Overlapped filtered multitone modulation and its optimization on VLIW DSP

Transcription

1 Pavel SILHAVY, Ondrej KRAJSA, Petr SYSEL, Martn KOUTNY Dept. of Telecommuncatons, Brno Unversty of Technology, Purynova 8, 6 Brno, Czech Republc () Overlapped fltered multtone modulaton and ts optmzaton on VLIW DSP Abstract. In recent years, the multcarrer modulatons (MCM) have been appled to wre and wreless transmsson systems. MCM enable a nearperfect utlzaton of the provded frequency band on metallc cables and they also effectvely elmnate multpath propagaton n terrestral transmsson. They are manly the mplementatons called Dscrete MultTone (DMT) and Orthogonal Frequency Dvson Multplexng (OFDM). These approaches have also dsadvantages, whch have led to seeng new approaches to the mplementaton of the MCM modulaton scheme. One of them s the Fltered MultTone Modulaton (FMT). In the artcle, the channel equalzaton n overlapped and non-overlapped FMT modulaton wll be compared. The optmal mplementaton of FMT on the VLIW DSP wll be ntroduced n the second part.optmzed mplementaton of flter ban wth the help of parallel processng s descrbed, and also frame wrtng/readng and ts synchronzaton are ntroduced. Streszczene. W ostatnch latach, w modulacjach multcarrer (MCM) zostały zastosowane systemy transmsj przewodowej bezprzewodowej.mcm umożlwaja nemal perfecyjne wyorzystane pasma częstotlwośc przewdzane w ablach a równeż suteczne wyelmnować welodrogowość w transmsj nazemnej. Sa to przede wszystm mplementacje o nazwe Dscrete welotonowy (DMT) Orthogonal Frequency Dvson Multplexng (OFDM). Metody te maja taże wady, tóre doprowadzły do poszuwana nowych sposobów podejśca do wdrożena systemu modulacj MCM. Jednym z nch jest fltrowane welotonowe modulacj (FMT). W drugej częśc artyułu została opsana optymalna mplementacja modulacj FMT. Wyorzystano ban fltrów z równoległym przetwarzanem, oraz odpowedne ram zapsu/odczytu oraz synchronzacj. (Welotonowa modulacja porywajaca sę MCM jej optymalzacja) Keywords: Mult-Carrer Modulaton (MCM), Fltered MultTone modulaton (FMT), Half-overlap subchannel Fltered MultTone Modulaton, Decson Feedbac equalzer (DFE), Very Long Instructon Word (VLIW), Implementaton, Dgtal Sgnal Processor (DSP). Słowa luczowe: modulacja MCM, welotonowa modulacja FMT. Introducton The DMT and OFDM modulatons are utlzed n data transmsson over metallc cables n ADSL, VDSL and PLC systems, but also n terrestral transmsson n the WLAN and WMAX technologes, and n several other applcatons. Last but not least, they are used for dgtal rado and televson broadcastng (DVB-T)[]. These modulatons enable a near-perfect utlzaton of the frequency band provded n metallc cables wth spectrally-shaped transmsson characterstcs, or an effcent suppresson of the nfluence of multpath propagaton on terrestral transmsson. Ther dsadvantages, whch are gven by the method of the mplementaton, nclude the suboptmal utlzaton of closely-spectrally-shaped channels, channels wth narrowband dsturbance, and the suboptmal realzaton of duplex transmsson. The realzaton of FDM duplex transmsson s suboptmal, because the frequency band n the transent area between downstream and upstream channels s not used optmally. The above dsadvantages are gven by the method of realzng the multcarrer modulaton (MCM), where the ndvdual symbols have been generated usng FFT and nserted one by one. Durng the symbol duraton the ampltudes and the phases of ndvdual carrers are constant and defned by the QAM constellaton dagram of the dmenson used. Between ndvdual symbols, the ampltudes and the phases of all the carrers have been changed and thus the spectrum of each carrer s the snc functon, wth the parameters gven by the square wndow of each symbol, the attenuaton of the frst sde-lobe beng -db. Thus each carrer affects a number of neghbourng sub-bands and, on the contrary, the narrowband dsturbance affects the data transmsson on a number of neghbourng carrers, whch are outsde the dsturbance frequency bandwdth. Furthermore, f the frequency-dvson duplex s used, addtonal flterng s necessary so that the ndvdual transmsson drectons do not affect each other. Paradoxcally, t s these flters that have the domnant nfluence on the appearance of nter-symbol nterference. The frequency bandwdth between ndvdual drectons s utlzed suboptmally, whch can be seen from the bt-loadng of each ADSL modem. For these reasons, alternatve approaches to the mplementaton have recently been nvestgated to mprove the above mentoned dsadvantages. More recently, a flter ban mplementaton approach to MCM has frequently been dscussed. Ths method s called Fltered MultTone modulaton (FMT) []. Fltered MultTone Modulaton The FMT modulaton represents the modulaton technque usng a ban of flters to dvde the frequency band. The complex values obtaned from QAM modulaton are, smlar to the DMT modulaton, the nputs of the modulaton system. The number of bts assgned to ndvdual carrers s, the same as wth the DMT modulaton, determned durng the ntalzaton accorcng to the dsturbance level and attenuaton of the transmsson channel. Furthermore, as wll be gven later, an effectve mplementaton can be realzed wth the help of the FFT algorthm and thus the ncreased computaton complexty s acceptable. The man dsadvantage s the many tmes hgher delay gven by addtonal flterng. Ths modulaton s commonly realzed as non-overlapped FMT, where the ndvdual sub-bands do not overlap each other. The suboptmal utlzaton of the frequency band between ndvdual sub-bands s another dsadvantage. Nevertheless, the overlapped FMT modulaton, ntroduced n [], can be realzed, where, smlar to the DMT modulaton, the ndvdual subchannels are mutually overlapped and thus the bandwdth s utlzed effectvely. However, the overlap s n the half-subchannel band only. Prncple of Fltered MultTone modulaton and demodulaton The basc structure of FMT modulator, ntroduced n [], realzes the crtcal sampled flter ban. Each complex nput X from the QAM modulators of ndvdual carrers s fltered by FIR flter h (n) of the order of γn, whch s derved from the low-band prototype flter: () where X x (n) = = = X h (n N), { X = ( ) X for =,.., for =,N PRZEGLAD ELEKTROTECHNICZNY (Electrcal Revew), ISSN -97, R. 87 NR / 45

2 X * DFE X' X IFFT P/S x(n) channel y(n) S/P * FFT DFE X' X - - -* DFE N X' N Fg.. The effectve realzaton of the FMT modulator and demodulator. Ths mplementaton s also of hgh computaton complexty. Fg. shows an effectve realzaton of the FMT modulator and demodulator, ntroduced n [4]. Ths mplementaton uses the FFT transform, each output of whch has been fltered by the so-called polyphase flter of the order g. The coeffcents of the polyphase flters g =[g (),..., g (γ )] can be obtaned from the prototype flter h(n) of the order of γn: () g (l) =h(ln + ), where l =..γ The prototype flter can be desgned by samplng the frequency characterstc () and applyng the optmal wndow. Useful wndows enablng the desgn of orthogonal flter bans are, for example, the Blacman wndow, the Blacmanharrs wndow, the Hammng wndow, the Hann wndow, the Nuttall wndow, and some others. () H(e jπft ) = { for T f T otherwse As mentoned above, the FMT modulaton can be mplemented as overlapped or non-overlapped. Fg. shows a comparson of DMT, non-overlapped and overlapped FMT modulatons. It can be seen from the fgure that, due to the overlap, DMT and overlapped FMT mae optmal use of the whole frequency band. In the case of non-overlapped FMT, the area between carrers has been unused. Moreover, the wder subchannels enable achevng a hgher attenuaton for lower polyphase ftter orders g n the case of overlapped FMT. The subchannels are separated perfectly n the case of non-overlapped FMT, thus a dsturbance or an nhomogenety n one subchannel does not affect the neghborng carrers. Magntude characterstcs [db] tone [ - ] Fg.. Example of the comparson of the spectra of DMT, nonoverlapped FMT wt = - Blacman wndow and overlapped FMT wt =6-Nuttall wndow. Equalzaton n FMT modulaton The prncple of FMT sgnal demodulaton can be seen n the rght-hand part of fgure. In the case of non-overlapped FMT, the ndvdual carrers are completely separated, thus no nter-carrer nterference (ICI) occurs. In the case of overlapped FMT, the suppresson of ICI has been ensured thans to the orthogonalty of the modulaton ban, analogously to the DMT modulaton. The nter-symbol nterference occurs even n the case of deal channel, whch s gven by the FMT modulaton prncple. To put t more exactly, the spectral shapng of ndvdual channels by addtonal flterng leads to the occurrence of ISI nterferences, whch have to be elmnated. Equalzaton to mnmze ISI nterference can be performed ndvdually for each subchannel n the frequency doman, because each carrer creates a separated complex channel. / Y Z K K X K w FF + Fg.. Decson Feedbac equalzer structure. w FB 46 PRZEGLAD ELEKTROTECHNICZNY (Electrcal Revew), ISSN -97, R. 87 NR /

3 In fgure the complex values of DFE (Decson Feedbac equalzer) equalzers are drawn for the st to N th channels. The DFE equalzer structure s shown n fgure. The DFE equalzer contans two dgtal FIR (Fnte Impulse Response) flters and a decson crcut. The feedforward flter (FF) wth the coeffcents w FF and of the order of M s to shorten the channel mpulse response to the feedbac flter (FB) length R. The feedforward flter s desgned to set the frst coeffcent of the shortened mpulse response of channel to unty. Wth the help of the feedbac flter (FB) wth the coeffcents w FB and of the order of R we subtract the rest of the shortened channel mpulse response. The dervaton of MMSE DFE equalzer soluton was publshed several tmes, e.g. [5]. In ths secton, the useful results of dervaton wll be recaptulated. The coeffcents of the equalzer flters for the gven delay Δ can be determned usng the equaton: (4) w FB = R X Y f f T R X Y f where matrx R X Y s:, w FF = ( H H H ) H H C H w FB (5) R X Y = I GH ( H H H ) H H G H matrx H s the convoluton matrx of the channel from whch we chose the shortened part n terms of delay parameter Δ wth the help of matrx G: +M samples {}}{ (6) G =dag(,...,,,...,,,..., ) }{{}}{{} Δ R and f s the column vector of length R wth element one n the frst poston: (7) f =[,,..., R ] To compare equalzaton n non-overlapped and overlapped FMT modulatons we realzed a seres of smulatons of varous FMT systems wth dfferent flter orders γ and desgn wndows. The comparatve parameter of the acheved mnmzatons was the summaton of the MSE of all the carrers used: (8) MSE = N = ( ) f T R X Y f Fgures 4 and 5 gve examples of the smulaton results. In fgure 4 the comparson s on the deal channel and n fgure 5 t s on the ANSI channel. In both examples the systems had N =carrers. Tests on dfferent channels proved that n the case of overlapped FMT modulaton a better MSE mnmzaton ant thus a better channel equalzaton can be acheved than n the case of non-overlapped FMT. The dfference n the fnte acheved mnmzatons s ordnal. In the case of a lower equalzer flter order a smaller mnmzaton s acheved for overlapped FMT too n comparson wth non-overlapped FMT. Overlapped modulaton appears to be a better choce due to not only the optmal frequency spectrum utlzaton, but also due to the equalzer complexty and the fnal mnmzaton value acheved. MSE [ - ] non-overlap γ=8 overlap γ=8 non-overlap γ= overlap γ= non-overlap γ= overlap γ= non-overlap γ=4 overlap γ= M [ - ], (R=M) Fg. 4. Comparson of acheved MSE of non-overlapped and overlapped FMT modulatons of systems wth dfferent flter orders γ and Nutall wndows on deal channel. MSE [ - ] non-overlap γ=8 overlap γ=8 non-overlap γ= overlap γ= non-overlap γ= overlap γ= non-overlap γ=4 overlap γ= R [ - ] (M=R) Fg. 5. Comparson of acheved MSE of non-overlapped and overlapped FMT modulaton of systems wth dfferent flter orders γ and Blacman wndows on ANSI channel. Optmal mplementaton of FMT on VLIW DSP Complers desgned for dgtal sgnal processors dffer from the ANSI-C or C++ standard n a few detals, whch n the ultmate result have a consderable effect on the speed and stablty of algorthm mplementaton. The basc dfference les n that the defned data types are fully adapted to the archtecture of dgtal sgnal processor. The number of data bts and the format of storng numbers n a gven code (mostly the two s complement) correspond to the actual storage of numbers n dgtal sgnal processor regsters. When optmzng the source code t s convenent ether to enter the nstructons of dgtal sgnal processor assembler drectly nto the C-language source code or to use the ntrnsc functons, whch are assembled as a sngle nstructon. In ths way, the crtcal parts of source code that the assembler s not able to analyze correctly can be optmzed. In parallel processng, the gven algorthm can be realzed smultaneously for several values of the nput sgnal. Usng parallel processng wll greatly ncrease the speed of algorthm processng. Implementaton of the system s realzed usng the TMSC67DSK development t wth the TMSC67 dgtal sgnal processor. The AIC audo codec taes care about data transmsson to the channel. The system dstngushes between odd and even sequences n the data feld and on ths bass dstrbutes data nto the rght or the left PRZEGLAD ELEKTROTECHNICZNY (Electrcal Revew), ISSN -97, R. 87 NR / 47

4 Algorthm.: S DEC( buf, len, wndow, sze) begn for to len f buff rp > wndow then return (true) buff rp ++; do comment: read ponter ncrementaton f buff rp == buff ep then buff rp = buff buff comment: end of cyclc buffer testng return (false) comment: t s not a sync buffer end channel. Ths advantage was used n the realzaton of the test mplementaton. The frst channel was thus used to ensure synchronzaton whle the second channel was used for the actual data transfer. The processng of transmtted data can be dvded nto several stages, whch can be mplemented separately. Frst, blocs of QAM modulaton symbols are generated from the nput bt sequence. The constellaton dagram s selected for each carrer whle establshng a connecton, usng the sgnal-to-nose rato. A Recommended tranng sequence s used when establshng the connecton. Symbols are assgned to bt sequences usng a loo-up table so that the transmttng power s the same for all constellaton dagrams. The next step on the transmtter sde s to mplement the IFFT,.e. the converson from the frequency doman to the tme doman. The DSPLIB lbrary, optmzed for the TMSC67 processor, was used n the mplementaton, namely the DSP_fft6x6 functon, whch wors wth 6-bt nput values of the float type and a 6-bt feld twddle-factor, also of the float type. The functon return value s then also float. Next, the flterng of the frame obtaned by IFFT and by a flter ban s mplemented. We can choose from several approaches to mplement the flter ban. The frst s flterng that corresponds exactly to Fg.,.e. flterng each th sample by a flter wth coeffcents correspondng to the polyphase flter n the th branch. Ths approach could be optmzed by usng the functons of the DSPLIB lbrary, but ths feature brngs a number of constrants on the length of each flter, and on data algnment[6]. Furthermore, t would be necessary to eep n memory a large number of sgnal samples. The second approach s flterng accordng to Fg.6 and example of realzaton n C s n example. The prototype flter s stored n the memory n one varable such that the sequence number of samples corresponds to the sequence number of data on each carrer. The nput sample ponter x and the ponter to the feld of prototype flter coeffcents h can be declared by the ey word const snce n the course of calculaton the nput sample value and the values of ndvdual flter coeffcents wll not change. The output sample value and the values of statespace varables wll, on the contrary, change durng calculaton and thus they cannot be declared by the ey word const. It s obvous from the algorthm structure that the ndvdual nput arguments represent mutually ndependent data structures, whch wll be stored n separate memory locatons. In that case t s of advantage to use the ey word restrct, Example. Flter ban for FMT n C vod ban flt ( const nt x[ restrct ], const nt h[ restrct ], short y[ restrct ], // frame length nt M, // overlap factor nt g){ nt ; } for (= ; < M g ; =+) { // sample n th poston (y+%m) += mpy( h[], x[ ]); // sample n th + poston (y+%m+) += mpyh ( h[ ], x[ ] ) ; } whch nforms the compler about the memory-ndependence of the varables. In case the output sample was entered nto the same memory feld as the nput samples (n-place processng), there would evdently be a dependence relaton between the n and out ponters and the restrct eyword could not be used n declarng the two arguments. Comparson of optmzed and non-optmzed mplementatons are n tables and. For the purposes of the ADC, the data has to be amplfed and converted to nteger data type. Ths data type s supported by the ADC and DAC converters. Also sortng and nsertng of synchronzaton too place whle convertng these data to values approprate for the transfer. The synchronzaton conssted n nsertng a synchronzaton pulse always at the begnnng of each multframe. The multframe contans a predefned number of frames. Ths value s 69 frames n ITU G.9, where the frst frame of the transmsson chan s used to synchronze the remanng 68 frames. Incomng frames are stored n a crcular buffer. Ths buffer can hold up to several multframes, but from the capacty pont of vew, ths value s set to 5. Two ndependent ponters, read and wrte, tae care of the read and wrte operatons from/to the cyclc buffer. Thus no overwrtng of data that have not been read should occur. After wrtng the data nto the recevng buffer, the startng pulse of multframe s dentfed. Ths s guaranteed by algorthm. By callng the s_dec functon the ponter to a defned structure buf s nserted nto the buffer. Ths structure contans ponters to all the necessary data unts n the mplementaton of readng. The current readng poston s tested after the callng. If ths poston corresponds to a predefned level of the synchronzaton pulse decson wndow, the algorthm evaluates that t s a synchronzaton pulse. If the current value of the test element does not match the level of the decson wndow, the algorthm ncrements the read ponter and contnues testng. If the read ponter ndcates the end of the cyclc buffer, the value of startng feld s assgned to ponter. The length of the test feld s always equal to the length of the defned frame. Thus no loop algorthm should occur here. In the event that wthn the gven frame no synchronzaton pulse was found, t was one of the transmsson frames. In the future ths testng wll be seen to by calculatng the number of receved frames and thus computatonal resources wll be saved. Subsequently the receved frames are fltered, just le n the transmtter, and the FFT s performed. 48 PRZEGLAD ELEKTROTECHNICZNY (Electrcal Revew), ISSN -97, R. 87 NR /

5 a) h h h h h h h h b) X X X X X - X - X - X - X - X - X - X - X -γ X -γ X -γ X -γ c) y y y y Fg. 6. Optmzed algorthm for mplementng FIR flter ban Table. Wthout optmzaton FFT DMT FMT γ =8 FMT γ =6 D-FMT γ =8 D-FMT γ = Conclusons In the artcle, non-overlapped FMT and overlapped FMT modulaton systems were presented. We mentoned the structure of the modulator and demodulator, and the possbltes of an equalzaton mplementaton based on the DFE equalzer ban. Results of the smulaton of complexty and acheved equalzaton results for both approaches were presented. Test results on dfferent channels proved that n the case of overlapped FMT modulaton a better MSE mnmzaton ant thus a better channel equalzaton can be acheved than n the case of non-overlapped FMT. An effectve mplementaton of ths modulaton usng the FFT algorthm was compared wth a drect mplementaton and a proposed optmzed mplementaton. The mplementaton effectveness was compared wth the number of multply and accumulate (MAC) nstructons and cycles that are necessary for calculatng one output frame. An optmzed mplementaton of FMT modulaton on DSP was also shown. Ths soluton conssts of two parts, namely the mplementaton of flter ban and the mplementaton of frame generaton, wrtng, readng, and synchronzaton. Both of these parts were descrbed wth examples of soluton n the C code. The proposed desgn was mplemented and tested on a TMSC67 development starter t. Fg. 7. Optmzed algorthm for mplementng FIR flter ban The process n the recever s exactly the opposte of the process n the transmtter. FFT DMT FMT γ =8 FMT γ = Table. Optmzed mplementaton Acnowledgements Ths wor was supported n part by Grant Agency of Czech Republc GACR project No. /9/846, by MSM 65 research program, and by Grant Agency of Brno Unversty of Technology No. FEKT-S--6.[?] REFERENCES [] Stuavec, R.; Kratochvl, T. Smulaton and Measurement of the Transmsson Dstortons of the Dgtal Televson DVB-T/H Part : Modulator for Dgtal Terrestral Televson. Radoengneerng,, ro?. 9,?., s ISSN: - 5. [] Cherubn G., Eelefterou E., Olcer S., Coff.M.. Flter ban modulaton technques for VHDSL. IEEE Communcaton Magazne, May, pp [] Slhavy, P. Half-overlap subchannel Fltered MultTone Modulaton wth the small delay. In The Seventh Internatonal Conference on Networng ICN 8. pp , Cancun, Mexco, IARIA, LCN 7949, Aprl 8. ISBN: [4] Berenguer, I., Wassel, J. I., FMT modulaton: recever flter ban defnton for the dervaton of an effcent mplementaton, IEEE 7th Internatonal OFDM Worshop, Hamburg, Germany, Sep.. [5] Sayed, Al H. Fundamentals of Adaptve Flterng, Wley, NJ, ISBN [6] Sysel, P.; Krajsa, O. Optmzaton of FIR flter mplementaton for FMT on VLIW DSP. In Proceedngs of the 4th Internatonal Conference on Crcuts, Systems and Sgnals (CSS ).. Corfu: WSEAS Press,. s ISBN: Authors: Ph.D. Pavel Slhavy, M.Sc. Ondrej Krajsa, Ph.D. Petr Sysel, M.Sc. Martn Koutny, Dept. of Telecommuncatons, Brno Unversty of Technology, Facultu of Electrcal Engneerng and Communcaton, Brno Unversty of Technology,ul. Purynova 8, 6 Brno, Czech Republc, emal: slhavy@feec.vutbr.cz, rajsao@feec.vutbr.cz, sysel@feec.vutbr.cz, outnym@feec.vutbr.cz PRZEGLAD ELEKTROTECHNICZNY (Electrcal Revew), ISSN -97, R. 87 NR / 49