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Filter Bank Based Transceiver Design for Ultrawideband

Itra Widebandlowed by intermediate speed analog-to-digital converterssample each subbandat Nyquist rate This architecture presents two important adtit allows a flexible de-desired performance; andg the underlying theory of time-frequency signal representationsperformance in terms of mean squarerateUWB receivers is their capabilioviderate time of arrival estimates, and thus accurate ranging and localization We address thispect by first analyzing synchronization schemes for Uwthen presenting a time ofal algorithm in the frequency domain, suitable for the filter bankbsequently, we describe algorithms for ranging and localization based on time of arrivald whichsignal detection and timefiers (LNAsprovide lowpass signalsADC stagebandpass filters are used, which have very good timeThe digital section is implemented with a hybrid architecture consisting ofprogrammable logic device(PLD) to handle the high aggrete, and a dgnal processor(SP)to implement signal processing algorithms in a flexible and easily re-als and channelulse radio technology, the transmitted signal consists of a series of low energbandwidth pulses p(t), with a duration in the order of hundreds of picoseconds Transmittedrum Ptral density(PSD)constraints set by regulatory bodies(Generic Harmonized European StandardRegarding Ultra-Wideband Transmission Systems, 2002) Seveeach trann symbol in order to achieve the necessary energy per bit

At the transmitter, bits aregrouped in data symbols and transmitted at symbol rate RTe whervals In turn, each frame interval is divided in N equally spacedalchip intervals In each frame intervis located in one of the Ne chip intervals In case that Pulse Position Modulation of orderM(M-PPMfurther diulation intervals of lengthpulse position and polarity, respectively, in each frame interval, with the purpose of satisfying the PSD mask A general expression for a waveform carrying a block of N, consecutivemodulation intervals within the chip interval, it may takend mand subsequently divided in frame and chip intervals, as in the IEEE 802 15 4a Standarcntechopen

Filter bank transceiver design for ultra widebandthe rake receiIn bothgeneralized class ofn signal projectionThe complexity of eacher is determined by the following factorsSize of the basis which is determines the number ofSampling frequency at each ADCch aDcRequirement that sampling clock is synchronized with received signalThis interpretation is useful to compare SR and RAKEthe table, N stands for the number of samples captured in each modulation intervalRecenBasis functiRAKE-M Bnp(t-r)l>1(=)e2m≥MB|≥B/MTable 2 Comparison of UwB Receivers as Generalized Filter BanksWe now compare the performance of the filter banker with the other recedscribed In terms of performance, one may look at the reconstruction MSE or the BER, whichare related by(29), Regarding the Ber, the ieee channel model type 3 is used, boundingchronized to the leading edge of the received signal The receiver settings used in theations are summarized in Table 3, which also reports the mean square error for each re-er it can be seen that a filter bankchieves the lowest mse if 4 or mewith 1Table 3 is shown in Fig

8 As it can be seen, the BER of the filter bank receiver approachesthe matched filter bound as the number of filters increases, and is lower than for the otherM>4 In the simulatiideal basis function with square pulses was usedfilter to have unlimited banif the basis functions do not form an orthogonal basis, further receiverO)show, however, that the perfoa filter banker using implementable Gaussian filters is4Estimatind localizationThe wide bandwidth used by UWB radio systems provides two fundamental advantages forlocalization applications, especially in short-range wireless networks On the one hand, diverity in frequencygnal powerpenetrate and go through obstacles This allows applications such as through-the-wntechopen

Itra WidebandNo, of ADc120 MHZFilter Bank mFilter bank me4591200Table 3 receiver settings fulationFig 8

Averaged BER curves in channel type 3 for the Filter Bank Receiver, SR receiver, andRAKE Receiver The matched filter bdue to the dispersive properties of different materials On the other hand,the theoreticalce achievable by an unbiased estimator)of time-delayestimator is inversely proportional to the rms bandwidth, also known as Gabor bandwidth,defined as:f2 P()IdfBRPdthere pthe Fourier transform of the pulsthe rms bandwidth using modulations whose power spectrumconcentrates a greater percentagearge RMS bantion of the pulses (less than one nanosecondentsimplies that the fundamental lower limit of thean IR-UWB timing estimator is dramatically small, and hence this explains the potentiality ofntechopen

Filter bank transceiver design for ultra widebandpurposese with sampling rates ae Nyquist rate, and thus the Cramer-Raodeed one of the most attractive featureUWBtential to alrate positioning Due to their large signal bandwidth, UWB signals exhibvery high time resolution This high time resolution allows receivers to resolve individualnodes the receiver needs to identify the first arriving path, which is associated to LOS prop-agation In a multipath scenario, the direct path may be masked in a multipath cluster, unual paths within that cluster

Therefore, time-basedystems This section addresses the estimation of timing measurements and their applicationtion for very broadband signal systems and continue withof the state-of-the-art onTOA estipecial attention is placed to the the filter bank receiver in order to derive suitable algorithmsfor TOA estimation of the LOS signal, emphasizing some of the main drawbacks linked to thereceiver architecture, and arguing for a frequency domain processing for the estimation of theTOA, particularly suitable for the filter-bank receiver, as shown in(Navarro Najar, 2007)The filter-bank architecture of the receiver falls very natuut represents the DFT components of theell-known higon spectral estimation methods can be applied directly to the fre-quency domain signal samples achieving very accurate timing estimation Finally, the sectionpositioning byparticular approach based on data fusion algorithmThis technique is partice for developing global posittical in uwBation systems, given that small timing errornformation at several levels: carrierHofulse radio uwb, based on ppm modulationtiming synchronizatThe synchronization technique to bereceiver architecture andonlthe position information by collecting the energy of the pulses Most of the research worn Ir-UWB implementation focuses on a non-coherent receiver because it has the advantageevertheless, we shall review the coherent techniques suitable for PPM modulated IR-UWBgnals to provide a benchmark for lower complexity techniques The basis carntechopen

Itra Widebandthe matched filter solutions, see(Oh Kim, 2008; Oh et al, 2009; Wu et al 2008), and( Kimet al, 2009) As introduced earlier, the advantages of coherent reception include:First, the coherent reception is important for frame acquisition and rangingte compared with a non-coherentwhicho accurate rangingdecoding can be performed during the header and payload intervals2002), proposing a CLEAN (see(Hogbom, 1974))basedre correlation algorithm; whilendeed be achieved, the iterative amplitude estimating and adjustingakes theutationally burdensome (Wu et al, 2007)optimizedude adjusting, which greatly reduced the computation complexity withresearchersconsidered detecting the direct path directly from the match-filtering outthe receivedgnal

In the work by(Chung Ha, 2003), the peak of match-filtering outas the location of the direct path, but this is onlbeing omnidirectional threshonducted in(Low005)anddifficulties for a practicalsed on phase-locked loops(PLLs) and baseband codetracking delay-locked loops(DLLs) However, because of the extremely low duty cycle and986)challenge motivates us to draw ofnventional PLL, delay locked loop, and code tracking loop theories to design appropriateequivalent timing locked loop for tracking of ultra-short IR-UWB impulsesSynchronization in UwB Systems with Dirty Templates(TDT) approach applied to PPM was presented in (Yang2006) The derivationgrate-and-dump operationfor PPM signalsI(t: T)P2k(t; T)dt VT EO,Ts)1)wherend a=b,TA is the PPM modulation index in (1) To see how (31)enables TDT,nsider its noise-free pawhere p(t; T)and p(t; T)represent the noise-free parts of r(t; T) and r(t; T), respectivelPr(t) hasro support upper bounded by the symbolduration t, we havet: T)=Ppk{t-△;τCntechopen

Filter bank transceiver design for ultra widebandand kkr Using (34), Appendix I of(Yang, 2006)shows that, when the PPM modulation indexatisfies A Tf, the noise-free part of x(k; T)in(31)simplifies to52kEA(t0)+(52k-52k+1)EB(towhere we have used the definitionsEA(to)=E/,P7()E首Non-data-aided TDTaveraging with respect to the random symbols Isk, the mean-square of x(k; T)isE。{x2(kER-3EA(to)EB(tosy product EA(to) EB(to))anis, at the cornIn(39), ER=EA(To)+EB(to)=Ef P?(t)dt is the constantergy of theaggregate template at the receiverthe bandpass-filtered zmbok-rateained by integrating and dumping the products of adjacent dirtytemplates"becomhere the noise term s(k; T) can be expressed as53(k;T)term S(k; T) can be well approximated as white Gaussian noise with zero mean and variance2≈2ERNBTsNO

Then, the mean square of the sampk: r) can be found asEsg{x2(k;)}=E2{x2(k;r}+Ex{2(k;r)}(E最-3E(6)E()+23)ntechopen

Itra Widebandhich is uniquely maximized when t =0, that is, when T To

Then, the non-data-aidedTDTwith its saestimator we have the fo(n-data-aided) unbiased and consistent estimator in the mesquare sense, as can be seen from the mean andof the cost functiok(; T)F2k-1(f; t)dt(49)2(E-3EA(0)E(60)+27)下(-3EE+)+(E最-3)It is worth emphasizing that the basic idea behind our TDT estimator is that EA(to)EB(to)isconstantd thus do not affect the peak-picking operationfinding toData-aided TDTand 2)when to =0, then x(k; t) only contributes noise if s2kdid thenould be designed such thatymbols are theHence, the trainingsequence for data-aided TDT is designed to comprise a repeated pattern(1, 0); that isIt can be easily verified that this pattern simplifies (40)Then, itsbecomesntechopen

Filter bank transceiver design for ultra widebandNotice that the estimator(48)relies on three major steps: correlation, aThe training sequence in(48)allows us to swap the order of these steps and alleviate the noiseffects Specifically, in the data-aided mode, it fIn other words, by taking the squared-mean instead of mean-square, theterm(55)is eliminated This observation leads us tolowing result of a timing algorithmtailored for our carefully designed training sequence一嗎(The mean and variance of this cost functi(K; T)=Ek-4EAto)EB(to)ER-4EA(to)EB(to)OnTOA as a particularSynchronization is seen as the timing information required formodulation while tois linked to identify the first arriving path, but in essence both require similar techni 2003)but has strong practical limitations due to the requirement of very high sampling rates andcomplexity Although different Ml approaches have

appeared in the literature that manage tomplexity considerably Lopez-Salcedo vazquez(2005); Yang Giannakis(2005)exist practical limitations for then positioning applications Efforts have beensteered towards near optimum less complex solutions, most of them based on time deapproacheshe majority of practical solutions for TOA estimation found in the literature can be broadlyheblock diagram isd in Fig 9 for an scheme based on a correlator/matchrespectively

Energy based TOA estimators receivedattention as a viable alternative to correlationbased methods( Cheong et al 2005: RabbachinPot require expensive pulse-shape estimation algorithms and representlexity systems The estimation scheme proposed and analyzedRabbachin et al, 2005)is representative of a large class of energy based TOA estimation algo-the incesignal is squared and integratedtime intervalsof thealgorithm and is also strongly related to its latency These schemes also consider additionalprocessing to improve signal qualityerlapping adjacindows are collected over several symbol perioThe location of the direct path is computedfirst interval where the energyntechopen

Filter bank transceiver design for ultra widebandymbols can be written aschi19 isamplitude of the /-th symbol and bresulting transmitted signal is shown in Figsequence ( b1TH Code sequence 10, 1, 1, 0) DS Code sequence(1, -1,1,-11order to fully understand the design principles of IR-UWB receiveunderstand the channel propagationthe transmitted signal In order to developties and established a modification of the traditional Saleh-valenzuela model (saleh valerzuela, 1987)as a statistical channel model for UwB According to this model, signal pathsastersining several rays with different gains(B,and rater index and path index inside each cluster respectively Theresulting baseband channel model is given byhe uwB channel has been characterized in iEEE 802 15 4a(Molisch et al 2004), where seral types of channels are described

Among other environments, channel types 3 and 4 modelindoor environment in line of sight (LOS)and non-line of sight (NLOS)configurations re-pectively The main challenge in UwB propagation stems from the fact that theutive in time since the transmitted pulse is very short, paths separatedsavable by the receiver, resulting in hundreds of paths forical propagation environments According to values provided in(Molisch et al, 2004), Tablechannel models 3 and 4 The first parameter ranges from 22 to 45, while the latter can be uto 13 ns Therefore, channel dispersion is very challenging for the receiver, botand in terms of channeloids the differentiation of paths in clusters In this model each ray is representby its amplitude(Br)and delay Tr, where r is the path index Then, the baseband channeh(1)=∑F6(-v)ntechopen

Itra WidebandCunnel environnentAug no, pathsI Indoor(office)NLOSOutdoor lo29173Outdoor NLOSTable 1 Time Dispersion of IEEE 802154a Channel Modelsof additive white gausnoise(AWGN)"(t)with variance of the received signal is given by(4)lay of the channel, tmaxthan thed even longer than the symbol interval Ts, causer,to evaluate the capabilities of capturing the received signal energyn differentroaches it is assumed that Tmax TA Note that with this assumptionulation intervals In thh()Ts-btT

-hT3 Filter Bank Receiver ArchiteAs it can be inferred from thedesigning a good receiver for UwB in dispeof uwb receivers, as we will see, these redwhich provide very good performance in traditional narrowband transmission, presentfilter bank architecture, which consists in splitting the UwB signal in several subbands andist rate This architecture aims at maxinthe received signalergy while keepingsee that the presenteday be obtained through a generalized filter bank interpretation3 1 Overview of Ultra wideband Receiversfirst approach, referreference(SR) Receiverignal with a locally generated template stmp(t)andtegration time2 The signal template Stmp(f)is generated with theure usedtransmitter,that isntechopen

Filter bank transceiver design for ultra widebandrIrFig 2 Stored Reference Receiverwherethe transmittedwith unitits the symbolles taken in each modulation interval, which is given by Nsr= TAffset, which is intentionally modeled tont thehe captured energy, particularlchannels After the analog correlator, the signal is sampled by an ADC at rate Nsr/T, ands operating on decision variables zi and zi, containing all samplestaken at each respective modulation interval Finally,variable is obtained ashere the weights w correspond to a whitened matched filter for reception with GaussianAnotheron approach to receive spread spectrum signals in a multipath propagationevironment is the RAKE Receiver, shown in Fig 3 The RAKE receiver useslators that lock at different multipath replicas(Zhu et al

, 2008) The output oon of the delay, amplitude, phase and shape (distortion) of the pulses at each individualarrival When the number of fingers Nrkto the number of resolvable paths, thisver constitutes in fact the matched fiver In practice, given the large numberble UwB paths,你relevant impact on its complexityFig 3 RAKE Receivercally generated replicas of the efysis of the RAKE rsimilar to that of the srntechopen

Itra WidebandkT+Fig 4 Energy Detector ReceiverrItFis 5 Transmitted Reference Receivegnal template of the k-th finger is constructed in the same way as the transmitted signal and*()=EEP(+-ITS-cTHTe-hT-Tknd t represents the k-th propagation path with largest energyNrk ADC converters sampling at symbol rate while Srersampling factoRAKE approach In both cases the number of samples taken in a modulation interval iscritical parameterIn the following we discuss two non-coherent approaches, namely theTransmitted Reference ReceiverRAKE and SR approachesdetector(EDreceiver does not correlate the received signal with a local template Inend adds up the received energy in each modulation interval to create the decision variables

Fig, 4 shows the main blocks that constitute the ed receiveCIR) To this end, the transmittederates a referpulse for each transmittedpulse The two pulses are separated an interval that is longer than thefor signal detection The receiver functional block diagdepicted5 The signalis correlated by a delayed version of itself, integrated and then sampled at rate T For eachmodulation interval Nor samples are collected, where Nir= 7, and then processed32 Time-tThe coherent recdescribed in the previous sectionanalogcorrelate it with the re-Thisconstraints on these structures, suchmber of fingers of the RAKErrelation) in the digital domain, where more cortures can be addressed if enough computing power is availablevazquez et al, 2003)for example) requires sampling thentechopen

Filter bank transceiver design for ultra widebandignal at Nyquist rate, which can be very challenging for signals with up to 10 GHz bandwidth An alternativeis considered in this section, where sampling is performed inby a discrete set offundamentay to represent a broad range of possibilities riesion of signalsest That is, given a signal s()choosing a set of functions yk(r)and &k(t)such that the(10)while the original signal is reconstructed as5here(10)is known as the analysis equin(11)is knesynthesis equation If 8k(f)=n(f), then(11)is known as the orthogonal series expansionf s(f), Otherwise, the functions Yk(f)and &k(t)are a set of biorthogonal functions with theh case do(t)by(Gabor, 1946) Instead oignal into equally sized segments and then perform the Fourier transform of each segmThe result provides local information altent on each time interval tperform the two-dimensional sampling on s(f)the time axis is divided into N equally sizedtervals of length T, which represent the time-domain sampling period Each segment of s(fis labeled as sn()anwhere n indexes the number ofamplitude

Since sn()is a time-limited signal, its Fourier transform Sn(f) can be expressedas the sequence of discrete samp∑S(kB)hereB=I is the sampling interval in the frequency domain Fig 6 shows an exampof the two-dimensional sampling grid The product BT defines the density of samples takenfrom the time-freqenergy distribution of the signal Nyquist density, defined as thetime-frequency product BT=1set of samples required for perfectnot all the signal energy is capturedntechopen

Itra Widebandg 6 Example of 2-dimenote by Sn m the two-dimensional samples of s(f) Indexes n and m represent the timend frequency domain sampling, respectively

Denoting sn(t)as the periodic signal obtainedby the sampling of Sn ()it fe(14)Therefore, the two-dimensional samples can be expressed as a function of the time-doing the synthesis equation of the series expansion, the reconstruction of the signal s(f)isgiven by()=∑∑Snm7mAssuming thatcounted number of frequency domaintaken on each intervalide a perfect signal reconstruction Limiting the number ofsamples on each interval to a finite number M leads to the M-th order represwhich is defined as the truncated series expansion,figure of merit of the quality of signal acquisition can be given in terms of the MSE of thetruncated series representation, which is given by∑ntechopen

Filter bank transceiver design for ultra wideband團Fig 7 Block diagram of a Filter Bank ReceiverTherefore, having the a priori knowledge of the signal bandwidth one can define M to achieveFilter Bank ReceiverThe fundaidea behind the filter bank receiver is to provide an implementation that aws us to obtain a highly accurate time-frequency representation of the received UwB signPulse Position Modulation(Padulation is used The signal length conveying a block of Np bits is Tp=NpTs

The chanered lower than the modulation interval The noise is assumed to be awgn with variancef the filter bankdimensional sampling stage by splitting the input signal into M paths and correlating it witthe basis function(18)be carried out with ortheachadulation interval are arranged in a vector The captured samples can be expressed afrequency domain The collected samples feo-dimensional set of samples Using(6)and(19)it follows that, whena given interval,z()of the I-th symbol, and z( the vector for the time interval corresponding to b,=1Thestatistics of z()and z1()are givntechopen

Itra Widebandb=0(D)(22)rs are combined to make the decision variable Defining the combining weights as w2matched filter solution(Kay, 1998), which defines the weights as wI The statisticsing(24)it follows that the BER for the filter bank receiver is given bBEProvided thset of functions ?n, m()constitute an orthogonal basis, and assuming thatthe noise vector is awgn the noise covariance matrix becomesIo and the ber is6)Note that the product zp can be expressed, in terms of the MSE of the M-th order repre-where Ha(/) is the Fourier transform of hp(on ('pr)

Therefore, the BER of the filter bankreceiver may also be expressed in terms of the reconstruction MSEAt this point it is interesting to look back at the SR and raKe receivers as implementationsmpling the recenal after correlating with a locally generated template While the SR Receiver implementsntechopen