THE IMPACT OF A WIDEBAND CHANNEL ON UWB SYSTEM DESIGN

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1 THE IMPACT OF A WIDEBAND CHANNE ON UWB SYSTEM DESIGN Mke S.W. Chen and Robert W. Brodersen Berkeley Wreless Research Center Berkeley, CA ABSTRACT The goal of ths work s to nvestgate the nqe system mplementaton sses assocated wth an ltra-wdeband channel. The paper begns wth channel models and from the characterstcs of these models, the cost of dong coherent detecton, ncldng channel estmaton and maxmm rato combnng, s analyzed and smlated. The reslts show that sng a sgnal bandwdth rangng over 5MHz to GHz has better system performance than sng the entre avalable 7 GHz bandwdth. It s also shown that matched flterng n UWB plays a more crtcal role than n a narrowband system. Fnally, the mpact of mperfect matched flterng s analyzed and smlated. I. INTRODUCTION Commncaton system desgn s strongly ted to the characterstcs of the wreless channel. Wthot good knowledge of the channel model, t s dffclt to come p wth relable system specfcatons and archtectres. In narrowband systems, the sgnal bandwdth s mch smaller than the carrer freqency. Therefore, central lmt theorem can be appled to channel modelng, where Ralegh and Rcan dstrbtons are the most commonly sed models [][]. However, as sgnal bandwdth scales p, assmptons that are made for narrowband system begn to break down. In secton II, we brefly revst mportant channel characterstcs, sch as freqency dependency and coherence tme, and dscss ther potental nflence on UWB system desgn. Some statstcal models reported n the lteratre are also smmarzed. In secton III, we apply these wdeband channel models to a coherent recever archtectre, whch can nherently take fll advantage of a wdeband sgnal. The performance of dong coherent detecton, manly channel estmaton and maxmm rato combnng, s analyzed. The analyzed recever archtectre makes se of a matched flter and near east Sqare Estmator (SE for lower system complexty, and performs hard decson at the end for BER analyss. Important system desgn parameters, sch as optmal sgnal bandwdth and energy captrng perod are explored throgh smlatons and analytcal eqatons. The work extends from the analytcal approach n [3], where a smple nform dstrbted channel model was assmed. Fnally, de to the freqency dependency of the wreless channel as well as estmaton error, a dscrepancy between ncomng sgnal waveform and matched flter response exsts, and degrades the total system performance. For nstance, the scattered waveform can vary de to dfferent geometry and type of objects [4][5]. The mpacts from these channel ncertantes are analyzed and smlated n secton IV. II. UWB CHANNE MODEING UWB s allowed to transmt between 3.GHz to.6ghz for ndoor commncaton systems [6]. The relatonshp between transmtted waveform,, and receved waveform, y(t, can be expressed as a fncton of channel gan, a (f,t and arrval tme (f,t of th mltpath: y( t a ( f, t φ ( t τ ( f, t ( Assmng the system s bandlmted to W, the above contnos tme relatonshp can be represented as a dscretetme verson sng the samplng theorem [7]. y[ m] m k k, m] k, mx ] [ m k] a ( f, m/ W e jπf cτ ( f, m/ W snc( k Wτ ( f, m/ W Next, some nsghts based on these eqatons are provded. Freqency dependency: In narrowband system, the data bandwdth, W, s assmed mch smaller than carrer freqency, f c. Therefore, the analyss n narrowband system assmes channel gan and delay, a (t and (t, are freqency ndependent wthn the bandwdth of nterest. Ths allows s to treat the receved sgnal as the smmatons of delayed and scaled versons of transmtted sgnals, whch s also known as the mltpath model. Bascally, the receved sgnal shape does not change over wreless channel. The recever can ths se an expected waveform as the matched flter response. ( of 6

2 However, the UWB sgnal bandwdth s so wde that the freqency dependency on tap gan and delay cannot be gnored. In other words, the receved sgnal waveform gets dstorted by the commncaton channels, sch as antenna pattern, propagaton throgh freqency selectve objects, crct mparments, etc. Ths phenomenon nspres s to do a frther analyss on ths plse shape ncertanty, whch s addressed n the later secton. Coherence tme: There are several reasons for the tme varaton of channel response. The frst one s Doppler spread, whch s the relatve dfference of Doppler shfts of every mltpath contrbtng to a certan dscrete channel tap. Doppler shft of the th mltpath can be expressed as f c, and s essentally the phase rotaton ntrodced by the carrer snsod as shown n Eq. (. Snce a plse-based UWB rado performs carrerless commncaton, there s no Doppler shft assocated wth the carrer. Path Path coherence tme nder m/sec scenaro s on the order of s of mllseconds to second, whch allows ample tme for channel estmaton. Another mportant factor casng tme varaton s the movement of mltpaths between dscrete channel taps, whch can be descrbed as, shown n Eq. (. The bandwdth n narrowband systems s mch smaller than the center freqency so that the movement of mltpaths s neglgble compared to Doppler spread. However, n UWB, the bandwdth s comparable to center freqency. Ths, the tme scale of mltpath movement s of the same order of magntde as the Doppler shft,.e. s of mllseconds to second n an ndoor envronment. The tme varaton of channel gan, a (f, t, depends on the free space attenaton. Assmng recever and transmtter move locally compared to the dstance between the two, the channel gan vares slowly compared to the prevos ones. From smple calclatons, the coherence tme s comparable to that of narrowband systems wth GHz center freqency. Note that the freqency dependence of the channel gan and delay can also be tme varyng. For example, f a freqency selectve object moves wthn the channel, t wll case a tme-varyng plse shape. In ndoor envronment, ths effect shold be neglgble. Fgre. Mltpaths arrve from all drectons.5 Delta K model Shown n Fgre, we assme all the mltpaths nformly come from all drectons. The channel response of one partclar tap s the smmaton of all the mltpaths that propagate abot the same dstance, d. Assmng the moble moves at speed, v, the channel response can be expressed as, d v A ( t cosθ t (3 c c As mentoned earler, there s no phase constrcton or destrcton for a carrerless UWB system. However, there s stll Doppler effect on the plse waveform, whch s a v freqency drft of ( cosθ. Gven an ndoor envronment wth m/sec movement, freqency drft effect s c neglgble de to the small rato to speed of lght, c. Therefore, we conclde that a carrerless UWB system does not sffer from Doppler spread. Even for a carrer-based UWB, sch as mlt-band OFDM approach, there s stll less Doppler spread compared to a narrowband system de to fewer mltpaths contrbtng to one channel tap. The x -8 Fgre One Realzaton of model ognormal x -8 Fgre 3 One Realzaton of ognormal Model of 6

3 Statstcal model: Several statstcal models are proposed n the IEEE 8.5 stdy grop. Becase UWB occpes a wder bandwdth, the nmber of mltpaths contrbtng to one channel tap s less than n narrowband systems. ess averagng effects mply Raylegh model s no longer stable. Dfferent partes have proposed ndvdal model that ft ther own measrement and are smmarzed as follows: ( Saleh-Valenzela Model (S-V: S-V model does not assme mltpaths arrve on each samplng tme. Two Posson processes are sed to descrbe the channel. The frst one s for the frst path of each path clster and the second one s for the paths wthn each clster. Tap magntde s Raylegh dstrbted [8]. ( -K model: Ths s proposed n [9]. A path arrves wthn tme draton accordng to a certan probablty. The tap magntde s lognormal dstrbted. It smlates dfferent envronment by changng dfferent parameters, as shown n []. (3 Nakagam model: Nakagam dstrbton s sally sed when the central lmt theorem does not hold []. (4 ognormal model: ognormal model assmes Raylegh dstrbton wth exponentally decayng power gan. Ths model s sed to verfy the analytcal analyss gven n ths paper. III. ANAYSIS AND SIMUATIONS OF COHERENT RECEIVER In order to explot the dversty gans from the large bandwdth n UWB, we need a coherent recever,.e. Rake combnng, at the cost of more complexty. In the followng sectons, we wll analyze the performance of coherent detecton n order to determne optmal sgnal bandwdth, as well as the nmber of mltpaths recever shold collect n the Rake combnng scheme. The tme perod whch recever captres mltpaths s referred as collecton tme n the followng sectons. UWB has a maxmm avalable bandwdth of 7.5 GHz. An mportant system specfcaton s that how mch bandwdth one shold se for optmal performance. Althogh wder transmsson bandwdth mples more dversty, the estmaton error wold ncrease f one fxed the total transmsson power. On the other hand, f the transmsson power ncreases n proporton wth the bandwdth, then t s not srprsng that the performance s always better by scalng p bandwdth, becase the estmaton error remans the same we dversty gan enhances the performance. From crct mplementaton perspectve, a low-power and low-cost UWB rado that adopts an ntegrated CMOS solton [] s however lmted by the maxmm otpt voltage. As a conseqence, the otpt power cannot be scaled p arbtrarly wth the bandwdth. Gven a powerconstraned system mplementaton, we fxed the total transmsson power for the followng analyss. A near east Sqare Error (SE estmator was sed for channel estmaton. Althogh SE estmator s not as optmal as MMSE, t does smplfy the hardware mplementaton. Pls, t s a robst estmator for any stochastc process to be estmated. Therefore, we choose SE n ths project, bt may stll explore the best estmator for UWB channel estmaton n the ftre. For the maxmm rato combnng scheme, SE estmaton reslt s sed as flter response, we a hard decson s made for error rate analyss. Channel estmaton: In the case of resolvable paths, we express the receved sgnal n vector form. y ] + w The receved vector,, s assmed orthogonal over dfferent resolvable path. As the bandwdth scales p, the nmber of resolvable paths shold ncrease. Note that UWB plse, bandlmted to W, has a certan shape and draton and may not meet the Nyqst crtera. Therefore, there cold be an ISI problem between samples spaced by /W. The followng analyss and smlaton assmes the plse energy s mostly confned wthn /W perod or a clean algorthm s adopted to mantan orthogonalty over dfferent channel taps. Before we perform SE estmaton, the ncomng sgnal s processed by a matched flter n order to project the sgnal nformaton onto the correct dmenson. In ths secton, we assme the recever perfectly knows the ncomng sgnal shape. In the next secton, we wll consder an mperfect matched flter, whch cases extra estmaton error. By mappng receved sgnal, y, onto sgnal dmenson,, we get sffcent statstcs, r ( (t, at path 3 of 6

4 r ( l y Next, extra processng gan s provded by averagng r ( K tmes, and the estmated channel response and the estmaton error for tap erved: combner. The channel models we sed were -K model and lognormal model. All the smlatons were compared to prevos error probablty analyss assmng random varable X s Gassan dstrbted. The channel we sed n the smlaton assmes a mean excess delay of 3 ns, and maxmm collecton tme of 5 ns. hˆ l σ ( No K + e No E( No + K k where ε s the sgnal energy; and No s the channel nose densty. r.4..8 BER.6.4. SE + CT ognormal Rake combnng: The error event of the Rake combnng sng the estmated channel response s when the recever detects zero we transmtter sends one, and vce versa. The error probablty can be expressed as, Pe P( V> V P( h ˆ[ ]( W W ] ε > P( X > where V, V (W, W s the detecton energy (nose energy wth and wthot sgnal exstence The smmaton of polynomal fnctons of tap coeffcents s not easy to compte. So, we treat the whole smmaton as a random varable X. By comptng the frst and second moment of X, one can gan some nsghts abot the error probablty fncton. The mean and varance of X s as follows, E( X ε E( No + ε E( NoK ( + NoNo VarX ( ( ( E( ε ( + No l ε E( + Smlatons: The followng smlaton reslts are based on a receved SNR of db. The nmber of extra averagng cycles, K, s. The hgh receved SNR s assmng there s processng gan already provded n order to redce the smlaton tme. The smaller the ncomng SNR, the more processng gan one shold provde to the channel estmator and Rake BW (GHz Fgre 4. BER vs. Bandwdth BER vs. bandwdth scalng As we ncreased the bandwdth from 5 MHz to 8 GHz, the resolvable paths also ncreased from 5 to 4 paths gven the delay spread of 5 ns. Snce the total transmsson power s crrently fxed, the smmaton of all tap power s always constant. In other words, the more paths n the system the less energy resdes n each path. Shown n Fgre 4, the BER goes p wth bandwdth after abot GHz, where the estmaton error overwhelms the dversty gan. Note that the analytcal eqatons wth CT assmptons (X s Gassan dstrbton match closely wth the smlaton reslts for lognormal model. The performance of -K model s mch worse, becase mltpaths do not exst for every dscrete tap. However, all channel models show that sng bandwdth more than GHz wold ncrease the error rate. BER vs. collecton tme The above example s smlated by collectng all mltpaths wthn 5 ns. Snce the power delay profle s assmed to be exponentally decayng, there s no beneft to collectng more than needed. The sgnal collected n the tal reslts n more estmaton error than sgnal energy. Therefore, we vary the collecton tme at dfferent freqences, shown n Fgre 5 and 6. The performance does not mprove mch after collectng ns for 8 GHz case, we ns s sffcent for 5 MHz BW. 4 of 6

5 BER BER vs. Rakng BW5MHz SE + CT ognormal # of Rakng Taps Fgre 5 BER vs. Collecton tme for 5 MHz sgnal BW p ( t s( t + w( t,where w ( t ~ N(, Wo / The otpt SNR of the matched flter s defned as the mean and varance rato at the otpt of the flter. The followng eqaton shows the relatonshp between otpt SNR wth these nondealtes, (t and w(t, and deal SNR assmng a perfect matched flter. SNR ot ( + Wo + + No SNR MF T s( t δ( t dt + T E b δ ( t dt E b + T s( t δ( t dt E b SNR deal BER vs. Rakng BW8GHz SE + CT ognormal The eqaton provdes nsghts of how mch SNR degradaton wold be cased by (t and w(t..35 BER # of Rakng Taps Fgre 6 BER vs. Collecton tme for 8 GHz sgnal BW IV. IMPACT OF DISTORTED MATCHED FITER As we descrbed n the channel characterstcs secton, there s more sgnfcant dstorton de to the wdeband channel snce the recever cannot perfectly match to the ncomng sgnal. In ths secton, we model the flter and analyze the performance degradaton. Modelng matched flter: The receved sgnal, y(t, s the combnaton of channel gan, h, and waveform dstorton, (t, pls whte Gassan nose, n(t, cased by ambent, crct or qantzaton nose. y ( t h ( s( t + δ ( t + n( t, where n ( t ~ N(, No / Meanwe, the matched flter response, p(t, matches to the orgnal expected waveform, s(t, pls whte Gassan nose, w(t, de to qantzaton error f a dgtal matched flter s adopted. Imperfect matched flter mpact on channel estmaton: We ncorporate the matched flter nondealty, (t, nto SE estmaton as follows, y r ] ( + δ + w y ] ε + ( w δ + ] Gven the fact that sgnal energy always gets attenated after channel propagaton, we have the followng neqalty, δ + δ < <,where δ The new estmaton error has been added by an extra term de to dstorted matched flter response: e e, org e, extra σ σ + σ,where σ e, extra E( ( No No + + We calclate the lower bond of the extra error. It s not nttve from the above eqaton. Therefore, we plot the orgnal (gray and extra (black estmaton error at each channel tap and compared wth two dfferent averagng cycles of dong SE channel estmaton, as shown n Fgre 7 and 8. 5 of 6

6 Fgre org extra for average cycles org extra for average cycles From the above reslts, the extra estmaton error de to dstorted matched flter gradally domnates the estmaton error as we try to get more accrate channel estmaton by performng more averagng cycles. Inttvely thnkng, ths s becase coherent detecton s based on the otcomes of the matched flter. If there s any nondealty n the matched flter, more averagng wll case error accmlaton, whch n trn degrades system performance. V. CONCUSION For a power-constraned system, t appears that sng 5 MHz to GHz sgnal bandwdth s adeqate for coherent detecton, and the optmal collecton tme shold be a fncton of mean excess delay. There s no beneft to collectng all the mltpaths, becase the power delay profle s sally exponentally decayng. The mpact of the matched flter nondealty has been analyzed and smlated. The reslts show that ths nondealty s a potental dffclty of mplementng a coherent UWB system. VI. ACKNOWEDGMENT The athors wold lke to thank Prof. Tse (UC Berkeley for valable dscssons. The project was spported by Army Research Offce, North Carolna(Award No. 6586, and ndstral members of the Berkeley Wreless Research Center. VII. REFERENCES [] T. Rappaport, S. Sedel, and K. Takamzawa, Statstcal channel mplse response models for factory an open plan bldng rado commncaton system desgn, IEEE Trans. Commn., Vol. 39, May 99, pp [] G. Trn, W. Jewell, and T. Johnston, Smlaton of rban vehcle-montorng systems, IEEE Trans. Vehclar Tech., Vol., No., Feb. 97, pp [3] E. Telatar, and D. Tse, Capacty and Mtal Informaton of Wdeband Mltpath Fadng Channels, IEEE Trans. Info. Theory, Vol. 46, Jl., pp [4] R. Q, A Stdy of the Ultra-Wdeband Wreless Propagaton Channel and Optmm UWB Recever Desgn, IEEE JSAC, Vol., No. 9, Dec., pp [5] Y. Zhang, M. Geyer, and E. Sptzer, Tme-Doman Waveform Development Drng Propagaton and Scatterng, Mcrowave and Optcal Technology etters, Vol. 6, No. 4, Ag., pp [6] FCC, Frst Report and Order, FCC -48, Feb. 4,. [7] D. Tse, EE9S Class Notes, UC Berkeley, Fall. [8] A. Saleh and R. Valenzela, A Statstcal Model for Indoor Mltpath Propagaton, IEEE JSAC, Vol. SAC-5, No., Feb. 987, pp [9] H. Szk, A Statstcal Model for Urban Rado Propagaton, IEEE Transactons on Commncatons, pp , Jly 977. [] H. Hashem, Implse Response Modelng of Indoor Rado Propagaton Channels, IEEE JSAC, Vol., No. 7, Sept. 993 pp [] A. Molsch, M. Wn, and D. Cassol, The Ultra- Wde Bandwdth Indoor Channel: from Statstcal Model to Smlatons, IEEE P8.5-/84-SG3a and IEEE P8.5-/85-SG3a. [] I. O Donnell, M. Chen, S. Wang and R. Brodersen, An Integrated, ow Power, Ultra-wdeband Transcever Archtectre for ow-rate, Indoor Wreless Systems, IEEE CAS, Workshop on Wreless Comm. and Networkng, Sep.. 6 of 6