DESIGN OF OPTIMIZED FIXED-POINT WCDMA RECEIVER

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1 7th European Sgnal Processng Conference (EUSIPCO 9) Glasgow, Scotland, August -8, 9 DESIGN OF OPTIMIZED FIXED-POINT WCDMA RECEIVER Ha-Nam Nguyen, Danel Menard, and Olver Senteys IRISA/INRIA, Unversty of Rennes, rue de Kerampont F-3 Lannon Emal: hanguyen@rsa.fr ABSTRACT To satsfy energy and complexty constrants, embedded wreless systems requre fxed-pont arthmetc mplementaton. To optmze the fxed-pont specfcaton, exstng approaches are based on fxed-pont smulatons to evaluate the performances. In ths paper, the approach used to optmze the fxed-pont specfcaton for a WCDMA recever s presented. The dynamc range and the fxed-pont accuracy are evaluated analytcally n our approach. The analytcal accuracy constrant expresson accordng to the bt error rate (BER) s proposed. The results show that the optmzed fxedpont specfcaton depends on the nput recever sgnal-to-nose rato (SNR).. INTRODUCTION Wreless communcaton s one of the most mportant sectors for dgtal sgnal processng (DSP) applcatons []. The low cost and low power termnal desgn s one of the key challenges n ths doman. New servces, such as mage, vdeo and Internet access requre hgher data rate. Consequently, the complexty of the baseband dgtal part s growng. Dfferent aspects have to be consdered to optmze the mplementaton cost and the power consumpton. Especally, the arthmetc aspects offer opportuntes to reduce the cost and the power consumpton. Effcent embedded wreless system mplementaton requres the use of fxed-pont arthmetc. Therefore, the vast majorty of embedded DSP applcatons s mplemented n fxed-pont archtectures [, 3, ]. Indeed, fxed-pont archtectures are cheaper and more energy effcent than floatng-pont archtectures because of ther lower data word-lengths. The fxed-pont converson process s made up of two man steps correspondng to the dynamc range estmaton and the fxedpont data word-length optmzaton. The am of ths optmzaton process s to mnmze the mplementaton cost as long as the applcaton performances are fulflled. To optmze the fxed-pont specfcaton, exstng approaches [, ] are based on fxed-pont smulatons to evaluate the performances. In [], the fxed-pont error s analyzed for a CDMA recever, but the performances n terms of bt error rate s also measured wth fxed-pont smulatons. To evaluate accurately the bt error rate, a great number of samples are needed. Each modfcaton of the fxed-pont data requres a new fxed-pont smulaton. Thus these approaches suffer from a major drawback whch s the long optmzaton tme. Consequently, the fxed-pont desgn space cannot be explored and multple wordlength approaches [5] cannot be used. In ths paper the approach used to optmze the fxed-pont specfcaton s presented for the case of a WCDMA recever. The WCDMA technology s used for the physcal layer of the Unversal Moble Telecommuncatons System (UMTS), one of the thrd generaton wreless communcaton systems. A new approach s proposed to estmate more accurately the data dynamc range. The propertes of the applcaton are taken nto account to reduce the pessmstc effects of classcal analytcal approaches lke nterval arthmetc. Then, the accuracy constrant used n the fxed-pont optmzaton problem s determned from the requred applcaton performances. For the bt error rate, the analytcal expresson of the accuracy constrant accordng to the bt error rate s proposed. The experment results show the opportunty to code the fxed-pont data accordng to the recever sgnal-to-nose rato. Our approach can be easly adapted to any communcaton system. The paper s organzed as follows. In Secton, the fxed-pont converson process s summarzed and the WCDMA recever s descrbed n Secton 3. The desgn of the symbol decoder module s detaled n Secton. Frst, the dynamc range estmaton s presented and secondly, the fxed-pont specfcaton optmzaton s descrbed. In Secton 5, the desgn of the searcher module s presented.. FIXED-POINT CONVERSION The fxed-pont converson can be dvded nto two man steps correspondng to bnary-pont poston determnaton and word-length optmzaton. The frst step corresponds to the determnaton of the nteger word-length of each datum. The number of bts wl for ths nteger part must allow the representaton of all the values taken by the data, and s obtaned from the data bound. Thus, frstly the dynamc range s evaluated for each datum. Then, these results are used to determne, for each datum, the bnary-pont poston whch mnmzes the nteger word-length and whch avods overflow. Moreover, scalng operatons are nserted n the applcaton to adapt the fxed-pont format of a datum to ts dynamc range or to algn the bnary-pont of the addton nputs. The second step corresponds to the determnaton of the fractonal word-length. The number of bts fwl for ths fractonal part defnes the computatonal accuracy, whch s usually measured by the output quantzaton nose power q. The mplementaton cost s mnmzed under the accuracy constrant P max e q. Let wl be an N-sze vector representng the N applcaton data word-lengths. Let C(wl) be the mplementaton cost and q (wl) be the computatonal accuracy obtaned for the word-length vector wl. The mplementaton cost C(wl) s mnmzed under the accuracy constrant P max e q : mn(c (wl)) such as q (wl) P max e q () To obtan reasonable optmzaton tmes, an analytcal approach s used to evaluate the fxed-pont accuracy. Moreover, n a wreless communcaton system, the performance s measured by the error rate. Therefore a relaton between the applcaton performance and the accuracy constrant must be done. An analytcal expresson of the maxmal quantzaton nose power accordng to the bt error rate at the Rake recever output s proposed. 3. PRESENTATION OF WCDMA WCDMA s the ar nterface of 3G moble telecommuncatons networks, whch s based on DS-CDMA (Drect Spread Code Dvson Multple Access) technology. In WCDMA, two layers of spreadng codes are used [3]: channelzaton codes and scramblng codes. The channelzaton codes C ch are based on the Orthogonal Varable Spreadng Factor (OV) technque to allow the change of spreadng factor and to mantan the orthogonalty between dfferent spreadng codes of dfferent lengths. The scramblng codes used EURASIP, 9 993

2 s (n) s(n) z c ch,q(n) C G(n) s(k) z 5 s (n) d c.ref(k) c ch,i (n) c ch,q(n) s5(k) acc I acc S out + accq ˆα Symbol decoder FIR FIR Channel estmaton Fgure : Data flow graph of the th fnger of the WCDMA Rake recever. n downlnk are long Gold codes C G. The nput data d t s multpled wth the spreadng codes, and the transmtted sgnal TXt s equal to TXt = d t C ch C G. In a mult-path Raylegh channel, the global receved sgnal s(n) s the sum of elementary sgnal s n (n) for dfferent channel paths. Let τ and α be respectvely the delay and the complex ampltude of th path n the channel. The global receved sgnal s(n) expresson s equal to ( ) s(n) = s n (n) + n n(n) = (α TX(n τ ) + n n (n)) () The term n n (n) represents the nose term made up of the recever thermal nose and the nterference of the other users. Ths term can be consdered gaussan wth varance σ n n. Assumng that a user has one DPDCH channel, d t C ch take values n {± ± }. Thus TX {±, ±}. For smplfcaton, TX s normalzed nto {±,±}, hence ts power s equal to one. By defnton, the sgnalto-nose rato s equal to SNR = /σ n n. For the WCDMA recever, the symbol decodng s carred out by a Rake recever to beneft from the mult-path fadng effects. The Rake recever concept s based on the combnaton of the dfferent mult-path components n order to mprove the qualty of symbol decson. Each mult-path sgnal s assgned to a fnger whch correlates the receved sgnal by the spreadng code shfted wth a delay τ. Demodulaton results from a weghted decson at the correlator outputs. Usng the maxmum lkelhood crtera, the symbol s estmated from the y(k) sgnal: y(k) = y (k) = α (k)r (k) (3) = = Thus, the fnger s made up of two man parts correspondng to the decodng symbol module and the channel estmaton module. The data flow graph of a fnger s presented n Fgure. The complex ampltude α of the th path s estmated by the plot sequence located n the control frame (DPCCH). Thanks to the complex multplcaton of the receved sgnal by the conjugate Gold code, the unscramblng operaton s performed. Then, the despreadng operaton from channelzaton code transforms the receved wde-band sgnal nto a narrow-band sgnal. Fnally, the estmated phase dstorton resultng of the transmsson channel s removed. Each fnger requres the knowledge of the th path delay τ to obtan the maxmal correlaton. Frst, the coarse tme delay estmaton s carred out wth the path searcher. Then, the fne synchronzaton of the code and the receved sgnal s made wth a Delay-Locked Loop (DLL). The data flow graph of the path searcher s presented n Fgure. The receved sgnal s multpled by dfferent shfted versons of the spreadng codes. A threshold s calculated on the average power, then peaks are determned. Each peak gves potentally a path component accordng to that shfted tme. x CM x acc s(n) L L C ch,q(n)c G(n) N=5: observaton wndow L=5: OV code length α<: threshold coeffcent + x pow N α N Fgure : Data flow graph of the path searcher.. Dynamc range estmaton. SYMBOL DECODER path(s) found The frst step of the fxed-pont converson process corresponds to nteger word-length determnaton. It s requred to determne each data dynamc range n ths step. An analytcal approach based on nterval arthmetc [] s used to estmate the dynamc and to guarantee no overflow. However, ths method sometmes overestmates the dynamc range f the applcaton propertes are not taken nto account. In a drect sequence spead-spectrum system, the sgnal-to-nose rato s partcularly low. Wth tens of smultaneous users n communcatons, the nose and nterference power s tens of tmes hgher than the useful sgnal. The dynamc range s manly due to the nose and nterference. In the despreadng process, the sgnal s summed up over the length L of spreadng sequence. The pure analytcal approach wll multply the dynamc range by L. But n fact, ths process multples manly the dynamc range of useful sgnal, not that of nose and nterference. From ths property, an approach s then proposed to determne more accurately the data dynamc range. Before the despreadng/correlaton process, the whole useful sgnal plus nose s consdered. After ths process, only the useful sgnal s taken nto account when calculatng the dynamc range. The dynamc range of dfferent data s computed from the Rake recever flow graph presented n Fgure. The nput s(n) consstng of desred sgnal s n (n) plus nose n n(n) s normalzed to have the maxmum ampltude one. Because a gaussan nose σn n has 99.7% of ts values n [ 3σ nn,3σ nn ], assumng the real and magnary parts of s n (n) are n the nterval [,], the nput s consdered to be n [ 3σ nn, + 3σ nn ]. The normalzaton process corresponds to the dvson of the nput by + 3σ nn. By propagatng the nput range n the flow graph, the followng results are obtaned. The dynamc range of the accumulator output acc I before normalzaton s equal to max( acc I ) =. + 3σ nn () The dynamc range of α correspondng to the channel estmaton module output s equal to max( α ) = + 3σ nn (5) The dynamc range of s out correspondng to the symbol estmaton module module s equal to max( s out ) = ( + 3σ nn ) () The dynamc range has been estmated wth our analytcal approach for dfferent SNR values and compared wth results obtaned from smulatons. The results are presented n Fgure 3 for the accumulator output (acc I ) and for the symbol decodng output (s out ). It s notced that from one to two bts dffer between estmated and smulated results. Nevertheless, the dynamc range evolutons accordng to the sgnal-to-nose rato are dentcal for analytcal and 99

3 smulaton based estmatons. Ths confrms the valdty of our approach to estmate the dynamc range n the WCDMA recever. The dfference between the two lnes can be explaned by the channel model used n the smulaton. If a sngle path channel model, for example, s used, the dfference s less than bt. Moreover, the analytcal estmatons are known to be more pessmstc. For the accumulaton output, n both smulaton and estmaton, there s a dfference of 3 bts between db and 5 db. For the fnger output, there s a dfference of bts between db and 5 db and of bts between db and 5 db. These results show the opportunty to adapt the data nteger word-length accordng to the sgnal-to-nose rato at the recever nput. Range (log) 8 acc (analytcal) acc (smulaton) output sgnal acc (smulaton) acc (analytcal) Sout (analytcal) E /N b Fgure 3: Estmated and smulaton based values of dynamc range for the decoder.. Word-length optmzaton In fxed-pont mplementaton, a mnmal computaton accuracy must be provded to guarantee that the system performances are mantaned. For the symbol decodng module as well as the whole system, the performances are evaluated wth the bt error rate so that the use of fnte precson does not modfy the referenced nfnte precson (BER ) more than ε. Suppose that the quantzaton nose power s q, the performance crteron can be wrtten as:.. Accuracy constrant BER BER Peq ( + ε)ber (7) Nose model The quantzaton nose can be modeled by a sum of dfferent nose sources propagatng throughout the system. Ths sum can be consdered as a sngle nose source e q at the system output. In [8], ths nose source ẽ q s valdated for a wde range of applcatons as the sum of a unform-dstrbuted nose and a gaussan nose ẽ q = υ(β e u + ( β) e n ) (8) where e u and e n are unform-dstrbuted nose and gaussan nose wth varance of, υ controls the varance (power) of the global nose and β [,] s a weght allowng the combnaton of two models. If there s a domnant quantzaton nose source, the output nose s farly a unform dstrbuton and β. In the other extremty, where each nose source contrbutes the same, β. Ths model s vald for every systems based on arthmetc operatons and usng roundng quantzaton mode. Computaton accuracy evaluaton To compute the power expresson of the output quantzaton nose, the technque presented n [7] s used. Gven that the code and the channel complex ampltude are constant for a frame, the system can be assumed to be lnear and tme nvarant. For the choce of the code and the channel complex ampltude, the worst case whch leads to the maxmal quantzaton nose power s consdered. The output quantzaton nose s a weghted sum of each nose source varance σq : = σq = K σe (9) wth K, the gan between the output and the nose source. The varance σ e of each nose source s obtaned from the quantzaton step q (the least sgnfcant bt weght) obtaned after quantzaton: σ e = q () Constrant determnaton In ths part, the expresson of the bt error rate BER Pe accordng to the output quantzaton nose power s presented. Ths expresson allows determnng the maxmum quantzaton nose power satsfed (7). Frstly, the case of a gaussan dstrbuton for the output quantzaton nose s consdered (β = ). Insde the system, multple roundng quantzaton noses e,e,...,e K are generated. If there s no domnant nose source, due to the central lmt theorem, the sum of these noses s then consdered gaussan and has the followng probablty densty functon (pdf): f q (x) = σ q π exp x σ q () In a WCDMA recever, the thermal nose and multple access nterference (MAI) can be modeled as a gaussan nose source f the transmsson channel s addtve whte Gaussan nose (AWGN) and there s no domnant nterferers [9]. In other cases, mproved gaussan approxmaton or alternatve method must be used. For smplcty, at frst, the receved sgnal s assumed to have two components correspondng to the desred sgnal and the gaussan nose and nterference. Thus, the output s the sum of the output quantzaton nose e q and the output recever nose n out. The expresson of the total nose probablty densty functon f n (x) s as follows: x f n (x) = σn out + σq exp π (σn out + σq ) () and the followng probablty dstrbuton functon F n (x): F n (x) = x + erf σn out + σq (3) Snce WCDMA uses BPSK/b-orthogonal transmsson, bt error rate can be calculated as follow: BER(σ q,σ nout ) = F n () = erfc σn out + σq = Q () σn out + σq From (7) and (), the condton for σ q s: σq ) (( erfc + ε)erfc σn σ nout out ( ( )) = Q ( + ε)q σn out σ nout (5) 995

4 Secondly, the case wth a domnant quantzaton nose has been consdered (β = ). In ths case, the nose dstrbuton s unform and ts pdf f q (x) s then as follows: f q (x) = q Id [ q, q ] () Thus the global nose, ncludng the gaussan nose source wth pdf f c, has the followng pdf: and the followng pdf: f n (x) = f c f q (x) = f c (t) f q (x t)dt (7) = ( erf x + q erf x q ) (8) q N N x F n (x) = q (erf t + q erf t q ) (9) N N In case of BPSK, the bt error probablty s: BER(σ q,σ nout ) = F n () () By the smlar way, the precson can be deduced from (7) and (). Snce there s no smple mathematcal expresson, the crteron s solved numercally. The accuracy constrant has been determned for dfferent sgnal-to-nose rato. The results are presented n Fgure. The lne P sout and P nout correspond to the desred sgnal s out (symbol) power and the output nose n out power respectvely. The dfference between the lnes P sout and P nout corresponds to the output sgnalto-nose rato. The dfference between the lnes P sout and q corresponds to the output sgnal-to-quantzaton nose rato (SQNR). The results show that the SQNR must be ncreased n order to keep the BER decreasng when the SNR ncreases. In such case, more accuracy s requred to reduce the decson errors due to fnte precson arthmetc Psout Pnout q (gaussan) q (unform) Table : Optmzed Rake recever word-lengths obtaned for dfferent SNR values acc s out accordng to the SNR. Between, db and db the word-lengths of the varables acc and s out ncrease respectvely by 8% and %. Optmzaton results show that, for a SNR varyng from db to db, potentally, up to % of energy consumpton can be saved f the fxed-pont specfcaton s adapted accordng to the SNR. 5. PATH SEACHER In ths secton the results obtaned for the path searcher are presented. 5. Range estmaton The prevous approach s used to estmate the dynamc range of the path searcher descrbed n Fgure. The nput data RX s normalzed nto [, ]. It s then multpled wth complex conjugate spreadng code C ch CG and results n the nterval [,] for each real and magnary part. For the accumulaton along wth L (OV code length) symbols only the sgnal s summed up sgnfcantly. Thus, the dynamc range s equal to max( x acc ) = L + 3σ () The dynamc range of x pow correspondng to the profle power s equal to max( x pow ) = 8 ( + 3σ) () The estmated and smulaton based dynamc range of each value s presented n Fgure 5. It s noteworthy that estmated and smulated results dffer of or bts. 8 Power Range (log) accumulaton crx accumulaton power profle power est. acc est. power Fgure : Sgnal and nose power levels accordng to the SNR.. Word-length optmzaton The optmzaton process presented n equaton () s carred-out wth the accuracy constrant defned n equaton (5). The optmzed word-lengths obtaned for dfferent SNR values are presented n Table. The results show that the optmzed word-lengths vary Fgure 5: Estmated and smulaton based values of range for the path searcher. 5. Precson evaluaton The path searcher module cannot use crtera presented n.. Ths module s based on the detecton theory and classcal crtera are 99

5 Table : Optmzed searcher word-lengths obtaned for dfferent SNR values x CM x acc x pow used to analyze the performance. The msdetectons (MD) correspondng to the non-detecton of an exstng path and the false alarms (FA) correspondng to the detecton of a non-exstng path are both measured. To analyze the path searcher performance, the mult-path Raylegh channel s consdered. The output of the path searcher before decson x pow s made up of three components correspondng to the sgnal s pow, the recever nose n pow and the output quantzaton nose e q. Compared to the Rake recever, the dstrbuton of the output sgnal s not straght. Two cases have to be consdered. When there s a path, the output value depends on the module of the complex ampltude α assocated to th path. Wthout path, the output values depend on the code propertes. In ths last case, the modelng of the output sgnal dstrbuton s complex. Thus the technque based on smulaton presented n [8] has been retaned to determne the accuracy constrant and a Monte Carlo method s used to measure the FA and MD values. A Raylegh channel model respectng the 3GPP channel case 3 [] wthout Doppler effect s used, correspondng to a mult-path fadng wth four path components (gan, delay): ( db, ns); (-3 db, ns); (- db, 5 ns); (-9 db, 78 ns). The evoluton of the false alarm accordng to the SNR are presented n Fgure for dfferent output quantzaton nose levels. The false alarms are more senstve to the quantzaton nose than the msdetectons. For the same quantzaton nose level, the mean of msdetected paths does not evolve and s very closed to the one n nfnte precson. Hence, the accuracy constrant s determned from the false alarm crtera, then the data word-lengths are optmzed. The results are presented n Table. The path searcher word-lengths, as same as the Rake recever, depend on the SNR values = 7 db = 75 db = 8 db = 85 db = 9 db 8 8. CONCLUSION For the embedded wreless system desgn, the arthmetc optmzaton aspect s one of the ways to reduce the mplementaton cost and the power consumpton. An approach has been proposed to optmze the fxed-pont specfcaton accordng to the requred applcaton performances. A new approach has been proposed to estmate more accurately the data dynamc range by explotng the applcaton propertes. The accuracy constrant has been determned from the requred applcaton performances. For the bt error rate, the analytcal expresson of the accuracy constrant accordng to the BER has been proposed. The results show that the fxed-pont specfcaton depends on the nput SNR. An approach n whch the fxedpont specfcaton s adapted dynamcally accordng to the nput recever SNR can be nvestgated. In the case of low SNR, lower word-length data can be used and energy can be saved. REFERENCES [] 3GPP. TS 5. V8.3.: Base Staton rado transmsson and recepton (FDD), 8. [] B. Evans. Modem Desgn, Implementaton, and Testng Usng NI s LabVIEW. In Natonal Instrument Academc Day, Berut, Lebanon, June 5. [3] J. Eyre and J. Ber. The evoluton of DSP processors. IEEE Sgnal Processng Magazne, 7():3 5, March. [] K. Han, I. Eo, K. Km, and H. Cho. Numercal word-length optmzaton for CDMA demodulator. In Proc. IEEE Internatonal Symposum on Crcuts and Systems (ISCAS ), volume, pages 9 93,. [5] N. Herve, D. Menard, and O. Senteys. Data wordlength optmzaton for FPGA synthess. IEEE Workshop on Sgnal Processng Systems (SPS 5), pages 3 8, 5. [] R. Kearfott. Interval computatons: Introducton, uses, and resources. Euromath Bulletn, ():95, 99. [7] D. Menard, R. Rocher, and O. Senteys. Analytcal Fxed- Pont Accuracy Evaluaton n Lnear Tme-Invarant Systems. IEEE Trans. Crcuts Syst. I, 55():397 38, Nov. 8. [8] D. Menard, R. Rocher, O. Senteys, and O. Serzel. Accuracy Constrant Determnaton n Fxed-Pont System Desgn. EURASIP Journal on Embedded Systems, 8(Artcle ID 58), 8. [9] M. Pursley. Performance Evaluaton for Phase-Coded Spread-Spectrum Multple-Access Communcaton Part I: System Analyss. IEEE Trans. Commun. [legacy, pre-988], 5(8): , 977. [] C. Sengupta, S. Das, J. R. Cavallaro, and B. Aazhang. Fxed pont error analyss of multuser detecton and synchronzaton algorthms for CDMA communcaton systems. In Proc. 998 IEEE Internatonal Conference on Acoustcs, Speech, and Sgnal Processng (ICASSP 98), pages 39 35, 998. [] W. Strauss. DSP chps take on many forms. DSP-FPGA.com Magazne, March. [] W. Strauss. Hangng up on analog and flexng Wreless/DSP muscles. Techncal report, Forward Concepts, 8. [3] K. Tachkawa. W-CDMA Moble Communcatons System. Wley,. [] H. Zhao, T. Ottosson, E. Strom, and A. Kdyarova- Shevchenko. Performance analyss of a fxed-pont successve nterference canceller for WCDMA. In Proc. th IEEE Vehcular Technology Conference (VTC -Fall), volume 3, pages 99 93, Sept.. Fgure : Mean of non-vald detected paths (false alarms) obtaned for dfferent SNR values 997

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