An Idea Whose Time Has Come

ltra-wideband (UWB) radio is a fast emerging technology with uniquely attractive features inviting major advances 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 Uoverlaying coexistent RF systems can operate using low-power ultra-short information bearing pulses. With similar regulatory processes currently under way in many countries worldwide, industry, government agencies, and academic institutions responded to this FCC ruling with rapidly growing research efforts targeting a host of exciting UWB applications: short-range very high-speed broadband access to the Internet, covert communication links, localization at centimeter-level accuracy, high-resolution ground-penetrating radar, through-wall imaging, precision navigation and 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 outlines research directions and challenges to be overcome. As signal processing expertise is expected to have major impact in research and development of UWB systems, emphasis is placed on DSP aspects.

Introduction UWB characterizes transmission systems with instantaneous spectral occu- pancy in excess of 500 MHz

Liuqing Yang and Georgios B. Giannakis

2626 IEEEEEE SIGNALSIGNAL PROCESSINGPROCESSING MAGAZINEMAGAZINE NONOVEMBERVEMBER 20042004 1053-5888/04/$20.00053-5888/04/$20.00©2004IEEE2004IEEE or a fractional bandwidth of more than 20%. (The frac- dia transmissions. Similar to the frequency reuse princi- tional bandwidth is defined as B/fc , where ple exploited by wireless cellular architectures, low- B := fH − fL denotes the −10 dB bandwidth and cen- power, short-range UWB communications are also ter frequency fc := ( fH + fL )/2 with fH being the potentially capable of providing high spatial capacity, in upper frequency of the −10 dB emission point, and fL terms of bits per second per square meter. In addition, the lower frequency of the −10 dB emission point. UWB connectivity is expected to offer a rich set of soft- According to [12], UWB systems with fc > 2.5 GHz ware-controllable parameters that can be used to design need to have a −10 dB bandwidth of at least 500 location-aware communication networks flexible to MHz, while UWB systems with fc < 2.5 GHz need to scale in rates and power requirements. have fractional bandwidth at least 0.20.) Such systems To fulfill these expectations, however, UWB research rely on ultra-short (nanosecond scale) waveforms that and development has to cope with formidable chal- can be free of sine-wave carriers and do not require IF lenges that limit their bit error rate (BER) perform- processing because they can operate at baseband. As ance, capacity, throughput, and network flexibility. information-bearing pulses with ultra-short duration Those include high sensitivity to synchronizing the have UWB spectral occupancy, UWB radios come with reception of ultra-short pulses, optimal exploitation of unique advantages that have long been appreciated by fading propagation effects with pronounced frequency- the radar and communications communities: i) enhanced selectivity, low-complexity constraints in decoding capability to penetrate through obstacles; ii) ultra high high-performance multiple access protocols, and strict precision ranging at the centimeter level; iii) potential for power limitations imposed by the desire to minimize very high data rates along with a commensurate increase interference among UWB communicators, and with in user capacity; and iv) potentially small size and pro- coexisting legacy systems, particularly GPS, unmanned cessing power. Despite these attractive features, interest air vehicles (UAVs), aircraft radar, and WLANs. These in UWB devices prior to 2001 was primarily limited to challenges call for advanced digital signal processing radar systems, mainly for military applications. With (DSP) expertise to accomplish tasks such as synchro- bandwidth resources becoming increasingly scarce, nization, channel estimation and equalization, multi- UWB radio was “a midsummer night’s dream’’ waiting user detection, high-rate high-precision low-power to be fulfilled. But things changed drastically in the analog/digital conversion (ADC), and suppression of spring of 2002, when the FCC released a spectral mask aggregate interference arising from coexisting legacy allowing (even commercial) operation of UWB radios at systems. As DSP theory, algorithms, and hardware the noise floor, but over an enormous bandwidth (up to advanced narrowband and broadband technology, DSP 7.5 GHz). is expected to play a similar role in pushing the fron- This huge “new bandwidth” opens the door for an tiers of emerging UWB applications. To this end, it is unprecedented number of bandwidth-demanding posi- important to understand features and challenges that tion-critical low-power applications in wireless commu- are unique to UWB signaling from a DSP perspective. nications, networking, radar imaging, and localization systems [64]. It also explains the rapidly increasing Regulatory Issues efforts undertaken by several research institutions, and Motivating Applications industry, and government agencies to assess and exploit Despite its renewed interest during the past decade, the potential of UWB radios in various areas. These UWB has a history as long as radio. When invented by include short-range, high-speed access to the Internet, Guglielmo Marconi more than a century ago, radio accurate personnel and asset tracking for increased safe- communications utilized enormous bandwidth as infor- ty and security, precision navigation, imaging of steel mation was conveyed using spark-gap transmitters. The reinforcement bars in concrete or pipes hidden inside next milestone of UWB technology came in the late walls, surveillance, and medical monitoring of the 1960s, when the high sensitivity to scatterers and low heart’s actual contractions. power consumption motivated the introduction of For wireless communications in particular, the FCC UWB radar systems [5], [45], [46]. Ross’ patent in regulated power levels are very low (below −41.3 dBm), 1973 set up the foundation for UWB communications. which allows UWB technology to overlay already avail- Readers are referred to [5] for an interesting and able services such as the global positioning system informative review of pioneer works in UWB radar and (GPS) and the IEEE 802.11 wireless local area net- communications. works (WLANs) that coexist in the 3.6−10.1 GHz In 1989, the U.S. Department of Defense (DoD) band. Although UWB signals can propagate greater coined the term “ultra wideband” for devices occupy- distances at higher power levels, current FCC regula- ing at least 1.5 GHz, or a −20 dB fractional bandwidth tions enable high-rate (above 110 MB/s) data trans- exceeding 25% [37]. Similar definitions were also missions over a short range (10−15 m) at very low adopted by the FCC notice of proposed rule making power. Major efforts are currently under way by the that regulated UWB recently. The rule making of UWB IEEE 802.15 Working Group for standardizing UWB was opened by FCC in 1998. The resulting First COMSTOCK

© wireless radios for indoor (home and office) multime- Report and Order (R&O) that permitted deployment

NOVEMBER 2004 IEEE SIGNAL PROCESSING MAGAZINE 27 of UWB devices was announced on 14 February and ing a vast quantity of sensory data in a timely manner. released in April 2002 [12]. Three types of UWB sys- Typically, energy is more limited in sensor networks tems are defined in this R&O: imaging systems, com- than in WPANs because of the nature of the sensing munication and measurement systems, and vehicular devices and the difficulty in recharging their batteries. radar systems. Spectral masks assigned to these applica- Studies have shown that current commercial Bluetooth tions are listed in Table 1. In particular, the FCC devices are less suitable for sensor network applications assigned bandwidth and spectral mask for indoor com- because of their energy requirements [62] and higher munications is illustrated in Figure 1. expected cost [2]. In addition, exploiting the precise Although currently only the United States permits localization capability of UWB promises wireless sensor operation of UWB devices, regulatory efforts are under networks with improved positioning accuracy. This is way both in Europe and in Japan. Market drivers for especially useful when GPSs are not available, e.g., due UWB technology are many even at this early stage, and to obstruction. are expected to include new applications in the next ▲ Imaging systems: Different from conventional radar few years. We outline here application trends where sig- systems where targets are typically considered as point nal processing tools will probably have considerable scatterers, UWB radar pulses are shorter than the target impact in UWB system development. dimensions. UWB reflections off the target exhibit not ▲ Wireless personal area networks (WPANs): Also known only changes in amplitude and time shift but also as in-home networks, WPANs address short-range (gen- changes in the pulse shape. As a result, UWB wave- erally within 10−20 m) ad hoc connectivity among forms exhibit pronounced sensitivity to scattering rela- portable consumer electronic and communication tive to conventional radar signals. This property has devices. They are envisioned to provide high-quality been readily adopted by radar systems (see e.g., [5] and real-time video and audio distribution, file exchange references therein) and can be extended to additional among storage systems, and cable replacement for home applications, such as underground, through-wall and entertainment systems. UWB technology emerges as a ocean imaging, as well as medical diagnostics and bor- promising physical layer candidate for WPANs, because der surveillance devices [55], [57]. it offers high-rates over short range, with low cost, high ▲ Vehicular radar systems: UWB-based sensing has the power efficiency, and low duty cycle. potential to improve the resolution of conventional ▲ Sensor networks: Sensor networks consist of a large proximity and motion sensors. Relying on the high number of nodes spread across a geographical area. ranging accuracy and target differentiation capability The nodes can be static, if deployed for, e.g., avalanche enabled by UWB, intelligent collision-avoidance and monitoring and pollution tracking, or mobile, if cruise-control systems can be envisioned. These sys- equipped on soldiers, firemen, or robots in military and tems can also improve airbag deployment and adapt emergency response situations. Key requirements for suspension/braking systems depending on road condi- sensor networks operating in challenging environments tions. UWB technology can also be integrated into include low cost, low power, and multifunctionality. vehicular entertainment and navigation systems by High data-rate UWB communication systems are well downloading high-rate data from airport off ramp, motivated for gathering and disseminating or exchang- road-side, or gas station UWB transmitters.

Table 1. FCC spectral mask for UWB systems.

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 960–1610 –75.3 –75.3 –65.3 –65.3 –53.3 –75.3 1610–1900 –53.3 –63.3 –53.3 –53.3 –51.3 1900–1990 –61.3 1990–3100 –51.3 –51.3 –41.3 –61.3 3100–10,600 –41.3 –41.3 –41.3 10,600–22,000 –51.3 22,000–29,000 –51.3 –61.3 –51.3 –51.3 –41.3 20,000–31,000 –51.3 >31,000 –61.3

Indoor/handled communication systems: fL , fH [3.1, 10.6] GHz; low-frequency imaging systems: fL , fH < 960 MHz; high-frequency imaging systems:

fL , fH [3.1, 10.6] GHz; medium-frequency imaging systems: fL , fH [1.99, 10.6] GHz; vehicular radar systems: fc > 24.075 GHz, fL , fH [22, 29] GHz.

28 IEEE SIGNAL PROCESSING MAGAZINE NOVEMBER 2004 UWB Communications at the Physical Layer −40 In this section, we outline physical layer issues of UWB −45 communication systems, including transmitter/receiver designs, synchronization, channel estimation, and mul- −50 tiple access schemes. In addition to the conventional 3.1 10.6 − single-band UWB transmissions, we will also discuss 55 1.99 recent multiband alternatives for power-efficient adher- −60 ence to FCC’s spectral mask, mitigation of narrowband interference (NBI), and relaxed sampling requirements. −65 Indoor Limit To appreciate UWB system designs, however, it is GPS Part 15 Limit − important to understand first the propagation charac- 70 Band UWB EIRP Emission Level in dBm teristics of the transmitted ultra-short waveform and −75 establish a realistic channel model. 0.96 1.61 100 101 Channel Modeling Frequency in GHz Since more than 80% of the envisioned commercial ▲ UWB applications will be indoor communications, we 1. FCC spectral mask for indoor commercial systems. will focus on indoor channels. The well-known Saleh- Valenzuela (S-V) indoor channel model was established firmed, the standardized channel model is basically a back in 1987 [50], based on measurements utilizing modified version of the S-V model [50]. To reach an low power ultra-short pulses (of width 10 ns and center analytically tractable channel model, the total number frequency 1.5 GHz) in a medium-size, two-story office of paths is defined as the number of multipath arrivals building. In the S-V model, multipath components with expected power within 10 dB from that of the arrive at the receiver in groups (clusters). Cluster strongest arrival. The Rayleigh distribution in the S-V arrivals are Poisson distributed with rate . Within channel model is replaced by the log-normal distribu- each cluster, subsequent arrivals are also Poisson dis- tion. The phases θm,n are also constrained to take values tributed with rate λ>. With αm,n denoting the gain 0 or π with equal probability to account for signal of the nth multipath component of the mth cluster, inversion due to reflection, yielding a real-valued chan- having phase θm,n, the channel impulse response can be nel model. With path gains normalized to have unit expressed as energy, a log-normal random variable is introduced to account for shadowing. Model parameters correspon- +∞ ding to several ranges are also provided in [14], for h(t) = α δ(t − τ ) l l both line-of-sight (LOS) and nonline-of-sight (NLOS) l =0 +∞ +∞ scenarios. The standardized UWB channel model in jθm,n [14] is claimed to better match the measurements. = αm,ne δ(t − Tm − τm,n), (1) m=0 n=0 However, the log-normal distribution and the shadow- ing factor render this model less tractable for theoreti- where Tm + τm,n (τm,0 = 0) denotes the arrival time of cal performance analysis and quantification of the the nth multipath component of the mth cluster, θm,n channel-induced diversity and coding gains. are independent uniform random variables over A typical realization of the channel impulse response [0, 2π), and αm,n are independent Rayleigh random generated using the channel model 2 [14] is shown in − /γ −τ /γ {α2 }= {α2 } Tm m,n variables with power E m,n E 0,0 e e , Figure 2. The number of multipath components is 315 where >γ. The number of clusters and multipath in this realization, spanning over a delay spread of about components may theoretically extend over infinite 50 ns. Let p(t) denote the transmitted pulse of duration time. However, the terms of the double sum in (1) Tp . After multipath propagation, the received waveform practically vanish for sufficiently large (m, n) with an is given by the convolution of p(t) with the physical ( ) exponentially decaying power profile. channel h t , and contains multiple delayed copies of ( ) ( ) = ( )( ) = L α ( − τ ) Lately, efforts have been made to characterize UWB p t ; i.e., g t : p h t l =0 l p t l , where channels with bandwidths exceeding 2 GHz. To come denotes convolution. Notice from Figure 2 that the {τ }L up with a statistical model, channel realizations are spacing among multipath delays l l =0 is in the order identified either in the frequency domain by frequency of nanoseconds. These delayed copies of p(t) in g (t) sweeping or in the time domain using impulsive signals. can be resolved from each other only if Tp is sufficiently In November 2002, the channel modeling subcommit- small, that is, if the transmit bandwidth B ≈ 1/Tp is tee of the IEEE 802.15.3a Task Group recommended sufficiently large. The transmitted and received wave- a channel model which captures the aforementioned forms corresponding to two Tp values are shown in works, as well as recent refinements [14]. Because the Figure 3, where the received waveforms were generated clustering phenomenon has been experimentally con- using the multipath delays and amplitudes of Figure 2.

NOVEMBER 2004 IEEE SIGNAL PROCESSING MAGAZINE 29 With Tp = 91 ns, we have B ≈ 11 MHz, and the Transmitter Design received waveform consists of a single distorted version Generally adopted spectrum shapers p(t) for UWB of p(t). With Tp = 0.55 ns, we have B ≈ 2 GHz, and communications include the Gaussian pulse, the the received waveform contains multiple resolvable Gaussian monocycle (first derivative of Gaussian pulse), copies of p(t). If the channel is known at the receiver, and the second derivative of the Gaussian pulse, as these resolvable copies can be combined coherently to depicted in Figure 4, along with their Fourier trans- provide multipath diversity. But before discussing forms (FTs). The reason behind the popularity of these receiver designs that collect this diversity, let us first pulses is twofold: i) Gaussian pulses come with the introduce UWB transmission schemes. smallest possible time-bandwidth product of 0.5, which maximizes range-rate resolution and ii) the Gaussian pulses are readily available from the antenna pattern [51]. With Tp at the subnanosecond 0.25 ( ) 0.2 scale, p t occupies UWB with 0.15 bandwidth B ≈ 1/Tp . As mentioned 0.1 before, and illustrated in Figure 0.05 3(b), such an ultra-short p(t) also 0 −0.05 gives rise to multiple resolvable

Amplitude −0.1 copies, and thus enables rich multi- −0.15 path diversity. −0.2 In a typical UWB system, each − 0.25 information-conveying symbol is 5101520253035404550 represented by a number of (N f ) Delay (ns) pulses, each transmitted per frame of duration Tf  Tp . Having N f ▲ 2. A typical realization of the channel impulse response generated using the IEEE frames, over which a single symbol 802.15.3 a channel model 2: NLOS channels with 0−4 m transmitter-receiver distance. is spread, reverses the commonly used terminology where a frame consists of multiple symbols (here multiple frames comprise a symbol). With M -ary modulation, log M 1 2 0.8 Transmitted Pulse message bits are transmitted during 0.6 Received Waveform a signaling interval of duration 0.4 Ts = N f Tf s that corresponds to a 0.2 bit rate R = log M/T . 0 b 2 s −0.2 Being real, baseband UWB trans- Amplitude −0.4 missions neither have to entail fre- −0.6 quency modulation nor phase − 0.8 modulation with M > 2. Conse- 1 050100 150 quently, symbol values can be trans- Time (ns) mitted by modulating the position and/or the amplitude of p(t). In (a) M -ary pulse position modulation 1 (PPM), M distinctly delayed pulses Transmitted Pulse { ( − )}M −1 0.8 p t m m=0 are employed, each 0.6 Received Waveform representing one symbol value. 0.4 Generally, the so-termed modula- 0.2 0 tion indices m are chosen such that −0.2 m = m with ≥ Tp , which cor- Amplitude −0.4 responds to an orthogonal PPM. In −0.6 binary PPM, the delay can also be −0.8 −1 chosen to minimize the correlation ( ) ( − ) 012345678910 p t p t dt [52]. As band- Time (ns) width efficiency drops with increas- (b) ing modulation size M , PPM is suitable for power-limited applica-

▲ 3. The transmitted and received waveforms corresponding to (a) Tp = 91 ns and (b) tions. In fact, PPM was almost

Tp = 0.55 ns. For illustration purposes, only the first 10 ns are shown in (b). exclusively adopted in the early

30 IEEE SIGNAL PROCESSING MAGAZINE NOVEMBER 2004 10 Gaussian Pulse 1 Gaussian Pulse Gaussian Monocycle Gaussian Monocycle 0 Scholtz Monocycle 0.8 Scholtz Monocycle 0.6 −10

0.4 −20 0.2 − 0 30

−0.2 Power (dB) −40

Amplitude (dB) −0.4 −50 −0.6 −0.8 −60 −1 −70 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 100 101 Time (ns) Frequency (GHz) (a) (b)

▲ 4. (a) Generally adopted pulse shapes in UWB communications; (b) Fourier transform of several pulse shapes. Pulse width: 0.7 ns.

development of UWB radios because negating ultra- b u(k) = 0, (2) models M -ary PAM. With binary sym- short pulses were difficult to implement. Another mod- bols, and b u(k) = 0, au(k) = 2su(k) − 1 corresponds to ulation scheme that does not require pulse negation is BPSK, and au(k) = su(k) corresponds to OOK [32], the so termed on-off keying (OOK), where symbol “1” [43], [69]. is represented by transmitting a pulse, and “0” by With TH codes, MA is achieved by altering the transmitting nothing. pulse position from frame to frame, according to the TH( ) As pulse negation became easier to implement, pulse sequence c u n . MA can also be enabled by modify- amplitude modulation (PAM) attracted more attention. ing the pulse amplitude from frame to frame. The latter In particular, when M = 2, antipodal pulses are used to allows for many other choices of alternative spreading represent binary symbols, as in binary phase shift key- codes which, individually or in combination with TH ing (BPSK) or bipolar signaling. Biorthogonal signal- codes, give rise to the following transmitted waveform ing by combining orthogonal PPM with binary PAM as [c.f. (2)]: well as orthogonal waveform and block orthogonal +∞ modulation schemes have also been reported [43]. ( ) = E  /  ( ) To allow for multi-user access (MA) to the UWB vu t u au n N f c u n = channel, time hopping (TH) was introduced early in n 0 · − − TH( ) −  /  , [52]. With TH, each pulse is positioned within each p t nTf c u n Tc b u n N f ( ) frame duration Tf according to a user-specific TH 3 TH( ) sequence c u n . Specifically, dividing each frame into Nc chips each of duration Tc , the uth user’s TH code where c u(n) is the user-specific “amplitude code” dur- TH( ) ∈ , − c u n [0 Nc 1] corresponds to a time shift of ing the nth frame. Depending on the spreading codes TH( ) c u n Tc during the nth frame [72]. Consequently, employed, the UWB systems are termed TH-UWB the uth user’s transmitted waveform is given by [52], direct-sequence (DS)-UWB [15], or baseband single-carrier/multicarrier (SC/MC)-UWB [66], [77], +∞ just to name a few. ( ) = E  /  vu t u au n N f In addition to facilitating multiple access, spreading = n 0 codes also shape the transmit spectrum. Analytical · − − TH( ) −  /  , p t nTf c u n Tc b u n N f expressions and simulated power spectral density (2) (PSD) for UWB transmissions are pursued in [44] and [70]. A PSD expression for TH-UWB allowing where Eu is the uth user’s energy per pulse at the trans- for both short and long spreading codes is derived mitter end. With su(k) ∈ [0, M − 1] denoting the M - in [44]. The effects of timing jitter on PSD of UWB ary information symbol transmitted by the uth user transmissions utilizing random TH codes and/or during the kth symbol duration, (2) subsumes several M -ary modulation can be found in [70]. In particu- modulation schemes. When b u(k) = su(k), and lar, let us consider “short” spreading codes that are au(k) = 1, (2) describes UWB transmissions with M - symbol-periodic with period N f . Let us now define ary PPM; when au(k) = 2su(k) + 1 − M , and the symbol level transmitted waveform for user u as

NOVEMBER 2004 IEEE SIGNAL PROCESSING MAGAZINE 31 − ( ) (n) ( ) = N f 1 ( − − TH( ) ) φ n = δ(n), and φ ( f ) = 1, ∀n pT,u t : n=0 p t nTf c u n Tc for TH- aa bb N f −1 UWB, p , (t) := c (n)p(t − nT ) for DS/SC/ T u n=0 u − f ( ) = N f 1 ( − ) MC-UWB, and pT,u t : n=0 p t nTf when no for binary PAM and spreading code is involved. Equation (2) then becomes √ +∞ (n) vu(t) = Eu = au(k)pT,u(t − kTs − b u(k)). Along φ = 1, ∀n, and k 0 aa the lines of [42, Chapter 4], it can be shown that the 1, n = 0 ( ) (n) PSD of vu t is φ ( f ) = 1 + cos(2πf ) bb , n = 0 2 E ∞ u 2 (n) (n) − j2π fnT ( ) = | , ( )| φ φ ( ) s ,( ) vv f PT u f aa bb f e 4 for binary PPM. Accordingly, the resultant PSD of Ts =−∞ 2 n vu(t) becomes [c.f. (4)]: vv( f ) = (Eu/Ts )|PT,u( f )| ( ) = (E / )| ( )|2 ( − for PAM and vv f u Ts PT,u f [ 1 φ(n) = { ( ) ( + )},φ(n)( ) = ( π ))/ + ( + ( π ))/( ) ∞ δ( − where aa : E au k au k n bb f : cos 2 f 2 1 cos 2 f 2Ts n=−∞ f − j2π f (b u (k)−b u (k+n)) E{e }, and PT,u( f ) := F{pT,u(t)} is k/Ts )] for PPM. the FT of pT,u(t). In particular, for independent identi- The shape of the vv( f ) for both modulations is cally distributed (i.i.d.) equiprobable binary symbols determined by PT,u( f ), which may contain spectral su(k) ∈{0, 1}, we have au(k) = 2su(k)−1, and b u(k) = 0 lines due to the repeated use of N f pulses in forming with PAM; and au(k) = 1, and b u(k) = su(k) with each symbol. Different from PAM, which is a zero- PPM. It then follows that mean linear modulation, additional spectral lines

10 10

0 0 − 10 −10 − 20 −20 − 30 −30

Power (dB) − 40 Power (dB) −40 − 50 −50 − 60 −60

−70 −70 024681012 024 6 81012 Frequency (GHz) Frequency (GHz) (a) (b)

10

0

−10

−20

−30

Power (dB) −40

−50

−60

−70 024681012 Frequency (GHz) (c)

▲ 5. Transmit PSD corresponding to (a) no spreading code, (b) random DS codes, and (c) random TH codes. Gaussian pulse with = . = = = Tp 0 4 ns. Nf 64, Tf 100 ns, Tc 2 ns.

32 IEEE SIGNAL PROCESSING MAGAZINE NOVEMBER 2004 emerge with PPM. Although the bandwidth of PT,u( f ) where is determined by the pulse shaper p(t), its shape, by L definition, relies not only on p(t), but also on the p (t) := α p (t − τ , ). (5) spreading codes utilized. The transmit PSD correspon- R l T l 0 l =0 ding to no spreading, random DS spreading, and ran- dom TH spreading with binary PAM are depicted in TH Figure 5. Notice how pronounced spectral lines are in Let us select Tf ≥ τL ,0 + Tp and c (0) ≥ TH Figure 5 where no spreading code is used. Figure 5(b) c (N f − 1) to confine the duration of pR(t) within and (c) confirms that both DS and TH spreading [0, Ts ) and thus avoid intersymbol interference (ISI). smooth the transmit PSD. It is also worth mentioning Without loss of generality, let us also confine the tim- that although the spectral lines cause “noise-like’’ inter- ing offset τ0 within a symbol duration, i.e., τ0 ∈ [0, Ts ). ference to narrowband services coexisting with UWB Notice that at the timing synchronization stage, the systems, they introduce cyclostationarity that one can multipath channel is unknown, and so is pR(t). exploit for timing offset estimation simply because Consequently, even with known training symbols a(k), these spectral lines originate from the underlying perio- the traditional approach of peak-picking the correlation dicity of the transmission. of 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 is Timing Synchronization not only suboptimum in the presence of dense multi- As defined in (1), the physical channel h(t) not only path, but also results in unacceptably slow acquisition captures multipath effects but also includes a delay speed and has prohibitive complexity when one has to (uncertainty) on the first arrival time τ0. For coherent perform exhaustive search over thousands of demodulation, timing synchronization is the first task bins/chips. There is clearly a need for low-complexity to be performed at the receiver to acquire and track the timing estimation methods in multipath-rich propaga- timing offset τ0. tion settings. To this end, a number of attempts have In fact, one of the major challenges at the UWB been proposed to improve acquisition speed and/or physical layer is the accuracy and speed of this synchro- performance in UWB radios. These attempts include: a nization step. As UWB systems employ low-power coarse bin reversal search for the noiseless case [22]; a ultra-short pulses (in the order of nanoseconds), timing coded beacon sequence in conjunction with a bank of requirements are stringent because even minor mis- correlators in the context of data-aided localization in alignments may result in lack of energy capture which the absence of multipath [13]; a ranging system that renders symbol detection impossible [59]. To better requires knowledge of the strongest path [26]; a non- understand the unique challenges in UWB timing, let data aided (a.k.a. blind) timing estimator that relies on us consider a single-user link with zero-mean, i.i.d. the cyclostationarity that arises in UWB transmissions M -ary PAM symbols a(k) having zero-mean and vari- with slow TH and sufficiently dense multipath [61]; σ 2 ance s . (Generalization to PPM is also possible.) and a data-aided maximum likelihood (ML) timing Dropping temporarily the subscript u, the received sig- algorithm using symbol- and frame-rate samples [60]. √nal after multipath propagation is [c.f. (3)]: r(t) = E ∞ ( ) L α ( − − τ ) + η( ) k=0 a k l =0 l pT t kTs l t , where UWB Timing with Dirty Templates (L + 1) is the number of effectively nonzero paths, To relax the rather restrictive assumptions in these each with amplitude αl and delay τl satisfying approaches, we have developed timing algorithms τl <τl +1 , ∀l . We assume that the channel is quasi- based on the novel concept of “dirty templates’’ [79]. {α }L {τ }L static, meaning that l l =0 and l l =0 remain invari- The idea is to rely on pairs of successive symbol-long ant per burst but may change from burst to burst; a(k), segments of r(t) taken at candidate time-shifts {α }L {τ }L η( ) τ ∈ , ) l l =0 and l l =0 are independent of the noise t [0 Ts and have one segment in each pair serve as a which is assumed zero-mean, wide-sense stationary but template for the other. Specifically, integrate-and-dump not necessarily white and/or Gaussian, as it consists of operations are performed on products of such segments both ambient noise and multi-user interference (MUI). to obtain symbol-rate samples: With respect to the first arrival time (timing offset) τ0, T other path delays can be uniquely described as: s xk(τ) = r(t + kTs + τ)r(t + (k − 1)Ts + τ)dt, τl ,0 := τl − τ0, ∀l ∈ [0, L ]. It is convenient to express 0 ( ) ( ) r t in terms of the aggregate pulse pR t at the receiver (6) which encompasses the transmit pulse, spreading codes and multipath effects: ∀k ∈ [1, +∞) and τ ∈ [0, Ts ). The symbol-long seg- ments r(t + kTs + τ) and r(t + (k − 1)Ts + τ), for ∈ , ) √ ∞ t [0 Ts are “dirty templates’’ because: i) they are r(t) = E a(k)pR(t − kTs − τ0) + η(t), noisy, ii) they are distorted by the unknown channel, and k=0 iii) they are subject to the unknown offset τ0. The latter

NOVEMBER 2004 IEEE SIGNAL PROCESSING MAGAZINE 33 2(τ) cancel the cross terms in xk we used that { ( ) ( )}= { 2( ) 2( )}=σ 4 = UWB characterizes transmission E a k a l 0 and E a k a l s , for k l . E (τ)˜ + E (τ)˜ = Ts 2 ( ) = E Now notice that A B 0 pR t dt : R is systems with instantaneous the constant energy of the unknown aggregate tem- E (τ)˜ − E (τ)˜ spectral occupancy in excess plate at the receiver and also that B A is uniquely maximized at τ˜ = 0, since EA (τ)˜ is minimized of 500 MHz or a fractional at τ˜ = 0 and EB (τ)˜ is maximized at τ˜ = 0, by definition. { 2(τ)} τ˜ = bandwidth of more than 20%. So, E xk is maximized when 0, or equivalently, τ = τ0. Compactly written, the approach for nondata τ = τ∈ , ) { 2(τ)} aided TDT yields: 0 arg max [0 Ts E xk . constitutes a major difference between the Timing tech- As usual, the ensemble mean must be replaced in nique based on dirty templates (TDT) and the transmit- practice by its consistent sample mean estimator ted reference (TR) approach [21] for channel estimation obtained from K symbol-long pairs of received seg- −1 K 2 (τ) and symbol demodulation, as we will detail in the ensu- ments: K k=1 x2k−1 . The number of samples K ing sections. To grasp the gist of TDT, let x¯k(τ) and required for reliable estimation can be reduced marked- r¯(t) denote the noise-free parts of xk(τ) and r(t). ly if a data aided approach is pursued [79]. The training Applying Cauchy-Schwartz’s inequality to (6) yields sequence {a(k)} for data-aided TDT comprises a repeated pattern (s, s, −s, −s ) with s being any M -ary PAM sym- Ts bol. This pattern is particularly attractive because it simpli- ¯ 2(τ) ≤ ¯2( + + τ) (τ) = (− )k 2 −E (τ)˜ + E (τ)˜ + ξ( ) xk r t kTs dt fies (7) to xk 1 s [ A B ] k . As 0 −1 K 2 a result, K = x − (τ) converges faster to Ts k 1 2k 1 2 E{x 2(τ)}=s 4[E (τ)˜ − E (τ)˜ ]2 + σ 2 , because now one × r¯ (t + (k − 1)Ts + τ)dt, k A B ξ σ 4 0 obviates convergence to s , that is necessary in the blind approach to remove unknown symbol effects where the equality holds ∀k if and only if (self-noise). The benefit with data-aided TDT is very r¯(t + kTs + τ) = λr¯(t + (k − 1)Ts + τ). But the latter rapid acquisition since only K = 1 pair of received is true ∀t ∈ [0, Ts ) if and only if τ = τ0. In words, the symbol-long segments carrying as few as four training cross correlation of successive symbol-long received seg- symbols, is sufficient; see also Figure 6. Summarizing, ments reaches a unique maximum magnitude if and consistent (non)data-aided TDT can be accomplished only if these segments are scaled versions of each other, in the absence of ISI even when TH codes are present which is achieved only at the correct timing; i.e., when and the UWB multipath channel is unknown, using τ = τ0. In its simplicity, this neat observation offers a “dirty’’ Ts -long segments of the received waveform as distinct criterion for timing synchronization that, for follows [79]: years, has relied on the idea that the autocorrelation of the noise-free template has a unique maximum at the K 2 correct timing; the latter has been the principle behind 2kTs τˆ0 = arg max r(t + τ)r(t + τ − Ts ) dt . τ∈[0,T ) ( − ) all existing narrowband and UWB timing schemes, s k=1 2k 1 Ts including the popular early-late gate algorithm [42]. (8) The TDT approach is different from these conventional synchronizers. It has fundamental implications to UWB and also to a number of other applications such as time- Both training and blind modes have low-complexity as delay and displacement estimation through unknown they require only symbol rate samples, but the data- time-dispersive media, where there is no undistorted aided mode enjoys also rapid acquisition relying on as template to rely on, even in the noise-free case. few as four training symbols [s, s, −s, −s ]. To establish its validity even in the presence of noise, The estimator in (8) enables timing synchronization we start by recalling that pR(t) has finite nonzero sup- at any desirable resolution constrained only by the port [0, Ts ). This implies that the noisy xk(τ) can be affordable complexity: i) coarse timing with low com- expressed as [c.f. (5) and (6)]: plexity, e.g., by picking the maximum over N f candi- date offsets τ = nTf , where integer n ∈ [0,N f ); ii) fine x (τ) = a(k) [a(k − 1)E (τ)˜ + a(k + 1)E (τ)˜ ] + ξ(k), timing with higher complexity at the chip resolution k A B τ = ∈ , ) ( ) with iTc , i [0 Nc ; and iii) adaptive timing 7 (tracking) with voltage-controlled clock (VCC) circuits; the preliminary tests in Figure 6 correspond to frame where ξ(k) denotes noise after correlation, level timing resolution. As the TDT algorithms only Ts Ts −˜τ E (τ)˜ := E p2 (t)dt,E (τ)˜ := E p2 (t)dt and require zero ISI, the condition T ≥ τ , + T can be A Ts −˜τ R B 0 R f L 0 p τ˜ := (τ0 − τ) mod Ts . The mean-square of xk(τ) in relaxed to allow for higher data rates, as long as guard ( ) { 2(τ)}=σ 4 E2 (τ)˜ + E2(τ)˜ + σ 2 = (σ 4/ ) 7 is E xk s [ A B ] ξ s 2 frames are inserted between symbols to avoid ISI, much 2 2 2 ×{[EA (τ)˜ + EB (τ)˜ ] + [EA (τ)˜ − EB (τ)˜ ] }+σξ , where to like zero-padding in narrowband systems [67].

34 IEEE SIGNAL PROCESSING MAGAZINE NOVEMBER 2004 0 10 100 K = 1 K = 1 K = 2 K = 2 K = 16 −1 K = 16 − 1 10 10 K = 64 K = 64 No Timing 10−2

10−2 Perfect − 10 3 Timing

Normalized MSE With

Average BER Timing 10−3 10−4 Acquisition

−5 10−4 10 −50 5101520 051015 20 25 30 35 SNR Per Pulse (dB) SNR Per Symbol (dB) (a) (b)

▲ 6. (a) Normalized MSE of τˆ0 in (8) and (b) average BER using TDT algorithm. Dashed (solid) curves correspond to (non) data-aided mode.

K Multi-User TDT k τˆd,0 = arg max (−1) The timing algorithms we have introduced are for a τ∈ , ) [0 Ts = peer-to-peer link where MUI is treated as noise. This k 1 ( + ) 2 is reasonable in a multi-user setting provided that user k 1 Ts × ( +τ) ( +τ − ) . separability is ensured through channelization. But in r t r t Ts dt kT such cases, user separation is sensitive to mistiming. s To illustrate how data-aided TDT can be extended to a multi-user setup, suppose one wishes to synchronize Simulations indicate that this multi-user TDT scheme to a single desired user (say user d) who is transmit- requires long training sequences. It is of interest to ting the training pattern (s, s, −s, −s ) and is received explore multi-user TDT algorithms that remain opera- in the presence of other asynchronous users commu- tional with short or even without training sequences. nicating information-bearing i.i.d. symbols. Equation Besides low-complexity timing algorithms that are (7) now becomes operational in realistic UWB multi-user settings, analyt- ical studies on system performance and capacity in the presence of timing errors are topics deserving further

Nu −1 investigation. In the context of narrowband receivers, xk(τ) = xu,k(τ) carrier synchronization and symbol timing issues have u=0 been investigated thoroughly [34]. Existing solutions − Nu 1 include the spectral line generating synchronizers, the = ( ) ( − )E (τ˜ ) au k [au k 1 u,A u ML approach, and the cyclostationary approach. u=0 Performance is benchmarked using the (modified) + ( + )E (τ˜ ) + ξ( ), au k 1 u,B u ] t Cramér-Rao bound (CRB) [34]. For wireless channels (9) that are strongly frequency selective and quasi-static over time, recent developments in multicarrier modula- tion have stimulated renewed interest in synchroniza- Ts 2 where E , (τ˜ ) := E p , (t)dt , E , (τ˜ ) := tion. Considering the time-frequency duality between u A u u Ts −˜τu u R u B u Ts −˜τu E 2 ( ) τ˜ = (τ , − τ) u 0 pu,R t dt and u : u 0 mod Ts are UWB and orthogonal frequency division multiplexing as before, but with symbols, channels and offsets (OFDM) systems, these works may prove valuable in being user dependent. The desired user’s samples at promoting a dual thrust for timing estimation of UWB the dirty-template correlator output obey xd,k(τ) = signals. [This duality refers to the fact that OFDM con- k 2 (−1) s [−Ed,A (τ˜d ) + Ed,B (τ˜d )] + ξ(t). Upon averaging veys information via impulse-like signals in the frequen- (without squaring), we obtain for the user under cy-domain (carriers), whereas a UWB system conveys k 2 training E{(−1) xd,k(τ)}=s [Ed,B (τ˜d ) − Ed,A (τ˜d )] ; information via impulse-like signals in the time-domain while for all other users transmitting zero-mean i.i.d. (ultra-short pulses).] k symbols we have E{(−1) xu,k(τ)}=0. This observa- Upon synchronization, the receiver can adjust its tion suggests the following multi-user TDT estimator timing according to the estimated first arrival time τˆ0. [c.f. (8)] In the following sections, we assume this estimate to be

NOVEMBER 2004 IEEE SIGNAL PROCESSING MAGAZINE 35 perfect. Consequently, the multipath delays with respect Concatenating the L r outputs from all fingers dur- to the adjusted receiver timing will be such that τ0 = 0. ing the nth frame we can form the block:

Rake Reception and Multipath Diversity x (n) := [x (n; 0) x (n; 1) ···x (n; L − 1)]T The most commonly used UWB receiver is a correla- u u u u r tion (matched filter) receiver [5], [52], where the = Euau(n/N f )c u(n)α˜ + ηη(n), (12) received signal is correlated with the transmitted pulse p(t). Conveying information with ultra-short pulses, UWB transmissions can resolve many paths, and are where α˜ and ηη(n) are L r × 1 vectors constructed by α˜ η( ; ) ∈ , − thus rich in multipath diversity (see Figure 3). This has stacking l r and n l r for l r [0 L r 1]. Recalling motivated research towards designing correlation-based that each symbol is conveyed by N f pulses, a total of Rake receivers to collect the available diversity [8]. N f L r correlator outputs must be collected, L r per frame, to decode one symbol. To this end, vectors (k+1)N −1 Frame- and Symbol-Rate Rake Receivers {x (n)} f corresponding to the kth symbol can u n=kN f For DS-, SC-, or MC-UWB systems with PAM modu- be concatenated into a vector of size N f L r × 1 as [c.f. lation, the continuous-time received waveform is given (12)]: by [c.f. (3)]

T ( ) = ν ( ) ( ) + η( ) y (k) := xT (kN ) ···xT (kN +N − 1) ru t u t h t t u u f u f f ∞ = Euau(k)(cu ⊗˜αα) + ηη(k), (13) = Eu au(n/N f )c u(n) g (t − nTf ) + η(t), n=0

(10) where ⊗ stands for Kronecker product, cu := ( ), ... , ( − ) T ηη( ) = ηT ( ), ... , [c u 0 c u N f 1 ] , and k : [ kN f ( ) = (  )( ) = L α ( − τ ) ηT ( + − ) T × where g t : p h t l =0 l p t l is the kN f N f 1 ] is the N f L r 1 noise vector that composite pulse-multipath channel. Since the frame consists of additive white Gaussian noise (AWGN), duration Tf is up to our disposal, we can choose the MUI, and NBI. Notice that the vector yu(k) in the frame duration longer than the maximum delay spread discrete-time equivalent input-output relationship (12) augmented by one pulse duration, i.e., Tf ≥ τL + Tp , contains nothing but the correlator outputs collected to avoid interframe interference (IFI). Rake receivers from L r fingers over N f consecutive frames correspon- with L r fingers sum up weighted outputs (diversity ding to the kth symbol. To decode a symbol, diversity combining) from a bank of L r correlators. For clarity, combining needs to be carried out. With the N f L r × 1 we will consider correlation and diversity combining weight vector β, diversity combining yields the decision T separately. During the nth frame, the template for the statistics for the kth symbol: z u(k) := β yu(k). τ˜ η( ) l r th correlator (Rake finger with delay l r ) is the pulse If the noise t is white, maximum ratio combining ( ) +˜τ p t delayed by nTf l r . Accordingly, the correlator (MRC) is optimal and gives rise to weight vector output of the l r th finger during the nth frame is βmf := cu ⊗ α˜ , which implements matched filtering (MF). In the presence of MUI and/or NBI, the noise η(t) is often colored, which renders MF weights subopti- +˜τ + nTf lr Tp ( ; ) = ( ) ( − −˜τ ) .( ) mal and motivates the use of minimum mean-square xu n l r ru t p t nTf l r dt 11 +˜τ β = E η+ nTf lr error (MMSE) weights: mmse : u[R T −1 Eu (cu ⊗˜α)(cu ⊗˜α) ] (cu ⊗˜αα), where Rη := E × {ηη(k)ηηT (k)} is the aggregate noise covariance matrix. It is τ˜ + α˜ = lr Tp ( ) ( −˜τ ) β Upon defining l r : τ˜ g t p t l r dt , it fol- worth clarifying that the MMSE weights consists +˜τ + lr mmse nTf lr Tp ( − ) ( − −˜τ ) = β lows that nT +˜τ g t mTf p t nTf l r dt of N f L r distinct elements, whereas mf consists of repe- α˜ δ( − ) f lr l r m n , where to establish the latter, we used that titions of L r distinct elements. Consequently, MF com- >τ + Tf L T√p . Substituting (10) into (11), we find bining has lower complexity than MMSE combining. ( ; ) = E ( / ) ( )α˜ + η( ; ) xu n l r uau n N f c u n l r n l r , where Established based on a two-step (correlation fol- η(n; l r ) is the sampled noise, at the correlator output lowed by weighted combination) approach, (11) of the l r th finger, during the nth frame. For each fin- requires frame-rate sampling per finger. Interestingly, ger to capture distinct multipath returns, finger delays receiver processing can be implemented even with sym- τ˜ −˜τ ≥ must satisfy l r l r −1 2Tp , which yields the maxi- bol rate sampling. To see this, recall first that the entries mum number of fingers L¯ :=τ /(2T ). In practice, of β (that is, [β] ∀n ∈ [0,N L − 1]) are the diversity ¯ r L p n f r L r ≤ L r is often chosen to trade off performance with combining weights. Rake reception that yields the complexity, leading to receiver options such as all Rake, decision statistics z u(k) can be realized by correlating partial Rake or selective Rake [71]. Notice that the fil- r (t) with the symbol-long template p¯ (t) = u − s N f 1 L −1 η( ; ) η( ) r β + ( − −˜τ ) tered and sampled n l r stays white if the noise t n=0 l =0 [ ]nLr l r p t nTf l r , and sampling τ˜ r = is white, since l r are spaced sufficiently apart. its output every Ts N f Tf seconds.

36 IEEE SIGNAL PROCESSING MAGAZINE NOVEMBER 2004 ¯ To generate the template ps (t), multiple analog poses a major challenge in UWB communications waveforms p(t) have to be generated and delayed because even if one opts to utilize only a few (say the accordingly. The delay accuracy will affect decoding ten strongest out of hundreds of) returns, accurate esti- performance. But different from pulse-rate sampling mation of the ten strongest channel gains and their cor- that requires precise timing at each sampling instance, responding delays is required. In a UWB channel with ¯ ps (t) needs to be generated only once during the chan- hundreds of multipath returns, channel estimation is nel coherence time. The latter provides the timing cir- oftentimes easier said than done. cuits sufficient time to stabilize and thus reduces timing jitter effects. Channel Estimation Although channel estimation is also critical in the con- Quantifying the UWB Channel’s Multipath Diversity text of narrowband and spread-spectrum (SS) systems Let us now quantify the order of the multipath diversity (see e.g., [63]), and the channel estimators developed collected by a Rake receiver with Lr fingers. To this for DS-CDMA can be adapted to UWB systems, the end, we assume that the channel, which is a realization formidably high sampling rates required by the latter of the S-V model, is perfectly known at the receiver. We motivates search for alternatives. The main reason is also take the noise to be white, and use the MF weights that the number of parameters to be estimated, i.e., the for MRC. With binary modulation, it is shown in [78] number of delays and amplitudes, can be as large as that the average BER is upper bounded as follows: 400 for a typical UWB indoor channel. Impulse response estimators for UWB channels have − Lr 1 2 been developed in [28] and [73] based on the ML cri- Pe ≤ E exp −ρα˜ /2 l r terion. The input-output channel identification algo- l r =0 − rithm in [73] uses a single transmitted pulse in the Lr 1 −1/2 2 −L r /2 absence of MUI; whereas the approaches in [28] form = 1 + ρE α˜ ≤ (AL ρ) ,(14) l r r impulse response estimates using either training sym- l r =0 bols (data-aided), or unknown information-conveying where ρ is the transmit signal-to-noise ratio (SNR), symbols (nondata-aided), treating MUI as white − 2 L r 1 AL is the geometric average of E{˜α } , and the Gaussian noise. Not surprisingly, [73] arrives at the r l r l r =0 second inequality holds at high SNR (ρ  1). Recall same channel estimator as the data-aided approach in − α L r 1 that l r = are the amplitudes of the effective chan- [28], under the assumption that all multipath compo- l r 0 |τ − τ | > ∀ = nel taps [c.f. (11)]. Equation (14) confirms that as the nents are resolvable, i.e., l 1 l 2 Tp , l 1 l 2 . number of fingers L r increases, the diversity order also Both data-aided (DA) and nondata-aided (NDA) chan- increases. Also notice that although N f L r samples are nel estimators are tested in [28] over a fixed channel collected in (13), the diversity order is only L r /2, with three multipath components, based on 100 sym- instead of N f L r /2, because the degrees of freedom are bols. Computational complexity of the ML channel only L r /2, and the factor 1/2 comes from the fact that estimators in [28] and [73] increases as the number of the UWB channel is real. The average BER correspon- multipath components increases, and becomes unaf- ding to binary PAM, and PPM for two values of the fordable for a realistic UWB indoor channel. Moreover, modulation index is plotted in Figure 7. As L r increas- sampling at subpulse rate is required to perform chan- es, the increase in diversity order is evident. nel estimation. In [28], the sampling rate of Two remarks are in order. First, the Rake reception 12.5/Tp ∼ 25/Tp Hz is suggested. With typical model we presented here is valid when TH is absent. A Tp = 0.7 ns, the sampling rate is in the formidable general Rake reception model along with a unifying signal-to-interference-and-noise ratio (SINR) analysis of low duty-cycle UWB access through multipath and 100 NBI can be found in [82]; see also [11] for a system Lr = 1 model based on oversampling. Secondly, even when − 1 TH is absent, DS-, SC- and MC-UWB may exhibit dif- 10 ferent diversity and coding gains when Tf <τL + Tp Lr = 4 −2 and IFI emerges. For further details in this direction, BER 10 readers are referred to [77]. Lr = 16 So far, we have outlined how Rake reception can 10−3 collect diversity, provided that the multipath channel Average − PPM (∆ = 1 ns) can be estimated at the receiver. Since the received 10 4 ( ) PPM (∆ = 0.156 ns) waveform ru t contains many delayed and scaled repli- PAM cas of the transmitted pulses, a large number of fingers is needed for energy capture. Performing Rake recep- 051015 20 25 30 tion with appropriate weights on individual fingers SNR (dB) entails estimation of the channel impulse response. This ▲ 7. Collecting multipath diversity with Rake reception (Tp = 0.7 ns).

NOVEMBER 2004 IEEE SIGNAL PROCESSING MAGAZINE 37 range of 17.9 ∼ 35.7 GHz. At the expense of addition- information conveying waveforms are nonoverlapping. al hardware, such rates can only be feasible with stag- The receiver then correlates r(t) with its delayed ver- gered sampling using a bank of polyphase ADCs with sion r(t − Tf ), to yield the symbol estimate [21]: accurate timing control. More recently, joint timing synchronization and channel estimation has been pursued. In [6], least sˆ = sign r(t)r(t − Tf ) dt ,(15) τ squares (LS) estimates of the timing offset 0 and the ( ) = L α ( − τ ) channel impulse response h t l =0 l t l are formed using Nyquist rate (subpulse rate) samples of which, in the absence of noise, yields sˆ = the received waveform. The clustered structure of the sign {s g 2(t)dt}=s . channel is taken into account in forming these esti- Equation (15) is reminiscent of the TDT estimator in mates. But in addition to oversampling, this approach (8). However, there are fundamental differences between entails rather restrictive assumptions which include the TR approach for channel estimation and symbol τ0 < Tf , τL ,0 < Tf , knowledge of the channel impulse demodulation and the TDT synchronizer. The first main response structure and order L. Aiming at sub-Nyquist difference is that TR assumes that noisy templates are sampling rate, [31] translates the channel impulse taken at the correct time instances; i.e., τ0 is known and response estimation problem into a harmonic retrieval corrected by τ = τ0; whereas templates in TDT are not problem. Under the condition τL ,0 < Tf and with the only noisy and distorted by the unknown channel, but knowledge of L, this method can only form an estimate also subject to the unknown τ0. Of course, the second of a circularly shifted h(t) with the unknown major difference is that TDT does not incur the 50% τ0(mod Tf ), simply because harmonic retrieval rate/energy loss of TR, where half of transmitted wave- approaches are blind to unknown circular shifts. In forms are used as pilots, regardless of the channel. other words, [31] cannot estimate timing offsets. To To optimize the emerging channel estimation per- this end, the FFT based approach in [68] combined formance-rate tradeoff, a so-called pilot waveform with a separate timing estimator offers a viable alterna- assisted modulation (PWAM) for UWB systems was tive for offline UWB channel estimation at least for developed in [81]. As depicted in Figure 8, pilot (a.k.a. PPM transmissions (similar to [6], [28], and [73]), training) pulses are inserted in PWAM, and an estimate high sampling requirements prevent online implemen- of the aggregate analog channel g (t) is formed at the tation of [68]. receiver by simply averaging over several received pilot waveforms (see also Figure 9). This estimate gˆ (t) can Transmitted Reference and PWAM Signaling then be used as a correlator template, to enable inte- To avoid the high sampling rate and computational grate-and-dump demodulation at frame rate (10 MHz complexity associated with the estimation of h(t), an with a typical Tf = 100 ns). alternative approach is to estimate the aggregate analog Clearly, TR is a special case of PWAM where a pilot channel g (t) = (p  h)(t). To this end, there has been pulse is inserted after every information pulse. Since the a renewed interest in the so termed TR signaling [54], correlator relies on a “noisy template,’’ one expects the whose application to UWB systems was proposed in error performance at the PWAM detector output to be [57] for radar detection, and in [21] for communica- similar to that of differential decoding. In the latter, tions. In TR systems, each information-conveying pulse each information symbol is detected by using a received is coupled with an unmodulated (a.k.a. pilot) pulse; symbol as a “noisy pilot’’ to eliminate the unknown e.g., per PAM symbol s ={±1}, we transmit channel gain from the subsequent received symbol. v(t) = p(t) + s · p(t − Tf ). After multipath propaga- Key parameters of PWAM include the number of tion, the received waveform is given by pilot pulses inserted per burst and the energy allocation r(t) = g (t) + s · g (t − Tf ) + η(t). With frame dura- among pilot and information-conveying pulses. These tion chosen to be Tf ≥ τL + Tp , the received pilot and parameters determine not only the channel estimation

ε √ p(np) η(t) sˆ(ns) − 1 r(t) Nf 1 × T p(t) + × ∫ f ∑ Detector × g(t) 0 ± 0 s(ns) = { 1} g(t) = p(t) h(t) Channel t = nsNfTf ε * √ s(ns) Estimator gˆ(t)

▲ 8. PWAM system block diagram. Es(ns) and Ep(np) denote the energy of information-conveying and pilot waveforms, respectively; η(t) ˆ is the additive noise; r(t) stands for the received waveform; and h(t) represents the estimate of h(t).

38 IEEE SIGNAL PROCESSING MAGAZINE NOVEMBER 2004 and symbol demodulation performance but also the allows it to span the gamut of power-limited to band- effective data rate. In fact, optimal parameters can be width-limited scenarios [81]. selected to not only minimize the mean-square channel Figure 10(a) depicts the average capacity correspon- estimation error and achieve the CRB but also maxi- ding to optimal (equi-SNR) PWAM, TR, and the case mize the average capacity [81]. For any given N f , Tf , of perfect channel estimate, with BPSK modulation. and number of waveforms per burst N =τc /Tf that The gap is evident, and is increasing as SNR increases. is determined by the channel coherence time τc , the Notice that after 10 dB, the average capacity corre- optimal number of pilot waveforms is given by sponding to PWAM approaches one, whereas that cor- Np = N −N f (N /N f −1) [81]. A fraction α of the responding to TR approaches 0.5 due to its inherent total energy per burst is assigned to pilot waveforms, 50% rate loss. With channel coherence time τc = 0.2 α = . = = with 05 at low SNR or small N , and ms, and Tf 100 ns, the burst size is N 2000, the α = N f /( N −Np + N f ) at high SNR or large N . average BER versus SNR ρ is plotted in Figure 10(b) Moreover, equispaced, equipowered pilot waveforms for both optimal PWAM and ideal channel estimate. maximize the average capacity as well as provide Random TH code is used, and the MUI is modeled as robustness to slow channel variations. In addition, allo- Gaussian noise [72]. When multiple users are present, cating the number of pilot pulses according to channel degradation in BER performance can be observed both coherence time, the flexibility inherent in PWAM with PWAM and with a perfect channel estimate.

Tx: Tf NfTf ......

Pilot Info. Conveying Waveforms Waveforms Rx: ......

gˆ(t) Analog Delay + Analog Delay + Element Element

▲ =τ / = + ¯ = 9. Channel estimation with PWAM (N c Tf 3Nf 3, Np 3).

1 100 Ideal Estimate 10−1 Optimal PWAM 0.8 Ideal Estimate Optimal PWAM 10−2 TR 0.6 10−3

0.4 Average BER 10−4 Nu = 50

0.2 10−5 Nu = 1 Average Capacity (Bit/Channel Use) 10−6 0 051015 20 25 051015 20 Nominal SNR ρ Nominal SNR ρ (dB) (a) (b)

▲ 10. (a) Average capacity versus SNR and (b) BER performance in the presence of MUI.

NOVEMBER 2004 IEEE SIGNAL PROCESSING MAGAZINE 39 Aiming at training-based channel estimation, PWAM Consider a single-user link with binary PAM with is reminiscent of the pilot symbol assisted modulation DS/SC/MC and/or TH spreading codes. Moreover, (PSAM), which was originally developed for bandlimit- let us differentially encode the binary PAM (BPSK) ed time-selective channels, and has recently been symbols a(k) as a˜(k) := a(k) · a˜(k − 1) and transmit extended to narrowband frequency-selective channels the encoded sequence a˜(k). The received waveform is [36]. Nevertheless, they differ in several aspects: i) then given by [c.f. (5)]: 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 equivalent r(t) = E a˜(k)pR(t − kTs − τ0) + η(t), frequency-selective channels, whereas PWAM recovers k=0 the equivalent continuous-time channel waveform; and iii) corresponding to one pilot symbol used in PSAM, where the timing offset τ0 = 0 in general. Performing PWAM allocates multiple pilot pulses across frames and the integrate-and-dump operations using dirty tem- is thus more flexible to strike desirable rate-performance plates as in (6), the symbol-rate samples are [c.f. (7)] tradeoffs arising with variable channel coherence time. Although TR was originally advocated for its low- T complexity, there has been a number of recent TR s xk = r(t + kTs )r(t + (k + 1)Ts ) dt improvements that trade off complexity for performance. 0 In the context of delay-hopped (DH-)TR, [84] proposes = a(k)EA (τ0) + a(k + 1)EB (τ0) + ξ(k), (16) an 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. In where we used the fact that a(k) = a˜(k)a˜(k − 1) in TR and PWAM, the continuous-time aggregate channel establishing the second equality. is estimated from the pilot waveforms only. Further If one opts to estimate the timing offset using, e.g., exploiting the channel information embedded in the the TDT approach, and compensate it (almost) perfect- information-conveying waveforms, ML and generalized ly, then (16) can be considered approximately with likelihood ratio tests (GLRTs) schemes were put forth in τ0 = 0. In this case, EA (0) = 0, EB (0) = ER and (16) [7]. Trading off complexity for performance, [7] turns boils down to xk = a(k + 1)ER + ξ(k), which can be out to be a channel impulse response estimator with high easily demodulated. In fact, (16) with τ0 = 0 shows that complexity as the ones in [28] and [73]. the differential UWB system in [7] and [19] can be viewed as a special case of the noncoherent approach. Differential and Noncoherent UWB This differential UWB receiver is semicoherent since it As both timing synchronization and channel estimation requires timing but bypasses channel estimation. The pose major challenges in UWB communications, non- performance of such a differential (DIFF) scheme is coherent UWB radios that bypass both of these chal- shown in Figure 11. It is worth stressing that with per- lenging tasks offer interesting alternatives to explore. fect timing and for the same information rate, differen- tial UWB outperforms TR simply because the latter uses 50% energy on pilots, as confirmed in Figure 11. But even when synchronization is attempted, timing 100 errors are inevitable and thus τ0 = 0. In this case, EA (τ0) and EB (τ0) are also nonzero and direct applica- 10−1 tion of differential demodulation will lead to consider- able performance degradation. Simulated performance Without Timing of DIFF-UWB and TR in the presence of timing offset 10−2 is shown in Figure 11. Notice that though TR is more robust against timing offsets than DIFF-UWB, both

Average BER yield unacceptable performance. However, we observe Perfect Timing 10−3 that the channel energies E (τ ) and E (τ ) in (16) can DIFF A 0 B 0 TR be viewed as the impulse response taps of an unknown VA first-order equivalent ISI channel [83]. This interesting −4 10 CML viewpoint motivates development of noncoherent algo- −50 5101520 rithms for joint symbol detection and estimation of the unknown equivalent channel based on the “dirty corre- E/σ2 (dB) lator’’ output samples in (16). It is worth stressing that ▲ 11. Performance of TR and differential (DIFF) UWB in the pres- only two equivalent channel taps are to be estimated ence and absence of timing offsets; and that of incoherent UWB with noncoherent UWB, as apposed to hundreds of radios using VA and CML demodulators in the presence of timing taps in the underlying UWB physical channel and the offsets. analog aggregate channel in TR and PWAM. Several

40 IEEE SIGNAL PROCESSING MAGAZINE NOVEMBER 2004 noncoherent schemes have been recently considered in where we used the fact that au(2n + 1) = au(2n), and [83]. One approach is the ML sequence demodulator b u(2n + 1) = b u(2n), ∀n ∈ [0,N f /2 − 1]. This UWB- using Viterbi’s algorithm (VA) along with its low-com- specific scheme is different from existing ST codes used plexity per-survivor variants. Further trading off per- for digital linear modulations [3] in three aspects. formance for complexity, decision-directed conditional ▲ i) Digital symbol-by-symbol versus analog within each ML (CML) alternatives are also explored in [83]. The symbol waveform. Existing STC schemes operate on digi- performance of noncoherent UWB using VA and CML tal symbols, whereas this UWB-tailored STC approach schemes is depicted in Figure 11. Bypassing both tim- encodes pulses within symbol waveforms; it is this UWB- ing synchronization and channel estimation, these non- specific aspect that enables enhanced space-multipath coherent algorithms exhibit as little as 3 dB loss in diversity gains; comparison with differential UWB with perfect timing. ▲ ii) Flat or ISI-inducing channels versus frequency-selec- tive channels: Existing STC schemes are designed either Multi-Antenna UWB Systems for flat, or, for ISI-inducing MIMO fading channels, We have seen how the error performance of UWB whereas this analog ST code is tailored for non-ISI radios can be boosted by collecting multipath diversity inducing UWB MIMO channels that are rich in multi- [8], [21], [81]. However, Rake reception in UWB may path diversity; require a large number of finger amplitudes and delays ▲ iii) Linear and nonorthogonal nonlinear modulations which are cumbersome to obtain [28], [73]. Avoiding versus linear and orthogonal nonlinear modulations with estimation of the channel’s impulse response, PWAM coherent or noncoherent reception. Existing STC schemes and TR require an analog delay line at the receiver entail linear modulators and coherent demodulators, which may not be easy to implement [13]. Differential except for the works of [20] that deal with the nonco- and noncoherent schemes enjoy low complexity at the herent case. However, the latter do not consider price of suboptimum performance. In a nutshell, orthogonal nonlinear modulations (orthogonal PPM) although rich multipath diversity is enabled with UWB that are of interest to UWB and lead to ST coding transmissions, its collection at the receiver may face schemes that guarantee full diversity and symbol implementation difficulties, especially when the channel detectability, even with noncoherent reception. variations are relatively rapid. With one receive and two transmit antennas and On the other hand, multi-antenna-based space-time PAM modulation in the absence of TH, it can be (ST) systems offer an effective means of enabling space shown that the average BER for binary modulations at diversity via spatial multiplexing, which has the poten- high receive-SNR ρ is upper bounded by [78]: tial to improve not only error performance, but also − capacity. Motivated by these attractive features, an ana- A L r log ST coding scheme was developed for UWB com- P ≤ L r ρ ,(18) e 2 munications in [78]. With the channel coherence time being at least one symbol duration τc ≥ Ts = N f Tf , the following ST coded matrix is transmitted: where L r is the number of Rake fingers, and AL r is the L −1 geometric average of E{˜α2 } r . Compared with (14), l r l r =0 N /2−1 f v00(n; t) v01(n; t) this ST coded transmission scheme doubles the diversity u u , ∀t ∈ [0, T )(17) order, but loses 3 dB coding gain, due to the power split v10(n; t) v11(n; t) s n=0 u u between the two antennas at the transmitter. In an indoor environment with low mobility, the channel kl ( ; ) τ where vu n t denotes the waveform transmitted from coherence time c is generally much larger than the the kth transmit antenna during the (2n + l )th frame frame duration Tf . This suggests employment of an duration. The matrix entries in (17) can be expressed interleaver in conjunction with ST coding. With the explicitly as multipath channel remaining invariant over one symbol duration T = N T , and changing independently from s f f 00( ; ) = ( ) ( ) − symbol to symbol, it is shown in [78] that using an vu n t au 2n c u 2n p t 2nTf interleaver with depth Nd ≤ N f yields an average BER −c TH(2n)T −b (2n) u c u upper bounded as follows: 01( ; ) = ( ) ( + ) −( + ) vu n t au 2n c u 2n 1 p t 2n 1 Tf − − TH( + ) − ( ) A Nd L r c u 2n 1 Tc b u 2n L r Pe ≤ ρ .(19) 2Nd v10(n; t) = a (2n)c (2n+1)p t −2nT u u u f TH ( ) −c (2n)T −b (2n) Achieving diversity Nd times that in 18 with the same u c u 11( ; ) =− ( ) ( ) −( + ) L r and identical channel estimation complexity, the vu n t au 2n c u 2n p t 2n 1 Tf price paid is decoding delay by Nd symbols and loss in − TH( + ) − ( ) , c u 2n 1 Tc b u 2n coding gain by a factor Nd .

NOVEMBER 2004 IEEE SIGNAL PROCESSING MAGAZINE 41 While enhancing the diversity gains by deploying an additional antenna, ST-coded multi-antenna UWB 0 10 radios can be implemented with conventional analog Rake receivers having a small number of fingers. ST- Lr = 1 UWB also enables noncoherent reception for joint − 10 1 diversity collection, which bypasses the cumbersome channel estimation task [78]. Figure 12 shows simulat- Lr = 16 ed performance of an ST-coded multi-antenna UWB −2 10 system with coherent and noncoherent reception in the BER presence of timing jitter. Simulations reveal consider- Lr = 4 able improvement in both BER, and enhanced immu- − 10 3 nity against timing jitter. The latter suggests theoretical Nt = 1, Nr = 1 analysis of its robustness against timing jitter, and the Nt = 2, Nr = 2 potential of multiple antennas to facilitate synchroniza- 10−4 051015 20 25 30 tion of UWB systems. SNR (dB) (a) Multiple Access and Interference Suppression In the presence of multiple users and overlaying nar- rowband systems, single user detection is typically sub- 100 optimal, and special effort is needed to cope with MUI Lr = 1 and/or NBI effects. This subsection will be devoted to 10−1 such issues.

Lr = 16 Lr = 4 Single-Carrier and Multicarrier Codes: 10−2 Let us recall the baseband multi-access UWB setup in ( )

BER (3) with the user-specific spreading codes c u n being 10−3 symbol-periodic with period N . We also normalize f − N f 1 2( ) = the spreading codes such that n=0 c u n N f . In −4 DS-UWB, orthogonal binary sequences c u(n) ∈{±1} 10 N −1 Nt = 1, Nr = 1 f ( ) ( ) = δ( − ) are employed: n=0 c u1 n c u2 n N f u1 u2 . Nt = 2, Nr = 2 Similar to TH-UWB, these codes are constant-modulus 051015 20 25 30 and have been used in e.g., [15], [48], [76]. However, SNR (dB) utilizing the entire bandwidth, they are not flexible in (b) handling NBI. To this end, digital single-carrier (SC-) and multicarrier (MC-)UWB have been introduced recently, for low-power low-duty-cycle baseband UWB 100 multiple access [77]. Nt = 1, Nr = 1 Casting the user-specific spreading codes c (n) into Nt = 2, Nr = 2 u N f × 1 vectors cu with user index u ∈ [0,N u − 1], the construction of SC/MC-UWB codes cu starts with N u = N f orthogonal baseband digital subcarriers ∀k ∈ [0,N f − 1]: BER

   2πn , = = / ,  cos k n 0, or, n N f 2 10−1  √ N f  2πn [fk ]n = 2 cos k , n ∈ [1,N f /2 − 1],  N f  √   π(2n−N f ) 2 sin k , n ∈ [N f /2 + 1,N f − 1], N f 051015 20 25 30 SNR (dB) (c) where [fk]n denotes the (n + 1) st entry of the column vector fk . The discrete-time Fourier transform (DTFT) ▲ 12. (a) Incoherent reception; (b) coherent reception in the of f contains sinc functions, as depicted in Figure k − { (o)}N f 1 absence of timing jitter; (c) coherent reception in the presence of 13(a). Now let cu u=0 denote any set of orthonor- = ( , , ) timing jitter (from top to bottom Lr 1 4 16 ). Timing jitter is mal spreading codes of length N f . User-specific codes modeled as exponentially distributed with mean 0.5 ns; Nt and Nr for baseband MC-UWB can then be constructed as lin- stand for the number of transmit and receive antennas, respectively. ear combinations of digital subcarriers

42 IEEE SIGNAL PROCESSING MAGAZINE NOVEMBER 2004 − Nf 1 = (o) .() cu cu k fk 20 k=0 5 Subcarrier 0 Subcarriers 1,3 Subcarrier 2 4.5 Notice that baseband SC-UWB is subsumed by − 4 (o) N f 1 (20), if one selects c = as distinct columns of a u u 0 3.5 N f ×N f identity matrix. (For each user (subcarrier) to 3 occupy exactly the same bandwidth, a 0.5/N f shift has to be introduced to the digital subcarriers as detailed in 2.5 [77].) Different from orthogonal frequency division 2

multiple access (OFDMA) in narrowband systems [67], Absolute Value 1.5 the baseband SC/MC codes in (20) are real. Spreading every symbol on a single digital subcarrier, each SC- 1 UWB user occupies 2Tf /Tp 2 frequency bands (see 0.5 Figure 13), and the resulting transmissions enjoy multi- 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 path diversity gains; whereas narrowband OFDMA sys- GHz tems have to resort to channel coding and/or (a) frequency hopping to mitigate frequency-selective fad- ing at the expense of (possibly considerable) bandwidth 0 overexpansion. 10 In [77], the performance of DS-, SC- and MC- −1 UWB is quantified in terms of diversity and coding 10 gains, when IFI is present but ISI is avoided by zero- −2 padding or cyclic-prefixing. Analysis shows that 10 SC/MC codes enable full multipath diversity gain, and −3 MC codes can further effect maximum coding gain. 10 no NBI Additionally, SC- and MC-UWB codes offer flexibility 10−4 DS–UWB: MMSE in handling (e.g., WLAN induced) NBI, simply by Average BER SC–UWB: MMSE avoiding the corresponding digital subcarriers. The MC–UWB: MMSE −5 DS–UWB: MF same flexibility in avoiding NBI is also present in the 10 SC–UWB: MF spectrally encoded (SE-) UWB system of [9]. With MC–UWB: MF 10−6 SC/MC codes, the ultrawide bandwidth is partitioned 02468101214 16 18 20 into segments, each corresponding to a digital carrier. Eu/N0 (dB) Likewise, SE-UWB also partitions the bandwidth into a (b) number of frequency bands (so-called frequency (o) “chips’’). A sequence of codes (much as cu in (20) for SC/MC-UWB) can then be applied on these “chips’’ 100 to enable MA. As a result, both SC/MC- and SE- UWB can avoid NBI affected frequency segments— 10−1 digital carriers in SC/MC-UWB and frequency “chips’’ in SE-UWB—by nulling the corresponding elements of 10−2 (o) the code vector cu . Constructed based on digital cos/sin functions, SC/MC-UWB facilitates low-com- 10−3 plexity implementation using standard discrete-cosine- DS−UWB: 1−Finger Rake − Average BER 4 transform (DCT) circuits. (This implementation 10 SC−UWB: 1−Finger Rake advantage also distinguishes them from the analog SC- MC−UWB: 1−Finger Rake − − − DS UWB: 4 Finger Rake UWB codes introduced in [66] that offer robustness 10 5 − − SC UWB: 4 Finger Rake against user asynchronism.) SE-UWB, on the other MC −UWB: 4−Finger Rake hand, can be implemented using surface acoustic wave 10−6 (SAW) devices [9]. As SC/MC-UWB, the resultant 0 51015202530 SE-UWB also enables multipath diversity by sweeping Eu/N0 (dB) (c) the ultra-wide bandwidth within pulse duration Tp , much as in fast frequency hopping (FH) systems. ▲ = Performance comparisons among DS, SC, and MC 13. (a) Subcarriers in baseband SC- and MC-UWB (Nf 4, / = ≈ . spreading codes, individually or in combination with Tf Tp 4, Tp 0 2 ns). Average BER corresponding to DS-, SC-, TH codes, have been carried out when NBI is pres- and MC-UWB over AWGN with NBI at the GPS band (center fre- ent, under a general SINR analysis framework that quency 1.2 GHz, bandwidth 20 MHz) in (b) AWGN channel; (c) allows for various Rake finger selections [82]. Several multipath channel (selective-Rake with MMSE combining).

NOVEMBER 2004 IEEE SIGNAL PROCESSING MAGAZINE 43 interesting conclusions can be drawn from these com- pulse stream [32], [42], [76]. In other words, the parisons. In particular, analytical and simulated results transmitted signal using PPM and TH codes can be show that MC-UWB provides code-independent BER expressed as [c.f. (2)]: performance in the presence of multipath and NBI effects, regardless of the Rake finger selection. The +∞ ( ) = E − + TH( ) − ( ) BER averaged over all codes is shown in Figure 13(b) vu t u p t nN c c u n Tc b u n n=0 for AWGN channels and in Figure 13(c) for multipath M−1 channels, both in the presence of NBI. From these = (m)( ), ( ) vu t 21 comparisons, baseband MC-UWB emerges as an m=0 attractive choice for antijam applications without √ (m)( ) = E +∞ (m)( ) − + nulling any subcarriers. This avoids additional process- where vu t : u n=0 b u n pm t nN c TH( ) (m)( ) = δ( ( ) − ) ing for collision detection or clear channel assessment c u n Tc with b u n : b u n m , and (CCA), and ensures small size transceivers with low pm (t) := p(t − m), ∀m ∈ [0, M − 1]. As to the TH( ) power consumption. nonlinear TH codes, the frame-rate sequence c u n Different from the WPAN multiband proposals that can be uniquely mapped to a chip-rate TH sequence ˜TH( ) = δ TH( / ) − ( ) rely on analog carriers (see, e.g., [4]), the SC/MC c u k : c u k Nc k mod Nc for the TH( ) codes achieve multiband transmission using baseband kth chip. When c u n has period N f , it can be veri- ˜TH( ) operations. Compared to analog multiband solutions fied that c u k has period N f Nc . But the chip-rate that entail multiple local oscillators, carrier-free multi- TH sequence can be viewed as a DS code with {0, 1} band SC/MC-UWB access not only enjoys low-com- entries, and thus enables representation of nonlinear plexity implementation but also avoids dealing with TH spreading with an equivalent linear DS spreading. carrier frequency offsets that are known to degrade Consequently, we have [c.f. (21)] error performance (of e.g., OFDMA) severely. The schemes we have discussed so far for UWB mul- +∞ tiple access are either constant modulus or provide ( ) ( ) v m (t) = E v m (k)p (t − kT ), robustness and flexibility against NBI. But with u u u m c k=0 DS/SC/MC spreading codes, perfect multi-user sepa- ration with N u = N f users is possible only if ≥ τ + (m)( ) = (m)( /( )) ˜TH( ) Tf L Tp , that is, when rate considerations allow where vu k : b u k NcN f c u k is the sym- (m,m)( ) = one to select a frame duration which is longer than the bol sequence after TH spreading. Let gu l : (    )(− )| maximum delay spread augmented by one pulse dura- pm h u pm t t=lTc of order L u be the chip-sam- tion. When TH spreading codes are employed, or when pled discrete time equivalent finite impulse response Tf <τL + Tp is chosen to achieve high data rates, the (FIR) channel. Then, the chip-sampled matched filter mutual orthogonality among users’ spreading codes is output of the mth branch at the receiver is destroyed after multipath propagation [15], [25]. This introduces MUI, which compromises capacity and Nu −1M−1Ld ( , ) ( ) error performance considerably [25], unless complex  ( )= E m m ( ) m ( − )+η  ( ), xm k u gu l vu k l m k receiver algorithms are employed to mitigate it. u=0 m=0l =0 Conventionally, MUI is treated as Gaussian noise, (22) and is suppressed statistically with the aid of (strict) power control [72]. However, when the number of users is not large enough, the Gaussian approximation where ηm (k) denotes the sampled noise and Ld := of MUI is not valid, especially with imperfect power maxu L u . It is shown in [32] and [76] that (22) can control [10], [16]. also be represented in vector-matrix form by utilizing block spreading in lieu of symbol spreading. The result- MUD for UWB Access ant input-output relationship is To improve upon the statistical MUI cancellation,

UWB-MA utilizing multi-user detection (MUD) was Nu −1 M−1 (m,m) ( )  ( ) = E m ( ) pursued in [32]. In fact, [32] established the first digi- xm i u Gu,0 vu i tal model for UWB-MA systems, where novel u=0 m=0  approaches were developed to account for the nonlin- (m ,m) (m) + G , v (i − 1) + η  (i). (23) ear PPM modulation and TH spreading. The digital u 1 u m model triggered the transition from analog UWB to digital UWB, and these novel approaches are used also Extracted from a continuous-time UWB transmission in recent UWB modeling attempts (see, e.g., [11]). with nonlinear PPM modulation and TH spreading, the Specifically, the continuous time UWB signal using digital model in (23) consists of only linear operations. nonlinear M -ary PPM modulation is viewed as M par- In addition, its serial form (22) and parallel (vector- allel branches each realizing a shifted version of the matrix) form (23) both capture MUI and ISI [manifested

44 IEEE SIGNAL PROCESSING MAGAZINE NOVEMBER 2004 as interblock interference (IBI) in (23)] after multipath Consequently, only the desired user’s spreading codes propagation. As a result, this digital model allows direct are required at the receiver, and a single-user detector adaptation of narrowband MUD to UWB systems. A is sufficient. As a result, deterministic MUI-resilient number of works have followed this approach. reception with low-complexity code-matched filtering Recursive MUD schemes are also pursued for DS-UWB becomes possible without loss of ML optimality, and systems, without assuming channel knowledge at the with full multipath diversity gains [76]. Figure 14 com- receiver [27]. It has been illustrated by simulations that pares the BER of MSBS-UWB with conventional TH- such recursive MUD receivers outperform Rake UWB using a Rake receiver [52], and with the receivers with finite fingers in suppressing both MUI MUD-UWB receiver [32], over two channel models and NBI. However, MUD-based schemes entail sam- [25], [50], [76]. In contrast to conventional TH- pling at subpulse rate of up to 16 GHz, they require an UWB, MSBS-UWB shows no degradation as the num- initializing training sequence of 500 symbols, and rely ber of users increases. With much lower complexity and on decision directed operation that is prone to error many more active users, it also outperforms the MUD- propagation. To ensure convergence, the channels for UWB multiple access system. all users must also remain invariant for a sufficiently long period (500 symbols) [27]. Single-Band or Carrier-Modulated Multiband? So far, we have focused on baseband UWB signaling, Multistage Block-Spread (MSBS) UWB Access which occupies a single UWB spectrum from near DC With chip duration Tc ≈ Tp and symbol duration up to a few GHz. Such carrier-free transmissions Ts = N f Nc Tc , the bandwidth expansion factor in a require minimal RF components. But since UWB typical UWB system is N f Nc . But the maximum num- radios occupy extremely broad bandwidth, they ber of users is N u = Nc with orthogonal TH, and inevitably overlay existing narrowband RF services, N u = N f with orthogonal DS/MC/SC, both of which such as GPS, federal aviation systems (FAS), and have lower user capacity than that allowed by the band- WLAN. To regulate coexistence, the FCC has released width expansion factor. There is certainly space for a spectral mask in its first UWB R&O that limits the improvement in terms of multi-user capacity. To this equivalent isotropic radiated power (EIRP) spectrum end, a promising so termed multistage block-spread density with which UWB radios are allowed to trans- (MSBS) design of spreading codes has been developed mit. To realize the attractive features of UWB radios [76]. With MSBS-UWB, the number of users that can under this FCC regulation, the following challenges be accommodated is N u = N f Nc by employing have to be addressed: DS/SC/MC codes in combination with TH codes. ▲ i) Operating below the noise floor, UWB radios More important, MSBS-UWB provides MUI-resilient must emit at low power. But as any other communica- performance, even after (possibly unknown) multipath tion system, the performance of a UWB system heavily propagation. Relying on two stages of block-spreading relies on the received SNR that is proportional to the and interleaving, the mutual orthogonality among transmit power. Maximization of the latter, however, users’ spreading codes is guaranteed even after propa- can be achieved only if the spectral shape of the FCC gation through frequency-selective multipath channels. mask is exploited in a power-efficient manner.

100 100

−1 − 10 10 1

10−2 − 10 2

−3

10 BER BER − 10 3 10−4 Conventional: 1 User MUD; Channel 1 Conventional: 2 Users − 10 4 MUD; Channel 2 10−5 Conventional: 3 Users Conventional: 4 Users MSBS; Channel 1 MSBS−UWB: 1−32 Users MSBS; Channel 2 10−6 10−5 02468101214161820 02468101214161820

Eb/N0 (dB) Eb/N0 (dB) (a) (b)

▲ 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.

NOVEMBER 2004 IEEE SIGNAL PROCESSING MAGAZINE 45 ▲ ii) To avoid interference to (and from) coexisting nar- pulses that are FCC mask compliant, [40] developed rowband systems, their corresponding frequency bands pulses in digital form that correspond to the dominant must be avoided. Since the nature and number of coexist- eigenvectors of a matrix, which is constructed by sam- ing services may change depending on the band used, the pling the FCC mask. The resulting pulses meet the avoidance mechanism should also be sufficiently flexible. FCC mask, but do not optimally exploit the allowable ▲ iii) Traditionally, UWB multiple access is achieved by bandwidth and power [see Figure 15(a)]. employing TH codes. User capacity of UWB radios can Unfortunately, converting the digital designs in [40] be further improved by partitioning the ultra-wide into analog form entails digital-to-analog (D/A) opera- bandwidth into subbands, allowing users to hop among tions at 64 GHz rate. Imposing minimum modification these subbands according to user-specific hopping pat- to the analog components of existing UWB transmit- terns. Since hopping should span subbands centered ters and aiming at pulses that not only meet, but also around different frequencies, UWB pulse shapers must optimally exploit the FCC mask, [29] introduced opti- be agile with respect to FH to enhance system capacity mal pulse shapers for UWB using the “workhorse’’ of and reinforce the low probability of interception and digital filter design methods, namely the Parks- detection (LPI/LPD). McClellan algorithm [39]. This idea is to start with All these requirements heavily rely on a basic trans- any continuous-time spectral shaping waveform pa(t), mitter module—the pulse shaper. Unfortunately, the including the Gaussian monocycle, and design the widely adopted Gaussian monocycle is not flexible pulse shaper as enough to meet these challenges [74]. To design pulse shapers with desirable spectral properties, two M−1 approaches can be employed: carrier-modulation p(t) := wm pa(t − mT0), (24) and/or baseband analog/digital filtering of the base- m=0 band pulse shaper. The former relies on local oscillators at the UWB transmitter and receiver, which being where wm are tap coefficients with spacing T0 . prone to mismatch give rise to carrier frequency off- Evidently, the choice of T0 affects wm , and thus the fea- set/jitter (CFO/CFJ). In multiband UWB systems sibility, optimality and complexity of the overall design. with FH, multiple CFO/CFJ emerge with this It is shown in [29] that T0 = 35.7 ps is suitable for approach. Although passing the (Gaussian) pulse optimal designs with full-band control, and T0 = 73 ps through a baseband analog filter can reshape the pulse for suboptimal designs that trade off performance for without introducing CFO/CFJ, it is well known that complexity. For any T0 value and pa(t) with FT Pa( f ), analog filters are not as flexible when compared to digi- [29] casts the pulse shaper design problem boils down tal filters, which are accurate and perfectly repeatable. to a digital filter design problem, where an M -tap FIR { }M −1 filter with coefficients wm m=0 is to be designed such π Optimal UWB Pulse Shapers that its DTFT magnitude |W (e j2 F )| approximates Pulse shapers respecting the FCC mask have been pro- D(F /T0), ∀F ∈ [0, 0.5], where D( f ) := Pd ( f )/ posed in [40] and [29]. Targeting multiple orthogonal |Pa( f )|, ∀ f ∈ [0, 0.5/T0] and Pd ( f ) can be chosen to

−35 −35 FCC Mask for Indoor Comm. Subband 1 A −40 −40 FCC Mask for Indoor Comm. Subband 2 B Subband 3 C −45 −45 D E −50 −50 − −55 55 − −60 60

er (dBm) −65 er (dBm) − 65 w w

Po −70 Po −70 − −75 75 − −80 80 − −85 85 − −90 90 0 5 10 15 0 5 10 15 Frequency (GHz) Frequency (GHz) (a) (b)

▲ 15. (a) Baseband pulse shapers and the FCC mask for indoor communications. A—Gaussian monocycle with Tp = 0.37 ns; B—Gaussian monocycle with Tp = 0.19 ns; C—a pulse shaper in [98]; D&E—pulse shapers in [99]; (b) Multiband UWB using baseband pulse shapers.

46 IEEE SIGNAL PROCESSING MAGAZINE NOVEMBER 2004 satisfy any desirable spectral mask specifica- tion. Instead of casting the UWB pulse −40 shaper design as a filter design problem, it is also possible to view it as a semi-definite pro- −45 gramming (SDP) optimization problem; see er (dBm) − [75] for SDP related designs. w 50

Pulse shapers designed according to (24) Po exploit the FCC spectral mask optimally, −55 and offer flexibility for (dynamic) avoidance 12345678910 11 12 Frequency (GHz) of NBI. Comparing three pulse shaper designs in Figure 15(a), it follows that, in FCC Mask for Indoor Communications ( ) GPS 802.11b/g 802.11a order for a Gaussian monocycle pa t to Multiple Subbands in Multiband UWB Band Band Band adhere to the FCC mask, it must transmit at Eu ≤ 0.506 Ts µJ when Tp = 0.37 ns, and at ▲ 16. Multiple subbands in multiband UWB. Eu ≤ 3.43 Ts µJ when Tp = 0.19 ns; pulse shaper C can transmit at Eu ≤ 0.25 Ts mJ, while pulse shapers D and E can transmit at rely on analog carriers, and thus have to deal with mul- Eu ≤ 0.88Ts mJ, and Eu ≤ 0.91Ts mJ, respectively [29]. tiple carrier frequency offsets (CFO) arising from the This shows that the optimal designs in [29] can offer mismatch of multiple transmit-receive oscillators. 2–3 orders of magnitude more power-efficient pulse Unless compensated for, CFO is known to degrade shapers. Furthermore, they are well suited for digital performance severely, especially in carrier-modulated implementation of subband hopping (or FH) codes, MC-UWB transmissions. For multiband UWB, carrier which are used with multiband UWB systems. The lat- frequency synchronization is more challenging because ter have gained popularity recently, because they can there are more than one carrier frequencies, especially replace the traditional TH codes for MA, or comple- when OFDM or fast frequency-hopping is employed ment them to enhance capacity and covertness [see across multiple bands. For this reason, multiband UWB Figure 15(b)]. calls for CFO sensitivity studies, low complexity CFO estimators, and per-subcarrier based channel estimation Multiband UWB Access modules. To this end, existing techniques for wideband Baseband pulses can also be modulated onto carrier(s) communications can serve as starting points. to higher frequency band(s). Recently, there has been Multiband UWB multiple access schemes also have an increasing interest in transmissions with multiple to be designed by taking all bands into consideration. subbands, which we henceforth term multiband UWB Notice that the carrier frequencies (center frequencies) (see e.g., [1], [4], [47]). In multiband UWB radios, of subbands in Figure 16 span a wide range from 3.35 pulses are modulated by several analog carriers to sub- GHz up to 10.35 GHz with a 500 MHz multiband bands 500−800 MHz wide (see Figure 16). partitioning. Consequently, the bands to the right Compared to Figure 15, it is evident that multiband (towards the 10.6 GHz end) tend to be more lossy UWB can make more efficient use of the FCC mask, than the bands to the left (towards the 3.1 GHz end). minimize interference to existing narrowband systems Therefore, an assignment confining each user to a sin- by flexible band selection, and facilitate future scalabili- gle fixed band will result in user-dependent perform- ty of the spectrum use. Moreover, since each band ance, and will not enable the full multipath diversity. In occupies only a fraction of the bandwidth of a single- a nutshell, a multiband based UWB-MA scheme must band transmission, the pulse shaper employed in multi- account for the following issues: i) flexibility to accom- band UWB can have much longer duration in time, modate various schemes (SC or MC) for multiple which in turn eases implementation of the ADC, and access, ii) capability to collect full multipath diversity, enables implementation with off-the-shelf (OTS) com- and iii) scalability in spectral efficiency (from low, to ponents capitalizing on existing mature technology for medium, and high data rates). wideband communications. As in single-band UWB, challenges facing multiband Cross-Band FLEX-UWB Access UWB systems include timing acquisition and channel To meet the aforementioned requirements, we have estimation. The (non)data aided timing algorithms for recently introduced a cross-band flexible UWB MA synchronization, and channel estimators, including scheme for high-rate multipiconet WPANs [80]. The TDT, TR and PWAM, we outlined for single-band so termed FLEX-UWB design is built on the basis of UWB apply also to multiband alternatives on a per band the MSBS-UWB approach we outlined earlier to basis. However, due to the introduction of multiple achieve resilience against MUI in an environment with carrier frequencies, new challenges arise. Recall that in multiple piconets. To allow for various selections of the baseband MC-UWB systems, multiple digital sub- spreading codes, FLEX-UWB relies on an FFT matrix × carriers are utilized; whereas multiband UWB radios FN s , of size N s N s , where N s denotes the number of

NOVEMBER 2004 IEEE SIGNAL PROCESSING MAGAZINE 47 1 2 Subband 1 3 4 s0 v0 1 s LCF v 2 1 1 Subband 2 s2 Coding v2 3 s3 v3 4 1 2 Subband 3 3 4 1 2 Subband 4 1 Piconet 12 Piconet 2 3 4

equency

3 Piconet 34 Piconet 4 Fr Time One OFDM Symbol Cyclic Duration Prefix

▲ 17. FLEX-UWB: cross-band LCF-OFDMA (sk: symbols; vk: coded symbols; number of subbands: 4; number of piconets: 4; total number of users Nu = 4; number of subcarriers per subband Ns = 4).

subcarriers per subband. Let N u denote the total num- As mentioned before, choosing {cu} to be columns of = / ber of users across all piconets, and define P : N s N u . the identity matrix IN u gives rise to FDMA. In particu- Built on the user-specific N u × 1 spreading code cu, the lar, replacing Tzp with an identity matrix IK , and select- basic block-spreading matrix is given by ing K = 1, (25) boils down to: C = F H (c ⊗ I ). u N s u P Such a code design, coupled with cyclic-prefix insertion H (removal) at the transmitter (receiver), corresponds to Cu := F (cu ⊗ IP ) ⊗ Tzp,(25) N s an orthogonal (O)FDMA UWB scheme, where each user occupies all P subcarriers of each subband [80]. It where IP is a P × P identity matrix, and Tzp is a is well known that OFDMA can be implemented effi- (K + Ld ) × K matrix that pads Ld zeros to a K × 1 ciently with the FFT module, but has to resort to (pos- vector, with K being the size of information symbol sibly considerable) bandwidth overexpansion to mitigate blocks, and Ld denoting the order of the discrete-time frequency-selective fading. To amend this problem, a equivalent channel. The resulting multiple access cross-band linear complex field (LCF) precoder is also scheme depends on the selection of the spreading introduced in [80]. (For tutorial treatments of LCF − { }N u 1 codes cu u=0 . Time-division multiple access (TDMA), (pre)coding, the reader is referred to [30] and [67].) where each user utilizes the whole bandwidth at differ- The transmission corresponding to FLEX-UWB with − { }N u 1 ent time slots, can be achieved by choosing cu u=0 as the LCF-OFDMA choice is depicted in the example of × = columns of FFT matrix FN u , of size N u N u . Figure 17, where each subband consists of N s 4 sub- Choosing the spreading codes as columns of a carriers, the first of which is assigned to piconet 1. The N u ×N u identity matrix results in frequency-division number of information symbols per block is four, which multiple access (FDMA), where each user utilizes part is the total number of subcarriers (across all subbands) of the bandwidth but can transmit all the time. And assigned to a single piconet. The symbol block is first − { }N u 1 with cu u=0 being any set of mutually orthogonal passed through an LCF encoder (a square matrix), vectors, code-division multiple access (CDMA) can be whose output is the coded symbol block v. Notice that achieved, where each user utilizes the entire bandwidth no redundancy is introduced here. The coded symbol all the time with a user-specific signature. It turns out block v is then evenly distributed to all subbands and that the code design (25) can be applied simultaneous- transmitted using an OFDMA scheme, which consists ly over all (or, selected) subbands, and guarantees: i) of selecting user-specific subcarriers, inverse FFT, and MUI-resilient UWB-MA; ii) full multipath diversity; cyclic-prefix insertion. and iii) bandwidth efficiency of K /(K + Ld ) [117]. Notice that the bandwidth efficiency of FLEX-UWB is Capacity in the UWB Regime the same as that of MSBS-UWB, and is tunable by Shortly after his landmark paper [53], Shannon pointed varying the symbol block size K , which also affects the out that as the bandwidth B grows, the AWGN chan- decoding delay. nel capacity approaches:

48 IEEE SIGNAL PROCESSING MAGAZINE NOVEMBER 2004 ∞ = ( ) CAWGN : lim CAWGN B B→∞ P P To fulfill expectations, UWB = lim B log 1 + = loge, →∞ B BN0 N 0 research and development has to cope with formidable challenges that limit their bit where P is the received power and N 0/2 is the noise P ∞ PSD. Evidently, given N 0 and , CAWGN benchmarks error rate performance, the maximum rate achievable. But how close practical capacity, throughput, and UWB systems come to this fundamental limit? And how UWB transceivers should be designed to approach network flexibility. it? For flat Rayleigh fading channels, it is known that as →∞ ∞ B , CAWGN can be achieved by frequency shift keying [17]. But as we discussed in Section III-A, UWB trans- τ ˜ { ,β }L˜ missions typically encounter multipath fading chan- time c . As L increases, more unknowns dl l l =1 nels. This motivates investigation of capacity issues for need to be estimated. If the number of unknowns is UWB channels with pronounced frequency selectivity. too large, negligible resources remain for conveying If such channels exhibit independent fading at differ- information, which drives the mutual information to ent frequency bins, it turns out that the achievable zero. An intuitive explanation is also possible for result { }L˜ mutual information for a fixed transmission power b). As dl l =1 represent delays of resolvable paths, one goes to zero as B increases, when spread spectrum sig- delay can be distinguished from its neighbors by the naling is used [33]. This result is quite intuitive pulse duration Tp . But this requires timing estimation because independent fading across frequency bins (tracking) with pulse-resolution accuracy. Since together with an increasing B implies infinite number Tp ≈ 1/B , it is expected that the resources will again be of independent multipath coefficients, whose estima- depleted by such stringent tracking requirements. As an ˜ tion then exhausts the power and bandwidth extreme example, consider L = 1 with β1 known. In resources. But Figures 2 and 3 suggest that even when this case, finding d1 amounts to the timing synchro- the number of resolvable multipath returns (L˜ ) increas- nization problem. As discussed earlier, reliable symbol es with increasing B (decreasing Tp ), the total number recovery is impossible once the waveform of duration of paths (L + 1) induced by the physical surroundings Tp is missed. As B grows, it is becoming increasingly { ,β }L˜ is practically finite. Let dl l l =1 denote the delays difficult to capture the shrinking pulse. and coefficients of the resolvable paths. Notice that The capacity results a) and b) corroborate the { ,β }L˜ dl l l =1 depend on, but are not necessarily identical demanding and challenging nature of UWB timing to, the delays and coefficients of the physical channel synchronization and channel estimation. They indicate {τ ,α }L ˜ { }L˜ l l l =0 . Evidently, L is upper bounded by that receiver knowledge of dl l =1 is particularly critical (L + 1) as B increases. To investigate the capacity in achieving capacity. The question is when the assump- { }L˜ behavior in such cases, consider a white-noise-modula- tions under a) are satisfied; i.e., when can dl l =1 be tion (WNM) signaling where the empirical autocorre- treated as known at the receiver? We know that lation of the transmitted waveform resembles that of τc ∝ 1/fc and that the time it takes for βl to move by white noise, and a quasi-static channel with coherence one tap (from dl to dl + Tp ) is proportional to time τ and maximum delay spread τ ,  τ . Then T ≈ 1/B . Therefore, when 1/B  1/f , the resolvable c L 0 c p ˜ c the following results are obtained in [58]: delays {d }L change much slower than the correspon- ˜ ˜ l l =1 ˜ ▲ { }L {β }L {β }L a) When dl l =1 are known but l l =1 are unknown, ding coefficients l l =1 and can be treated as if they the achievable mutual information using WNM signaling can be “tracked’’ at the receiver. In other words, result ˜ ˜ is lower and upper bounded by [1 − (L /Lc )× a) requires the fractional bandwidth satisfy B/fc  1. ( + ˜ / ˜ ) ∞ ( ˜ / ˜ ) ∞ log 1 L c L ]CAWGN and L c L CAWGN, respectively, This may be the case with multiband UWB systems where L˜ := Pτ /N . Consequently, if L˜  L˜ then with relatively large f , but is not satisfied by baseband ˜ ˜ c ˜c ˜0 c c (L /Lc ) log(1 + Lc /L ) ≈ 0 and the achievable mutual UWB systems. information approaches C ∞ ; whereas if L˜  L˜ then The spread-spectrum and WNM systems we dis- ˜ ˜ AWGN c Lc /L ≈ 0 and the achievable mutual information is neg- cussed so far use transmissions with no duty cycle; i.e., ligibly small. Tf = Tp . In low-duty-cycle UWB systems, however, we ˜ ▲ { }L  b) When dl l =1 are unknown (regardless of whether have Tf Tp . How does duty-cycling affect capacity {β }L˜ l l =1 are known or not), the upper bound on the in the UWB regime? Let us first define the duty-cycle mutual information using WNM signaling decays to 0 parameter θ: with θ ∈ (0, 1], transmission occurs only like 1/B, even when L˜ = 1 and β is known. during one period τ out of the total of τ /θ seconds; ˜ 1 c c In result a), Lc essentially captures the available and the system sleeps when not transmitting. resources, namely the SNR P/N 0 and the coherence Interestingly, as FSK that is “peaky’’ in frequency is

NOVEMBER 2004 IEEE SIGNAL PROCESSING MAGAZINE 49 capacity achieving in flat-fading channels, duty-cycled network, sustained link networks (SLN) were proposed signals that are “peaky’’ in time are capacity achieving in [24] as a MAC layer scheme. In SLN, the physical in multipath channels [41], [65]. In fact, it follows layer links are maintained for the lifetime of the logical from results a) and b) that WNM and PPM can both link between two nodes. Taking advantage of the low ∞ achieve CAWGN when they are “duty-cycled’’ with duty-cycle nature of conventional UWB communica- θ → 0 [41]: tions, especially at low bit rate, [24] also developed a ˜ ▲ { }L A) As long as dl l =1 are known at the receiver, then full-duplex scheme, which results in a tradeoff between the number of transceiver units and the bit rate. ( ) → ∞ , UWB allows for accurate localization, especially in lim CWNM B CAWGN B→∞ environments where GPS encounters satellite visibility ˜ if lim L /B → 0, constrains. Such a precise positioning information can be B→∞ ∞ utilized to develop location-aware networking. In other lim C (B) → C , →∞ PPM AWGN words, improved coexistence with other piconets/sys- B tems and reduced power consumption can be achieved if lim L˜ log log B/ log B → 0. B→∞ by scaling personal operating space based on UWB local- ization. Furthermore, for a prescribed average power, ˜ ▲ { }L B) If dl l =1 are also unknown at the receiver, then the peak power is inversely proportional to the pulse rep- etition frequency (PRF), which induces a range-rate  → ∞ , tradeoff. Based on accurate localization information, a  CAWGN  ˜ promising direction for UWB systems is to adjust data if limB→∞ L log B/B → 0 lim CWNM(B) ∞ rates on a per packet, or a per link basis. As a result, the B→∞  < C ,  AWGN unique features of UWB may lead to power-efficient, ˜ / → λ> , if limB→∞ L B 0 location-aware adaptive routing protocols.  ∞ Fast timing techniques will allow for quick computa-  → C ,  AWGN tion and tracking of the relative positions among sen- if L˜ = 1 lim CPPM(B) sors, which would be beneficial for position-assisted B→∞  → 0, ˜ node selection, and information relaying with mini- if lim →∞ L / log B →∞. B mum energy consumption. Idle or partially functional nodes can also be utilized as relays to ensure fault-toler- Notice that WNM and PPM signaling systems can ant networking. This approach has the potential to tolerate different bandwidth scaling factors as the num- improve performance, while saving power. ber of resolvable paths L˜ increases. Also, when timing To facilitate variable bit rate sessions and fair-queuing knowledge is not available, these factors are further bandwidth guarantees (those cannot be simultaneously reduced. These results are established for real UWB accommodated by fixed-assignment or random access {β }L˜ channels with l l =1 being i.i.d. It would be interest- alternatives), a two-phase demand assignment MAC ing to see how the correlation and power profile of the could be pursued. This layer-integrating design could channel affect these scaling factors. start at the network scheduling which is to be performed by the “master user’’ of the piconet. Similar to a general- UWB at the Networking Layer ized process sharing policy [38], [49], [56], the sched- Along with flexibility requirements at the physical layer, uler associates “slave user’’ u with a service-dependent the open access network paradigm requires redefinition weight Fu that determines percentage of bandwidth allo- of upper layers in the UWB system architecture. In the cation Bu . During the first phase (TDMA contention same way Internet protocol (IP) has succeeded in glu- based reservation), the intention of the slave user to ing together heterogeneous networks, UWB and the transmit along with the requested Fu is communicated open radio access paradigm offer the potential for inte- to the scheduler via mini-slots, while the master user grating heterogeneous wireless access networks. To responds with mini-slots containing each user’s ID with reach this goal, one needs to first address the following the corresponding code assignment. During the second question regarding the next-to-physical medium access phase, users transmit (possibly at different rates) multi- control (MAC) layer: What, if any, UWB specific fea- media information. The MSBS and FLEX spreading tures may be required within the MAC? codes we outlined earlier are good choices for this stage, Utilizing TH, conventional UWB systems provide because they not only assure MUI/multipath-resilient covertness and are considered as the physical layer for operation but also enable multirate transmissions with future tactical wireless networks [24]. However, the high full-diversity, fine rate resolution, and easy rate switching precision synchronization required by UWB systems capability [67], [76], [80]. necessitates long acquisition headers at higher power, Existing dynamic resource allocation schemes could especially when simple serial searching algorithms are also be adopted to UWB settings, especially when loca- adopted due to the size and processing power of UWB tion information and partial channel state information transceivers. To improve covertness in a UWB-based (CSI) become available (or can be predicted) at the trans-

50 IEEE SIGNAL PROCESSING MAGAZINE NOVEMBER 2004 mitter. Optimization criteria can involve maxi- mization of sum-capacity, or, minimization of symbol error rate bounds, under a prescribed transmit-power budget. Moreover, ST codes and/or steerable antenna arrays (beamform- ers) can also be adjusted for packet-fair sched- uling and flexible UWB allocation along the lines of [78]. Another interesting direction is to couple resource allocation with routing considera- (a) (b) tions by distributing resources among nodes in an optimal fashion. On these subjects, one of the key elements is the exploitation of information from lower layers. For example, link quality maps provided by the channel estimation and error control algorithms are expected to play a critical role in routing establishment. Due to channel fading, routes in a wireless network are inherently unstable (c) and prone to link failures. This has an adverse effect on the ability of networks to ▲ 18. (a) The Trinity chip set released by Xtreme Spectrum Inc.; (b) The Mobile support applications with stringent quality of ad hoc Network (MANET) by MultiSpectral Solutions Inc.; (c) the PUlsON family service (QoS) requirements. Exploitation of marketed by Time Domain Corporation. the extra diversity offered by multipath routes of the UWB channel calls for an ana- lytical framework for multipath routing in (un)coordi- mask more effectively, but entail more extensive IF pro- nated networking environment. For UWB links, cessing at rather high frequencies, and a number of multipath routing is particularly attractive, because it oscillators at both the transmitter and the receiver. For can provide path failure protection, load balancing, any given UWB system, comparative studies need to be while at the same time reduce the transmission delay by carried out when multiple implementation alternatives distributing traffic among a set of available paths. (analog versus digital) exist. For instance, channel esti- mation and correlation in TDT, TR, and PWAM sys- Implementation Issues tems can be implemented either with analog delay Any practical UWB system design should take into lines, or, with digital delay elements after AD convert- account implementation feasibility and complexity ing the analog waveform. Avoiding analog delay lines, issues, including ADC speed and correlator bandwidth. the latter requires formidable sampling. Analyses and An overview on these issues can be found in [18]. In tradeoff studies of these alternatives are either per- particular, to reduce time-to-market, UWB designs formed [8], [81], or are underway [23]. It is also with analog components should utilize commonplace worth mentioning that the complexity reduction at building blocks, e.g., low noise amplifiers (LNAs), mix- higher hierarchies is often times more effective than at ers, ADCs, digital-to-analog converters (DACs), and lower hierarchies. For instance, about 60% of the total phase locked loops (PLLs), for which standard figure of number of gates are dedicated to channel estimation. merit production tests are available. Currently, ana- This number can certainly be reduced to some degree log/RF circuits are mostly implemented in high per- by applying digital circuit design techniques. On the formance SiGe platforms, whereas digital/base-band other hand, adopting more efficient channel estimation circuits are implemented in CMOS. The latter is superi- techniques might reduce dramatically the number of or in terms of both power consumption and cost. At gates. These are areas where VLSI-SP expertise can the same time, DSP based designs also enjoy process have considerable impact in UWB algorithms and portability, low sensitivity to component variability, as implementation. well as benefits from Moore’s law. A system design free System designs tailored for UWB as mentioned in of RF components will facilitate system-on-a-chip preceding sections also entail challenges to UWB cir- (SoC) implementation in CMOS, which shrinks as cuitry implementation. Successful implementation of CMOS scales down from 0.18 µm to 0.13 µm and both carrier-free baseband and carrier-modulated multi- 0.09 µm. In this aspect, different system designs score band UWB calls for high-efficiency UWB antennas, and differently. The conventional single-band UWB systems tight jitter requirements. To this end, there is a rich lit- mostly rely on base-band carrier-free transmissions, and erature in UWB Radar, and emerging works in commu- therefore require no IF processing. Whereas the recent- nications. High-rate transmissions require fast automatic ly emerged multiband UWB systems utilize the FCC gain control (AGC) response, as well as improved ADC

NOVEMBER 2004 IEEE SIGNAL PROCESSING MAGAZINE 51 speed. In [35], a channelized ADC with CMOS imple- resources in handling the challenges facing UWB com- mentation is advocated. As mentioned before, multi- munications. On the other hand, digital signal process- band solutions with carrier modulated pulses utilize the ing techniques have matured for conventional RF FCC allowable bandwidth efficiently. Hopping among communications, and a large body of literature has multiple frequency bands requires high performance grown from recent advances in narrowband and wide- local oscillators and switching circuits as well as UWB band wireless communications. Understanding the antennas. Implementation of such systems with low unique properties and challenges of UWB communica- power consumption and low cost requires integration of tions, and applying competent signal processing tech- RF and baseband circuitry into a single CMOS chip, niques are vital to conquering the obstacles towards which hinges upon the solution of the “touchy issue’’ of developing exciting UWB applications. It is clear that substrate noise mitigation. Further development of innovative research in this area will pay handsome divi- UWB systems will also benefit from increased SP dends in meeting the future challenges and demands of expertise to enable modulation/demodulation, syn- the dynamic communications industry. chronization, channel estimation, error control coding, as well as cross-layer functionalities. Acknowledgments A number of companies have already announced This article was prepared through collaborative partici- UWB prototype products for various applications: the pation in the Communications and Networks Trinity chip set released by Xtreme Spectrum Inc. for Consortium sponsored by the U.S. Army Research streaming video applications; the Mobile ad hoc Network Laboratory under the Collaborative Technology (MANET) by MultiSpectral Solutions Inc.; and the Alliance Program, Cooperative Agreement DAAD19- PulsON family marketed by Time Domain Corporation 01-02-0011. This work was also supported by the NSF for personnel and asset tracking systems (see Figure 18). Grant EIA-0324864.

Closing Remarks Liuqing Yang received her B.S. degree in electrical engi- Just a year after announcing the First R&O, FCC neering from Huazhong University of Science and affirmed rules to authorize the deployment of UWB Technology, Wuhan, China, in 1994, and her M.Sc. and technology and sponsored several demonstrations of Ph.D. degrees in electrical and computer engineering UWB devices on 13 February 2003. During this from the University of Minnesota in 2002 and 2004, assemblage, seven companies demonstrated 12 UWB respectively. Since August 2004, she has been an assistant systems, which cover applications from communica- professor with the Department of Electrical and tions, through-wall and/or ground-penetrating Radar, Computer Engineering at the University of Florida. Her and localization. At the same time, a number of special general research interests include communications, signal issues in journals and special sessions in various confer- processing and networking. Currently, she has a particu- ences are devoted to UWB research and development. lar interest in ultra-wideband communications. Her IEEE sponsors a Working Group for standardization research encompasses synchronization, channel estima- and a biennial workshop in Ultra-Wideband Systems tion, equalization, multiple access, space-time coding, and Technology (UWBST), where the number of sig- and multicarrier systems. nal processing and communications researchers increas- es rapidly. All these justify well that indeed UWB is an Georgios B. Giannakis received his diploma in electrical idea “whose time has come.’’ engineering from the National Technical University of To realize this idea, however, UWB research and Athens, Greece, in 1981 and an M.Sc. in electrical development has to cope with challenges that limit engineering in 1983, an M.Sc. in mathematics in 1986, their performance, capacity, throughput, network flexi- and a Ph.D. in electrical engineering in 1986, all from bility, implementation complexity, and cost. Those the University of Southern California. He joined the include precise and rapid synchronization in a multi- University of Virginia in 1987. Since 1999 he has been user (and possibly ad hoc) environment, modeling of a professor with the Department of Electrical and UWB channel variations, low complexity channel esti- Computer Engineering at the University of Minnesota, mation and multipath diversity collection, UWB-MA where he holds an ADC Chair in Wireless schemes that facilitate MUI/NBI suppression, and Telecommunications. His general interests span the their corresponding multi-user detectors, UWB-tai- areas of communications and signal processing, estima- lored MAC layer schemes, high-speed high-precision tion and detection theory, time-series analysis, and sys- A/D and D/A converter designs, high-frequency oscil- tem identification, on which he has published more lators, and high efficiency UWB antennas. than 200 journal papers, 350 conference papers, and To fully exploit the benefits of UWB systems, two edited books. He received many awards, including enhanced interdisciplinary links need to be established the 2000 IEEE Signal Processing Society’s Technical across the signal processing, communications, and Achievement Award. He was editor-in-chief for IEEE networking communities. Today, research in signal pro- Signal Processing Letters, associate editor for IEEE cessing for UWB is still at its infancy, offering limited Transactions on Signal Processing, and served many

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