ltra-wideband (UWB) radio is a fast emerging technology with uniquely attractive features inviting majoradvances in wireless communications, networking, radar, imaging, and positioning systems. By its rule-making proposal in 2002, the Federal Communications Commission (FCC) in the United States essen-tially unleashed huge “new bandwidth’’ (3.6–10.1 GHz) at the noise floor, where UWB radios
overlaying coexistent RF systems can operate using low-power ultra-short information bearing pulses. With similarregulatory processes currently under way in many countries worldwide, industry, government agencies, and academicinstitutions responded to this FCC ruling with rapidly growing research efforts targeting a host of exciting UWBapplications: short-range very high-speed broadband access to the Internet, covert communication links, localizationat centimeter-level accuracy, high-resolution ground-penetrating radar, through-wall imaging, precision navigationand asset tracking, just to name a few. This tutorial focuses on UWB wireless communications at the physical layer.It overviews the state-of-the-art in channel modeling, transmitters, and receivers of UWB radios, and outlinesresearch directions and challenges to be overcome. As signal processing expertise is
expected to have major impact in research and development of UWBsystems, emphasis is placed on DSP aspects.
IntroductionUWB characterizes transmission systems
with instantaneous spectral occu-pancy in excess of 500 MHz
UAn Idea Whose Time Has Come
or a fractional bandwidth of more than 20%. (The frac-tional bandwidth is defined as B/fc , whereB := fH − fL denotes the −10 dB bandwidth and cen-ter frequency fc := ( fH + fL )/2 with fH being theupper frequency of the −10 dB emission point, and fLthe lower frequency of the −10 dB emission point.According to [12], UWB systems with fc > 2.5 GHzneed to have a −10 dB bandwidth of at least 500MHz, while UWB systems with fc < 2.5 GHz need tohave fractional bandwidth at least 0.20.) Such systemsrely on ultra-short (nanosecond scale) waveforms thatcan be free of sine-wave carriers and do not require IFprocessing because they can operate at baseband. Asinformation-bearing pulses with ultra-short durationhave UWB spectral occupancy, UWB radios come withunique advantages that have long been appreciated bythe radar and communications communities: i) enhancedcapability to penetrate through obstacles; ii) ultra highprecision ranging at the centimeter level; iii) potential forvery high data rates along with a commensurate increasein user capacity; and iv) potentially small size and pro-cessing power. Despite these attractive features, interestin UWB devices prior to 2001 was primarily limited toradar systems, mainly for military applications. Withbandwidth resources becoming increasingly scarce,UWB radio was “a midsummer night’s dream’’ waitingto be fulfilled. But things changed drastically in thespring of 2002, when the FCC released a spectral maskallowing (even commercial) operation of UWB radios atthe noise floor, but over an enormous bandwidth (up to7.5 GHz).
This huge “new bandwidth” opens the door for anunprecedented number of bandwidth-demanding posi-tion-critical low-power applications in wireless commu-nications, networking, radar imaging, and localizationsystems [64]. It also explains the rapidly increasingefforts undertaken by several research institutions,industry, and government agencies to assess and exploitthe potential of UWB radios in various areas. Theseinclude short-range, high-speed access to the Internet,accurate personnel and asset tracking for increased safe-ty and security, precision navigation, imaging of steelreinforcement bars in concrete or pipes hidden insidewalls, surveillance, and medical monitoring of theheart’s actual contractions.
For wireless communications in particular, the FCCregulated power levels are very low (below −41.3 dBm),which allows UWB technology to overlay already avail-able services such as the global positioning system(GPS) and the IEEE 802.11 wireless local area net-works (WLANs) that coexist in the 3.6−10.1 GHzband. Although UWB signals can propagate greaterdistances at higher power levels, current FCC regula-tions enable high-rate (above 110 MB/s) data trans-missions over a short range (10−15 m) at very lowpower. Major efforts are currently under way by theIEEE 802.15 Working Group for standardizing UWBwireless radios for indoor (home and office) multime-
dia transmissions. Similar to the frequency reuse princi-ple exploited by wireless cellular architectures, low-power, short-range UWB communications are alsopotentially capable of providing high spatial capacity, interms of bits per second per square meter. In addition,UWB connectivity is expected to offer a rich set of soft-ware-controllable parameters that can be used to designlocation-aware communication networks flexible toscale in rates and power requirements.
To fulfill these expectations, however, UWB researchand development has to cope with formidable chal-lenges that limit their bit error rate (BER) perform-ance, capacity, throughput, and network flexibility.Those include high sensitivity to synchronizing thereception of ultra-short pulses, optimal exploitation offading propagation effects with pronounced frequency-selectivity, low-complexity constraints in decodinghigh-performance multiple access protocols, and strictpower limitations imposed by the desire to minimizeinterference among UWB communicators, and withcoexisting legacy systems, particularly GPS, unmannedair vehicles (UAVs), aircraft radar, and WLANs. Thesechallenges call for advanced digital signal processing(DSP) expertise to accomplish tasks such as synchro-nization, channel estimation and equalization, multi-user detection, high-rate high-precision low-poweranalog/digital conversion (ADC), and suppression ofaggregate interference arising from coexisting legacysystems. As DSP theory, algorithms, and hardwareadvanced narrowband and broadband technology, DSPis expected to play a similar role in pushing the fron-tiers of emerging UWB applications. To this end, it isimportant to understand features and challenges thatare unique to UWB signaling from a DSP perspective.
Regulatory Issues and Motivating ApplicationsDespite its renewed interest during the past decade,UWB has a history as long as radio. When invented byGuglielmo Marconi more than a century ago, radiocommunications utilized enormous bandwidth as infor-mation was conveyed using spark-gap transmitters. Thenext milestone of UWB technology came in the late1960s, when the high sensitivity to scatterers and lowpower consumption motivated the introduction ofUWB radar systems [5], [45], [46]. Ross’ patent in1973 set up the foundation for UWB communications.Readers are referred to [5] for an interesting andinformative review of pioneer works in UWB radar andcommunications.
In 1989, the U.S. Department of Defense (DoD)coined the term “ultra wideband” for devices occupy-ing at least 1.5 GHz, or a −20 dB fractional bandwidthexceeding 25% [37]. Similar definitions were alsoadopted by the FCC notice of proposed rule makingthat regulated UWB recently. The rule making of UWBwas opened by FCC in 1998. The resulting FirstReport and Order (R&O) that permitted deployment
of UWB devices was announced on 14 February andreleased in April 2002 [12]. Three types of UWB sys-tems are defined in this R&O: imaging systems, com-munication and measurement systems, and vehicularradar systems. Spectral masks assigned to these applica-tions are listed in Table 1. In particular, the FCCassigned bandwidth and spectral mask for indoor com-munications is illustrated in Figure 1.
Although currently only the United States permitsoperation of UWB devices, regulatory efforts are underway both in Europe and in Japan. Market drivers forUWB technology are many even at this early stage, andare expected to include new applications in the nextfew years. We outline here application trends where sig-nal processing tools will probably have considerableimpact in UWB system development.▲ Wireless personal area networks (WPANs): Also knownas in-home networks, WPANs address short-range (gen-erally within 10−20 m) ad hoc connectivity amongportable consumer electronic and communicationdevices. They are envisioned to provide high-qualityreal-time video and audio distribution, file exchangeamong storage systems, and cable replacement for homeentertainment systems. UWB technology emerges as apromising physical layer candidate for WPANs, becauseit offers high-rates over short range, with low cost, highpower efficiency, and low duty cycle. ▲ Sensor networks: Sensor networks consist of a largenumber of nodes spread across a geographical area.The nodes can be static, if deployed for, e.g., avalanchemonitoring and pollution tracking, or mobile, ifequipped on soldiers, firemen, or robots in military andemergency response situations. Key requirements forsensor networks operating in challenging environmentsinclude low cost, low power, and multifunctionality.High data-rate UWB communication systems are wellmotivated for gathering and disseminating or exchang-
ing a vast quantity of sensory data in a timely manner.Typically, energy is more limited in sensor networksthan in WPANs because of the nature of the sensingdevices and the difficulty in recharging their batteries.Studies have shown that current commercial Bluetoothdevices are less suitable for sensor network applicationsbecause of their energy requirements [62] and higherexpected cost [2]. In addition, exploiting the preciselocalization capability of UWB promises wireless sensornetworks with improved positioning accuracy. This isespecially useful when GPSs are not available, e.g., dueto obstruction.▲ Imaging systems: Different from conventional radarsystems where targets are typically considered as pointscatterers, UWB radar pulses are shorter than the targetdimensions. UWB reflections off the target exhibit notonly changes in amplitude and time shift but alsochanges in the pulse shape. As a result, UWB wave-forms exhibit pronounced sensitivity to scattering rela-tive to conventional radar signals. This property hasbeen readily adopted by radar systems (see e.g., [5] andreferences therein) and can be extended to additionalapplications, such as underground, through-wall andocean imaging, as well as medical diagnostics and bor-der surveillance devices [55], [57].▲ Vehicular radar systems: UWB-based sensing has thepotential to improve the resolution of conventionalproximity and motion sensors. Relying on the highranging accuracy and target differentiation capabilityenabled by UWB, intelligent collision-avoidance andcruise-control systems can be envisioned. These sys-tems can also improve airbag deployment and adaptsuspension/braking systems depending on road condi-tions. UWB technology can also be integrated intovehicular entertainment and navigation systems bydownloading high-rate data from airport off ramp,road-side, or gas station UWB transmitters.
IEEE SIGNAL PROCESSING MAGAZINE28 NOVEMBER 2004
Equivalent Isotropically Radiated Power (EIRP) [dBm]Frequency Indoor Hand Held Low Freq. High Freq. Med. Freq. Vehicular[MHz] Comm. Comm. Imaging Imaging Imaging Radar<960 15.209 limits 15.209 limits 15.209 limits 15.209 limits 15.209 limits 15.209 limits
UWB Communications at the Physical LayerIn this section, we outline physical layer issues of UWBcommunication systems, including transmitter/receiverdesigns, synchronization, channel estimation, and mul-tiple access schemes. In addition to the conventionalsingle-band UWB transmissions, we will also discussrecent multiband alternatives for power-efficient adher-ence to FCC’s spectral mask, mitigation of narrowbandinterference (NBI), and relaxed sampling requirements.To appreciate UWB system designs, however, it isimportant to understand first the propagation charac-teristics of the transmitted ultra-short waveform andestablish a realistic channel model.
Channel ModelingSince more than 80% of the envisioned commercialUWB applications will be indoor communications, wewill focus on indoor channels. The well-known Saleh-Valenzuela (S-V) indoor channel model was establishedback in 1987 [50], based on measurements utilizinglow power ultra-short pulses (of width 10 ns and centerfrequency 1.5 GHz) in a medium-size, two-story officebuilding. In the S-V model, multipath componentsarrive at the receiver in groups (clusters). Clusterarrivals are Poisson distributed with rate �. Withineach cluster, subsequent arrivals are also Poisson dis-tributed with rate λ > �. With αm,n denoting the gainof the nth multipath component of the mth cluster,having phase θm,n , the channel impulse response can beexpressed as
h (t ) =+∞∑
l =0
αl δ(t − τl )
=+∞∑
m=0
+∞∑
n=0
αm,ne jθm,n δ(t − Tm − τm,n), (1)
where Tm + τm,n (τm,0 = 0) denotes the arrival time ofthe nth multipath component of the mth cluster, θm,nare independent uniform random variables over[0, 2π), and αm,n are independent Rayleigh randomvariables with power E{α2
m,n} = E{α20,0}e−Tm/γ e−τm,n/γ ,
where > γ . The number of clusters and multipathcomponents may theoretically extend over infinitetime. However, the terms of the double sum in (1)practically vanish for sufficiently large (m, n) with anexponentially decaying power profile.
Lately, efforts have been made to characterize UWBchannels with bandwidths exceeding 2 GHz. To comeup with a statistical model, channel realizations areidentified either in the frequency domain by frequencysweeping or in the time domain using impulsive signals.In November 2002, the channel modeling subcommit-tee of the IEEE 802.15.3a Task Group recommendeda channel model which captures the aforementionedworks, as well as recent refinements [14]. Because theclustering phenomenon has been experimentally con-
firmed, the standardized channel model is basically amodified version of the S-V model [50]. To reach ananalytically tractable channel model, the total numberof paths is defined as the number of multipath arrivalswith expected power within 10 dB from that of thestrongest arrival. The Rayleigh distribution in the S-Vchannel model is replaced by the log-normal distribu-tion. The phases θm,n are also constrained to take values0 or π with equal probability to account for signalinversion due to reflection, yielding a real-valued chan-nel model. With path gains normalized to have unitenergy, a log-normal random variable is introduced toaccount for shadowing. Model parameters correspon-ding to several ranges are also provided in [14], forboth line-of-sight (LOS) and nonline-of-sight (NLOS)scenarios. The standardized UWB channel model in[14] is claimed to better match the measurements.However, the log-normal distribution and the shadow-ing factor render this model less tractable for theoreti-cal performance analysis and quantification of thechannel-induced diversity and coding gains.
A typical realization of the channel impulse responsegenerated using the channel model 2 [14] is shown inFigure 2. The number of multipath components is 315in this realization, spanning over a delay spread of about50 ns. Let p(t ) denote the transmitted pulse of durationTp . After multipath propagation, the received waveformis given by the convolution of p(t ) with the physicalchannel h (t ), and contains multiple delayed copies ofp(t ); i.e., g (t ) := (p h )(t ) = ∑L
l =0 αl p(t − τl ) , where denotes convolution. Notice from Figure 2 that thespacing among multipath delays {τl }L
l =0 is in the orderof nanoseconds. These delayed copies of p(t ) in g (t )can be resolved from each other only if Tp is sufficientlysmall, that is, if the transmit bandwidth B ≈ 1/Tp issufficiently large. The transmitted and received wave-forms corresponding to two Tp values are shown inFigure 3, where the received waveforms were generatedusing the multipath delays and amplitudes of Figure 2.
IEEE SIGNAL PROCESSING MAGAZINENOVEMBER 2004 29
▲ 1. FCC spectral mask for indoor commercial systems.
100 101
−75
−70
−65
−60
−55
−50
−45
−40
Frequency in GHz
UW
B E
IRP
Em
issi
on L
evel
in d
Bm
Indoor LimitPart 15 Limit
0.96 1.61
1.993.1 10.6
GPSBand
With Tp = 91 ns, we have B ≈ 11 MHz, and thereceived waveform consists of a single distorted versionof p(t ). With Tp = 0.55 ns, we have B ≈ 2 GHz, andthe received waveform contains multiple resolvablecopies of p(t ). If the channel is known at the receiver,these resolvable copies can be combined coherently toprovide multipath diversity. But before discussingreceiver designs that collect this diversity, let us firstintroduce UWB transmission schemes.
Transmitter DesignGenerally adopted spectrum shapers p(t ) for UWBcommunications include the Gaussian pulse, theGaussian monocycle (first derivative of Gaussian pulse),and the second derivative of the Gaussian pulse, asdepicted in Figure 4, along with their Fourier trans-forms (FTs). The reason behind the popularity of thesepulses is twofold: i) Gaussian pulses come with thesmallest possible time-bandwidth product of 0.5, which
maximizes range-rate resolution andii) the Gaussian pulses are readilyavailable from the antenna pattern[51]. With Tp at the subnanosecondscale, p(t ) occupies UWB withbandwidth B ≈ 1/Tp . As mentionedbefore, and illustrated in Figure3(b), such an ultra-short p(t ) alsogives rise to multiple resolvablecopies, and thus enables rich multi-path diversity.
In a typical UWB system, eachinformation-conveying symbol isrepresented by a number of (N f )pulses, each transmitted per frame ofduration Tf � Tp . Having N fframes, over which a single symbolis spread, reverses the commonlyused terminology where a frameconsists of multiple symbols (heremultiple frames comprise a symbol).With M -ary modulation, log2 Mmessage bits are transmitted duringa signaling interval of durationTs = N f Tf s that corresponds to abit rate Rb = log2 M/Ts .
Being real, baseband UWB trans-missions neither have to entail fre-quency modulation nor phasemodulation with M > 2. Conse-quently, symbol values can be trans-mitted by modulating the positionand/or the amplitude of p(t ). InM -ary pulse position modulation(PPM), M distinctly delayed pulses{p(t − �m)}M −1
m=0 are employed, eachrepresenting one symbol value.Generally, the so-termed modula-tion indices �m are chosen such that�m = m� with � ≥ Tp , which cor-responds to an orthogonal PPM. Inbinary PPM, the delay � can also bechosen to minimize the correlation∫
p(t )p(t − �)dt [52]. As band-width efficiency drops with increas-ing modulation size M , PPM issuitable for power-limited applica-tions. In fact, PPM was almostexclusively adopted in the early
IEEE SIGNAL PROCESSING MAGAZINE30 NOVEMBER 2004
▲ 3. The transmitted and received waveforms corresponding to (a) Tp = 91 ns and (b)Tp = 0.55 ns. For illustration purposes, only the first 10 ns are shown in (b).
▲ 2. A typical realization of the channel impulse response generated using the IEEE802.15.3 a channel model 2: NLOS channels with 0−4 m transmitter-receiver distance.
0 1 2 3 4 5 6 7 8 9 10
0
−1−0.8−0.6−0.4−0.2
0.20.40.60.8
1
Am
plitu
de
Time (ns)
(b)
Transmitted PulseReceived Waveform
0 50 100 1501
−0.8−0.6−0.4
−0.20
0.20.40.60.8
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5 10 15 20 25 30 35 40 45 50
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plitu
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development of UWB radios because negating ultra-short pulses were difficult to implement. Another mod-ulation scheme that does not require pulse negation isthe so termed on-off keying (OOK), where symbol “1”is represented by transmitting a pulse, and “0” bytransmitting nothing.
As pulse negation became easier to implement, pulseamplitude modulation (PAM) attracted more attention.In particular, when M = 2, antipodal pulses are used torepresent binary symbols, as in binary phase shift key-ing (BPSK) or bipolar signaling. Biorthogonal signal-ing by combining orthogonal PPM with binary PAM aswell as orthogonal waveform and block orthogonalmodulation schemes have also been reported [43].
To allow for multi-user access (MA) to the UWBchannel, time hopping (TH) was introduced early in[52]. With TH, each pulse is positioned within eachframe duration Tf according to a user-specific THsequence c T H
u (n). Specifically, dividing each frame intoNc chips each of duration Tc , the uth user’s TH codec T H
u (n) ∈ [0,Nc − 1] corresponds to a time shift ofc T H
u (n)Tc during the nth frame [72]. Consequently,the uth user’s transmitted waveform is given by
vu(t ) =√Eu
+∞∑
n=0
au(�n/N f �)
· p(t − nTf − c TH
u (n)Tc − bu(�n/N f �)�
),
(2)
where Eu is the uth user’s energy per pulse at the trans-mitter end. With su(k) ∈ [0, M − 1] denoting the M -ary information symbol transmitted by the uth userduring the kth symbol duration, (2) subsumes severalmodulation schemes. When bu(k) = su(k) , andau(k) = 1, (2) describes UWB transmissions with M -ar y PPM; when au(k) = 2su(k) + 1 − M , and
bu(k) = 0, (2) models M -ary PAM. With binary sym-bols, and bu(k) = 0, au(k) = 2su(k) − 1 corresponds toBPSK, and au(k) = su(k) corresponds to OOK [32],[43], [69].
With TH codes, MA is achieved by altering thepulse position from frame to frame, according to thesequence c TH
u (n). MA can also be enabled by modify-ing the pulse amplitude from frame to frame. The latterallows for many other choices of alternative spreadingcodes which, individually or in combination with THcodes, give rise to the following transmitted waveform[c.f. (2)]:
vu(t ) =√Eu
+∞∑
n=0
au(�n/N f �) c u(n)
· p(t − nTf − c TH
u (n)Tc − bu(�n/N f �)�
),
(3)
where c u(n) is the user-specific “amplitude code” dur-ing the nth frame. Depending on the spreading codesemployed, the UWB systems are termed TH-UWB[52], direct-sequence (DS)-UWB [15], or basebandsingle-carrier/multicarrier (SC/MC)-UWB [66], [77],just to name a few.
In addition to facilitating multiple access, spreadingcodes also shape the transmit spectrum. Analyticalexpressions and simulated power spectral density(PSD) for UWB transmissions are pursued in [44]and [70]. A PSD expression for TH-UWB allowingfor both short and long spreading codes is derivedin [44]. The effects of timing jitter on PSD of UWBtransmissions utilizing random TH codes and/orM -ary modulation can be found in [70]. In particu-lar, let us consider “short” spreading codes that aresymbol-periodic with period N f . Let us now definethe symbol level transmitted waveform for user u as
IEEE SIGNAL PROCESSING MAGAZINENOVEMBER 2004 31
▲ 4. (a) Generally adopted pulse shapes in UWB communications; (b) Fourier transform of several pulse shapes. Pulse width: 0.7 ns.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Time (ns)
(a)
Am
plitu
de (
dB)
Gaussian PulseGaussian MonocycleScholtz Monocycle
100 101−70
−60
−50
−40
−30
−20
−10
0
10
Frequency (GHz)
(b)
Pow
er (
dB)
Gaussian PulseGaussian MonocycleScholtz Monocycle
IEEE SIGNAL PROCESSING MAGAZINE32 NOVEMBER 2004
pT ,u(t ) := ∑N f −1n=0 p(t − nTf − c TH
u (n)Tc ) for TH-UWB, pT ,u(t ) := ∑N f −1
n=0 c u(n)p(t − nTf ) for DS/SC/MC-UWB, and pT ,u(t ) := ∑N f −1
n=0 p(t − nTf ) when nospreading code is involved. Equation (2) then becomesvu(t ) = √
Eu∑+∞
k=0 au(k)pT ,u(t − kTs − bu(k)�). Alongthe lines of [42, Chapter 4], it can be shown that thePSD of vu(t ) is
�vv( f ) = Eu
Ts|PT ,u( f )|2
∞∑n=−∞
φ(n)aa φ
(n)
b b ( f )e− j2π f nTs , (4)
where φ(n)aa := E{au(k)au(k + n)}, φ(n)
b b ( f ) :=E{e− j2π f (bu(k)−bu(k+n))�} , and PT ,u( f ) := F{pT ,u(t )} isthe FT of pT ,u(t ). In particular, for independent identi-cally distributed (i.i.d.) equiprobable binary symbolssu(k) ∈ {0, 1}, we have au(k) = 2su(k)−1, and bu(k) = 0with PAM; and au(k) = 1, and bu(k) = su(k) withPPM. It then follows that
φ(n)aa = δ(n), and φ
(n)bb ( f ) = 1, ∀n
for binary PAM and
φ(n)aa = 1,∀n, and
φ(n)
b b ( f ) ={
1, n = 01 + cos(2π�f )
2, n �= 0
for binary PPM. Accordingly, the resultant PSD ofvu(t ) becomes [c.f. (4)]: �vv( f ) = (Eu/Ts )|PT ,u( f )|2for PAM and �vv( f ) = (Eu/Ts )|PT ,u( f )|2[(1−cos(2π�f ))/2 + (1+ cos (2π�f ))/(2Ts )
∑∞n=−∞ δ( f −
k/Ts )] for PPM.The shape of the �vv( f ) for both modulations is
determined by PT ,u( f ), which may contain spectrallines due to the repeated use of N f pulses in formingeach symbol. Different from PAM, which is a zero-mean linear modulation, additional spectral lines
▲ 5. Transmit PSD corresponding to (a) no spreading code, (b) random DS codes, and (c) random TH codes. Gaussian pulse withTp = 0.4 ns. Nf = 64, Tf = 100 ns, Tc = 2 ns.
0 2 4 6 8 10 12−70
−60
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−10
0
10
Frequency (GHz)
(a)
Pow
er (
dB)
0 2 4 6 8 10 12
0
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Frequency (GHz)
(b)
Pow
er (
dB)
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0
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−50
−40
−30
−20
−10
10
Frequency (GHz)
(c)
Pow
er (
dB)
IEEE SIGNAL PROCESSING MAGAZINENOVEMBER 2004 33
emerge with PPM. Although the bandwidth of PT ,u( f )
is determined by the pulse shaper p(t ), its shape, bydefinition, relies not only on p(t ), but also on thespreading codes utilized. The transmit PSD correspon-ding to no spreading, random DS spreading, and ran-dom TH spreading with binary PAM are depicted inFigure 5. Notice how pronounced spectral lines are inFigure 5 where no spreading code is used. Figure 5(b)and (c) confirms that both DS and TH spreadingsmooth the transmit PSD. It is also worth mentioningthat although the spectral lines cause “noise-like’’ inter-ference to narrowband services coexisting with UWBsystems, they introduce cyclostationarity that one canexploit for timing offset estimation simply becausethese spectral lines originate from the underlying perio-dicity of the transmission.
Timing SynchronizationAs defined in (1), the physical channel h (t ) not onlycaptures multipath effects but also includes a delay(uncertainty) on the first arrival time τ0. For coherentdemodulation, timing synchronization is the first taskto be performed at the receiver to acquire and track thetiming offset τ0.
In fact, one of the major challenges at the UWBphysical layer is the accuracy and speed of this synchro-nization step. As UWB systems employ low-powerultra-short pulses (in the order of nanoseconds), timingrequirements are stringent because even minor mis-alignments may result in lack of energy capture whichrenders symbol detection impossible [59]. To betterunderstand the unique challenges in UWB timing, letus consider a single-user link with zero-mean, i.i.d.M -ary PAM symbols a(k) having zero-mean and vari-ance σ 2
s . (Generalization to PPM is also possible.)Dropping temporarily the subscript u, the received sig-nal after multipath propagation is [c.f. (3)]: r(t ) =√E
∑∞k=0 a(k)
∑Ll =0 αl pT (t − kTs − τl ) + η(t ) , where
(L + 1) is the number of effectively nonzero paths,each with amplitude αl and delay τl satisfyingτl < τl +1, ∀l . We assume that the channel is quasi-static, meaning that {αl }L
l =0 and {τl }Ll =0 remain invari-
ant per burst but may change from burst to burst; a(k),{αl }L
l =0 and {τl }Ll =0 are independent of the noise η(t )
which is assumed zero-mean, wide-sense stationary butnot necessarily white and/or Gaussian, as it consists ofboth ambient noise and multi-user interference (MUI).With respect to the first arrival time (timing offset) τ0,other path delays can be uniquely described as:τl ,0 := τl − τ0, ∀l ∈ [0, L ]. It is convenient to expressr(t ) in terms of the aggregate pulse pR(t ) at the receiverwhich encompasses the transmit pulse, spreading codesand multipath effects:
r(t ) =√E
∞∑k=0
a(k)pR(t − kTs − τ0) + η(t ),
where
pR(t ) :=L∑
l =0
αl pT (t − τl ,0). (5)
Let us select Tf ≥ τL ,0 + Tp and c TH(0) ≥c TH(N f − 1) to confine the duration of pR(t ) within[0, Ts ) and thus avoid intersymbol interference (ISI).Without loss of generality, let us also confine the tim-ing offset τ0 within a symbol duration, i.e., τ0 ∈ [0, Ts ).
Notice that at the timing synchronization stage, themultipath channel is unknown, and so is pR(t ) .Consequently, even with known training symbols a(k),the traditional approach of peak-picking the correlationof r(t ) with pR(t ) to estimate τ0 is not applicable.Instead of pR(t ), one could correlate r(t ) with pT (t )and look for the maximum. Evidently, this approach isnot only suboptimum in the presence of dense multi-path, but also results in unacceptably slow acquisitionspeed and has prohibitive complexity when one has toper form exhaustive search over thousands ofbins/chips. There is clearly a need for low-complexitytiming estimation methods in multipath-rich propaga-tion settings. To this end, a number of attempts havebeen proposed to improve acquisition speed and/orperformance in UWB radios. These attempts include: acoarse bin reversal search for the noiseless case [22]; acoded beacon sequence in conjunction with a bank ofcorrelators in the context of data-aided localization inthe absence of multipath [13]; a ranging system thatrequires knowledge of the strongest path [26]; a non-data aided (a.k.a. blind) timing estimator that relies onthe cyclostationarity that arises in UWB transmissionswith slow TH and sufficiently dense multipath [61];and a data-aided maximum likelihood (ML) timingalgorithm using symbol- and frame-rate samples [60].
UWB Timing with Dirty TemplatesTo relax the rather restrictive assumptions in theseapproaches, we have developed timing algorithmsbased on the novel concept of “dirty templates’’ [79].The idea is to rely on pairs of successive symbol-longsegments of r(t ) taken at candidate time-shiftsτ ∈ [0, Ts ) and have one segment in each pair serve as atemplate for the other. Specifically, integrate-and-dumpoperations are performed on products of such segmentsto obtain symbol-rate samples:
xk(τ) =∫ Ts
0r(t + kTs + τ)r(t + (k − 1)Ts + τ)dt ,
(6)
∀k ∈ [1,+∞) and τ ∈ [0, Ts ). The symbol-long seg-ments r(t + kTs + τ) and r(t + (k − 1)Ts + τ) , fort ∈ [0, Ts ) are “dirty templates’’ because: i) they arenoisy, ii) they are distorted by the unknown channel, andiii) they are subject to the unknown offset τ0. The latter
constitutes a major difference between the Timing tech-nique based on dirty templates (TDT) and the transmit-ted reference (TR) approach [21] for channel estimationand symbol demodulation, as we will detail in the ensu-ing sections. To grasp the gist of TDT, let xk(τ) andr(t ) denote the noise-free parts of xk(τ) and r(t ).Applying Cauchy-Schwartz’s inequality to (6) yields
x 2k (τ) ≤
∫ Ts
0r2(t + kTs + τ)dt
×∫ Ts
0r2(t + (k − 1)Ts + τ)dt ,
where the equality holds ∀k if and only ifr(t + kTs + τ) = λr(t + (k − 1)Ts + τ). But the latteris true ∀t ∈ [0, Ts ) if and only if τ = τ0. In words, thecross correlation of successive symbol-long received seg-ments reaches a unique maximum magnitude if andonly if these segments are scaled versions of each other,which is achieved only at the correct timing; i.e., whenτ = τ0. In its simplicity, this neat observation offers adistinct criterion for timing synchronization that, foryears, has relied on the idea that the autocorrelation ofthe noise-free template has a unique maximum at thecorrect timing; the latter has been the principle behindall existing narrowband and UWB timing schemes,including the popular early-late gate algorithm [42].The TDT approach is different from these conventionalsynchronizers. It has fundamental implications to UWBand also to a number of other applications such as time-delay and displacement estimation through unknowntime-dispersive media, where there is no undistortedtemplate to rely on, even in the noise-free case.
To establish its validity even in the presence of noise,we start by recalling that pR(t ) has finite nonzero sup-port [0, Ts ). This implies that the noisy xk(τ) can beexpressed as [c.f. (5) and (6)]:
E{a(k)a(l )} = 0 and E{a2(k)a2(l )} = σ 4s , for k �= l .
Now notice that EA (τ ) + EB (τ ) = ∫ Ts
0 p2R(t )dt := ER is
the constant energy of the unknown aggregate tem-plate at the receiver and also that EB (τ ) − EA (τ ) isuniquely maximized at τ = 0, since EA (τ ) is minimizedat τ = 0 and EB (τ ) is maximized at τ = 0, by definition.So, E{x 2
k (τ)} is maximized when τ = 0, or equivalently,τ = τ0. Compactly written, the approach for nondataaided TDT yields: τ0 = arg maxτ∈[0,Ts ) E{x 2
k (τ)}.As usual, the ensemble mean must be replaced in
practice by its consistent sample mean estimatorobtained from K symbol-long pairs of received seg-ments: K −1 ∑K
k=1 x 22k−1(τ). The number of samples K
required for reliable estimation can be reduced marked-ly if a data aided approach is pursued [79]. The trainingsequence {a(k)} for data-aided TDT comprises a repeatedpattern (s , s ,−s ,−s ) with s being any M -ary PAM sym-bol. This pattern is particularly attractive because it simpli-fies (7) to xk(τ) = (−1)k s 2[−EA (τ )+ EB (τ )] + ξ(k). Asa result, K −1 ∑K
k=1 x 22k−1(τ) converges faster to
E{x 2k (τ)} = s 4[EA (τ ) − EB (τ )]2 + σ 2
ξ , because now oneobviates convergence to σ 4
s , that is necessary in theblind approach to remove unknown symbol effects(self-noise). The benefit with data-aided TDT is veryrapid acquisition since only K = 1 pair of receivedsymbol-long segments carrying as few as four trainingsymbols, is sufficient; see also Figure 6. Summarizing,consistent (non)data-aided TDT can be accomplishedin the absence of ISI even when TH codes are presentand the UWB multipath channel is unknown, using“dirty’’ Ts -long segments of the received waveform asfollows [79]:
τ0 = arg maxτ∈[0,Ts )
K∑k=1
(∫ 2kTs
(2k−1)Ts
r (t + τ )r (t + τ − Ts ) dt
)2
.
(8)
Both training and blind modes have low-complexity asthey require only symbol rate samples, but the data-aided mode enjoys also rapid acquisition relying on asfew as four training symbols [s , s ,−s ,−s ].
The estimator in (8) enables timing synchronizationat any desirable resolution constrained only by theaffordable complexity: i) coarse timing with low com-plexity, e.g., by picking the maximum over N f candi-date offsets τ = nTf , where integer n ∈ [0,N f ); ii) finetiming with higher complexity at the chip resolutionwith τ = iTc , i ∈ [0,Nc ); and iii) adaptive timing(tracking) with voltage-controlled clock (VCC) circuits;the preliminary tests in Figure 6 correspond to framelevel timing resolution. As the TDT algorithms onlyrequire zero ISI, the condition Tf ≥ τL ,0 + Tp can berelaxed to allow for higher data rates, as long as guardframes are inserted between symbols to avoid ISI, muchlike zero-padding in narrowband systems [67].
IEEE SIGNAL PROCESSING MAGAZINE34 NOVEMBER 2004
UWB characterizes transmissionsystems with instantaneousspectral occupancy in excessof 500 MHz or a fractionalbandwidth of more than 20%.
Multi-User TDTThe timing algorithms we have introduced are for apeer-to-peer link where MUI is treated as noise. Thisis reasonable in a multi-user setting provided that userseparability is ensured through channelization. But insuch cases, user separation is sensitive to mistiming.To illustrate how data-aided TDT can be extended toa multi-user setup, suppose one wishes to synchronizeto a single desired user (say user d) who is transmit-ting the training pattern (s , s ,−s ,−s ) and is receivedin the presence of other asynchronous users commu-nicating information-bearing i.i.d. symbols. Equation(7) now becomes
xk(τ) =Nu−1∑u=0
xu,k(τ)
=Nu−1∑u=0
au(k) [au(k − 1)Eu,A (τu)
+au(k + 1)Eu,B (τu)] + ξ(t ),(9)
where Eu,A (τu) := Eu∫ Ts
Ts −τup2
u,R(t )dt , Eu,B (τu) :=Eu
∫ Ts −τu
0 p2u,R(t )dt and τu := (τu,0 − τ) mod Ts are
as before, but with symbols, channels and offsetsbeing user dependent. The desired user’s samples atthe dirty-template correlator output obey xd,k(τ) =(−1)k s 2[−Ed,A (τd) + Ed,B (τd)] + ξ(t ) . Upon averaging(without squaring), we obtain for the user undertraining E{(−1)k xd,k(τ)} = s 2[Ed,B (τd) − Ed,A (τd)] ;while for all other users transmitting zero-mean i.i.d.symbols we have E{(−1)k xu,k(τ)} = 0. This observa-tion suggests the following multi-user TDT estimator[c.f. (8)]
τd,0 = arg maxτ∈[0,Ts )
[K∑
k=1
(−1)k
×∫ (k+1)Ts
kTs
r(t +τ)r(t +τ −Ts )dt
]2
.
Simulations indicate that this multi-user TDT schemerequires long training sequences. It is of interest toexplore multi-user TDT algorithms that remain opera-tional with short or even without training sequences.
Besides low-complexity timing algorithms that areoperational in realistic UWB multi-user settings, analyt-ical studies on system performance and capacity in thepresence of timing errors are topics deserving furtherinvestigation. In the context of narrowband receivers,carrier synchronization and symbol timing issues havebeen investigated thoroughly [34]. Existing solutionsinclude the spectral line generating synchronizers, theML approach, and the cyclostationary approach.Performance is benchmarked using the (modified)Cramér-Rao bound (CRB) [34]. For wireless channelsthat are strongly frequency selective and quasi-staticover time, recent developments in multicarrier modula-tion have stimulated renewed interest in synchroniza-tion. Considering the time-frequency duality betweenUWB and orthogonal frequency division multiplexing(OFDM) systems, these works may prove valuable inpromoting a dual thrust for timing estimation of UWBsignals. [This duality refers to the fact that OFDM con-veys information via impulse-like signals in the frequen-cy-domain (carriers), whereas a UWB system conveysinformation via impulse-like signals in the time-domain(ultra-short pulses).]
Upon synchronization, the receiver can adjust itstiming according to the estimated first arrival time τ0.In the following sections, we assume this estimate to be
IEEE SIGNAL PROCESSING MAGAZINENOVEMBER 2004 35
▲ 6. (a) Normalized MSE of τ0 in (8) and (b) average BER using TDT algorithm. Dashed (solid) curves correspond to (non) data-aided mode.
0 5 10 15 20 25 30 35
10−5
10−4
10−3
10−2
10−1
100
SNR Per Symbol (dB)
(b)
Ave
rage
BE
R
K = 1K = 2K = 16K = 64
No Timing
WithTimingAcquisition
PerfectTiming
−5 0 5 10 15 20
10−4
10−3
10−2
10−1
100
SNR Per Pulse (dB)
(a)
Nor
mal
ized
MS
EK = 1K = 2K = 16K = 64
perfect. Consequently, the multipath delays with respectto the adjusted receiver timing will be such that τ0 = 0.
Rake Reception and Multipath DiversityThe most commonly used UWB receiver is a correla-tion (matched filter) receiver [5], [52], where thereceived signal is correlated with the transmitted pulsep(t ). Conveying information with ultra-short pulses,UWB transmissions can resolve many paths, and arethus rich in multipath diversity (see Figure 3). This hasmotivated research towards designing correlation-basedRake receivers to collect the available diversity [8].
Frame- and Symbol-Rate Rake ReceiversFor DS-, SC-, or MC-UWB systems with PAM modu-lation, the continuous-time received waveform is givenby [c.f. (3)]
ru(t ) = νu(t ) � h (t ) + η(t )
=√Eu
∞∑n=0
au(�n/N f �)c u(n)g (t − nTf ) + η(t ),
(10)
where g (t ) := (p � h )(t ) = ∑Ll =0 αl p(t − τl ) is the
composite pulse-multipath channel. Since the frameduration Tf is up to our disposal, we can choose theframe duration longer than the maximum delay spreadaugmented by one pulse duration, i.e., Tf ≥ τL + Tp ,to avoid interframe interference (IFI). Rake receiverswith Lr fingers sum up weighted outputs (diversitycombining) from a bank of Lr correlators. For clarity,we will consider correlation and diversity combiningseparately. During the nth frame, the template for thel r th correlator (Rake finger with delay τl r ) is the pulsep(t ) delayed by nTf + τl r . Accordingly, the correlatoroutput of the l r th finger during the nth frame is
xu(n; l r ) =∫ nTf +τlr +Tp
nTf +τlr
ru(t )p(t − nTf − τl r )dt . (11)
Upon defining αl r := ∫ τlr+Tp
τlrg (t )p(t − τl r )dt , it fol-
lows that ∫ nTf +τlr +Tp
nTf +τlrg (t − mTf )p(t − nTf − τl r )dt =
αl r δ(m − n), where to establish the latter, we used thatTf > τL + Tp . Substituting (10) into (11), we findxu(n; l r ) = √
Euau(�n/N f �)c u(n)αl r + η(n; l r ) , whereη(n; l r ) is the sampled noise, at the correlator outputof the l r th finger, during the nth frame. For each fin-ger to capture distinct multipath returns, finger delaysmust satisfy τl r − τl r −1 ≥ 2Tp , which yields the maxi-mum number of fingers L r := �τL /(2Tp)�. In practice,Lr ≤ L r is often chosen to trade off performance withcomplexity, leading to receiver options such as all Rake,partial Rake or selective Rake [71]. Notice that the fil-tered and sampled η(n; l r ) stays white if the noise η(t )is white, since τl r are spaced sufficiently apart.
Concatenating the Lr outputs from all fingers dur-ing the nth frame we can form the block:
xu(n) := [xu(n; 0) xu(n; 1) · · · xu(n; Lr − 1)]T
=√Euau(�n/N f �)c u(n)ααα + ηηη(n), (12)
where ααα and ηηη(n) are Lr × 1 vectors constructed bystacking αl r and η(n; l r ) for l r ∈ [0, Lr − 1]. Recallingthat each symbol is conveyed by N f pulses, a total ofN f Lr correlator outputs must be collected, Lr perframe, to decode one symbol. To this end, vectors{xu(n)}(k+1)N f −1
n=kN fcorresponding to the kth symbol can
be concatenated into a vector of size N f Lr × 1 as [c.f.(12)]:
yu(k) := [xT
u (kN f ) · · · xTu (kN f +N f − 1)
]T
=√Euau(k)(cu ⊗ ααα) + ηηη(k), (13)
where ⊗ stands for Kronecker product, cu :=[c u(0), . . . , c u(N f − 1)]T , and ηηη(k) := [ηηηT (kN f ), . . . ,
ηηηT (kN f +N f − 1)]T is the N f Lr × 1 noise vector thatconsists of additive white Gaussian noise (AWGN),MUI, and NBI. Notice that the vector yu(k) in thediscrete-time equivalent input-output relationship (12)contains nothing but the correlator outputs collectedfrom Lr fingers over N f consecutive frames correspon-ding to the kth symbol. To decode a symbol, diversitycombining needs to be carried out. With the N f Lr × 1weight vector βββ, diversity combining yields the decisionstatistics for the kth symbol: zu(k) := βββT yu(k).
If the noise η(t ) is white, maximum ratio combining(MRC) is optimal and gives rise to weight vectorβmf := cu ⊗ ααα , which implements matched filtering(MF). In the presence of MUI and/or NBI, the noiseη(t ) is often colored, which renders MF weights subopti-mal and motivates the use of minimum mean-squareerror (MMSE) weights: βββmmse := Eu[Rη+Eu (cu ⊗ α)(cu ⊗ α)T ]−1(cu ⊗ ααα) , where Rη := E ×{ηηη(k)ηηηT (k)} is the aggregate noise covariance matrix. It isworth clarifying that the MMSE weights βββmmse consistsof N f Lr distinct elements, whereas βββmf consists of repe-titions of Lr distinct elements. Consequently, MF com-bining has lower complexity than MMSE combining.
Established based on a two-step (correlation fol-lowed by weighted combination) approach, (11)requires frame-rate sampling per finger. Interestingly,receiver processing can be implemented even with sym-bol rate sampling. To see this, recall first that the entriesof βββ (that is, [βββ]n ∀n ∈ [0,N f Lr − 1]) are the diversitycombining weights. Rake reception that yields thedecision statistics zu(k) can be realized by correlatingru(t ) with the symbol-long template p s (t ) =∑N f −1
n=0∑Lr −1
l r =0 [βββ]nLr +l r p(t − nTf − τl r ) , and samplingits output every Ts = N f Tf seconds.
IEEE SIGNAL PROCESSING MAGAZINE36 NOVEMBER 2004
To generate the template p s (t ), multiple analogwaveforms p(t ) have to be generated and delayedaccordingly. The delay accuracy will affect decodingperformance. But different from pulse-rate samplingthat requires precise timing at each sampling instance,p s (t ) needs to be generated only once during the chan-nel coherence time. The latter provides the timing cir-cuits sufficient time to stabilize and thus reduces timingjitter effects.
Quantifying the UWB Channel’s Multipath DiversityLet us now quantify the order of the multipath diversitycollected by a Rake receiver with Lr fingers. To thisend, we assume that the channel, which is a realizationof the S-V model, is perfectly known at the receiver. Wealso take the noise to be white, and use the MF weightsfor MRC. With binary modulation, it is shown in [78]that the average BER is upper bounded as follows:
Pe ≤Lr −1∏
l r =0
E[exp
(−ρα2l r/2
)]
=Lr −1∏
l r =0
(1 + ρE
{α2
l r
})−1/2 ≤ (ALr ρ)−Lr /2, (14)
where ρ is the transmit signal-to-noise ratio (SNR),ALr is the geometric average of
{E{α2
l r}}Lr −1
l r =0 , and thesecond inequality holds at high SNR (ρ � 1). Recallthat
{αl r
}Lr −1l r =0 are the amplitudes of the effective chan-
nel taps [c.f. (11)]. Equation (14) confirms that as thenumber of fingers Lr increases, the diversity order alsoincreases. Also notice that although N f Lr samples arecollected in (13), the diversity order is only Lr/2,instead of N f Lr/2, because the degrees of freedom areonly Lr/2, and the factor 1/2 comes from the fact thatthe UWB channel is real. The average BER correspon-ding to binary PAM, and PPM for two values of themodulation index is plotted in Figure 7. As Lr increas-es, the increase in diversity order is evident.
Two remarks are in order. First, the Rake receptionmodel we presented here is valid when TH is absent. Ageneral Rake reception model along with a unifyingsignal-to-interference-and-noise ratio (SINR) analysisof low duty-cycle UWB access through multipath andNBI can be found in [82]; see also [11] for a systemmodel based on oversampling. Secondly, even whenTH is absent, DS-, SC- and MC-UWB may exhibit dif-ferent diversity and coding gains when Tf < τL + Tpand IFI emerges. For further details in this direction,readers are referred to [77].
So far, we have outlined how Rake reception cancollect diversity, provided that the multipath channelcan be estimated at the receiver. Since the receivedwaveform ru(t ) contains many delayed and scaled repli-cas of the transmitted pulses, a large number of fingersis needed for energy capture. Performing Rake recep-tion with appropriate weights on individual fingersentails estimation of the channel impulse response. This
poses a major challenge in UWB communicationsbecause even if one opts to utilize only a few (say theten strongest out of hundreds of) returns, accurate esti-mation of the ten strongest channel gains and their cor-responding delays is required. In a UWB channel withhundreds of multipath returns, channel estimation isoftentimes easier said than done.
Channel EstimationAlthough channel estimation is also critical in the con-text of narrowband and spread-spectrum (SS) systems(see e.g., [63]), and the channel estimators developedfor DS-CDMA can be adapted to UWB systems, theformidably high sampling rates required by the lattermotivates search for alternatives. The main reason isthat the number of parameters to be estimated, i.e., thenumber of delays and amplitudes, can be as large as400 for a typical UWB indoor channel.
Impulse response estimators for UWB channels havebeen developed in [28] and [73] based on the ML cri-terion. The input-output channel identification algo-rithm in [73] uses a single transmitted pulse in theabsence of MUI; whereas the approaches in [28] formimpulse response estimates using either training sym-bols (data-aided), or unknown information-conveyingsymbols (nondata-aided), treating MUI as whiteGaussian noise. Not surprisingly, [73] arrives at thesame channel estimator as the data-aided approach in[28], under the assumption that all multipath compo-nents are resolvable, i.e., |τl1 − τl2 | > Tp , ∀l1 �= l2 .Both data-aided (DA) and nondata-aided (NDA) chan-nel estimators are tested in [28] over a fixed channelwith three multipath components, based on 100 sym-bols. Computational complexity of the ML channelestimators in [28] and [73] increases as the number ofmultipath components increases, and becomes unaf-fordable for a realistic UWB indoor channel. Moreover,sampling at subpulse rate is required to perform chan-nel estimation. In [28], the sampling rate of12.5/Tp ∼ 25/Tp Hz is suggested. With typicalTp = 0.7 ns, the sampling rate is in the formidable
range of 17.9 ∼ 35.7 GHz. At the expense of addition-al hardware, such rates can only be feasible with stag-gered sampling using a bank of polyphase ADCs withaccurate timing control.
More recently, joint timing synchronization andchannel estimation has been pursued. In [6], leastsquares (LS) estimates of the timing offset τ0 and thechannel impulse response h (t ) = ∑L
l =0 αl (t − τl ) areformed using Nyquist rate (subpulse rate) samples ofthe received waveform. The clustered structure of thechannel is taken into account in forming these esti-mates. But in addition to oversampling, this approachentails rather restrictive assumptions which includeτ0 < Tf , τL ,0 < Tf , knowledge of the channel impulseresponse structure and order L. Aiming at sub-Nyquistsampling rate, [31] translates the channel impulseresponse estimation problem into a harmonic retrievalproblem. Under the condition τL ,0 < Tf and with theknowledge of L, this method can only form an estimateof a circularly shifted h (t ) with the unknownτ0(mod Tf ) , simply because harmonic retrievalapproaches are blind to unknown circular shifts. Inother words, [31] cannot estimate timing offsets. Tothis end, the FFT based approach in [68] combinedwith a separate timing estimator offers a viable alterna-tive for offline UWB channel estimation at least forPPM transmissions (similar to [6], [28], and [73]),high sampling requirements prevent online implemen-tation of [68].
Transmitted Reference and PWAM SignalingTo avoid the high sampling rate and computationalcomplexity associated with the estimation of h (t ), analternative approach is to estimate the aggregate analogchannel g (t ) = (p � h )(t ). To this end, there has beena renewed interest in the so termed TR signaling [54],whose application to UWB systems was proposed in[57] for radar detection, and in [21] for communica-tions. In TR systems, each information-conveying pulseis coupled with an unmodulated (a.k.a. pilot) pulse;e.g., per PAM symbol s = {±1} , we transmitv(t ) = p(t ) + s · p(t − Tf ). After multipath propaga-tion, the received waveform is given byr(t ) = g (t ) + s · g (t − Tf ) + η(t ) . With frame dura-tion chosen to be Tf ≥ τL + Tp , the received pilot and
information conveying waveforms are nonoverlapping.The receiver then correlates r(t ) with its delayed ver-sion r(t − Tf ), to yield the symbol estimate [21]:
s = sign{∫
r(t )r(t − Tf )dt}
, (15)
which, in the absence of noise, yields s =sign {s∫ g 2(t )dt } = s .
Equation (15) is reminiscent of the TDT estimator in(8). However, there are fundamental differences betweenthe TR approach for channel estimation and symboldemodulation and the TDT synchronizer. The first maindifference is that TR assumes that noisy templates aretaken at the correct time instances; i.e., τ0 is known andcorrected by τ = τ0; whereas templates in TDT are notonly noisy and distorted by the unknown channel, butalso subject to the unknown τ0. Of course, the secondmajor difference is that TDT does not incur the 50%rate/energy loss of TR, where half of transmitted wave-forms are used as pilots, regardless of the channel.
To optimize the emerging channel estimation per-formance-rate tradeoff, a so-called pilot waveformassisted modulation (PWAM) for UWB systems wasdeveloped in [81]. As depicted in Figure 8, pilot (a.k.a.training) pulses are inserted in PWAM, and an estimateof the aggregate analog channel g (t ) is formed at thereceiver by simply averaging over several received pilotwaveforms (see also Figure 9). This estimate g (t ) canthen be used as a correlator template, to enable inte-grate-and-dump demodulation at frame rate (10 MHzwith a typical Tf = 100 ns).
Clearly, TR is a special case of PWAM where a pilotpulse is inserted after every information pulse. Since thecorrelator relies on a “noisy template,’’ one expects theerror performance at the PWAM detector output to besimilar to that of differential decoding. In the latter,each information symbol is detected by using a receivedsymbol as a “noisy pilot’’ to eliminate the unknownchannel gain from the subsequent received symbol.
Key parameters of PWAM include the number ofpilot pulses inserted per burst and the energy allocationamong pilot and information-conveying pulses. Theseparameters determine not only the channel estimation
IEEE SIGNAL PROCESSING MAGAZINE38 NOVEMBER 2004
▲ 8. PWAM system block diagram. Es(ns) and Ep(np) denote the energy of information-conveying and pilot waveforms, respectively; η(t)is the additive noise; r(t) stands for the received waveform; and h(t) represents the estimate of h(t).
p(t)
p(np)
g(t)
ChannelEstimator ˆ
Detector
1 r(t )
g(t ) = p(t) * h(t )
√
+ ×
(t )
g(t )t = nsNfTf
Tf0∫ ∑
Nf −1
0s(ns) = {±1}
××
ηε
s(ns)√ε
s(ns)
and symbol demodulation performance but also theeffective data rate. In fact, optimal parameters can beselected to not only minimize the mean-square channelestimation error and achieve the CRB but also maxi-mize the average capacity [81]. For any given N f , Tf ,and number of waveforms per burst N = �τc /Tf � thatis determined by the channel coherence time τc , theoptimal number of pilot waveforms is given byNp = N −N f (�N /N f � − 1) [81]. A fraction α of thetotal energy per burst is assigned to pilot waveforms,with α = 0.5 at low SNR or small N , andα = √
N f /(√
N −Np + √N f ) at high SNR or large N .
Moreover, equispaced, equipowered pilot waveformsmaximize the average capacity as well as providerobustness to slow channel variations. In addition, allo-cating the number of pilot pulses according to channelcoherence time, the flexibility inherent in PWAM
allows it to span the gamut of power-limited to band-width-limited scenarios [81].
Figure 10(a) depicts the average capacity correspon-ding to optimal (equi-SNR) PWAM, TR, and the caseof perfect channel estimate, with BPSK modulation.The gap is evident, and is increasing as SNR increases.Notice that after 10 dB, the average capacity corre-sponding to PWAM approaches one, whereas that cor-responding to TR approaches 0.5 due to its inherent50% rate loss. With channel coherence time τc = 0.2ms, and Tf = 100 ns, the burst size is N = 2000, theaverage BER versus SNR ρ is plotted in Figure 10(b)for both optimal PWAM and ideal channel estimate.Random TH code is used, and the MUI is modeled asGaussian noise [72]. When multiple users are present,degradation in BER performance can be observed bothwith PWAM and with a perfect channel estimate.
▲ 10. (a) Average capacity versus SNR and (b) BER performance in the presence of MUI.
0 5 10 15 200
0.2
0.4
0.6
0.8
1
Nominal SNR ρ
(a)
Ave
rage
Cap
acity
(B
it/C
hann
el U
se)
Ideal EstimateOptimal PWAMTR
0 5 10 15 20 25
Nominal SNR ρ (dB)
(b)
10−6
10−5
10−4
10−3
10−2
10−1
100
Ave
rage
BE
R
Nu = 1
Nu = 50
Ideal EstimateOptimal PWAM
Aiming at training-based channel estimation, PWAMis reminiscent of the pilot symbol assisted modulation(PSAM), which was originally developed for bandlimit-ed time-selective channels, and has recently beenextended to narrowband frequency-selective channels[36]. Nevertheless, they differ in several aspects: i)PSAM applies to narrowband channels with ISI, where-as PWAM estimates UWB channels that entail no ISI;ii) PSAM estimates the taps of discrete-time equivalentfrequency-selective channels, whereas PWAM recoversthe equivalent continuous-time channel waveform; andiii) corresponding to one pilot symbol used in PSAM,PWAM allocates multiple pilot pulses across frames andis thus more flexible to strike desirable rate-performancetradeoffs arising with variable channel coherence time.
Although TR was originally advocated for its low-complexity, there has been a number of recent TRimprovements that trade off complexity for performance.In the context of delay-hopped (DH-)TR, [84] proposesan ML receiver whose implementation requires the auto-correlation of the physical channel h (t ) at various delays,and calls for a systematic signal design methodology. InTR and PWAM, the continuous-time aggregate channelis estimated from the pilot waveforms only. Furtherexploiting the channel information embedded in theinformation-conveying waveforms, ML and generalizedlikelihood ratio tests (GLRTs) schemes were put forth in[7]. Trading off complexity for performance, [7] turnsout to be a channel impulse response estimator with highcomplexity as the ones in [28] and [73].
Differential and Noncoherent UWB As both timing synchronization and channel estimationpose major challenges in UWB communications, non-coherent UWB radios that bypass both of these chal-lenging tasks offer interesting alternatives to explore.
Consider a single-user link with binary PAM withDS/SC/MC and/or TH spreading codes. Moreover,let us differentially encode the binary PAM (BPSK)symbols a(k) as a(k) := a(k) · a(k − 1) and transmitthe encoded sequence a(k). The received waveform isthen given by [c.f. (5)]:
r(t ) =√E
∞∑k=0
a(k)pR(t − kTs − τ0) + η(t ),
where the timing offset τ0 �= 0 in general. Performingthe integrate-and-dump operations using dirty tem-plates as in (6), the symbol-rate samples are [c.f. (7)]
xk =∫ Ts
0r(t + kTs )r(t + (k + 1)Ts )dt
= a(k)EA (τ0) + a(k + 1)EB (τ0) + ξ(k), (16)
where we used the fact that a(k) = a(k)a(k − 1) inestablishing the second equality.
If one opts to estimate the timing offset using, e.g.,the TDT approach, and compensate it (almost) perfect-ly, then (16) can be considered approximately withτ0 = 0. In this case, EA (0) = 0, EB (0) = ER and (16)
boils down to xk = a(k + 1)ER + ξ(k), which can beeasily demodulated. In fact, (16) with τ0 = 0 shows thatthe differential UWB system in [7] and [19] can beviewed as a special case of the noncoherent approach.This differential UWB receiver is semicoherent since itrequires timing but bypasses channel estimation. Theperformance of such a differential (DIFF) scheme isshown in Figure 11. It is worth stressing that with per-fect timing and for the same information rate, differen-tial UWB outperforms TR simply because the latter uses50% energy on pilots, as confirmed in Figure 11.
But even when synchronization is attempted, timingerrors are inevitable and thus τ0 �= 0. In this case,EA (τ0) and EB (τ0) are also nonzero and direct applica-tion of differential demodulation will lead to consider-able performance degradation. Simulated performanceof DIFF-UWB and TR in the presence of timing offsetis shown in Figure 11. Notice that though TR is morerobust against timing offsets than DIFF-UWB, bothyield unacceptable performance. However, we observethat the channel energies EA (τ0) and EB (τ0) in (16) canbe viewed as the impulse response taps of an unknownfirst-order equivalent ISI channel [83]. This interestingviewpoint motivates development of noncoherent algo-rithms for joint symbol detection and estimation of theunknown equivalent channel based on the “dirty corre-lator’’ output samples in (16). It is worth stressing thatonly two equivalent channel taps are to be estimatedwith noncoherent UWB, as apposed to hundreds oftaps in the underlying UWB physical channel and theanalog aggregate channel in TR and PWAM. Several
IEEE SIGNAL PROCESSING MAGAZINE40 NOVEMBER 2004
▲ 11. Performance of TR and differential (DIFF) UWB in the pres-ence and absence of timing offsets; and that of incoherent UWBradios using VA and CML demodulators in the presence of timingoffsets.
−5 0 5 10 15 20
10−4
10−3
10−2
10−1
100
E/σ2 (dB)
Ave
rage
BE
R
Without Timing
Perfect Timing DIFFTRVACML
noncoherent schemes have been recently considered in[83]. One approach is the ML sequence demodulatorusing Viterbi’s algorithm (VA) along with its low-com-plexity per-survivor variants. Further trading off per-formance for complexity, decision-directed conditionalML (CML) alternatives are also explored in [83]. Theperformance of noncoherent UWB using VA and CMLschemes is depicted in Figure 11. Bypassing both tim-ing synchronization and channel estimation, these non-coherent algorithms exhibit as little as 3 dB loss incomparison with differential UWB with perfect timing.
Multi-Antenna UWB SystemsWe have seen how the error performance of UWBradios can be boosted by collecting multipath diversity[8], [21], [81]. However, Rake reception in UWB mayrequire a large number of finger amplitudes and delayswhich are cumbersome to obtain [28], [73]. Avoidingestimation of the channel’s impulse response, PWAMand TR require an analog delay line at the receiverwhich may not be easy to implement [13]. Differentialand noncoherent schemes enjoy low complexity at theprice of suboptimum performance. In a nutshell,although rich multipath diversity is enabled with UWBtransmissions, its collection at the receiver may faceimplementation difficulties, especially when the channelvariations are relatively rapid.
On the other hand, multi-antenna-based space-time(ST) systems offer an effective means of enabling spacediversity via spatial multiplexing, which has the poten-tial to improve not only error performance, but alsocapacity. Motivated by these attractive features, an ana-log ST coding scheme was developed for UWB com-munications in [78]. With the channel coherence timebeing at least one symbol duration τc ≥ Ts = N f Tf ,the following ST coded matrix is transmitted:
N f /2−1∑n=0
[v00
u (n; t )v10
u (n; t )v01
u (n; t )v11
u (n; t )
], ∀t ∈ [0, Ts ) (17)
where vklu (n; t ) denotes the waveform transmitted from
the kth transmit antenna during the (2n + l )th frameduration. The matrix entries in (17) can be expressedexplicitly as
v00u (n; t ) = au(2n)c u(2n)p
(t −2nTf
−c T Hu (2n)Tc −bu(2n)�
)v01
u (n; t ) = au(2n)c u(2n+1)p(t −(2n+1)Tf
−c T Hu (2n+1)Tc −bu(2n)�
)
v10u (n; t ) = au(2n)c u(2n+1)p
(t −2nTf
−c T Hu (2n)Tc −bu(2n)�
)v11
u (n; t ) = − au(2n)c u(2n)p(t −(2n+1)Tf
−c T Hu (2n+1)Tc −bu(2n)�
),
where we used the fact that au(2n + 1) = au(2n), andbu(2n + 1) = bu(2n), ∀n ∈ [0,N f /2 − 1]. This UWB-specific scheme is different from existing ST codes usedfor digital linear modulations [3] in three aspects.▲ i) Digital symbol-by-symbol versus analog within eachsymbol waveform. Existing STC schemes operate on digi-tal symbols, whereas this UWB-tailored STC approachencodes pulses within symbol waveforms; it is this UWB-specific aspect that enables enhanced space-multipathdiversity gains; ▲ ii) Flat or ISI-inducing channels versus frequency-selec-tive channels: Existing STC schemes are designed eitherfor flat, or, for ISI-inducing MIMO fading channels,whereas this analog ST code is tailored for non-ISIinducing UWB MIMO channels that are rich in multi-path diversity; ▲ iii) Linear and nonorthogonal nonlinear modulationsversus linear and orthogonal nonlinear modulations withcoherent or noncoherent reception. Existing STC schemesentail linear modulators and coherent demodulators,except for the works of [20] that deal with the nonco-herent case. However, the latter do not considerorthogonal nonlinear modulations (orthogonal PPM)that are of interest to UWB and lead to ST codingschemes that guarantee full diversity and symboldetectability, even with noncoherent reception.
With one receive and two transmit antennas andPAM modulation in the absence of TH, it can beshown that the average BER for binary modulations athigh receive-SNR ρ is upper bounded by [78]:
Pe ≤(
ALr
2ρ
)−Lr
, (18)
where Lr is the number of Rake fingers, and ALr is thegeometric average of
{E{α2
l r}}Lr −1
l r =0 . Compared with (14),this ST coded transmission scheme doubles the diversityorder, but loses 3 dB coding gain, due to the power splitbetween the two antennas at the transmitter. In anindoor environment with low mobility, the channelcoherence time τc is generally much larger than theframe duration Tf . This suggests employment of aninterleaver in conjunction with ST coding. With themultipath channel remaining invariant over one symbolduration Ts = N f Tf , and changing independently fromsymbol to symbol, it is shown in [78] that using aninterleaver with depth Nd ≤ N f yields an average BERupper bounded as follows:
Pe ≤(
ALr
2Ndρ
)−Nd Lr
. (19)
Achieving diversity Nd times that in (18) with the sameLr and identical channel estimation complexity, theprice paid is decoding delay by Nd symbols and loss incoding gain by a factor Nd .
IEEE SIGNAL PROCESSING MAGAZINENOVEMBER 2004 41
While enhancing the diversity gains by deploying anadditional antenna, ST-coded multi-antenna UWBradios can be implemented with conventional analogRake receivers having a small number of fingers. ST-UWB also enables noncoherent reception for jointdiversity collection, which bypasses the cumbersomechannel estimation task [78]. Figure 12 shows simulat-ed performance of an ST-coded multi-antenna UWBsystem with coherent and noncoherent reception in thepresence of timing jitter. Simulations reveal consider-able improvement in both BER, and enhanced immu-nity against timing jitter. The latter suggests theoreticalanalysis of its robustness against timing jitter, and thepotential of multiple antennas to facilitate synchroniza-tion of UWB systems.
Multiple Access and Interference SuppressionIn the presence of multiple users and overlaying nar-rowband systems, single user detection is typically sub-optimal, and special effort is needed to cope with MUIand/or NBI effects. This subsection will be devoted tosuch issues.
Single-Carrier and Multicarrier Codes: Let us recall the baseband multi-access UWB setup in(3) with the user-specific spreading codes c u(n) beingsymbol-periodic with period N f . We also normalizethe spreading codes such that
∑N f −1n=0 c 2
u(n) = N f . InDS-UWB, orthogonal binary sequences c u(n) ∈ {±1}are employed:
∑N f −1n=0 c u1(n)c u2(n) = N f δ(u1 − u2) .
Similar to TH-UWB, these codes are constant-modulusand have been used in e.g., [15], [48], [76]. However,utilizing the entire bandwidth, they are not flexible inhandling NBI. To this end, digital single-carrier (SC-)and multicarrier (MC-)UWB have been introducedrecently, for low-power low-duty-cycle baseband UWBmultiple access [77].
Casting the user-specific spreading codes c u(n) intoN f × 1 vectors cu with user index u ∈ [0,Nu − 1], theconstruction of SC/MC-UWB codes cu starts withNu = N f orthogonal baseband digital subcarriers∀k ∈ [0,N f − 1]:
[fk]n =
cos(
2πnN f
k)
, n = 0, or, n = N f /2,√
2 cos(
2πnN f
k)
, n ∈ [1,N f /2 − 1],√
2 sin(
π(2n−N f )
N fk)
, n ∈ [N f /2 + 1,N f − 1],
where [fk]n denotes the (n + 1) st entry of the columnvector fk . The discrete-time Fourier transform (DTFT)of fk contains sinc functions, as depicted in Figure13(a). Now let {c(o)u }N f −1
u=0 denote any set of orthonor-mal spreading codes of length N f . User-specific codesfor baseband MC-UWB can then be constructed as lin-ear combinations of digital subcarriers
IEEE SIGNAL PROCESSING MAGAZINE42 NOVEMBER 2004
▲ 12. (a) Incoherent reception; (b) coherent reception in theabsence of timing jitter; (c) coherent reception in the presence oftiming jitter (from top to bottom Lr = (1, 4, 16)). Timing jitter ismodeled as exponentially distributed with mean 0.5 ns; Nt and Nr
stand for the number of transmit and receive antennas, respectively.
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Nt = 1, Nr = 1
Lr = 1
Lr = 1
Lr = 4
Lr = 4
Lr = 16
Lr = 16
Nt = 2, Nr = 2
Nt = 1, Nr = 1Nt = 2, Nr = 2
Nt = 1, Nr = 1Nt = 2, Nr = 2
cu =N f −1∑
k=0
[c(o)
u]
k fk . (20)
Notice that baseband SC-UWB is subsumed by(20), if one selects
{c(o)
u
}N f −1u=0 as distinct columns of a
N f ×N f identity matrix. (For each user (subcarrier) tooccupy exactly the same bandwidth, a 0.5/N f shift hasto be introduced to the digital subcarriers as detailed in[77].) Different from orthogonal frequency divisionmultiple access (OFDMA) in narrowband systems [67],the baseband SC/MC codes in (20) are real. Spreadingevery symbol on a single digital subcarrier, each SC-UWB user occupies 2Tf /Tp � 2 frequency bands (seeFigure 13), and the resulting transmissions enjoy multi-path diversity gains; whereas narrowband OFDMA sys-tems have to resort to channel coding and/orfrequency hopping to mitigate frequency-selective fad-ing at the expense of (possibly considerable) bandwidthoverexpansion.
In [77], the performance of DS-, SC- and MC-UWB is quantified in terms of diversity and codinggains, when IFI is present but ISI is avoided by zero-padding or cyclic-prefixing. Analysis shows thatSC/MC codes enable full multipath diversity gain, andMC codes can further effect maximum coding gain.Additionally, SC- and MC-UWB codes offer flexibilityin handling (e.g., WLAN induced) NBI, simply byavoiding the corresponding digital subcarriers. Thesame flexibility in avoiding NBI is also present in thespectrally encoded (SE-) UWB system of [9]. WithSC/MC codes, the ultrawide bandwidth is partitionedinto segments, each corresponding to a digital carrier.Likewise, SE-UWB also partitions the bandwidth into anumber of frequency bands (so-called frequency“chips’’). A sequence of codes (much as c(o)
u in (20) forSC/MC-UWB) can then be applied on these “chips’’to enable MA. As a result, both SC/MC- and SE-UWB can avoid NBI affected frequency segments—digital carriers in SC/MC-UWB and frequency “chips’’in SE-UWB—by nulling the corresponding elements ofthe code vector c(o)
u . Constructed based on digitalcos/sin functions, SC/MC-UWB facilitates low-com-plexity implementation using standard discrete-cosine-transform (DCT) circuits. (This implementationadvantage also distinguishes them from the analog SC-UWB codes introduced in [66] that offer robustnessagainst user asynchronism.) SE-UWB, on the otherhand, can be implemented using surface acoustic wave(SAW) devices [9]. As SC/MC-UWB, the resultantSE-UWB also enables multipath diversity by sweepingthe ultra-wide bandwidth within pulse duration Tp ,much as in fast frequency hopping (FH) systems.
Performance comparisons among DS, SC, and MCspreading codes, individually or in combination withTH codes, have been carried out when NBI is pres-ent, under a general SINR analysis framework thatallows for various Rake finger selections [82]. Several
IEEE SIGNAL PROCESSING MAGAZINENOVEMBER 2004 43
▲ 13. (a) Subcarriers in baseband SC- and MC-UWB (Nf = 4,Tf/Tp = 4, Tp ≈ 0.2 ns). Average BER corresponding to DS-, SC-,and MC-UWB over AWGN with NBI at the GPS band (center fre-quency 1.2 GHz, bandwidth 20 MHz) in (b) AWGN channel; (c)multipath channel (selective-Rake with MMSE combining).
interesting conclusions can be drawn from these com-parisons. In particular, analytical and simulated resultsshow that MC-UWB provides code-independent BERperformance in the presence of multipath and NBIeffects, regardless of the Rake finger selection. TheBER averaged over all codes is shown in Figure 13(b)for AWGN channels and in Figure 13(c) for multipathchannels, both in the presence of NBI. From thesecomparisons, baseband MC-UWB emerges as anattractive choice for antijam applications withoutnulling any subcarriers. This avoids additional process-ing for collision detection or clear channel assessment(CCA), and ensures small size transceivers with lowpower consumption.
Different from the WPAN multiband proposals thatrely on analog carriers (see, e.g., [4]), the SC/MCcodes achieve multiband transmission using basebandoperations. Compared to analog multiband solutionsthat entail multiple local oscillators, carrier-free multi-band SC/MC-UWB access not only enjoys low-com-plexity implementation but also avoids dealing withcarrier frequency offsets that are known to degradeerror performance (of e.g., OFDMA) severely.
The schemes we have discussed so far for UWB mul-tiple access are either constant modulus or providerobustness and flexibility against NBI. But withDS/SC/MC spreading codes, perfect multi-user sepa-ration with Nu = N f users is possible only ifTf ≥ τL + Tp , that is, when rate considerations allowone to select a frame duration which is longer than themaximum delay spread augmented by one pulse dura-tion. When TH spreading codes are employed, or whenTf < τL + Tp is chosen to achieve high data rates, themutual orthogonality among users’ spreading codes isdestroyed after multipath propagation [15], [25]. Thisintroduces MUI, which compromises capacity anderror performance considerably [25], unless complexreceiver algorithms are employed to mitigate it.
Conventionally, MUI is treated as Gaussian noise,and is suppressed statistically with the aid of (strict)power control [72]. However, when the number ofusers is not large enough, the Gaussian approximationof MUI is not valid, especially with imperfect powercontrol [10], [16].
MUD for UWB AccessTo improve upon the statistical MUI cancellation,UWB-MA utilizing multi-user detection (MUD) waspursued in [32]. In fact, [32] established the first digi-tal model for UWB-MA systems, where novelapproaches were developed to account for the nonlin-ear PPM modulation and TH spreading. The digitalmodel triggered the transition from analog UWB todigital UWB, and these novel approaches are used alsoin recent UWB modeling attempts (see, e.g., [11]).Specifically, the continuous time UWB signal usingnonlinear M -ary PPM modulation is viewed as M par-allel branches each realizing a shifted version of the
pulse stream [32], [42], [76]. In other words, thetransmitted signal using PPM and TH codes can beexpressed as [c.f. (2)]:
vu(t ) =√Eu
+∞∑n=0
p(t − (
nNc + c T Hu (n)
)Tc − bu(n)�
)
=M −1∑m=0
v(m)u (t ), (21)
where v(m)u (t ) := √
Eu∑+∞
n=0 b (m)u (n)pm
(t − (
nNc +c T H
u (n))Tc
)with b (m)
u (n) := δ(bu(n) − m) , andpm(t ) := p(t − m�) , ∀m ∈ [0, M − 1]. As to thenonlinear TH codes, the frame-rate sequence c T H
u (n)
can be uniquely mapped to a chip-rate TH sequencec T H
u (k) := δ(c T H
u (�k/Nc �) − (k mod Nc ))
for thekth chip. When c T H
u (n) has period N f , it can be veri-fied that c T H
u (k) has period N f Nc . But the chip-rateTH sequence can be viewed as a DS code with {0, 1}entries, and thus enables representation of nonlinearTH spreading with an equivalent linear DS spreading.Consequently, we have [c.f. (21)]
v(m)u (t ) =
√Eu
+∞∑k=0
v(m)u (k)pm(t − kTc ),
where v(m)u (k) := b (m)
u (�k/(NcN f )�)c T Hu (k) is the sym-
bol sequence after TH spreading. Let g (m ′,m)u (l ) :=
(pm � hu � pm ′)(−t )|t=l Tc of order Lu be the chip-sam-pled discrete time equivalent finite impulse response(FIR) channel. Then, the chip-sampled matched filteroutput of the m ′th branch at the receiver is
xm ′(k)=Nu−1∑u=0
M −1∑m=0
Ld∑l =0
√Eu g (m ′,m)
u (l )v(m)u (k− l )+ηm ′(k),
(22)
where ηm ′(k) denotes the sampled noise and Ld :=maxu Lu . It is shown in [32] and [76] that (22) canalso be represented in vector-matrix form by utilizingblock spreading in lieu of symbol spreading. The result-ant input-output relationship is
xm ′(i) =Nu−1∑u=0
M −1∑m=0
√Eu
[G(m ′,m)
u,0 v(m)u (i)
+ G(m ′,m)u,1 v(m)
u (i − 1)]
+ ηηηm ′(i). (23)
Extracted from a continuous-time UWB transmissionwith nonlinear PPM modulation and TH spreading, thedigital model in (23) consists of only linear operations.In addition, its serial form (22) and parallel (vector-matrix) form (23) both capture MUI and ISI [manifested
IEEE SIGNAL PROCESSING MAGAZINE44 NOVEMBER 2004
as interblock interference (IBI) in (23)] after multipathpropagation. As a result, this digital model allows directadaptation of narrowband MUD to UWB systems. Anumber of works have followed this approach.Recursive MUD schemes are also pursued for DS-UWBsystems, without assuming channel knowledge at thereceiver [27]. It has been illustrated by simulations thatsuch recursive MUD receivers outperform Rakereceivers with finite fingers in suppressing both MUIand NBI. However, MUD-based schemes entail sam-pling at subpulse rate of up to 16 GHz, they require aninitializing training sequence of 500 symbols, and relyon decision directed operation that is prone to errorpropagation. To ensure convergence, the channels forall users must also remain invariant for a sufficientlylong period (500 symbols) [27].
Multistage Block-Spread (MSBS) UWB AccessWith chip duration Tc ≈ Tp and symbol durationTs = N f Nc Tc , the bandwidth expansion factor in atypical UWB system is N f Nc . But the maximum num-ber of users is Nu = Nc with orthogonal TH, andNu = N f with orthogonal DS/MC/SC, both of whichhave lower user capacity than that allowed by the band-width expansion factor. There is certainly space forimprovement in terms of multi-user capacity. To thisend, a promising so termed multistage block-spread(MSBS) design of spreading codes has been developed[76]. With MSBS-UWB, the number of users that canbe accommodated is Nu = N f Nc by employingDS/SC/MC codes in combination with TH codes.More important, MSBS-UWB provides MUI-resilientperformance, even after (possibly unknown) multipathpropagation. Relying on two stages of block-spreadingand interleaving, the mutual orthogonality amongusers’ spreading codes is guaranteed even after propa-gation through frequency-selective multipath channels.
Consequently, only the desired user’s spreading codesare required at the receiver, and a single-user detectoris sufficient. As a result, deterministic MUI-resilientreception with low-complexity code-matched filteringbecomes possible without loss of ML optimality, andwith full multipath diversity gains [76]. Figure 14 com-pares the BER of MSBS-UWB with conventional TH-UWB using a Rake receiver [52], and with theMUD-UWB receiver [32], over two channel models[25], [50], [76]. In contrast to conventional TH-UWB, MSBS-UWB shows no degradation as the num-ber of users increases. With much lower complexity andmany more active users, it also outperforms the MUD-UWB multiple access system.
Single-Band or Carrier-Modulated Multiband?So far, we have focused on baseband UWB signaling,which occupies a single UWB spectrum from near DCup to a few GHz. Such carrier-free transmissionsrequire minimal RF components. But since UWBradios occupy extremely broad bandwidth, theyinevitably overlay existing narrowband RF services,such as GPS, federal aviation systems (FAS), andWLAN. To regulate coexistence, the FCC has releaseda spectral mask in its first UWB R&O that limits theequivalent isotropic radiated power (EIRP) spectrumdensity with which UWB radios are allowed to trans-mit. To realize the attractive features of UWB radiosunder this FCC regulation, the following challengeshave to be addressed:▲ i) Operating below the noise floor, UWB radiosmust emit at low power. But as any other communica-tion system, the performance of a UWB system heavilyrelies on the received SNR that is proportional to thetransmit power. Maximization of the latter, however,can be achieved only if the spectral shape of the FCCmask is exploited in a power-efficient manner.
IEEE SIGNAL PROCESSING MAGAZINENOVEMBER 2004 45
▲ 14. (a) BER comparison of a conventional UWB-MA system with a MSBS-UWB system; (b) BER versus SNR for zero-forcing (ZF) receiv-er with Nf = 8, Nc = 4. Number of active users: four in MUD-UWB system, 32 in MSBS-UWB system.
▲ ii) To avoid interference to (and from) coexisting nar-rowband systems, their corresponding frequency bandsmust be avoided. Since the nature and number of coexist-ing services may change depending on the band used, theavoidance mechanism should also be sufficiently flexible.▲ iii) Traditionally, UWB multiple access is achieved byemploying TH codes. User capacity of UWB radios canbe further improved by partitioning the ultra-widebandwidth into subbands, allowing users to hop amongthese subbands according to user-specific hopping pat-terns. Since hopping should span subbands centeredaround different frequencies, UWB pulse shapers mustbe agile with respect to FH to enhance system capacityand reinforce the low probability of interception anddetection (LPI/LPD).
All these requirements heavily rely on a basic trans-mitter module—the pulse shaper. Unfortunately, thewidely adopted Gaussian monocycle is not flexibleenough to meet these challenges [74]. To design pulseshapers with desirable spectral properties, twoapproaches can be employed: carrier-modulationand/or baseband analog/digital filtering of the base-band pulse shaper. The former relies on local oscillatorsat the UWB transmitter and receiver, which beingprone to mismatch give rise to carrier frequency off-set/jitter (CFO/CFJ). In multiband UWB systemswith FH, multiple CFO/CFJ emerge with thisapproach. Although passing the (Gaussian) pulsethrough a baseband analog filter can reshape the pulsewithout introducing CFO/CFJ, it is well known thatanalog filters are not as flexible when compared to digi-tal filters, which are accurate and perfectly repeatable.
Optimal UWB Pulse ShapersPulse shapers respecting the FCC mask have been pro-posed in [40] and [29]. Targeting multiple orthogonal
pulses that are FCC mask compliant, [40] developedpulses in digital form that correspond to the dominanteigenvectors of a matrix, which is constructed by sam-pling the FCC mask. The resulting pulses meet theFCC mask, but do not optimally exploit the allowablebandwidth and power [see Figure 15(a)].Unfortunately, converting the digital designs in [40]into analog form entails digital-to-analog (D/A) opera-tions at 64 GHz rate. Imposing minimum modificationto the analog components of existing UWB transmit-ters and aiming at pulses that not only meet, but alsooptimally exploit the FCC mask, [29] introduced opti-mal pulse shapers for UWB using the “workhorse’’ ofdigital filter design methods, namely the Parks-McClellan algorithm [39]. This idea is to start withany continuous-time spectral shaping waveform pa(t ),including the Gaussian monocycle, and design thepulse shaper as
p(t ) :=M −1∑
m=0
wm pa(t − mT0), (24)
where wm are tap coef ficients with spacing T0 .Evidently, the choice of T0 affects wm , and thus the fea-sibility, optimality and complexity of the overall design.It is shown in [29] that T0 = 35.7 ps is suitable foroptimal designs with full-band control, and T0 = 73 psfor suboptimal designs that trade off performance forcomplexity. For any T0 value and pa(t ) with FT Pa( f ),[29] casts the pulse shaper design problem boils downto a digital filter design problem, where an M -tap FIRfilter with coefficients {wm}M −1
m=0 is to be designed suchthat its DTFT magnitude |W (e j2πF )| approximatesD(F/T0) , ∀F ∈ [0, 0.5], where D( f ) := Pd( f )/
|Pa( f )|, ∀ f ∈ [0, 0.5/T0] and Pd( f ) can be chosen to
IEEE SIGNAL PROCESSING MAGAZINE46 NOVEMBER 2004
▲ 15. (a) Baseband pulse shapers and the FCC mask for indoor communications. A—Gaussian monocycle with Tp = 0.37 ns; B—Gaussianmonocycle with Tp = 0.19 ns; C—a pulse shaper in [98]; D&E—pulse shapers in [99]; (b) Multiband UWB using baseband pulse shapers.
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−70
−65
−60
−55
−50
−45
−40
−35
Frequency (GHz)
(b)
Pow
er (
dBm
)
FCC Mask for Indoor Comm. Subband 1Subband 2Subband 3
satisfy any desirable spectral mask specifica-tion. Instead of casting the UWB pulseshaper design as a filter design problem, it isalso possible to view it as a semi-definite pro-gramming (SDP) optimization problem; see[75] for SDP related designs.
Pulse shapers designed according to (24)exploit the FCC spectral mask optimally,and offer flexibility for (dynamic) avoidanceof NBI. Comparing three pulse shaperdesigns in Figure 15(a), it follows that, inorder for a Gaussian monocycle pa(t ) toadhere to the FCC mask, it must transmit atEu ≤ 0.506 Ts µJ when Tp = 0.37 ns, and atEu ≤ 3.43 Ts µJ when Tp = 0.19 ns; pulseshaper C can transmit at Eu ≤ 0.25 Ts mJ,while pulse shapers D and E can transmit atEu ≤ 0.88Ts mJ, and Eu ≤ 0.91Ts mJ, respectively [29].This shows that the optimal designs in [29] can offer2–3 orders of magnitude more power-efficient pulseshapers. Furthermore, they are well suited for digitalimplementation of subband hopping (or FH) codes,which are used with multiband UWB systems. The lat-ter have gained popularity recently, because they canreplace the traditional TH codes for MA, or comple-ment them to enhance capacity and covertness [seeFigure 15(b)].
Multiband UWB AccessBaseband pulses can also be modulated onto carrier(s)to higher frequency band(s). Recently, there has beenan increasing interest in transmissions with multiplesubbands, which we henceforth term multiband UWB(see e.g., [1], [4], [47]). In multiband UWB radios,pulses are modulated by several analog carriers to sub-bands 500−800 MHz wide (see Figure 16).Compared to Figure 15, it is evident that multibandUWB can make more efficient use of the FCC mask,minimize interference to existing narrowband systemsby flexible band selection, and facilitate future scalabili-ty of the spectrum use. Moreover, since each bandoccupies only a fraction of the bandwidth of a single-band transmission, the pulse shaper employed in multi-band UWB can have much longer duration in time,which in turn eases implementation of the ADC, andenables implementation with off-the-shelf (OTS) com-ponents capitalizing on existing mature technology forwideband communications.
As in single-band UWB, challenges facing multibandUWB systems include timing acquisition and channelestimation. The (non)data aided timing algorithms forsynchronization, and channel estimators, includingTDT, TR and PWAM, we outlined for single-bandUWB apply also to multiband alternatives on a per bandbasis. However, due to the introduction of multiplecarrier frequencies, new challenges arise. Recall that inthe baseband MC-UWB systems, multiple digital sub-carriers are utilized; whereas multiband UWB radios
rely on analog carriers, and thus have to deal with mul-tiple carrier frequency offsets (CFO) arising from themismatch of multiple transmit-receive oscillators.Unless compensated for, CFO is known to degradeperformance severely, especially in carrier-modulatedMC-UWB transmissions. For multiband UWB, carrierfrequency synchronization is more challenging becausethere are more than one carrier frequencies, especiallywhen OFDM or fast frequency-hopping is employedacross multiple bands. For this reason, multiband UWBcalls for CFO sensitivity studies, low complexity CFOestimators, and per-subcarrier based channel estimationmodules. To this end, existing techniques for widebandcommunications can serve as starting points.
Multiband UWB multiple access schemes also haveto be designed by taking all bands into consideration.Notice that the carrier frequencies (center frequencies)of subbands in Figure 16 span a wide range from 3.35GHz up to 10.35 GHz with a 500 MHz multibandpartitioning. Consequently, the bands to the right(towards the 10.6 GHz end) tend to be more lossythan the bands to the left (towards the 3.1 GHz end).Therefore, an assignment confining each user to a sin-gle fixed band will result in user-dependent perform-ance, and will not enable the full multipath diversity. Ina nutshell, a multiband based UWB-MA scheme mustaccount for the following issues: i) flexibility to accom-modate various schemes (SC or MC) for multipleaccess, ii) capability to collect full multipath diversity,and iii) scalability in spectral efficiency (from low, tomedium, and high data rates).
Cross-Band FLEX-UWB AccessTo meet the aforementioned requirements, we haverecently introduced a cross-band flexible UWB MAscheme for high-rate multipiconet WPANs [80]. Theso termed FLEX-UWB design is built on the basis ofthe MSBS-UWB approach we outlined earlier toachieve resilience against MUI in an environment withmultiple piconets. To allow for various selections ofspreading codes, FLEX-UWB relies on an FFT matrixFNs , of size Ns ×Ns , where Ns denotes the number of
IEEE SIGNAL PROCESSING MAGAZINENOVEMBER 2004 47
▲ 16. Multiple subbands in multiband UWB.
1 2 3 4 5 6 7 8 9 10 11 12
−40
−45
−50
−55
Frequency (GHz)
Pow
er (
dBm
)
FCC Mask for Indoor CommunicationsMultiple Subbands in Multiband UWB
GPSBand
802.11b/gBand
802.11aBand
subcarriers per subband. Let Nu denote the total num-ber of users across all piconets, and define P := Ns /Nu .Built on the user-specific Nu × 1 spreading code cu , thebasic block-spreading matrix is given by
Cu := [FH
Ns(cu ⊗ IP )
] ⊗ Tzp , (25)
where IP is a P × P identity matrix, and Tzp is a(K + Ld) × K matrix that pads Ld zeros to a K × 1vector, with K being the size of information symbolblocks, and Ld denoting the order of the discrete-timeequivalent channel. The resulting multiple accessscheme depends on the selection of the spreadingcodes {cu}Nu−1
u=0 . Time-division multiple access (TDMA),where each user utilizes the whole bandwidth at differ-ent time slots, can be achieved by choosing {cu}Nu−1
u=0 ascolumns of FFT matrix FNu , of size Nu ×Nu .Choosing the spreading codes as columns of aNu ×Nu identity matrix results in frequency-divisionmultiple access (FDMA), where each user utilizes partof the bandwidth but can transmit all the time. Andwith {cu}Nu−1
u=0 being any set of mutually orthogonalvectors, code-division multiple access (CDMA) can beachieved, where each user utilizes the entire bandwidthall the time with a user-specific signature. It turns outthat the code design (25) can be applied simultaneous-ly over all (or, selected) subbands, and guarantees: i)MUI-resilient UWB-MA; ii) full multipath diversity;and iii) bandwidth efficiency of K /(K + Ld) [117].Notice that the bandwidth efficiency of FLEX-UWB isthe same as that of MSBS-UWB, and is tunable byvarying the symbol block size K , which also affects thedecoding delay.
As mentioned before, choosing {cu} to be columns ofthe identity matrix INu gives rise to FDMA. In particu-lar, replacing Tzp with an identity matrix IK , and select-ing K = 1, (25) boils down to: Cu = FH
Ns(cu ⊗ IP ).
Such a code design, coupled with cyclic-prefix insertion(removal) at the transmitter (receiver), corresponds toan orthogonal (O)FDMA UWB scheme, where eachuser occupies all P subcarriers of each subband [80]. Itis well known that OFDMA can be implemented effi-ciently with the FFT module, but has to resort to (pos-sibly considerable) bandwidth overexpansion to mitigatefrequency-selective fading. To amend this problem, across-band linear complex field (LCF) precoder is alsointroduced in [80]. (For tutorial treatments of LCF(pre)coding, the reader is referred to [30] and [67].)The transmission corresponding to FLEX-UWB withthe LCF-OFDMA choice is depicted in the example ofFigure 17, where each subband consists of Ns = 4 sub-carriers, the first of which is assigned to piconet 1. Thenumber of information symbols per block is four, whichis the total number of subcarriers (across all subbands)assigned to a single piconet. The symbol block is firstpassed through an LCF encoder (a square matrix),whose output is the coded symbol block v. Notice thatno redundancy is introduced here. The coded symbolblock v is then evenly distributed to all subbands andtransmitted using an OFDMA scheme, which consistsof selecting user-specific subcarriers, inverse FFT, andcyclic-prefix insertion.
Capacity in the UWB RegimeShortly after his landmark paper [53], Shannon pointedout that as the bandwidth B grows, the AWGN chan-nel capacity approaches:
IEEE SIGNAL PROCESSING MAGAZINE48 NOVEMBER 2004
▲ 17. FLEX-UWB: cross-band LCF-OFDMA (sk: symbols; vk: coded symbols; number of subbands: 4; number of piconets: 4; total numberof users Nu = 4; number of subcarriers per subband Ns = 4).
1234123412341234
LCFCoding
1 2
3 4
Piconet 1 Piconet 2
Piconet 3 Piconet 4
Subband 1
Subband 2
Subband 3
Subband 4
v0v1v2v3
s0s1s2s3
Freq
uenc
y
Time One OFDM SymbolDuration
CyclicPrefix
C ∞AWGN := lim
B→∞CAWGN(B )
= limB→∞
B log(
1 + PBN0
)= P
N0log e ,
where P is the received power and N0/2 is the noisePSD. Evidently, given N0 and P , C∞
AWGN benchmarksthe maximum rate achievable. But how close practicalUWB systems come to this fundamental limit? Andhow UWB transceivers should be designed to approachit? For flat Rayleigh fading channels, it is known that asB → ∞, C∞
AWGN can be achieved by frequency shiftkeying [17].
But as we discussed in Section III-A, UWB trans-missions typically encounter multipath fading chan-nels. This motivates investigation of capacity issues forUWB channels with pronounced frequency selectivity.If such channels exhibit independent fading at differ-ent frequency bins, it turns out that the achievablemutual information for a fixed transmission powergoes to zero as B increases, when spread spectrum sig-naling is used [33]. This result is quite intuitivebecause independent fading across frequency binstogether with an increasing B implies infinite numberof independent multipath coefficients, whose estima-tion then exhausts the power and bandwidthresources. But Figures 2 and 3 suggest that even whenthe number of resolvable multipath returns (L ) increas-es with increasing B (decreasing Tp ), the total numberof paths (L + 1) induced by the physical surroundingsis practically finite. Let {dl , βl }L
l =1 denote the delaysand coefficients of the resolvable paths. Notice that{dl , βl }L
l =1 depend on, but are not necessarily identicalto, the delays and coefficients of the physical channel{τl , αl }L
l =0 . Evidently, L is upper bounded by(L + 1) as B increases. To investigate the capacitybehavior in such cases, consider a white-noise-modula-tion (WNM) signaling where the empirical autocorre-lation of the transmitted waveform resembles that ofwhite noise, and a quasi-static channel with coherencetime τc and maximum delay spread τL ,0 � τc . Thenthe following results are obtained in [58]:▲ a) When {dl }L
l =1 are known but {βl }Ll =1 are unknown,
the achievable mutual information using WNM signalingis lower and upper bounded by [1 − (L /Lc )×log (1 + L c /L )]C∞
AWGN and (L c /L )C∞AWGN, respectively,
where Lc := Pτc /N0 . Consequently, if L � Lc then(L /Lc ) log(1 + Lc /L ) ≈ 0 and the achievable mutualinformation approaches C∞
AWGN; whereas if L � Lc thenLc /L ≈ 0 and the achievable mutual information is neg-ligibly small.▲ b) When {dl }L
l =1 are unknown (regardless of whether{βl }L
l =1 are known or not), the upper bound on themutual information using WNM signaling decays to 0like 1/B , even when L = 1 and β1 is known.
In result a), Lc essentially captures the availableresources, namely the SNR P/N0 and the coherence
time τc . As L increases, more unknowns {dl , βl }Ll =1
need to be estimated. If the number of unknowns istoo large, negligible resources remain for conveyinginformation, which drives the mutual information tozero. An intuitive explanation is also possible for resultb). As {dl }L
l =1 represent delays of resolvable paths, onedelay can be distinguished from its neighbors by thepulse duration Tp . But this requires timing estimation(tracking) with pulse-resolution accuracy. SinceTp ≈ 1/B , it is expected that the resources will again bedepleted by such stringent tracking requirements. As anextreme example, consider L = 1 with β1 known. Inthis case, finding d1 amounts to the timing synchro-nization problem. As discussed earlier, reliable symbolrecovery is impossible once the waveform of durationTp is missed. As B grows, it is becoming increasinglydifficult to capture the shrinking pulse.
The capacity results a) and b) corroborate thedemanding and challenging nature of UWB timingsynchronization and channel estimation. They indicatethat receiver knowledge of {dl }L
l =1 is particularly criticalin achieving capacity. The question is when the assump-tions under a) are satisfied; i.e., when can {dl }L
l =1 betreated as known at the receiver? We know thatτc ∝ 1/fc and that the time it takes for βl to move byone tap (from dl to dl + Tp ) is proportional toTp ≈ 1/B . Therefore, when 1/B � 1/fc , the resolvabledelays {dl }L
l =1 change much slower than the correspon-ding coefficients {βl }L
l =1 and can be treated as if theycan be “tracked’’ at the receiver. In other words, resulta) requires the fractional bandwidth satisfy B/fc � 1.This may be the case with multiband UWB systemswith relatively large fc , but is not satisfied by basebandUWB systems.
The spread-spectrum and WNM systems we dis-cussed so far use transmissions with no duty cycle; i.e.,Tf = Tp . In low-duty-cycle UWB systems, however, wehave Tf � Tp . How does duty-cycling affect capacityin the UWB regime? Let us first define the duty-cycleparameter θ : with θ ∈ (0, 1], transmission occurs onlyduring one period τc out of the total of τc /θ seconds;and the system sleeps when not transmitting.Interestingly, as FSK that is “peaky’’ in frequency is
IEEE SIGNAL PROCESSING MAGAZINENOVEMBER 2004 49
To fulfill expectations, UWBresearch and development hasto cope with formidablechallenges that limit their biterror rate performance,capacity, throughput, andnetwork flexibility.
capacity achieving in flat-fading channels, duty-cycledsignals that are “peaky’’ in time are capacity achievingin multipath channels [41], [65]. In fact, it followsfrom results a) and b) that WNM and PPM can bothachieve C ∞
AWGN when they are “duty-cycled’’ withθ → 0 [41]:▲ A) As long as {dl }L
l =1 are known at the receiver, then
limB→∞
CWNM(B ) → C ∞AWGN,
if limB→∞
L /B → 0,
limB→∞
CPPM(B ) → C ∞AWGN,
if limB→∞
L log log B/√
log B → 0.
▲ B) If {dl }Ll =1 are also unknown at the receiver, then
limB→∞
CWNM(B )
→ C ∞AWGN,
if limB→∞ L log B/B → 0< C ∞
AWGN,
if limB→∞ L /B → λ > 0,
limB→∞
CPPM(B )
→ C ∞AWGN,
if L = 1→ 0,
if limB→∞ L / log B → ∞.
Notice that WNM and PPM signaling systems cantolerate different bandwidth scaling factors as the num-ber of resolvable paths L increases. Also, when timingknowledge is not available, these factors are furtherreduced. These results are established for real UWBchannels with {βl }L
l =1 being i.i.d. It would be interest-ing to see how the correlation and power profile of thechannel affect these scaling factors.
UWB at the Networking LayerAlong with flexibility requirements at the physical layer,the open access network paradigm requires redefinitionof upper layers in the UWB system architecture. In thesame way Internet protocol (IP) has succeeded in glu-ing together heterogeneous networks, UWB and theopen radio access paradigm offer the potential for inte-grating heterogeneous wireless access networks. Toreach this goal, one needs to first address the followingquestion regarding the next-to-physical medium accesscontrol (MAC) layer: What, if any, UWB specific fea-tures may be required within the MAC?
Utilizing TH, conventional UWB systems providecovertness and are considered as the physical layer forfuture tactical wireless networks [24]. However, the highprecision synchronization required by UWB systemsnecessitates long acquisition headers at higher power,especially when simple serial searching algorithms areadopted due to the size and processing power of UWBtransceivers. To improve covertness in a UWB-based
network, sustained link networks (SLN) were proposedin [24] as a MAC layer scheme. In SLN, the physicallayer links are maintained for the lifetime of the logicallink between two nodes. Taking advantage of the lowduty-cycle nature of conventional UWB communica-tions, especially at low bit rate, [24] also developed afull-duplex scheme, which results in a tradeoff betweenthe number of transceiver units and the bit rate.
UWB allows for accurate localization, especially inenvironments where GPS encounters satellite visibilityconstrains. Such a precise positioning information can beutilized to develop location-aware networking. In otherwords, improved coexistence with other piconets/sys-tems and reduced power consumption can be achievedby scaling personal operating space based on UWB local-ization. Furthermore, for a prescribed average power,the peak power is inversely proportional to the pulse rep-etition frequency (PRF), which induces a range-ratetradeoff. Based on accurate localization information, apromising direction for UWB systems is to adjust datarates on a per packet, or a per link basis. As a result, theunique features of UWB may lead to power-efficient,location-aware adaptive routing protocols.
Fast timing techniques will allow for quick computa-tion and tracking of the relative positions among sen-sors, which would be beneficial for position-assistednode selection, and information relaying with mini-mum energy consumption. Idle or partially functionalnodes can also be utilized as relays to ensure fault-toler-ant networking. This approach has the potential toimprove performance, while saving power.
To facilitate variable bit rate sessions and fair-queuingbandwidth guarantees (those cannot be simultaneouslyaccommodated by fixed-assignment or random accessalternatives), a two-phase demand assignment MACcould be pursued. This layer-integrating design couldstart at the network scheduling which is to be performedby the “master user’’ of the piconet. Similar to a general-ized process sharing policy [38], [49], [56], the sched-uler associates “slave user’’ u with a service-dependentweight Fu that determines percentage of bandwidth allo-cation Bu . During the first phase (TDMA contentionbased reservation), the intention of the slave user totransmit along with the requested Fu is communicatedto the scheduler via mini-slots, while the master userresponds with mini-slots containing each user’s ID withthe corresponding code assignment. During the secondphase, users transmit (possibly at different rates) multi-media information. The MSBS and FLEX spreadingcodes we outlined earlier are good choices for this stage,because they not only assure MUI/multipath-resilientoperation but also enable multirate transmissions withfull-diversity, fine rate resolution, and easy rate switchingcapability [67], [76], [80].
Existing dynamic resource allocation schemes couldalso be adopted to UWB settings, especially when loca-tion information and partial channel state information(CSI) become available (or can be predicted) at the trans-
IEEE SIGNAL PROCESSING MAGAZINE50 NOVEMBER 2004
mitter. Optimization criteria can involve maxi-mization of sum-capacity, or, minimization ofsymbol error rate bounds, under a prescribedtransmit-power budget. Moreover, ST codesand/or steerable antenna arrays (beamform-ers) can also be adjusted for packet-fair sched-uling and flexible UWB allocation along thelines of [78].
Another interesting direction is to coupleresource allocation with routing considera-tions by distributing resources among nodesin an optimal fashion. On these subjects, oneof the key elements is the exploitation ofinformation from lower layers. For example,link quality maps provided by the channelestimation and error control algorithms areexpected to play a critical role in routingestablishment. Due to channel fading, routesin a wireless network are inherently unstableand prone to link failures. This has anadverse effect on the ability of networks tosupport applications with stringent quality ofservice (QoS) requirements. Exploitation ofthe extra diversity offered by multipathroutes of the UWB channel calls for an ana-lytical framework for multipath routing in (un)coordi-nated networking environment. For UWB links,multipath routing is particularly attractive, because itcan provide path failure protection, load balancing,while at the same time reduce the transmission delay bydistributing traffic among a set of available paths.
Implementation IssuesAny practical UWB system design should take intoaccount implementation feasibility and complexityissues, including ADC speed and correlator bandwidth.An overview on these issues can be found in [18]. Inparticular, to reduce time-to-market, UWB designswith analog components should utilize commonplacebuilding blocks, e.g., low noise amplifiers (LNAs), mix-ers, ADCs, digital-to-analog converters (DACs), andphase locked loops (PLLs), for which standard figure ofmerit production tests are available. Currently, ana-log/RF circuits are mostly implemented in high per-formance SiGe platforms, whereas digital/base-bandcircuits are implemented in CMOS. The latter is superi-or in terms of both power consumption and cost. Atthe same time, DSP based designs also enjoy processportability, low sensitivity to component variability, aswell as benefits from Moore’s law. A system design freeof RF components will facilitate system-on-a-chip(SoC) implementation in CMOS, which shrinks asCMOS scales down from 0.18 µm to 0.13 µm and0.09 µm. In this aspect, different system designs scoredifferently. The conventional single-band UWB systemsmostly rely on base-band carrier-free transmissions, andtherefore require no IF processing. Whereas the recent-ly emerged multiband UWB systems utilize the FCC
mask more effectively, but entail more extensive IF pro-cessing at rather high frequencies, and a number ofoscillators at both the transmitter and the receiver. Forany given UWB system, comparative studies need to becarried out when multiple implementation alternatives(analog versus digital) exist. For instance, channel esti-mation and correlation in TDT, TR, and PWAM sys-tems can be implemented either with analog delaylines, or, with digital delay elements after AD convert-ing the analog waveform. Avoiding analog delay lines,the latter requires formidable sampling. Analyses andtradeoff studies of these alternatives are either per-formed [8], [81], or are underway [23]. It is alsoworth mentioning that the complexity reduction athigher hierarchies is often times more effective than atlower hierarchies. For instance, about 60% of the totalnumber of gates are dedicated to channel estimation.This number can certainly be reduced to some degreeby applying digital circuit design techniques. On theother hand, adopting more efficient channel estimationtechniques might reduce dramatically the number ofgates. These are areas where VLSI-SP expertise canhave considerable impact in UWB algorithms andimplementation.
System designs tailored for UWB as mentioned inpreceding sections also entail challenges to UWB cir-cuitry implementation. Successful implementation ofboth carrier-free baseband and carrier-modulated multi-band UWB calls for high-efficiency UWB antennas, andtight jitter requirements. To this end, there is a rich lit-erature in UWB Radar, and emerging works in commu-nications. High-rate transmissions require fast automaticgain control (AGC) response, as well as improved ADC
IEEE SIGNAL PROCESSING MAGAZINENOVEMBER 2004 51
▲ 18. (a) The Trinity chip set released by Xtreme Spectrum Inc.; (b) The Mobilead hoc Network (MANET) by MultiSpectral Solutions Inc.; (c) the PUlsON familymarketed by Time Domain Corporation.
(a) (b)
(c)
speed. In [35], a channelized ADC with CMOS imple-mentation is advocated. As mentioned before, multi-band solutions with carrier modulated pulses utilize theFCC allowable bandwidth efficiently. Hopping amongmultiple frequency bands requires high performancelocal oscillators and switching circuits as well as UWBantennas. Implementation of such systems with lowpower consumption and low cost requires integration ofRF and baseband circuitry into a single CMOS chip,which hinges upon the solution of the “touchy issue’’ ofsubstrate noise mitigation. Further development ofUWB systems will also benefit from increased SPexpertise to enable modulation/demodulation, syn-chronization, channel estimation, error control coding,as well as cross-layer functionalities.
A number of companies have already announcedUWB prototype products for various applications: theTrinity chip set released by Xtreme Spectrum Inc. forstreaming video applications; the Mobile ad hoc Network(MANET) by MultiSpectral Solutions Inc.; and thePulsON family marketed by Time Domain Corporationfor personnel and asset tracking systems (see Figure 18).
Closing RemarksJust a year after announcing the First R&O, FCCaffirmed rules to authorize the deployment of UWBtechnology and sponsored several demonstrations ofUWB devices on 13 February 2003. During thisassemblage, seven companies demonstrated 12 UWBsystems, which cover applications from communica-tions, through-wall and/or ground-penetrating Radar,and localization. At the same time, a number of specialissues in journals and special sessions in various confer-ences are devoted to UWB research and development.IEEE sponsors a Working Group for standardizationand a biennial workshop in Ultra-Wideband Systemsand Technology (UWBST), where the number of sig-nal processing and communications researchers increas-es rapidly. All these justify well that indeed UWB is anidea “whose time has come.’’
To realize this idea, however, UWB research anddevelopment has to cope with challenges that limittheir performance, capacity, throughput, network flexi-bility, implementation complexity, and cost. Thoseinclude precise and rapid synchronization in a multi-user (and possibly ad hoc) environment, modeling ofUWB channel variations, low complexity channel esti-mation and multipath diversity collection, UWB-MAschemes that facilitate MUI/NBI suppression, andtheir corresponding multi-user detectors, UWB-tai-lored MAC layer schemes, high-speed high-precisionA/D and D/A converter designs, high-frequency oscil-lators, and high efficiency UWB antennas.
To fully exploit the benefits of UWB systems,enhanced interdisciplinary links need to be establishedacross the signal processing, communications, andnetworking communities. Today, research in signal pro-cessing for UWB is still at its infancy, offering limited
resources in handling the challenges facing UWB com-munications. On the other hand, digital signal process-ing techniques have matured for conventional RFcommunications, and a large body of literature hasgrown from recent advances in narrowband and wide-band wireless communications. Understanding theunique properties and challenges of UWB communica-tions, and applying competent signal processing tech-niques are vital to conquering the obstacles towardsdeveloping exciting UWB applications. It is clear thatinnovative research in this area will pay handsome divi-dends in meeting the future challenges and demands ofthe dynamic communications industry.
AcknowledgmentsThis article was prepared through collaborative partici-pation in the Communications and NetworksConsortium sponsored by the U.S. Army ResearchLaboratory under the Collaborative TechnologyAlliance Program, Cooperative Agreement DAAD19-01-02-0011. This work was also supported by the NSFGrant EIA-0324864.
Liuqing Yang received her B.S. degree in electrical engi-neering from Huazhong University of Science andTechnology, Wuhan, China, in 1994, and her M.Sc. andPh.D. degrees in electrical and computer engineeringfrom the University of Minnesota in 2002 and 2004,respectively. Since August 2004, she has been an assistantprofessor with the Department of Electrical andComputer Engineering at the University of Florida. Hergeneral research interests include communications, signalprocessing and networking. Currently, she has a particu-lar interest in ultra-wideband communications. Herresearch encompasses synchronization, channel estima-tion, equalization, multiple access, space-time coding,and multicarrier systems.
Georgios B. Giannakis received his diploma in electricalengineering from the National Technical University ofAthens, Greece, in 1981 and an M.Sc. in electricalengineering in 1983, an M.Sc. in mathematics in 1986,and a Ph.D. in electrical engineering in 1986, all fromthe University of Southern California. He joined theUniversity of Virginia in 1987. Since 1999 he has beena professor with the Department of Electrical andComputer Engineering at the University of Minnesota,where he holds an ADC Chair in WirelessTelecommunications. His general interests span theareas of communications and signal processing, estima-tion and detection theory, time-series analysis, and sys-tem identification, on which he has published morethan 200 journal papers, 350 conference papers, andtwo edited books. He received many awards, includingthe 2000 IEEE Signal Processing Society’s TechnicalAchievement Award. He was editor-in-chief for IEEESignal Processing Letters, associate editor for IEEETransactions on Signal Processing, and served many
IEEE SIGNAL PROCESSING MAGAZINE52 NOVEMBER 2004
positions within the IEEE Signal Processing Society,including secretary of the Conference Board and mem-ber of the Publications Board and the Board ofGovernors. He is also a member of the Proceedings ofthe IEEE editorial board and the steering committee ofIEEE Transactions on Wireless Communications.
References[1] G.R. Aiello and G.D. Rogerson, “Ultra-wideband wireless systems,” IEEE
Microwave Mag., vol. 4, no. 2, pp. 36–47, 2003.
[2] I.F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, “A survey onsensor networks,” IEEE Commun. Mag., vol. 40, no. 8, pp. 102–114, 2002.
[3] S.M. Alamouti, “A simple transmit diversity technique for wireless commu-nications,” IEEE J. Select. Areas Commun., vol. 16, no. 8, pp. 1451–1458,1998.
[4] J. Balakrishnan, A. Batra, and A. Dabak, “A multi-band OFDM system forUWB communication,” in Proc. Conf. Ultra-Wideband Systems andTechnologies, Reston, VA, 2003, pp. 354–358.
[5] T.W. Barrett, “History of ultra wideband (UWB) radar and communica-tions: Pioneers and innovators,” in Proc. Progress in ElectromagneticsSymposium, Cambridge, MA, 2000.
[6] C. Carbonelli, U. Mengali, and U. Mitra, “Synchronization and channelestimation for UWB signals,” in Proc. Global Telecommunications Conf.,San Francisco, CA, 2003, pp. 764–768.
[7] Y. Chao and R.A. Scholtz, “Optimal and suboptimal receivers for Ultra-wideband transmitted reference systems,” in Proc. GlobalTelecommunications Conf., San Francisco, CA, 2003, pp. 744–748.
[8] J.D. Choi and W.E. Stark, “Performance of ultra-wideband communica-tions with suboptimal receivers in multipath channels,” IEEE J. Select.Areas Commun., vol. 20, no. 9, pp. 1754–1766, 2002.
[9] C.R.C.M. da Silva and L.B. Milstein, “Spectral-encoded UWB communica-tion systems,” in Proc. Conf. Ultra-Wideband Systems and Technologies,Reston, VA, 2003, pp. 96–100.
[10] G. Durisi and G. Romano, “On the validity of Gaussian approximation tocharacterize the multiuser capacity of UWB TH PPM,” in Proc. Conf.Ultra-Wideband Systems and Technologies, Baltimore, MD, 2002, pp.157–161.
[11] G. Durisi, A. Tarable, J. Romme, and S. Benedetto, “A general method forerror probability computation of UWB systems for indoor multiuser com-munications,” J. Commun. Networks, vol. 5, no. 4, pp. 354–364, 2003.
[12] FCC First Report and Order: In the matter of Revision of Part 15 of theCommission’s Rules Regarding Ultra-Wideband Transmission Systems,FCC 02–48, April 2002.
[13] R. Fleming, C. Kushner, G. Roberts, and U. Nandiwada, “Rapid acquisi-tion for Ultra- Wideband localizers,” in Proc. Conf. Ultra-WidebandSystems and Technologies, Baltimore, MD, 2002, pp. 245–250.
[14] J.R. Foerster, Channel Modeling Sub-committee Report Final, IEEEP802.15-02/368r5-SG3a, IEEE P802.15 Working Group for WPAN,2002.
[15] J.R. Foerster, “The performance of a direct-sequence spread ultra wide-band system in the presence of multipath, narrowband interference, andmultiuser interference,” in Proc. Conf. Ultra-Wideband Systems andTechnologies, Baltimore, MD, 2002, pp. 87–92.
[16] A.R. Forouzan, M. Nasiri-Kenari, and J.A. Salehi, “Performance analysisof time-hopping spread-spectrum multiple-access systems: Uncoded andcoded schemes,” IEEE Trans. Wireless Commun., vol. 1, no. 4, pp.671–681, 2002.
[17] R.G. Gallager, Information Theory and Reliable Communication. NewYork: Wiley, 1968.
[18] R. Harjani, J. Harvey, and R. Sainati, “Analog/RF physical layer issues forUWB systems,” in Proc. the 17th Int. Conf. VLSI Design, Mumbai, India,
2004, pp. 941–948.
[19] M. Ho, V. Somayazulu, J. Foerster, and S. Roy, “A differential detectorfor an Ultra-Wideband communications system,” in Proc. VehicularTechnology Conf., Birmingham, AL, 2002, pp. 1896–1900.
[20] B.M. Hochwald and T.L. Marzetta, “Unitary space-time modulation formultiple-antenna communications in Rayleigh flat fading,” IEEE Trans.Inform. Theory, vol. 46, no. 2, pp. 543–564, 2000.
[21] R.T. Hoctor and H.W. Tomlinson, “An overview of delay-hopped, trans-mitted-reference RF communications,” in G.E. Research and DevelopmentCenter, Technical Information Series, 2002, pp. 1–29.
[22] E.A. Homier and R.A. Scholtz, “Rapid acquisition of Ultra-Widebandsignals in the dense multipath channel,” in Proc. Conf. Ultra-WidebandSystems and Technologies, Baltimore, MD, 2002, pp. 105–110.
[23] S. Hoyos, B. Sadler, and G. Arce, “On the performance of low complexitydigital receivers for Ultra-Wideband communication systems,” in Proc.Collaborative Tech. Alliances Conf., College Park, MD, 2003, pp. 211–215.
[24] S.S. Kolenchery, K. Townsend, and J.A. Freebersyser, “A novel impulseradio network for tactical wireless communications,” in Proc. MILCOMConf., Bedford, MA, 1998, pp. 59–65.
[25] H. Lee, B. Han, Y. Shin, and S. Im, “Multipath characteristics of impulseradio channels,” in Proc. Vehicular Technology Conf., Tokyo, Japan, Spring2000, pp. 2487–2491.
[26] J.S. Lee, C. Nguyen, and T. Scullion, “New uniplanar subnanosecondmonocycle pulse generator and transformer for time-domain microwaveapplications,” IEEE Trans. Microwave Theory Tech., vol. 49, no. 6, pp.1126–1129, 2001.
[27] Q. Li and L.A. Rusch, “Multiuser detection for DS-CDMA UWB in thehome environment,” IEEE J. Select. Areas Commun., vol. 20, no. 9, pp.1701–1711, 2002.
[28] V. Lottici, A. D’Andrea, and U. Mengali, “Channel estimation for ultra-wideband communications,” IEEE J. Select. Areas Commun., vol. 20, no.9, pp. 1638–1645, 2002.
[29] X. Luo, L. Yang, and G.B. Giannakis, “Designing optimal pulse-shapersfor ultra-wideband radios,” J. Commun. Networks, vol. 5, no. 4, pp.344–353, 2003.
[30] X. Ma and G.B. Giannakis, “Complex field coded MIMO systems:Performance, rate, and tradeoffs,” Wireless Commun. Mobile Comput., vol.2, no. 7, pp. 693–717, 2002.
[31] I. Maravic, J. Kusuma, and M. Vetterli, “Low-sampling rate UWB channelcharacterization and synchronization,” J. Commun. Networks, vol. 5, no. 4,pp. 319–327, 2003.
[32] C.L. Martret and G.B. Giannakis, “All-digital impulse radio for wirelesscellular systems,” IEEE Trans. Commun., vol. 50, no. 9, pp. 1440–1450,2002.
[33] M. Médard and R.G. Gallager, “Bandwidth scaling for fading channels,”IEEE Trans. Inform. Theory, vol. 48, no. 4, pp. 840–852, 2002.
[34] U. Mengali and A. D’Andrea, Synchronization Techniques for DigitalReceivers. New York: Plenum, 1997.
[35] W. Namgoong, “A channelized digital ultrawideband receiver,” IEEETrans. Wireless Commun., vol. 2, no. 3, pp. 502–510, 2003.
[36] S. Ohno and G.B. Giannakis, “Capacity maximizing MMSE-optimalpilots and precorders for wireless OFDM over rapidly fading channels,”IEEE Trans. Inform. Theory, vol. 50, no. 9, pp. 2138–2145, 2004.
[37] Assessment of Ultra-Wideband (UWB) Technology, OSD/DARPA,Ultra-Wideband Radar Review Panel, R-6280, July 13, 1990.
[38] A.K. Parekh and R.G. Gallager, “A generalized processor sharingapproach to flow control in integrated services networks: The single-nodecase,” IEEE/ACM Trans. Networking, vol. 1, no. 3, pp. 344–357, 1993.
[39] T.W. Parks and J.H. McClellan, “Chebyshev approximation for nonrecur-sive digital filters with linear phase,” IEEE Trans. Circuit Theory, vol. 19,no. 2, pp. 189–194, 1972.
IEEE SIGNAL PROCESSING MAGAZINENOVEMBER 2004 53
[40] B. Parr, B. Cho, K. Wallace, and Z. Ding, “A novel ultra-wideband pulsedesign algorithm,” IEEE Commun. Letters., vol. 7, no. 5, pp. 219–221, 2003.
[41] D. Porrat and D. Tse, “Bandwidth scaling in ultra wideband communica-tions,” in Proc. 41st Allerton Conf., Univ. of Illinois at U-C, Monticello,IL, 2003.
[42] J. Proakis, Digital Communications, 4th ed. New York: McGraw-Hill, 2001.
[43] F. Ramirez-Mireles and R.A. Scholtz, “N-orthogonal time-shift-modulatedsignals for ultra wide bandwidth impulse radio modulation,” in Proc. IEEEMini Conf. Communication Theory, Phoenix, AZ, 1997, pp. 245–250.
[44] J. Romme and L. Piazzo, “On the power spectral density of time-hoppingimpulse radio,” in Proc. Conf. Ultra-Wideband Systems and Technologies,Baltimore, MD, 2002, pp. 241–244.
[45] G.F. Ross, “The transient analysis of multiple beam feed networks forarray systems,” Ph.D. dissertation, Polytechnic Institute of Brooklyn,Brooklyn, NY, 1963.
[46] G.F. Ross and K.W. Robbins, Base-band radiation and reception system,U.S. Patent 3,739,392, June 12, 1973.
[47] E. Saberinia and A.H. Tewfik, “Pulsed and non-pulsed OFDM UltraWideband wireless personal area networks,” in Proc. Conf. Ultra-WidebandSystems and Technologies, Reston, VA, 2003, pp. 275–279.
[48] B.M. Sadler and A. Swami, “On the performance of UWB and DS -spreadspectrum communication systems,” in Proc. Conf. Ultra-Wideband Systemsand Technologies, Baltimore, MD, 2002, pp. 289–292.
[49] D. Saha, S. Mukherjee, and S.K. Tripathi, “Carry-over round robin: asimple cell scheduling mechanism for ATM networks,” IEEE Trans.Networking, vol. 6, no. 6, pp. 779–796, 1998.
[50] A.A.M. Saleh and R.A. Valenzuela, “A statistical model for indoor multi-path propagation,” IEEE J. Select. Areas Commun., vol. 5, no. 2, pp.128–137, 1987.
[51] H.G. Schantz and L. Fullerton, “The diamond dipole: A Gaussianimpulse antenna,” in Proc. IEEE Int. Symp. Antennas and PropagationSociety, vol. 4, Boston, MA, 2001, pp. 100–103.
[52] R.A. Scholtz, “Multiple access with time-hopping impulse modulation,”in Proc. MILCOM Conf., Boston, MA, 1993, pp. 447–450.
[53] C.E. Shannon, “A mathematical theory of communication,” Bell Syst.Tech. J., vol. 27, pp. 379–423, 623–656, 1948.
[54] M.K. Simon, Spread Spectrum Communications Handbook. New York:McGraw-Hill, 1985.
[55] E.M. Staderini, “UWB radars in medicine,” IEEE Aerosp. Electron. Syst.Mag., vol. 17, no. 1, pp. 13–18, 2002.
[56] A. Stamoulis and G.B. Giannakis, “Deterministic time-varying packet fairqueueing for integrated services networks,” J. VLSI Signal Processing, vol.30, no. 1–3, pp. 71–87, 2002.
[58] I.E. Telatar and D.N.C. Tse, “Capacity and mutual information of wide-band multipath fading channels,” IEEE Trans. Inform. Theory, vol. 46, no.4, pp. 1384–1400, 2000.
[59] Z. Tian and G.B. Giannakis, “BER sensitivity to mis-timing in Ultra-Wideband communications,” IEEE Trans. Signal Processing, to be published.
[60] Z. Tian and G.B. Giannakis, “Data-aided ML timing acquisition in Ultra-Wideband radios,” in Proc. Conf. Ultra-Wideband Systems and Technologies,Reston, VA, 2003, pp. 142–146.
[61] Z. Tian, L. Yang, and G.B. Giannakis, “Symbol timing estimation inUltra-Wideband communications,” in Proc. Asilomar Conf. Signals,Systems, and Computers, Pacific Grove, CA, 2002, pp. 1924–1928.
[62] S. Tilak, N.B. Abu-Ghazaleh, and W. Heinzelman, “A taxonomy of wire-less micro-sensor network models,” Mobile Computing Commun. Rev., vol.6, no. 2, pp. 28–36, 2002.
[63] V. Tripathi, A. Mantravadi, and V.V. Veeravalli, “Channel acquisition forwideband CDMA signals,” IEEE J. Select. Areas Commun., vol. 18, no. 8,pp. 1483–1494, 2000.
[64] S. Verdú, “Wireless bandwidth in the making,” IEEE Commun. Mag., vol.38, no. 7, pp. 53–58, 2000.
[65] S. Verdú, “Spectral efficiency in the wideband regime,” IEEE Trans.Inform. Theory, vol. 48, no. 6, pp. 1319–1343, 2002.
[66] Z. Wang, “Multi-carrier ultra-wideband multiple-access with goodresilience against multiuser interference,” in Proc. Conf. Info. Sciences andSystems, Baltimore, MD, 2003.
[67] Z. Wang and G.B. Giannakis, “Wireless multicarrier communications:Where Fourier meets Shannon,” IEEE Signal Processing Mag., vol. 17, no.3, pp. 29–48, 2000.
[68] Z. Wang and X. Yang, “Ultra wide-band communications with blindchannel estimation based on first-order statistics,” in Proc. Int. Conf.Acoustics, Speech, and Signal Processing, Montreal, Quebec, Canada, 2004,pp. 529–532.
[69] M.L. Welborn, “System considerations for Ultra-Wideband wireless net-works,” in Proc. IEEE Radio Wireless Conf., Boston, MA, 2001, pp. 5–8.
[70] M.Z. Win, “On the power spectral density of digital pulse streams gener-ated by m-ary cyclostationary sequences in the presence of stationary tim-ing jitter,” IEEE Trans. Commun., vol. 46, no. 9, pp. 1135–1145, 1998.
[71] M.Z. Win, G. Chrisikos, and N.R. Sollenberger, “Performance of rakereception in dense multipath channels: implications of spreading bandwidthand selection diversity order,” IEEE J. Select. Areas Commun., vol. 18, no.58, pp. 1516–1525, 2000.
[72] M.Z. Win and R.A. Scholtz, “Ultra wide bandwidth time-hoppingspread-spectrum impulse radio for wireless multiple access communica-tions,” IEEE Trans. Commun., vol. 48, no. 4, pp. 679–691, 2000.
[73] M.Z. Win and R.A. Scholtz, “Characterization of Ultra-Wide bandwidthwireless indoor channels: a communication-theoretic view,” IEEE J. Select.Areas Commun., vol. 20, no. 9, pp. 1613–1627, 2002.
[74] P. Withington, “Impulse radio overview,” [Online]. Available:http://user.it.uu.se/~carle/Notes/UWB.pdf
[75] X. Wu, Z. Tian, T.N. Davidson, and G.B. Giannakis, “Optimal waveformdesign for UWB radios,” in Proc. Int. Conf. Acoustics, Speech, and SignalProcessing, Montreal, Canada, 2004, pp. 521–524.
[76] L. Yang and G.B. Giannakis, “Multi-stage block-spreading for impulseradio multiple access through ISI channels,” IEEE J. Select. AreasCommun., vol. 20, no. 9, pp. 1767–1777, 2002.
[77] L. Yang and G.B. Giannakis, “Digital-carrier multi-band user codes forbaseband UWB multiple access,” J. Commun. Networks, vol. 5, no. 4, pp.374–385, 2003.
[78] L. Yang and G.B. Giannakis, “Analog space-time coding for multi-anten-na Ultra-Wideband transmissions,” IEEE Trans. Commun., vol. 52, no. 3,pp. 507–517, 2004.
[79] L. Yang and G.B. Giannakis, “Blind UWB timing with a dirty template,”in Proc. Int. Conf. Acoustics, Speech, and Signal Processing, Montreal,Quebec, Canada, 2004, pp. 509–512.
[80] L. Yang and G.B. Giannakis, “Cross-band flexible UWB multiple accessfor high-rate multi-piconet WPANs,” in Proc. Asilomar Conf. Signals,Systems, and Computers, Pacific Grove, CA, 2004.
[81] L. Yang and G.B. Giannakis, “Optimal pilot waveform assisted modula-tion for Ultra-Wideband communications,” IEEE Trans. WirelessCommun., vol. 3, no. 4, pp. 1236–1249, 2004.
[82] L. Yang and G.B. Giannakis, “A general model and SINR analysis of lowduty-cycle UWB access through multipath with NBI and Rake reception,”IEEE Trans. Wireless Commun., to be published.
[83] L. Yang, G.B. Giannakis, and A. Swami, “Noncoherent ultra-widebandradios,” in Proc. MILCOM Conf., Monterey, CA, 2004.
[84] H. Zhang and D.L. Goeckel, “Generalized transmitted-reference UWBsystems,” in Proc. Conf. Ultra-Wideband Systems and Technologies, Reston,VA, 2003, pp. 147–151.
