Journal of VLSI Signal Processing 43, 59–71, 2006

c© 2006 Springer Science + Business Media, LLC. Manufactured in The Netherlands.

DOI: 10.1007/s11265-006-7280-4

An Analog/Digital Baseband Processor Design of a UWB ChannelizedReceiver for Transmitted Reference Signals

LEI FENG AND WON NAMGOONGDepartment of Electrical Engineering, University of Southern California

e-mail: {leifeng; namgoong}@usc.edu

Abstract. The frequency channelized receiver enables the use of practical analog-to-digital converters (ADC)to digitize ultra-wideband (UWB) signals. The design issues of the analog and digital baseband processor forthe channelized receiver in a UWB transmitted reference (TR) system are investigated. In the analog part, thereceiver performance is shown to be weakly dependent on the analog filter bandwidth, the filter order, and the ADCoversampling ratio assuming white input noise. In the digital part, the coarse acquisition performance is shownto be significantly better in a channelized receiver than in a fullband receiver. The implementation issues for finesynchronization and correlation window length are also studied.

Keywords: Ultra-wideband, transmitted reference, channelized receiver, analog-to-digital converter, coarseacquisition, synchronization

1. Introduction

Ultra-wideband (UWB) impulse radio, which operatesby transmitting very short pulses with bandwidth onthe order of several gigahertz, enjoys numerous ad-vantages compared to narrowband systems includingrobustness to multipath fading and potential for achiev-ing high capacity. Its very wide bandwidth, however,poses several new challenges to communication sys-tem designers [1]. Channel estimation and synchro-nization appear to be the two major problems. The dif-ficulty of channel estimation arises from the dense mul-tipath environment. Synchronization becomes a chal-lenge because of the low duty cycle and the ultra-shortnature of the transmitted pulse, both of which introducenon-negligible timing and frequency offset betweenpulses.

The above mentioned challenges motivate a receiverthat digitizes the received UWB signals as early as pos-sible so that advanced digital processing techniques canbe applied. Since designing a single ADC to operate at

the signal Nyquist rate is not practical, parallel ADCarchitectures with each ADC operating at a fraction ofthe Nyquist rate need to be employed. To sample at afraction of the Nyquist rate, a frequency channelizedreceiver based on hybrid filter banks (i.e., continuous-time analysis filters and discrete-time synthesis filters)has been proposed in [2]. Among the advantages of thefrequency channelized receivers compared to the moreconventional time channelized (i.e., time-interleavedADC) receivers are the ease of designing the sam-ple/hold circuitries, greater robustness to jitter/phasenoise, and reduced ADC dynamic range requirements.The main drawback of the frequency channelized re-ceiver, however, is the slow convergence speed, whichcan be problematic in time-varying UWB wireless en-vironment [3].

Transmitted reference (TR) modulation schemeshave been proposed because of the ease of channelestimation in a dense multipath environment and thelow implementation complexity [4]. In one versionof TR system, referred to as the averaged TR system

60 Feng and Namgoong

[5], a fixed number of reference pulses precede datamodulated pulses in each transmission block. The pulserate is set so that there is no interference betweenconsecutive pulses. Assuming that the channel is con-stant for a block duration, the reference pulses are av-eraged to estimate the channel response. This channelestimate is then used to recover the transmitted databy simply correlating with the data pulses. In the fre-quency channelized receiver, data detection in a TRsystem can be achieved by simply averaging the ref-erence pulse responses in each of the subband chan-nels independently and using them to correlate the datapulses [8].

In this paper, we address the analog/digital base-band design issues of the TR UWB channelized re-ceiver. As designing bandpass filters with high centerfrequency is difficult, channelization is achieved usinga bank of mixers operating at equally spaced frequen-cies and lowpass filters to decompose the analog inputsignal into subbands [2]. Ideally, the analog lowpassfilter should satisfy the power complementary condi-tion [8]. In practice, the filters are only approximatelypower complementary because of the difficulties in de-signing such filters and the uncertainties due to processand temperature variations. Hence, the receiver sensi-tivity to the filter order and the cutoff frequency areinvestigated. In addition, the ADC resolution and sam-pling requirements are studied. Mono-bit ADCs are ofspecial interest because of its potential for low powerdesign.

After digitization, the receiver must first acquirethe initial synchronization parameters from the in-coming pulses. Achieving acquisition is difficult inUWB systems due to the high pulse timing sensitiv-ity and the large intervals between pulses [11][12].Several fast acquisition schemes have been proposed[11][14][15][16]. In this paper, we show that the fre-quency channelized receiver naturally leads to fast ac-quisition in TR systems. Coarse acquisition in a TRsystem is achieved by performing a two-dimensionalsearch for the pulse arrival time and the interval be-tween consecutive pulses. The acquisition hypothesisvariable is obtained by correlating between consecu-tive pulses in each subband, squaring to remove thephase uncertainty, then summing. For comparison, afull-band receiver, which is equivalent to a one-subbandchannelized receiver, is also considered. In the channel-ized receiver, the reduced bandwidth in each subbandwidens the correlation peak, allowing the search incre-ment to be correspondingly increased. Consequently,

the search space in the channelized receiver is reduced,resulting in a significantly faster acquisition time thanthat of a fullband receiver.

After the initial acquisition, the received signal goesthrough fine synchronization and detection. The tim-ing synchronization is composed of an interpolator,a Mueller and Muller (M&M) timing error detector(TED) and a numerically controlled oscillator (NCO)[10]. As the correlation window length is important ina TR system due to the “noise cross noise” term in thecorrelation [17], the length is adaptively adjusted. Thewindow length effects are simulated.

The paper is organized as follows. Section 2 presentsthe UWB TR system model. The low-pass filter andADC requirements of the channelizer are presented inSection 3. Coarse acquisition is discussed in Section4, while Section 5 describes fine synchronization anddetection. Section 6 draws conclusions.

2. System Model

To satisfy the FCC spectral mask, several pulse shapeshave been proposed [6][7]. In this paper, we use the5th-derivative of the Gaussian pulse

ptr (t) = Ac

(− t5

√2πλ5

+ t3

√2πλ3

− t√2πλ

)e

t2

2λ2

(1)

where Ac is a constant and λ of 51ps to fill the FCCspectral mask in the 3.1–10.6GHz band. Since de-signing a receiver to support the entire UWB bandmay be difficult, we subsequently assume a morepractical pulse with a bandwidth of 1.5GHz (3.1–4.6GHz), which is obtained by filtering the pulse re-sponse in (1) with a fourth order Chebyshev band-pass filter. The resulting pulse waveform is shown inFig. 1.

After passing through the multipath channel, the re-ceived pulse is s(t). In each transmission block, the firstNr pulses are reference pulses and the remaining Nd aredata pulses. To simplify the problem, we assume thatthe pulses are transmitted in fixed time intervals and thatthe interval is sufficiently large to prevent inter-pulseinterference between consecutive pulses. The channelis assumed to be constant during a transmission block.A block of received signal is

r (t) =Nr −1∑k=0

s(t−kT )+Nr +Nd−1∑

k=Nr

aks(t−kT )+n(t) (2)

An Analog/Digital Baseband Processor Design 61

-1 0 1 2 3 4 5 6 7-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Time (ns)

UW

B P

uls

e

Figure 1. The transmitted pulse with 1.5GHz bandwidth.

where ak is the kth transmitted antipodal symbol,n(t) is the additive noise, and T is the frame period(pulse repetition period). The channel estimation canbe achieved by averaging the first Nr pulses. The es-timated pulse is then correlated with the other framesignals to detect the data. The short pulse duration in-dicates that the detection is very sensitive to timingoffset.

2.1. Full-Band Receiver

Since the signal pulse energy falls within the 3.1–10.6GHz FCC spectral mask, the received signal is firstmixed to the baseband so to relax the ADC samplingrequirements. Denoting the mixer frequency as f f , theith sample of the kth pulse is

xk[i] = e− j2π f f t (aks(t − kT ) + n(t))|t=k(T +ε)+iTs

= ake− j2π f f kT sfull(kε + iTs) + nfull,k[i] (3)

where Ts is the sampling period and T + ε is thereceiver’s estimate of the pulse repetition period T.The fullband signal sfull(t) = s(t)e− j2π f f t and noisenfull,k[i] = n(t)e− j2π f f t |t=k(T +ε)+iTs .

2.2. Channelized Receiver

An M subband channelizer is shown in Fig. 2. The re-ceived signal r (t) is downconverted by a set of equallyspaced mixers at frequencies f0, f1, . . . , fM−1, filteredby the lowpass filter H (ω), then sampled by ADCsoperating at 1/M of the full-band receiver samplingfrequency. The channelized receiver ADC samplingfrequency fsub is 1/(MTs). The ith sample of the kthpulse in the mth subband can be shown to be

xk,m[i] = {[aks(t − kT ) + n(t)]e− j2π fm t }⊗ h(t)|t=k(T +ε)+i MTs

= ake− j2π fm kT sm(kε + i MTs) + nm,k[i]

(4)

Figure 2. An M subband UWB Channelizer.

62 Feng and Namgoong

where sm(t) = [s(t)⊗(h(t)e j2π fm t )]e− j2π fm t , nm,k[i] =n(t)e− jωm t ⊗h(t)|t=k(T +ε)+i MTs , and h(t) is the impulseresponse of the lowpass filter.

3. Channelizer

In this section, the design requirements of the analoglowpass filter and the ADCs in the frequency chan-nelized receiver are explored. The performance is ana-lyzed assuming perfect synchronization.

3.1. Analog Lowpass Filter

In order to preserve the simple averaging and correlat-ing detection structure of TR system, the subband filtershould satisfy the power complementary condition andthe sampling frequency should be high enough so tobe free from aliasing [8]. The power complementarycondition to be satisfied is

M−1∑m=0

∣∣∣H (ω − 2π fm)∣∣∣2

= 1 (5)

In practice, the filters are only approximately powercomplementary because of the difficulties in designing

Figure 3. BER sensitivity to analysis filter cutoff frequency.

such filters and the uncertainties due to process andtemperature variations. Although perfect power com-plementary analysis filters can be designed by appropri-ately cascading analog and digital filters as described in[8], we consider approximately power complementaryanalog analysis filters with no digital filters to simplifythe receiver complexity.

The analog lowpass filter order affects the amountof aliasing from sampling and the amount of overlapbetween adjacent subbands. To quantify the loss inperformance when approximately power complemen-tary analog analysis filters are used, the bit-error-rate(BER) curves of a 3-subband channelized receiver forTR with four training pulses and using the CM1 chan-nel model provided in IEEE P802.15-02/368r5-SG3aare plotted in Fig. 3. The horizontal axis denotes thefilter cutoff frequency normalized by half the differ-ence between consecutive mixer frequencies. Higherfilter orders are obtained by cascading identical firstorder filters. The received Eb/N0, which is the ratio ofthe single pulse energy (Eb) to the noise spectral den-sity (N0), is 10dB. The signal bandwidth is 1.5 GHz(3.1–4.6 GHz) and the ADC sampling frequency is2/3 GHz with each mixer frequency separated by500 MHz. In Fig. 3, the BER of a channelized receiverwith power complementary analysis filter is plotted forreference.

An Analog/Digital Baseband Processor Design 63

As is clear from Fig. 3, the channelized receiver withapproximately power complementary filters achievethe lowest BER (which is close to the ideal channel-ized receiver with power complementary filters) whenthe normalized cutoff frequency is approximately one.The minimum is also reasonably broad, suggesting thatthe channelizer is not very sensitive to slight variationsin the filter response. The small difference among theminima implies that high order filters are not necessarywhen the input noise is white. In the presence of nar-rowband interference, however, sharp filters are neededto isolate the effects of the interferer as explained in [2].In the remainder of this paper, we assume that a fourthorder lowpass filter is used.

3.2. Analog-to-Digital Converter

The quantization requirements of the frequency chan-nelized receiver is illustrated in Fig. 4. The BER curvesfor the TR system with four training pulses are plottedas a function of Eb/N0 for different quantization levels.The ADC sampling frequency is 2/3GHz, and the prop-agation channel model is assumed to be CM1. The BERof a full-band receiver, operating at 2GHz, is shown forcomparison. Except for the infinite-bit ADC receivers,

0 2 4 6 8 10 1210

-6

10-5

10-4

10-3

10-2

10-1

100

BE

R

Eb/N

0(dB)

IdealChannelized Inf-bitFullband Inf-bitChannelized 3-bitFullband 3-bitChannelized 1-bitFull band 1-bit

Figure 4. ADC resolution effects with 4 reference pulses.

the channelized receiver slightly outperforms the full-band receiver when the same ADC resolution is used.This improvement is due to the reduced quantizationnoise resulting from the reduction in signal power fromthe channelization process.

In Fig. 4, three bits are sufficient to achieve per-formance comparable to a channelized receiver withinfinite-bit ADC resolution. When 1-bit ADCs areused, the loss in performance compared to an infinite-bit channelized receiver is 2-3dB. Despite this loss inperformance, the 1-bit ADC receiver is especially at-tractive because of the resulting hardware simplicity.A simple comparator can be used as an ADC and noautomatic gain controller (AGC) is needed in each ofthe subband channel.

As increasing the sampling frequency reduces theeffect of the quantization noise and aliasing from sam-pling, the performance of the channelized receiver canbe improved by increasing the oversampling factor. InFig. 5, the BER is plotted for different ADC samplingfrequencies (1, 1.33 and 2), which are normalized bythe mixer frequency difference of 500MHz. Both 1-bitand infinite-bit ADCs are simulated. The lowest nor-malized ADC sampling frequency that provides suf-ficient statistics of the received signal is one. Whileincreasin the normalized sampling frequency beyond

64 Feng and Namgoong

0 2 4 6 8 10 1210

-6

10-5

10-4

10-3

10-2

10-1

100

BE

R

Eb/N

0(dB)

1-bit, Ratio 11-bit, Ratio 1.331-bit, Ratio 2Inf-bit, Ratio 1Inf-bit, Ratio 1.33Inf-bit, Ratio 2

Figure 5. BER performance with different ADC sampling rates. ADCs sample signal at 1, 1.33 and 2 times the minimum sampling frequency.

1.33 for the infinite-bit ADC receiver shows no perfor-mance improvement, the 1-bit ADC receiver perfor-mance improves with increasing sampling frequency.The largest incremental improvement in performance,however, occurs when the normalized sampling fre-quency is slightly increased from one. Hence, we sub-sequently assume that the normalized ADC samplingfrequency is 1.33.

4. Coarse Acquisition

Since the transmitter and receiver clocks are not syn-chronized, the receiver must first perform coarse ac-quisition to estimate the pulse arrival time τ0 and thepulse repetition period T before detection. To reducethe “noise cross noise” term, a time window is ap-plied to each pulse in order to capture only the highsignal-to-noise ratio part. The acquisition parameters

τ0 T

window 1 window 2

Figure 6. Acquisition parameters.

(τ0 and T) are shown in Fig. 6. τ0 is searched by slidingthe two windows within the pulse repetition period Twhile keeping their interval constant. Since the trans-mitter and receiver clocks are incommensurate, onlya nominal value of T is available at the receiver. Theacquisition procedure of T is to change the timing off-set between two windows in the range correspondingto the clock uncertainty. For each tentative value of τ0,the pulse repetition period (T) is searched from all pos-sible time offsets by a certain step. The total numberof search states is the multiplication of the numbers oftwo possible values.

In a full-band receiver, the coarse acquisition isachieved by first correlating the conjugate of the win-dowed kth pulse with the windowed (k + 1)st pulse.The cross-correlation value is squared to remove anyphase ambiguity. If the resulting hypothesis variableexceeds a certain threshold, the receiver enters the

An Analog/Digital Baseband Processor Design 65

fine synchronization mode. If the resulting value isbelow the threshold, the receiver changes the tenta-tive values of τ0 and/or T before continuing the searchprocess.

The coarse acquisition process in the channelizedreceiver is similar to that in the full-band receiver. Ineach subband, the conjugate of the windowed kth pulseis correlated with the windowed (k + 1)st pulse. Thecross-correlation value in each subband is squared thensummed. The estimates of both τ0 and T are variedduring the acquisition process. Coarse acquisition iscompleted when the resulting hypothesis variable ex-ceeds a certain threshold. Compared to the full-bandreceiver, the squaring and summing operation in eachsubband reduces the probability of detection PD for agiven PF, which is the false alarm probability whensignal is absent in both pulses. Despite this degrada-tion, the overall coarse acquisition time improves be-cause the frequency channelization process reduces thenumber of search bins. Since the reduced bandwidth ineach subband channel widens the correlation peak byapproximately the number of subbands M, the searchincrement (or bin) can be increased by M, resultingin a reduction of the search space by a factor of M.Assuming no degradation in the detection probabilityPD, the acquisition time reduces by almost M times. An

Figure 7. The hypothesis variables of a fullband signal and 3-subband channelized signals with respect to timing offset between two windows.

example of the correlation for a fullband and 3-subbandfrequency channelized receiver is plotted in Fig. 7 as afunction of the offset time assuming CM1 channel andno additive noise. Note that in addition to the widen-ing of the correlation peak, multiple side-lobes emergein the frequency channelized receiver, resulting in in-creased false alarm probabilities.

In this section, the acquisition performance of boththe full-band and channelized receivers are analyzed.Serial-search algorithm is considered, that is, only onestate is checked for a pulse period T. If successful ac-quisition is not reached at current state l, state l + 1 issearched in the next period.

4.1. Hypothesis Testing in a Full-Band Receiver

The hypothesis testing is performed to decide whethercorrect acquisition is achieved when searching overall the states. The search states are labeled by l =0, 1, . . . , L1. The l = 0 state corresponds to the correctacquisition state. For simplicity, we assume all pulsesare unmodulated. At the lth state, the samples in thewindowed kth pulse given in (3) can be representedas a Nw dimension vector e jθl,k (sl,k + nl,k), where sl,k

is the signal vector, nl,k is the complex noise vectorwith covariance matrix N0I(= 2σ 2I) with I being an

66 Feng and Namgoong

identity matrix, and θl,k is the mixer phase for the kthpulse at the lth state. θl,k is time varying due to trans-mitter and receiver clock uncertainty. Correlating withthe windowed (k + 1)st pulse, the resulting signal is

Yl = e j(θl,k+1−θl,k ) (sHl,ksl,k+1 + sH

l,knl,k+1

+ nHl,ksl,k+1 + nH

l,knl,k+1) (6)

where the superscript H stands for conjugate transpose.The first term in the parenthesis on the right hand side of(6) is the signal component and the remaining terms arethe noise components. The second and third terms are“signal cross noise” terms and are zero mean Gaussiannoise. The fourth term, which is the “noise cross noise”term, is also approximately Gaussian by the CentralLimit Theorem, since the noise in different pulses isindependent. The magnitude of the mean of Yl is

El, full = ∣∣sHl,ksl,k+1

∣∣ (7)

and the variance of all the noise is

σ 2l, full = |sl,k |2σ 2 + |sl,k+1|2σ 2 + Nwσ 4 (8)

To remove the phase ambiguity, the hypothesis vari-able is obtained by squaring the correlated signal

Jl, full = |Yl |2 (9)

The hypothesis variable Jl, full is then compared to athreshold to determine whether the signal is present.Jl, full has a central/noncentral chi-square distributionwith two degrees of freedom depending on whether thesignal is present or not. Denoting the threshold as γ ,the probability that the hypothesis variable exceeds γ

is [13]

Pl, full =∫ ∞

γ /σ 2l, full

e−(x+μl, full ) I0(2√

xμl, full)dx (10)

where μl, full = E2l, full/σ

2l, full and I0 is zeroth order

modified Bessel function of the first kind. Since thecorrect acquisition state is 0, P0, full is the detectionprobability and Pl, full(l = 1, . . . , L1) are false alarmprobabilities.

4.2. Hypothesis Testing in a Channelized Receiver

The search states are labeled by l = 0, 1, . . ., L2. Thel = 0 state corresponds to the correct acquisition state.

In the channelized receiver, Nw/M samples are col-lected at a rate of 1/(MTe) for each pulse. The searchincrement step for time offset T is MTe instead of Te

as in the fullband receiver. Because of the increasedsearch increment step, the number of channelized re-ceiver search states is reduced by M compared to afullband receiver, that is, L1 = M L2.

The ADC samples in the mth subband of the win-dowed kth pulse is represented in vector form ase jθl,k,m (sl,k,m + nl,k,m), where sl,k,m is the signal vector,nl,k,m is the noise vector and θl,k,m is the mth subbandmixer phase. After correlating with mth subband of thewindowed (k + 1)st pulse then summing all the sub-band correlation signals, the hypothesis variable of thechannelized receiver is

Jl,ch =M−1∑m=0

|(sl,k,m + nl,k,m)H (sl,(k+1),m + nl,(k+1),m)|2

(11)

As in the full-band receiver, the hypothesis variableJl,ch is compared with a threshold to determine whetherthe signal is present. Assuming that the noise among thesubbands is uncorrelated, Jl,ch becomes the summationof M independent and chi-square distributed randomvariables. The probability density function (PDF) ofJl,ch is the convolution of M chi-square PDFs, each ofwhich corresponds to the squared correlation signal ina subband. The false alarm and detection probabilities,Pl,ch(l = 1, . . . , L2) and P0,ch , can then be readilyobtained by integrating the PDF of Jl,ch .

4.3. Acquisition Performance Comparison

Following the similar steps as in [13], the single-dwell serial-search mean acquisition time of a fullbandreceiver in terms of T is

Tacq, full = 2L1 − (L1 − 1)P0, full

2P0, full

+κ(1 − P0, full)

L1∑l=1

Pl, full

P0, full

+κ

L1∑l=1

l Pl, full

L1

(12)

where κ is false alarm penalty. In the channelized re-ceiver, the mean acquisition time is similar to (12) ex-

An Analog/Digital Baseband Processor Design 67

Figure 8. The operating characteristic of the decision device.

cept that Pl, full(l = 0, . . . , L2) and L1 are replaced byPl,ch and L2, respectively.

To understand the operating characteristic of the de-cision device in both receivers, the detection probabilityPD, and the false alarm probability when signal is ab-sent in both pulses PF are plotted in Fig. 8. The receivedEb/N0 = 5dB or 15dB. The channelized receiver hasthree sub-bands. For a given PF, the PD of the full-bandreceiver is higher than that of the channelized receiver,because of the loss due to the squaring and summingof the subband signals.

Although PD is lower for a given PF, an importantadvantage of the frequency channelized receiver is thatthe number of bins to search is reduced by approxi-mately M as explained earlier. The net result of thesetwo contradictory effects is that the ratio of the meanacquisition time between the channelized and the full-band receivers depends on number of subbands andEb/N0. Using (12), the acquisition time ratios at Eb/N0

of 5dB and 15dB are plotted in Fig. 9 as a function ofnumber of subbands for a CM1 channel. To computethe acquisition time, we assume that the penalty asso-ciated with a false alarm is five time units, i.e., κ = 5.The mean acquisition time is shorter in a channelizedreceiver than in a fullband receiver due to the reducedsearch space. As the number of subbands increases,however, the reduction in mean acquisition time suf-

fers from diminishing returns because of the increasein false alarm probability.

5. Fine Synchronization and Detection

After initial acquisition, the receiver enters the finesynchronization mode, where the timing adjustmentfeedback loop is initiated to reduce the timing error.The loop, which operates at the symbol rate, adjuststhe sampling times (using digital interpolators) to syn-chronize with the transmitter. Once synchronization isachieved, channel estimation can be performed by av-eraging the reference pulses. Correlation length can beupdated by calculating the signal power in the timebins before and after the current correlation window.The digital receiver structure is shown in Fig. 10. Thephase rotation caused by incommensurate clocks canbe estimated and compensated (e− j θ̂km term in the fig-ure) based on the timing loop parameters since timingand phase have a constant relationship.

5.1. Timing Adjustment Loop

The transmitted data symbol period T and the receiverclock period Tr = T + ε are incommensurate due tothe free running oscillators in the transmitter and the re-ceiver. After initial acquisition, the timing adjustment

68 Feng and Namgoong

Figure 9. Acquisition time ratio between channelized receivers and a fullband receiver.

loop compensates the remaining timing offset by shift-ing all samples in a frame by an integer period of α aswell as a fractional period of μ. (α+μ)MTs is the tim-ing offset with respect to the first pulse. μ is estimatedby the M&M TED, loop filter and NCO [10].

When 1-bit ADCs are employed to simplify the re-ceiver complexity, the interpolator generates a multi-bit output, since 1-bit can not represent samples at thefractional period. The multibit output is in the formof two’s complement. The pulse correlation function

Figure 10. Digital receiver structure.

of the 1-bit, 2-bit and 3-bit interpolator output areshown in Fig. 11. They have timing accuracy of 1,1/2 and 1/6 of sampling period, respectively. The 3-bit output interpolator is adopted to achieve the tim-ing accuracy of 1/6 sampling period. Since the inputto the interpolator is 1-bit data, a linear interpolatoris adequate. Due to the limited timing accuracy, thelinear interpolator is implemented as a combinationallogic with two 1-bit sample inputs and one 3-bit timinginput.

An Analog/Digital Baseband Processor Design 69

0 0.2 0.4 0.6 0.8 10.2

0.4

0.6

0.8

1

Fractional Sampling Period

Corr

ela

tion

1-bit2-bit3-bit

Figure 11. The interpolator output correlation.

+WT

1 Tr/

+ – nco_out

N.. rs

μ

3 bit_

Figure 12. NCO in timing adjustment loop.

Figure 13. Correlation length effects for CM1 channels.

A loop filter is used to update the control word of thetiming loop NCO WT . In the NCO, the control worddetermines the ratio between the transmitter symbolperiod T and the receiver symbol period Tr

WT = T

Tr(13)

which is typically a value close to an integer. Afunctional block diagram of the NCO is shown inFig. 12. The NCO register nco out is updated eachTr . nco out represents the required timing shift interms of Tr . Since the interpolator needs timing infor-mation in terms of Ts , nco out is divided by a knowninteger Nrs to produce α and μ. Nrs is defined asNrs = Tr/Ts . By selecting an appropriate Nrs , the di-vision could be simplified to a shift. Due to the highsampling rate and low duty cycle pulse, Nrs can bevery large. Although not shown, a 20-bit NCO registerand a 3-bit μ for interpolation achieves near optimalperformance.

5.2. Length of the Correlation Window

The correlation length needs to be dynamically updateddepending on the UWB channel. If the length is too

70 Feng and Namgoong

short, the receiver is not collecting sufficient signal en-ergy. If the length is too long, extra noise is introduced.The correlation length effects on BER for CM1 channelare plotted in Fig. 13. The simulation is performed with1-bit ADC at Eb/N0 of 10dB, 12dB and 14dB. Thecorrelation window is selected so to minimize BER.The optimum window size for the CM1 channel is inthe 10ns to 20ns range. To achieve good performancefor different channels, the length of the correlationwindow needs to be dynamically updated accordingto the channel conditions. A 5ns window step appearsadequate.

To update the correlation length, the partial correla-tion values in two extra bins are calculated. One bin isbefore the correlation window and the other bin is afterthe window. The correlations of the two bins togetherwith those of the first and the last bins of the correlationwindow are compared with a threshold (i.e. 50% of theaverage bin correlation in the current correlation win-dow). A bin with correlation larger than the thresholdafter multiple frames should remain or be added to thecorrelation window. A bin with correlation smaller thanthe threshold should be removed from the correlationwindow.

6. Conclusions

The baseband processor design of a channelized re-ceiver for UWB TR systems is investigated in this pa-per. The channelized receiver achieves near optimalperformance for small ADC oversampling ratio de-spite reasonably large variations in analog filter band-width. The acquisition performance of the channel-ized receiver is superior to that of a fullband receiverbecause of the reduced search space of the channel-ized receiver. Fine synchronization is implementedwith linear interpolators and digital NCOs. The effectsof correlation window length are also investigated bysimulation.

Acknowledgments

This work was supported in part by the Army ResearchOffice under contract number DAAD19-01-1-0477 andNational Science Foundation under contract numberECS-0134629.

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An Analog/Digital Baseband Processor Design 71

Lei Feng received the B.S. and M.S. degree in electrical engineer-

ing from Peking University, Beijing, in 1997 and 2000, respectively.

He is currently working toward the Ph.D degree in electrical engi-

neering at University of Southern California, Los Angeles, CA. His

doctoral research focuses on the design of wideband communication

transceivers for wireless and wireline applications.

Won Namgoong received the BS degree in Electrical Engineering

and Computer Science from the University of California at Berkeley

in 1993, and the MS and Ph.D. degrees in Electrical Engineering

from Stanford University in 1995 and 1999, respectively. In 1999,

he joined the faculty of the Electrical Engineering Department at

the University of Southern California, where he is an Assistant Pro-

fessor. His current research areas include wireless/wireline commu-

nication systems, signal processing systems, RF circuits, and low-

power/high-speed circuits. In 2002, he received the National Science

Foundation (NSF) CAREER Award.