, Analyss and propertes of tme-varyng modfed DFT flter bans, EURASIP Journal on Advanes n Sgnal Proessng, vol. 6, pp. -2, De [8] N. J. Flege, odfed DFT polyphase SBC flter bans wth almost perfet Reonstruton, n Pro. IEEE. Int. Conf. Aousts, Speeh and Sgnal Proessng Adelade, Australa, Apr. 994, vol. 2, pp [9] N. J. Flege, Closed form desgn of prototype flters for lnear phase DFT polyphase flter bans, n Pro. ISCAS, Chago, USA, ay 993. [0] T. Karp and N. J. Flege, DFT flter bans wth perfet reonstruton, n Pro. IEEE Int. Symp. Cruts and Systems, Seattle, WA, ay, 995, pp, [] T. Karp, and N. J. Flege, Computatonal effent realzaton of DFT Flter bans, n Pro. EURASIP European Sgnal Proessng Conf. Treste, Italy, Sept. 996, pp [2] T. Karp and N. J. Flege, odfed DFT flter bans wth perfet reonstruton, IEEE Trans.on CS-: Analog and Dgtal Sgnal Proessng, vo. 46, pp , Nov.,999. Guangyu Wang was born n Chna, n 964. He reeved hs BS degree n rado engneerng from Chongqng Unversty of Posts and Teleommunatons (CQUPT, Chna n 985 and hs S degree n Teleommunaton Engneerng from Bejng Unversty of Posts and Teleommunatons, Chna n 988. From 988 to 995, he engaged n the researh of ommunaton system n CQUPT. He reeved hs PhD degree n 999 n Eletral Engneerng from Kel Unversty n Germany. And then he engaged n postdotoral wor n Erlangen-Nuremberg Unversty. Sne 2007, he s an adjunt Professor n Chongqng Unversty of Posts and Teleommunatons n Chna. Prof. Wang s the founder of the theory of tme-varyng multrate flter ban. In reent years, he publshed ten SCI papers about the tme-varyng flter ban theory. Wewe Zhang was born n Chna, n 987. She reeved her BS degree n Eletron Informaton Engneerng from Nanjng Insttute of Tehnology, Chna n 200. Currently she s worng on her S degree n ommunaton tehnology n Chongqng Unversty of Posts and Teleommunatons. Her researh nterests are multarrer modulaton tehnques for moble ommunaton, mult-rate dgtal sgnal proessng and flter ban theory. Ka Shao was born n Chna, n 977. He reeved hs BS degree n Computer Sene Eduaton from Southwest Chna Normal Unversty, Chna n 2000 and hs S degree n Teleommunaton and Computer Networs Engneerng from London South Ban Unversty, UK n He s urrently worng towards hs PhD degree n Communaton n Tampere Unversty of Tehnology, Fnland. In September 2000, he joned Chongqng Unversty of Posts and Teleommunatons (CQUPT n Chna. Hs man researh nterests are multarrer modulaton tehnques for moble ommunaton, mult-rate dgtal sgnal proessng and flter ban theory. Lng Zhuang was born n Chna, n 978. She s an Assoate Professor sne 200 n the College of Communaton and Informaton Engneerng, Chongqng Unversty of Posts and Teleommunatons, Chna. She reeved her BS degree and S degree n 2000 and 2003, respetvely, both n Communaton Engneerng from Chongqng Unversty of Posts and Teleommunatons. She reeved her PhD degree n 2009 n Control Theory and Control Engneerng from the Chongqng Unversty. Her man researh nterests are multarrer modulaton tehnque for moble ommunaton, mult-rate dgtal sgnal proessng, flter ban theory and neural networs. 203 Engneerng and Tehnology Publshng 657