DESIGN OF OPTIMIZED FIXED-POINT WCDMA RECEIVER

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 s presented for the case of a WCDMA recever. In our approach an analytcal approach s used to evaluate the dynamc range and the fxed-pont accuracy. Moreover for the bt error rate (BER), the analytcal expresson of the accuracy constrant accordng to the BER s proposed. The results show that the optmzed fxed-pont specfcaton depends on the nput recever Sgnal-to-Nose rato.. INTRODUCTION Wreless communcaton doman s one of the most mportant sectors for Dgtal Sgnal Processng (DSP) applcatons []. The desgn of low cost and low power termnals s one of the key challenges n ths doman. New servces are provded (mage, vdeo, Internet access) and requre hgh 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 mplementaton of embedded wreless systems requres the use of fxed-pont arthmetc. Therefore, the vast majorty of embedded DSP applcatons s mplemented n fxed-pont archtectures [,, ]. Indeed, fxed-pont archtectures are cheaper and more energy effcent than floatng-pont archtectures because ther data word-lengths are lower. 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 fullfled. To optmze the fxed-pont specfcaton, exstng approaches [3, 3] 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 BER s also measured wth fxed-pont smulatons. To evaluate accurately the BER, 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 can not be explored and multple word-length approaches [] can not be used. In ths paper the approach used to optmze the fxed-pont specfcaton s presented for the case of a WCDMA recever. Ths technology s used for the physcal layer of the thrd generaton of wreless communcaton systems (UMTS). 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 (BER), the analytcal expresson of the accuracy constrant accordng to the BER s proposed. The experment results show the opportunty to code the fxed-pont data accordng to the recever Sgnal-to-Nose Rato (SNR). 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 an 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 modules correspondng to bnary-pont poston determnaton and wordlength optmzaton.the frst part corresponds to the determnaton of the nteger part 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 values. Thus, frstly the dynamc range s evaluated for each datum. Then, these results are used to determne, for each data, the bnary-pont poston whch mnmzes the nteger part 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 part corresponds to the determnaton of the fractonal part word-length. The number of bts f wl for ths fractonal part defnes the computatonal accuracy. Thus, the data wordlengths are optmzed. The output quantzaton nose power P e s the metrc used to evaluate the fxed-pont computaton accuracy. The mplementaton cost s mnmzed under the accuracy constrant Pe max. Let wl be an N-sze vector ncludng the word-length of the N applcaton data. Let C(wl) be the mplementaton cost and P e (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 : mn(c (wl)) such as P e (wl) P max e () To obtan reasonable optmzaton tmes, an analytcal approach s used to evaluate the fxed-pont accuracy. Moreover, a lnk between the applcaton performances and the accuracy constrant must be done. An analytcal expresson of the maxmal quantzaton nose power accordng to the performances s proposed for the BER at the rake recever output. 3. PRESENTATION OF WCDMA WCDMA s a standard for the thrd-generaton of cellular network whch s based on DS-CDMA (Drect Spread Code Dvson Multple Access) technology. In WCDMA, two layers of spreadng codes are used [5]: channelzaton code and scramblng code. The channelzaton code C ch s used to acheve orthogonalty between channels when tme-shft s equal to zero. The scramblng codes used n uplnk are 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

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. 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 and s 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 (SNR) s equal to : SNR = E b N = σ n n (3) For the WCDMA recever, the symbol decodng s carred-out by a rake recever to beneft from the effects of mult-path fadng. The concept of the rake recever s based on the combnaton of the dfferent mult-path components n order to mprove the qualty of the decson on the symbol. Each mult-path sgnal s processed by a fnger whch correlates the receved sgnal by a spreadng code algned wth the delay τ of the mult-path sgnal. The mult-path components can be consdered as uncorrelated when the delay exceeds a chp perod. Demodulaton results of a weghted decson at the correlator outputs. Usng the maxmum lkelhood crtera the symbol s estmated from the y(k) sgnal N p N p y(k) = y (k) = α (k)r (k) () = = 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 symbol decoder module s presented n Fgure. The complex ampltude α of the th path s estmated wth the help of the known plot sequence located n the control frame (DPCCH). Thanks to the complex multplcaton of the receved sgnal by the conjugate of the Kasam code the unscramblng operaton s performed. Then, the despreadng operaton from OV code transforms the wde band receved 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 delay τ of the th path 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. 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 the determnaton of the data nteger word-length. Ths step requres to determne each data dynamc range. 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 de-spreadng 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 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 de-spreadng/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 the 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 of both real and magnary parts one. Because a gaussan nose σn n has 99.7% of ts values n the nterval [ 3σ nn,3σ nn ], assumng the real and magnary parts of s n (n) are n the nterval [,], the nput s consdered n the nterval [ 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 (5) The dynamc range of α correspondng to the output of the channel estmaton module s equal to max( α ) = + 3σ nn () The dynamc range of s out correspondng to the output of the channel estmaton module s equal to max( s out ) = ( + 3σ nn ) (7) 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 evolutons of the dynamc range accordng to the SNR are dentcal for analytcal and 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. In both smulaton and estmaton, for the accumulaton output, 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 nteger part of the data accordng to the SNR at the recever nput. Range (log) 8 acc (analytcal) acc (smulaton) output sgnal acc (smulaton) acc (analytcal) Sout (analytcal) 5 5 5 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 (BER) so that the use of fnte precson does not modfy the reference nfnte precson BER (BER ) more than ε. Suppose that the power of quantzaton nose e q s P e, the performance crteron can be wrtten as: BER P e ( + ε)ber (8).. Accuracy constrant 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 ẽ 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 ) (9) 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. Constrant determnaton In ths part, the expresson of the bt error rate BER(P e ) accordng to the output quantzaton nose power P e s presented. Ths expresson allows determnng the maxmum quantzaton nose power satsfyng (8). Frst 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): where f q (x) = σ q π exp x σ q () σq K = σe () = In a WCDMA recever, the thermal nose and multple-access nterference can be modeled as a gaussan nose source f the transmsson channel s 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, bterror rate can be calculated as follow: BER(σ q,σ nout ) = F n () = erfc σn out + σq = Q () σn out + σq From (8) and (), the condton for σ q s: σq ) (( erfc + ε)erfc σn σ nout out ( )) = Q (( + ε)q σn σ out (5) nout Secondly, the case wth a domnant quantzaton nose has been consdered (β = ). In ths case, the nose dstrbuton s unform and ts probablty densty functon f q (x) s then as follows: f q (x) = q Id [ q, q ] () Thus the global nose has the followng probablty densty functon: 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

Power (db) 3 35 5 5 Psout Pnout (gaussan) (unform)..3 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 accordng to the SNR. Between, db and db the word-length of the varables acc and s out are ncreased of respectvely 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. 55 E b /N (db) 3 5 7 9 3 5 7 9 acc 5 7 7 7 7 9 9 9 s out 7 7 7 8 9 9 9 9 9 5 3 5 7 8 9 b Table : Optmzed word-lengths of the rake recever obtaned for dfferent SNR values Fgure : Sgnal and nose power levels accordng to the SNR and the followng probablty dstrbuton functon: x F n (x) = q (erf t + q erf t q ) (9) N N In case of BPSK, the probablty of bt error s: BER(σ q,σ nout ) = F n () () By the smlar way, the precson can be deduced from Equaton 8 and Equaton. Snce there s no smple mathematcal expresson, the crteron s solved numercally. The accuracy constrant has been determned for dfferent SNR values. The results are presented n Fgure. The lne P sout and P nout correspond to the level (power) respectvely of the desred sgnal s out (symbol) and the recever nose n out at the system output. The dfference between the lnes P sout and P nout corresponds to the output sgnal-to-nose rato (SNR). The dfference between the lnes P sout and corresponds to the output sgnal-to-quantzaton nose rato (SQNR). The results show that to decrease the BER when the SNR ncreases, the SQNR must be ncreased. More accuracy s requred to reduce the decson errors due to fnte precson arthmetc... 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 σ q : P e = K σe () 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 (LSB weght) obtaned after quantzaton σ e = q () 5. PATH SEACHER In ths secton the results obtaned for the path searcher are presented. 5. Range estmaton The approach used for the rake-recever to estmate the dynamc range s used for the path searcher descrbed n Fgure. The nput data RX s normalzed nto [,]. It s then multpled wth complex conjugate of spreadng code C ch CG and results n the nterval [, ] for each real and magnary part. For the accumulaton along wth L symbols (L: OV code length) only the sgnal s summed up sgnfcantly. Thus, the dynamc range s equal to max( x acc ) = L + 3σ (3) 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. 5. Precson evaluaton The path searcher module can not use crtera presented n.. Ths module s based on the decson theory and classcal crtera are used to analyze the performances. 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 measured. To analyze the path searcher performances, 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 modelzaton 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 approach s used to measure the FA and MD values.

8 accumulaton E b /N (db) 3 5 7 9 3 5 7 9 x CM 8 8 8 8 8 8 8 8 9 9 9 x acc 3 3 3 3 x pow 7 7 7 8 9 9 Range (log) Table : Optmzed word-lengths of the searcher obtaned for dfferent SNR values 8 crx accumulaton power profle power est. acc est. power 5 5 5 b (BER), the analytcal expresson of the accuracy constrant accordng to the BER has been proposed. The results show that the fxedpont specfcaton depends on the nput SNR. An approach n whch the fxed-pont 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. Fgure 5: Estmated and smulaton based values of range for the path searcher. The evoluton of the false-alarm accordng to the SNR are presented n Fgure for dfferent levels of output quantzaton nose. The false-alarms are more senstve than the ms-detectons to the quantzaton nose. For the same level of quantzaton nose, the mean number of ms-detected paths does not evolve and s very closed to the case of nfnte precson. Thus, the accuracy constrant s determned from the false alarm crtera and then the data word-lengths are optmzed. The results are presented n Table. Lke for the rake recever, the word-lengths depend on the SNR values..8.7..5..3.. False alarms = 7 db = 75 db = 8 db = 85 db = 9 db 8 8 Fgure : Mean number of non-vald detected paths (false alarm) obtaned for dfferent SNR values. CONCLUSION For the desgn of embedded wreless systems, the optmzaton arthmetc aspects s one of the way 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 REFERENCES [] B. Evans. Modem Desgn, Implementaton, and Testng Usng NI s LabVIEW. In Natonal Instrument Academc Day, Berut, Lebanon, June 5. [] J. Eyre and J. Ber. The evoluton of DSP processors. IEEE Sgnal Processng Magazne, 7():3 5, March. [3] K. Han, I. Eo, K. Km, and H. Cho. Numercal word-length optmzaton for CDMA demodulator. In Crcuts and Systems,. ISCAS. The IEEE Internatonal Symposum on, volume,. [] N. Herve, D. Menard, and O. Senteys. Data wordlength optmzaton for FPGA synthess. Sgnal Processng Systems Desgn and Implementaton, 5. IEEE Workshop on, pages 3 8, 5. [5] H. Holma and A. Toskala. WCDMA for UMTS: Rado Access for Thrd Generaton Moble Communcatons. Wley,. [] 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 Transactons on Crcuts and Systems I: Regular Papers,, 55(), November 8. [8] D. Menard, R. Rocher, O. Senteys, and O. Serzel. Accuracy Constrant Determnaton n Fxed-Pont System Desgn. EURASIP Journal on Embedded Systems, Accepted for publcaton n 8. [9] M. Pursley. Performance Evaluaton for Phase-Coded Spread- Spectrum Multple-Access Communcaton Part I: System Analyss. Communcatons, IEEE Transactons on [legacy, pre-988], 5(8):795 799, 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 n Proc. of 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] H. Zhao, T. Ottosson, E. Strom, and A. Kdyarova- Shevchenko. Performance analyss of a fxed-pont successve nterference canceller for wcdma. Vehcular Technology Conference,. VTC-Fall. IEEE th, 3:99 93 Vol. 3, Sept..