Hindawi Publishing CorporationEURASIP Journal on Wireless Communications and NetworkingVolume 2008, Article ID 436865, 13 pagesdoi:10.1155/2008/436865

Research ArticleAsynchronous Two-Way Ranging Using Tomlinson-HarashimaPrecoding and UWB Signaling

Chih-Yu Wen,1 Jun-Koh Chen,1 and William A. Sethares2

1 The Department of Electrical Engineering, Graduate Institute of Communication Engineering, National Chung Hsing University,Taichung 402, Taiwan

2 The Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, 1415 Engineering Drive,Madison, WI 53706-1691, USA

Correspondence should be addressed to Author please provide, Author please provide

Received 22 August 2007; Revised 9 November 2007; Accepted 7 January 2008

Recommended by Biao Chen

This paper demonstrates two methods which simultaneously undertake synchronization and ranging based on a time-of-arrivalapproach with bidirectional communication to bypass the need for accurate synchronous clocking. In order to alleviate multipatheffects, Tomlinson-Harashima precoding and UWB signaling are used to measure the distance between pairs of sensors. Theproposed schemes are shown to be effective under certain assumptions and the analysis is supported by simulation and numericalstudies.

Copyright © 2008 Chih-Yu Wen et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. INTRODUCTION

In many sensor network applications, it is useful or even1required for sensors to be aware of their locations [1–5].Due to the low-power, lower-cost, and simple configurationrequirements of wireless sensor networks, GPS devices, ac-curate synchronous clocks, and manually configuring loca-tion information into each sensor during deployment maybe precluded. However, accurate relative location estimatesare achievable by relying on precise distance measurementsbetween neighboring sensors [6–13].

Previous work [14] suggests that bidirectional signalingcan be used to bypass the use of expensive clocks, but theanalysis is limited by the assumption that only the line-of-sight (LOS) path exists. However, in real radio channels,there may exist multiple transmission paths between the sen-sors. In order to investigate the effect of this multipath inter-2ference on the distance estimations, this paper augments theprevious schemes by utilizing channel estimation [15, 16],a Tomlinson-Harashima (TH) precoding (the modulo in-verse filter [17]), and ultra-wideband (UWB) signaling fordistance measurement in static multipath channels based onthe time-of-arrival (TOA) methodology. Two distributed so-lutions are described for distance estimation in ad-hoc sen-

sor networks: (1) asynchronous ranging via TH precoding(ARTHP) and (2) asynchronous ranging via ultra-wideband(ARUWB). For the ARTHP method, channel informationand a module inverse filter are used to combat the multipatheffect and maximize the correlator output so that the estima-tor can carry out the range measurement accurately (detailedin Section 2). For the ARUWB method, the two-way UWBcommunication system is used to provide precise TOA esti-mates in multipath channels (detailed in Section 3). In thispaper, the two proposed solutions integrate time synchro-nization, information processing, and ranging task to com-plete joint synchronization and ranging for wireless ad-hocsensor networks with two-way communications.

Preequalization techniques are used principally in datatransmission systems to combat the effect of interferencecaused by nonideal (multipath) channels. This paper pro-poses the application of TH precoding to the estimation ofdistance between pairs of sensors using bidirectional com-munication links over multipath channels. Assume that thechannel characteristics do not vary significantly with time.Therefore, given the channel state information in the trans-mitter, it is possible to precode the information prior totransmission such that the problems which are generally in-herent with the equalization at the receiver, such as the noise

2 EURASIP Journal on Wireless Communications and Networking

enhancement, can be avoided. The key point in TH precod-ing is the nonlinear modulo-arithmetic operation to guaran-tee the stability of the precoder.

TH precoding is derived from linear preequalization atthe transmitter. Disregarding the modulo congruence, THprecoding transforms the ISI channel H(z) to a memorylessone and the system overall behavior is well approximated bythe AWGN model. In [18, 19] a new precoding technique,called flexible precoding (FLP) or distribution-preservingprecoding, is proposed. Unlike TH precoding, FLP resembleslinear equalization at the receiver. The disadvantage of lin-ear equalization is that noise is filtered with 1/H(z) and thedesired precoding gain is lost. Compared with FLP, the per-formance of TH precoding has lower precoding loss and theimplementation of TH precoding has simpler circuitry com-plexity. However, TH recoding requires the channel knowl-edge, which may limit its usage in randomly time-varyingwireless channels. To avoid this drawback, a feedback chan-nel, which continuously updates the channel state informa-tion, may be applied. These feedback channels are usuallyavailable in standardized wireless communication systems.

For TH precoding, the following are three possible sce-narios. In the first, the transmitter and receiver share thesame incorrect channel state information. In the second, thereceiver has perfect channel knowledge but the transmitterhas an incorrect channel estimate. In the third, channel stateinformation is only available at the transmitter. In this work,given a pair of sensors, sensor A, and sensor B, the third sce-nario is considered where sensor B estimates the channel us-ing a training sequence sent by sensor A, inverts the chan-nel impulse response, and then sends the preequalized signalback to sensor A. This allows sensor A to accurately estimatethe distance. Current literature on ranging using preequal-ization techniques for wireless sensor networks is limited. Re-lated work in different precoding scenarios can be found in[20–26] and the references therein.

Besides the preequalization technique, a two-way TOA-based ranging technique with UWB signaling is proposedand the performance on ranging in UWB systems is studied.UWB radiolocation functionality usually relies on the abil-ity to perform precise estimates of the TOA. Different TOAestimation methods for UWB propagation signals are inves-tigated in [27–32]. Notice that the above research on rangingin UWB systems focuses on simulation and measurementsof UWB ranging and positioning or on theoretical accuracyof UWB synchronization and ranging for UWB signals withno specific application IEEE 802.15.3a/4a [33–35] signal for-mats. On the other hand, the CRLBs for several UWB signalformats are derived to complement the previous literature onUWB ranging by providing a theoretical framework for theanalysis of achievable ranging accuracy [36]. In addition, aglobal distributed solution is proposed to enable the simulta-neous performance of time synchronization and positioningin UWB ad-hoc networks [37]. It is demonstrated that a co-operative and distributed maximization of the log-likelihoodof range estimates can reduce the uncertainty on estimatedpositions in comparison with classical distributed weightedleast squares approaches. However, the analysis in [36] is im-practical since it does not take the effect of clock parameters

into account. In [37], although the described solution con-siders the clock-dependent ranging error, the operation ofthe proposed synchronization scheme and the diffusion al-gorithm that ensures the convergence of clock parameters arecomplex for ad-hoc networks.

In general, ranging accuracy depends on precise timesynchronization, time stamp reading, and information man-agement such as computation and signal processing. Thispaper presents an estimation-theoretic analysis of the pro-posed measurement mechanisms to assess the achievable es-timation accuracy. Two main ranging errors are considered:(1) the clock-dependent ranging error and (2) the signal-to-noise- (SNR-) dependent ranging error. These two rangingerrors are examined carefully to assess their impact on theTOA ranging accuracy.

The rest of the paper is organized as follows. Section 2describes the ARTHP method and analyzes the ranging ac-curacy. Section 3 presents the ARUWB approach and assessesthe estimation accuracy for both AWGN and multipath chan-nels. Then, Section 4 addresses the performance of the pro-posed ranging approaches and discusses the trade-offs be-tween ARTHP and ARUWB in terms of energy consumption,circuitry and computational complexity, and ranging accu-racy. Finally, Section 5 draws conclusions and shows futureresearch directions.

2. ASYNCHRONOUS RANGING VIA THPRECODING (ARTHP)

This section describes the Asynchronous Ranging via THPrecoding (ARTHP) technology to examine the effect ofmultipath interference on ranging problems. The proposedmethod outlines one way to estimate the distance using chan-nel estimation and the notion of cooperation between pairsof wireless sensors. Given two sensors A and B, sensor A ini-tiates communication by sending a training sequence. Then,sensor B carries out a channel estimation based on maximiz-ing the output of the correlator. Based on channel estimation,sensor B generates a modified training sequence for corre-lating with the training sequence sent from sensor A. Oncesensor B detects the peak of the correlator output, it triggersa time counter and initiates the TH precoding. After receiv-ing the signal from sensor B, sensor A stops the timer basedon the performance of the correlator output and calculatesthe propagation time tab. Thus, sensor B estimates the chan-nel and applies the TH precoding using a training sequencesent by sensor A, and allows A to accurately estimate the dis-tance. The basic principle of the ARTHP method is capturedin Figure 1.

(i) Sensor A sends training sequence s(t) for channel esti-mation and time synchronization in sensor B.

(ii) Sensor B carries out a channel estimation based onmaximizing the output of the correlator and time syn-chronization using the time stamps of transmissionand reception in sensors A and B.

(iii) Based on the channel estimation, sensor B generatesa modified training sequence y2(t) that can be used to

Chih-Yu Wen et al. 3

Sensor A Channel Sensor B

S(t) y1(t) rB∫MTc0 (·)

Local trainingsequence

y2(t)Trigger the counter Trigger the counter

tab

tA0 tB2

Channelestimation

tab tobs =MTc tpro

tA1 tB3

Sensor A Sensor BChannel

∫MTc0 (·)

S(t) S′(t) S(t)TH-precoding

Stop the counter

S(t)Stop the counter and

compute the delay time

tobs =MTc tab tdel = tpro + tobs tpro

tA5 tB4

Figure 1: The ARTHP method: block diagram of a bidirectional communication and distance measurement system using channel estimationand TH precoding.

Sensor An(t)

Sensor B

S(t) y1(t)rB(t)∫MTc

0 (·)Channelh(t)

y2(t)

Channelestimation

h(t)

S(t)

Figure 2: The correlator structure using channel information.

correlate with the received training sequence y1(t) sentfrom A. The correlator output of sensor B, rB(t), is

rB =∫MTc

0y1(t)y2(t)dt, (1)

where Tc represents the time interval between symbolsand MTc is the correlation time.

(iv) Once sensor B detects the peak of the correlator out-put, it triggers a time counter, initiates the TH precod-ing, and records the processing delay. Then, sensor Btransmits the preequalized signal and the delay infor-mation back to sensor A.

(v) After receiving the signal from sensor B, sensor A stopsthe timer based on the performance of the correlatoroutput and calculates the propagation time tab.

This method shows that time delay estimation is possiblewithout synchronous clocking. Based on the system architec-ture in Figure 1, the following subsections explore the impact

of the TH precoding and the correlation procedure on rang-ing accuracy.

2.1. TH precoding with channel knowledge

Since preequalization and correlator performance play crit-ical roles in the distance measurement, the performance ofthe TH precoding in sensor B and the correlator output ofsensor A are analyzed to help understand the behavior ofthe method. The precoder structure is shown in Figure 3.The modulo operation QI(·) is defined as QI(a) = a + b,where b is the unique integer multiple of I for which QI(a) ∈(−I/2, I/2]. Assuming that the channel impulse responseH(Z) is an mth order FIR filter, the approximation of theestimated channel impulse response H(Z) is given by

H(Z) =m−1∑n=0

gnZ−n �

m−1∑n=0

(gn + ∆gn

)Z−n, (2)

where gn and gn are the coefficients of channel impulse re-sponse H(Z) and estimated channel impulse response H(Z),respectively. Note that the difference ∆gn between gn and gndepends on channel estimation errors.

According to Figure 3, the output of the modulo opera-tion Xk(Z) in sensor B is

Xk(Z) = Sk(Z) + Xk(Z)(1− H(Z)

)− lkI

= Sk(Z)− lkI

H(Z),

(3)

4 EURASIP Journal on Wireless Communications and Networking

where lk is an integer. Therefore, the received signal Pk(Z) insensor A is

Pk(Z) = Xk(Z)H(Z) + Nk(Z)

= (Sk(Z)− lkI)·H(Z)

H(Z)+ Nk(Z)

= (Sk(Z)− lkI)·∑m−1

n=0 gnZ−n∑m−1

n=0 gnZ−n+ Nk(Z),

(4)

where Nk(Z) is the received noise.As a result of modulo reduction and providing that the

magnitude of the input data and I are chosen such thatSk(Z) � Pk(Z), the data output is

Sk(Z) � Pk(Z)(mod I) (5)

� Sk(Z)·∑m−1

n=0 gnZ−n∑m−1

n=0 gnZ−n+ N ′

k(Z) (6)

= Sk(Z)·∞∑n=0

cnZ−n + N ′

k(Z), (7)

where

cn =

g0

g0, n = 0(gn −

∑ nj=1g j cn− j

)g0

, n ≥ 1.(8)

Note that the coefficient cn can be shown to be bounded interms of the estimation errors using mathematical induction.Hence, there exists an upper bound δ for tap gain errorscaused by channel estimation errors and an upper bound Bfor cn (n ≥ 1), which is multiple of δ/|g0|.

By optimal L2 finite impulse response (FIR) approxima-tion [39], a discrete infinite impulse response (IIR) which isanalytic in {|z| > ρ, ρ < 1} (i.e., possessing a power series inZ−1 convergent on the unit circle),

F(Z) =∞∑n=0

fnZ−n (9)

with fn = cn, can be approximated by a discrete q-coefficientfinite impulse response (denoted by FIR(q))

F(Z) =q−1∑n=0

fnZ−n, (10)

where fn = cn.Given a high SNR and small channel estimation errors,

the coefficient c0 in (8) is approaching one such that the sig-nal term is dominant in (7). Therefore, the noise may be as-sumed to be negligible in this case. Therefore, based on (10),the data output Sk(Z) can be further approximated by

Sk(Z) = Sk(Z)·q−1∑n=0

cnZ−n. (11)

Then the correlator output of sensor A, rA, is given by

rA =∫MTc

0

q−1∑n=0

cns(t − nTc

)s(t)dt

=MTc +q−1∑n=1

cn

∫MTc

0s(t − nTc

)s(t)dt

=MTc +q−1∑n=1

cnRnA,

(12)

where

RnA =

∫MTc

0s(t − nTc

)s(t)dt. (13)

From the derivation in [40–43], the distribution of RnA is

given by

RnA∼N

(0, MTc

(1− 2

∣∣εn∣∣ + 2ε2n

)), (14)

where εn = (∆τ/Tc)±NεTc denotes the normalized fractionaltiming offset between the two training sequences for the nthcomponent. Note that Nεn is the smallest integer such thatεn ∈ (−1, 1). Therefore, given the channel information, thedistribution of rA is

rA∼N(µrA , σ2

rA

), (15)

where µrA = MTc and σ2rA =

∑ q−1n=1c

2nMTc(1 − 2|εn| + 2ε2

n).Hence, as channel estimation errors approach zero (i.e.,B, δ→0), we have

limB,δ→0

rA =MTc. (16)

With the TH precoding in sensor B, the correlator outputrA converges to MTc when the channel estimation errors ap-proach zero. On the other hand, without precoding in sensorB, the distribution of rA can be expressed by the same formas in (15) with cn = gn. Clearly, the precoding greatly reducesthe variance in the correlator output.

2.2. Analysis of ranging accuracy

The fundamental limitation on the ranging accuracy of theestimates is related to the form of the signal and the clock,including signal bandwidth, signal-to-noise ratio (SNR), andtiming calibration. Assume that the random range error andrange bias error from propagation conditions are negligible.The range-measurement accuracy may be characterized bythe measurement error

σR =(σ2S + σ2

clock

)1/2, (17)

where σS is the SNR-dependent random ranging accuracyand σclock is the clock-dependent random ranging accuracy.Note that σS relates the accuracy of synchronous distance es-timates to the signal-to-noise ratio and the effective band-width of the signal. The expression of σclock is the added in-accuracy due to the asynchronous clocking mechanism.

Chih-Yu Wen et al. 5

Sensor B nk Sensor A

S(Z) X(Z) P(Z) S(Z)rA(t)QN (·) Channel

H(Z)QN (·) Correlator

Sk Xk SkSk

S(Z)1− H(Z)

Figure 3: Tomlinson-Harashima precoding and linearized description.

2.2.1. Clock-dependent ranging accuracy

Suppose that sensors A and B are equipped with clocks thatare asynchronous in both frequency and phase. The randomvariable T denotes the sensor estimate of the true t; thus Tab

is an estimate of the true time tab and TAi is an estimate of the

time tai as measured by the clock of sensor A. From Figure 1,the estimated transmission time is

Tab = TA5 − TA

del − TA1 − TA

obs

2, (18)

where TAdel = Z·TB

del, TBdel = TB

pro + TBobs, and Z = (TA

1 −TA

0 )/(TB3 − TB

2 ). Note that all measurements TAi and TB

j areassumed to be independent normal random variables withthe same variance σ2 caused by the measurement error in theclock. This normality assumption is justified in [44] whenthe clock skew is small. Z is a scale factor that representshow much faster or slower clock A moves than clock B; TA

obsand TB

obs are the estimated observation time of the corre-lators in sensors A and B with distributions N (tAobs, σ

2TA

obs)

and N (tBobs, σ2TB

obs), respectively; TB

pro is the estimated process-

ing time of the TH precoder in sensor B with distributionN (tBpro, σ2

TBpro

). Since σ2TA

obs, σ2

TBobs

, and σ2TB

proare related to the

timing resolution of the clock, we may further express σ2TA

obs,

σ2TB

obs, and σ2

TBpro

as the variance 2σ2. Thus, the distribution of

the estimated delay time TBdel is given by TB

del∼N (µTBdel

, σ2TBdel

),

where µTBdel= tBpro + tBobs = tBdel and σ2

TBdel= σ2

TBpro

+ σ2TB

obs= 4σ2.

Since the measurement errors are small, which are the properconditions for the Gaussian approximation derived in [45–47], the distribution of TA

del is

TAdel∼N

(µZµTB

del, 4µ2

Zσ2 + tBdel

2σ2Z

). (19)

Therefore, the distribution of Tab can be sensibly approxi-mated by

Tab∼N(µTab

, σ2Tab

), (20)

where µTab= (1/2)(tA5 − µZt

Bdel − tA1 − tAobs) and σ2

Tab=

(1/4)[(4+4µ2Z)σ2 +tBdel

2σ2Z]. Thus, the clock-dependent rang-

ing accuracy σclock is given by

σ2clock = σ2

Dab= c2σ2

Tab. (21)

2.2.2. SNR-dependent ranging accuracy

The SNR-dependent ranging accuracy of the distance mea-surement is influenced by the error sources such as channel

estimation, correlator performance, and signal format. Dueto channel estimation errors, sensor B may possess erroneouschannel information, which may degrade the performance ofthe TH precoder. Since the operation of the ARTHP methodis complex, in this paper the channel estimation is assumedto be accurate (i.e., the variance of the correlator is negligi-ble and the proper correlation peak is chosen) such that theanalysis of the proposed approach can be simplified. In thiscase, the communication channel reduces to an AWGN chan-nel with direct path only. Accordingly, the accuracy of syn-chronous distance estimates [48–50] is related to the signal-to-noise ratio, the distance, and the effective bandwidth ofthe signal, which is given by

σS ≥ c·dab2βe√

2SNR, (22)

where βe is the effective bandwidth of the signal [50].Hence, from (21) and (22), the estimation error is

σR =(σ2S + σ2

clock

)1/2 ≥√√√√ c2d2

ab

8β2eSNR

+ c2σ2Tab

. (23)

3. ASYNCHRONOUS RANGING VIA UWB

An alternative approach is to use a two-way TOA-basedranging technique with UWB signaling. In standard UWBsystems, the preamble of a packet can be used to achievetime synchronization. Considering the cooperation betweena pair of sensors, in the ARUWB protocol, time calibrationis carried out by bidirectional communication without usingpreamble patterns to compensate the phase and frequency ofa clock.

Suppose that sensors A and B are equipped with clocks(oscillators) that are assumed to be asynchronous in bothfrequency and phase. Denote tai and tbj as the time stamps

in sensors A and B, respectively; let tadel and tbdel be the delaytime in sensors A and B, respectively; tab is the signal propa-gation time. The estimation of the ARUWB method proceedsas shown in Figure 4.

(i) Sensor A transmits a message, which is a rangingsequence comprising K symbols and containing thetimes ta0 and ta1 (the times indicated on its clock at thestart and the end of the transmission, resp.).

(ii) Sensor B receives the first symbol at time tb2 (which istab seconds after it is transmitted) and receives the lastsymbol at time tb3 .

6 EURASIP Journal on Wireless Communications and Networking

Clock of sensor A

TimeClock of sensor B

ta0 ta1 ta5

tb2 tb3 tb4

tab

B transmits tadel

and time stamp tb4(= ta1 + tab + tadel)

B receivesmessage

(= ta1 + tab)

B receivesmessage

(= ta0 + tab)

tab tabtadel =Z·tbdel

A receivesmessage

(= ta1 + 2tab + tadel)A transmits

time stamps ta0 and ta1

Figure 4: The ARUWB method: sensor A receives its reply at ta5 ; this is equal to ta1 + 2tab + tadel, from which A can estimate tab and hence thedistance; in this variation, sensor B can calculate the difference between its clock (tb3 − tb2 ) and A’s clock using the time-stamped informationin A’s messages (ta1 − ta0).

(iii) Sensor B calibrates its clock to A’s using the differencesta1 − ta0 (which is known from A’s message) and tb3 − tb2(the arrival times).

(iv) Some time tdel later, sensor B transmits the time tadel =z·tbdel that has elapsed since reception of A’s messagealong with the time stamp tb4 (the time on B’s clockwhen it transmits). These times are adjusted (if neces-sary) using the scale factor z = (ta1 − ta0)/(tb3 − tb2).

(v) Sensor A receives the reply from sensor B when itsclock reads ta5 (the time indicated on its clock at thestart of the reception). The transmission time tab canbe calculated as

tab = ta5 − ta1 − tadel

2. (24)

Notice that the clock calibration is achieved by trans-mitting a ranging sequence using bidirectional UWB links.Based on the estimation procedures, the ranging perfor-mance is analyzed considering clock-dependent estimationaccuracy and SNR-dependent estimation accuracy for bothAWGN and multipath channels in the following subsections.

3.1. ARUWB in AWGN channels

3.1.1. Clock-dependent ranging accuracy

Referring to Figure 4 and using a Gaussian approximation(which is justified in [45–47]), the distribution of the esti-mated distance Dab can be well approximated by

Dab∼N(µDab

, σ2Dab

)(25)

with µDab= c·µTab

= dab and σ2Dab

= c2σ2Tab

= (c2/4)[(2 +

2µ2Z)σ2 + tbdel

2σ2Z], where c is the propagation speed of the sig-

nal; σ is the timing resolution; µZ and σ2Z are the mean and

variance of the random variable Z, respectively; µTaband σ2

Tab

are the mean and variance of the random variable, the trans-mission time Tab, respectively. Note that the mean of randomvariable Dab is the true value of the distance between sensorsA and B and the variance of Dab depends on the variance ofthe timing measurement σ , the characteristic of the clock-adjustment factor Z, and the time delay tbdel.

Therefore, the clock-dependent ranging accuracy σclock isgiven by

σ2clock = σ2

Dab= c2σ2

Tab, (26)

which is derived as in (25).

3.1.2. SNR-dependent ranging accuracy

For ranging applications using UWB signals, in this work theCRLB for UWB signal formats derived in [36] are used toassess the SNR-dependent ranging accuracy. Given a distancedab and a channel transfer function, the synchronous rangingaccuracy is given by

σS ≥ c

4π

√√√√ N0

2T∫ fHfLf 2∣∣H( f ,dab

)∣∣2PSDMASK( f )df

, (27)

with channel transfer function

H(f ,dab

) = α0(τ0,dab

)e j2π f τ0 , (28)

where α0(τ0,dab) is the attenuation factor, which depends onboth distance and propagation delay and may be determinedbased on channel characteristics; T is the transmission time;[ fL, fH] is frequency range of the signal; PSDMASK( f ) is thepower emission mask. Note that in this paper PSDMASK( f ) isassumed to be a constant equal to G0 = −41.3 dbm/MHz asregulated by the FCC [36].

For the purpose of comparison, an ideal channel with atransfer function independent of frequency and dependent

Chih-Yu Wen et al. 7

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

−1.5 −1 −0.5 0 0.5 1 1.5 2 2.5

With TH precodingWithout TH precoding

(a)

0

2

4

6

8

10

29 29.5 30 30.5 31

Estimated distance (m)

0

0.2

0.4

0.6

0.8

1

29 29.5 30 30.5 31

The distribution of distance measurement

(b)

Figure 5: The distributions of correlator outputs of sensor A with/without TH precoding (15) with the timing offset ∆τ = 0.5Tc, MTc = 0.5,and q = 10 (left); the distribution of distance measurement in multipath channels using TH precoding (23) with a timing resolution of 1 ns(right top) and 0.1 nanosecond (right bottom): q = 10, tab= 10−7, tb4 = 3, tb3 = 2, tAobs = 0.2, tb2 = 1.25, ta1 = 0.75, and ta0 = 0.25 second.

upon distance between transmitter and receiver as the in-verse of the square of distance dab is considered to evaluatethe sensitivity of the ranging performance to the multipatheffect. Equation (22) therefore can be further expressed as

σS ≥ c·dab4π

√3N0

2TG0(f 3H − f 3

L

) (29)

with the effective bandwidth of the signal

βe =√

34π2T

(f 3H − f 3

L

) , (30)

where T is equal to (ta1 − ta0), N0 = 2.935 × 10−11 W/Hz,G0 = 7.413 × 10−14 W/Hz, and fH and fL are the highestand lowest frequency of UWB frequency bands, respectively.Note that the ranging accuracy in different UWB signal for-mats are related to the difference in bandwidth and the centerfrequency.

Thus, for an ideal channel, the estimation error σR, givenby the root-sum-square of the error components, is

σR =(σ2S + σ2

clock

)1/2 ≥√√√√ 3N0c2d2

ab

32π2TG0(f 3H − f 3

L

) + c2σ2Tab

.

(31)

3.2. ARUWB in multipath channels

3.2.1. Clock-dependent ranging accuracy

In multipath channels, the time stamp of the received sig-nal is determined by the timing resolution and the propaga-

tion delay. Applying the Gaussian approximation, the distri-bution of the estimated distance Dab is

Dab∼N(µDab

, σ2Dab

)(32)

with µDab= c·(µTab

+ τl) = dab + cτl and σ2Dab

= c2σ2Tab

=(c2/4)[(2+2µ2

Z)σ2+tbdel2σ2Z], where τl is the propagation delay

of the lth multipath component. Again the clock-dependentranging accuracy σclock is

σ2clock = σ2

Dab= c2σ2

Tab. (33)

Observe that when the LOS path is significantly attenu-ated, the distance measurement might be biased by an incor-rect choice of multipath component as derived in (32). Onthe other hand, given a signal with a large SNR and band-width in an environment with a dominant LOS path andmoderate multipath, the estimated propagation time maybe unbiased with a correct choice of the signal arrival timesuch that the clock-dependent ranging accuracy in multipathchannels is close to that in AWGN channels. Thus, the aboveanalysis suggests that in a strong multipath environment, theclock-dependent ranging accuracy might be dominated bythe multipath effect instead of the timing resolution as inAWGN channels.

3.2.2. SNR-dependent ranging accuracy

Based on (27), the synchronous ranging accuracy can be fur-ther derived as

σS ≥ c·dab4π

√3N0

2TG0(f 3H − f 3

L

)·η, (34)

8 EURASIP Journal on Wireless Communications and Networking

0

20

40

60

80

100

120

Stan

dard

devi

atio

n(c

m)

0 5 10 15 20 25 30 35

dab (m)

DS-UWB high band (ideal)DS-UWB low band (ideal)MB-OFDM band 1 (ideal)MB-OFDM band 2 (ideal)MB-OFDM band 3 (ideal)

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MB-OFDM band 2 (LOS)MB-OFDM band 3 (LOS)

(b)

Figure 6: The synchronous ranging accuracy of the ARUWB method with fixed observation time T = 1.83 microseconds and varyingdistance dab (from the first perspective) in ideal and AWGN channels (29) (left) and a multipath channel with a dominant LOS path (34)(right).

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(b)

Figure 7: The synchronous ranging accuracy of the ARUWB method with fixed distance dab = 30 m and varying SNR (from the secondperspective) in ideal and AWGN channels (29) (left) and a multipath channel with a dominant LOS path (34) (right).

Chih-Yu Wen et al. 9

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DS-UWB low band (LOS path)MB-OFDM band 1 (LOS path)

MB-OFDM band 2 (LOS path)

MB-OFDM band 3 (LOS path)

(b)

Figure 8: The distribution of asynchronous distance measurement using the ARUWB method with a timing resolution of 0.1 nanosecond:tab= 10−7, tb4 = 0.3 + 2.92 µs, tb3 = 0.3 + 1.92 µs, tb2 = 0.3, ta1 = 0.25 + 1.83 µs, and ta0 = 0.25, in ideal and AWGN channels (31) (left) and amultipath channel with a dominant LOS path (37) (right).

where

η = 1dab·

√√√√√ ∫ fHfLf 2 PSDMASK( f )df∫ fH

fLf 2∣∣H( f ,dab

)∣∣2PSDMASK( f )df

(35)

with channel transfer function

H(f ,dab

) = N−1∑k=0

αk(τk,dab

)e j2π f τk . (36)

Observe that the first term in (34) is the SNR-dependentranging accuracy in an ideal channel and the second term ηcan be considered as the performance loss due to the mul-tipath effect, which is examined via numerical studies inSection 4.

From (33) and (34), the measurement error σR can beexpressed as follows:

σR =(σ2S + σ2

clock

)1/2 ≥√√√√ 3N0c2d2

ab

32π2TG0(f 3H − f 3

L

)·η2 + c2σ2Tab

.

(37)

4. SIMULATION AND NUMERICAL RESULTS

This section demonstrates the performance of the proposeddistance measurement algorithms. Assume that the propaga-tion time is tab= 10−7 s (i.e., the true distance is dab = 30 m)for all distance measurement settings.

The first set of experiments evaluates the performance ofthe distance measurement using channel estimation with THprecoding. Note that the choice of the {tai , tbj } values is purelyarbitrary in order to show that the proposed technique is ableto joint synchronization and ranging with two-way commu-nications. Figure 5(left) depicts the corresponding correlatoroutput of sensor A. Observe that the correlator output rAwithout pre-equalization may have larger variance than withTH precoding due to the multipath effects.

Assume the transmitted waveform is a simple rectangularpulse with a zero phase characteristic,

a(t) = rect

(t

tp

), (38)

where tp is the pulse width. In our case, tp = Tc.Figure 5(right) shows the typical performance of the asyn-chronous bidirectional distance measurement scheme usingTH precoding in multipath channels with the parameters de-tailed in the caption and the clocks providing a resolutionbased on the symbol rates of the training sequence, 1 Giga-symbol per second (Gsps) (i.e., 1 nanosecond) and 10 Gsps(i.e., 0.1 nanosecond), respectively. Observe that as the dis-tance dab = 30 m, the σab is about 6 cm with a timing resolu-tion 0.1 nanosecond. Note that an accurate clock with com-plicated hardware is required for distance estimation using a

10 EURASIP Journal on Wireless Communications and Networking

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(a)

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(b)

Figure 9: The comparison of the asynchronous distance measurement applying the ARUWB method (using (31) and (37)) with the samesettings in Figure 8 and the UWB ranging solution in [37] (using (11) and (17)), in ideal and AWGN channels (left) and a multipath channelwith a dominant LOS path (right).

higher symbol rate (higher timing resolution) though pro-viding a higher measurement accuracy.

The second set of experiments examines the performanceof the ARUWB method in both AWGN and multipath chan-nels with synchronous clocking. The purpose of these exper-iments is to explore the influence of multipath effects on theranging performance. The two-ray ground reflection modelwith the same parameters used in the ARTHP method isconsidered to evaluate the corresponding measurement er-rors. Two perspectives are investigated to compare the rang-ing accuracy using different UWB signal formats: (1) rang-ing accuracy with fixed observation time T and varying dis-tance dab; (2) ranging accuracy with fixed distance dab andvarying observation time T (i.e., with varying SNR). Fromthe first perspective, Figure 6 depicts the synchronous rang-ing error, which is proportional to the distance between apair of sensors. Observe that for the UWB signalings, a DS-UWB high-band signal has the best ranging accuracy due toits higher frequency band and larger operation bandwidthand a MB-OFDM Band 1 signal has the worst ranging accu-racy because of its lower frequency band and smaller opera-tion bandwidth. As shown in Figure 6, when the distance dabis equal to 30 m, the standard deviation σdab of a DS-UWBhigh-band signal is about 1.8 cm, 12 cm, and 30 cm in ideal(left), AWGN (left), and multipath (right) channels, respec-tively. Therefore, given time synchronization, the ARUWB

method with DS-UWB High Band signals may be a good ap-proach for ranging.

From the second perspective and (29), note that theestimation error is dominated by the factor T( f 3

H − f 3L ),

which implies that operation frequencies and observationtime will determine the estimation accuracy. Given a SNR,MB-OFDM signals have larger observation times comparedwith DS-UWB signals since the signal energy is given by Es =T·PSDMASK·( fH − fL). Figure 7 shows that, again, the pro-posed method using UWB High Band signals with time syn-chronization may have better ranging performance in bothAWGN (left) and multipath (right) channels.

The third set of experiments studies the performanceof the ARUWB method in multipath channels with asyn-chronous clocking. Since the channel experimental param-eters highly depend on the measured environment, in thisset of experiments the two-ray ground reflection model ischosen. The parameters for the channel configuration areα0 = 0.8, α1 = 0.5, τ0 = 0 ns, and τ1 = 5 ns. Figure 8 il-lustrates the impact of time synchronization and multipatheffects on the distance measurement. Applying the ARUWBmethod with a DS-UWB High Band signal and given a tim-ing resolution 0.1 ns, the standard deviation σdab of the es-timation is about 30 cm, 50 cm, and 80 cm in ideal (left),AWGN (left) and multipath (right) channels, respectively.Note that though a DS-UWB High Band signal has the best

Chih-Yu Wen et al. 11

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DS-UWB high band (ARTHP)DS-UWB high band (Denis)DS-UWB high band (ARUWB)MB-OFDM band 3 (Denis)MB-OFDM band 3 (ARUWB)

Figure 10: The distributions of the distance measurement in a mul-tipath channel with a dominant LOS path using the UWB rangingmethod in [37, equation (17)], the ARTHP (23), and ARUWB (37)approaches with UWB signaling given the parameters detailed inthe captions of Figures 8 and 9.

ranging accuracy in an ideal channel, all of the UWB sig-nal formats have roughly the same estimation performanceas shown in Figure 8(left), which implies that the clock-dependent ranging error may dominate the ranging mea-surement under the circumstances of asynchronous clockingin an ideal channel. However, as shown in Figure 8(right),compared with the clock-dependent ranging error, the SNR-dependent ranging error may dominate estimation perfor-mance in multipath channels due to the performance losscaused by multipath effects.

Figure 9 compares the ARUWB method and a UWBranging solution [37] in an ideal channel and a multipathchannel with a dominant LOS path via bi-directional com-munications. Given the same settings as detailed in the cap-3tion of Figure 8 and based on (31) and (37) in Section 3 and[37, equations (11) and (17)] with WLOS = 0.61, WGLOS = 1,WELOS = 0, σLOS = 0.0068, WNLOS = 0.39, WGNLOS = 1,WENLOS = 0, and σNLOS = 0.0102 [38], the performancestudies show that the measurement results of these two tech-niques are very closed. It is important to remark that theexisting UWB approach [37] considers clock-dependent er-rors and multipath effects and uses a probabilistic modelto describe the weights of different multipath componentssuch that the ranging performance can be investigated basedon the channel scenarios. However, many assumptions aremade when analyzing the clock-dependent errors and the de-scriptions of parameter settings, such as how to obtain theSNR-dependent errors and how to set the weights for dif-

ferent multipath components, are not clear. In the ARUWBmethod, the clock-dependent error is studied and time syn-chronization mechanism is performed. Moreover, based onthe framework in [36], the SNR-dependent errors are fur-ther derived under different channel scenarios. Consideringthe clock-dependent and SNR-dependent estimation errors,the proposed UWB method illustrates a sensible way to assessthe ranging performance via bi-directional communications.

For the ARTHP and ARUWB methods, although rang-ing performance seems to be better in the ARTHP method(with channel information), the performance improvementis achieved at the cost of consuming signal resources forobtaining channel knowledge. Hence, a fair comparison ofthe proposed techniques with and without channel informa-tion requires considering longer signal duration and moresignal energy for the ARUWB technique (without channelknowledge). As a result, the following evaluation is madegiven the same energy consumption in each method. As-sume the transmission path is symmetric and the radiodissipates Eelec in the transmitter or receiver circuitry andEpro in the information processing. Based on the estima-tion procedures in the ARTHP method, the radio expends:E(ARTHP) = 6Eelec(ARTHP) + 5Epro(ARTHP), including the opera-tions for communication and signal processing such as sig-nal transmission and reception, channel estimation, corre-lation, TH precoding, and range-measurement calculation.Similarly, for the ARUWB method, the total energy con-sumption is E(ARUWB) = 4Eelec(ARUWB) + 2Epro(ARUWB), whichis dissipated for signal transmission and reception, timingcalibration, and distance estimation. Since computation ismuch cheaper than communication, we have E(ARTHP) ≈6Eelec(ARTHP) and E(ARUWB) ≈ 4Eelec(ARUWB), which may de-cide the relationship between Eelec(ARTHP) and Eelec(ARUWB) fora given energy.

Given the above settings, Figure 10 shows that the perfor-mance of the ARTHP method with DS-UWB High Band sig-nals is superior to that of the ARUWB method with differentUWB signal formats due to the contributions of multipathto the distance estimations. Note that the ARTHP methoddoes not require any signaling for the ranging task. Com-pared with the ARUWB method, the system architecture ofthe ARTHP approach has greater circuitry requirement andcomputational complexity due to channel estimation andTH precoding. From Figures 6 to 10, observe that underthe circumstance of a dominant LOS path, the ARUWB ap-proach may be a good technique for sensor ranging; on theother hand, if the LOS path is attenuated significantly, theARTHP approach may be preferred since the multipath ef-fect can be canceled out by the preequalization.

5. CONCLUSION

This paper presents two decentralized methods which si-multaneously undertake synchronization and ranging basedon an asynchronous two-way TOA approach for wirelessad-hoc sensor networks. These asynchronous and cooper-ative communication procedures may simplify the compu-tational and circuitry complexity of the ranging estimationin each sensor. In order to alleviate the multipath effect,

12 EURASIP Journal on Wireless Communications and Networking

Tomlinson-Harashima precoding and UWB signaling areused for the distance measurement between pairs of sensors.In the ARTHP technique, an algorithm is presented to cancelthe channel effect, which is crucial to the ranging accuracy.In the ARUWB method, the range-measurement accuracyhighly benefits from the well-known features of UWB sig-naling such as in communication and radio-location appli-cations to provide precise time-of-arrival estimates in multi-path channels. Sensible settings for the ranging problems us-ing the ARTHP and ARUWB approaches are presented andthe proposed mechanisms are simulated and analyzed to as-sess the accuracy of the distance estimation. Depending onthe measurement accuracy, the parameters in each techniquecan be determined to achieve desired performance.

For the two proposed ranging solutions, tradeoffs arefound between model complexity, energy consumption,computational complexity, and sensible model description inreal systems. Future plans will involve generalizing the meth-ods to consider certain failure scenarios and to explore thesensitivity of the proposed schemes to system models andnetwork operation.

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14 EURASIP Journal on Wireless Communications and Networking

Composition Comments

1. Please provide the corresponding author and his/her e-mail address.

2. We changed “signalling” to the highlighted “signaling”in the main title. Please check similar cases throughout.

3. Please check the accuracy of the highlighted part.Please check similar cases throughout.

4. We split this reference to [15, 16]. Please check.

5. Please note that the URL is not accessible.