Maximal Operating Distance Estimation for

Ranging in IEEE 802.15.4a Ultra Wideband

Thomas Gigl⋆•, Florian Troesch◦, Josef Preishuber-Pfluegl•, and Klaus Witrisal⋆

{thomas.gigl, witrisal}@tugraz.at, troeschf@nari.ee.ethz.ch, j.preishuber-pfluegl@cisc.at⋆Signal Processing and Speech Communication Laboratory, Graz University of Technology, Austria

•CISC Semiconductor, Design and Consulting GmbH, Austria◦Communication Technology Laboratory, Swiss Federal Institute of Technology (ETH) Zurich, Switzerland

Abstract—The IEEE 802.15.4a standard for wireless sensornetworks is designed for highly accurate ranging with impulseradio Ultra Wideband (UWB) signals. The standard is designedfor coherent and non-coherent (energy detector) receivers, thusthe choice of complexity is left to the implementer. In thispaper, the maximal operating distance is analyzed for ranging,using a coherent receiver and an energy detector under FCC/ECregulations. The analysis is based on the working points of thereceivers and a link budget calculation. The preamble of thestandard is defined by several parameters, which influence theallowed FCC transmit power, the free space losses and thus themaximal operating distance. It is shown which code and channelcombinations achieve the largest operating distance. The bestperformance is achieved by using long spreaded codes, wherecoherent receivers can achieve a maximal operating distance upto several thousand meters and energy detectors up to severalhundred meters.

I. INTRODUCTION

The IEEE 802.15.4a standard [1] is a standard for wireless

sensor networks with sub-meter ranging accuracy even in

indoor environments. The physical layer is defined for bi-

directional communications based on impulse radio ultra-

wideband signals. A two-way time-of-arrival ranging scheme

is proposed. The standard allows the usage of high complexity

coherent receivers and low-complexity energy detectors. The

used preamble sequences show perfect autocorrelation prop-

erties for both receiver types [2].

Energy detectors promise low-cost and low-power consump-

tion. On the other hand, a performance loss [3] and more

vulnerability to interfering signals occur [4]. Sub-Nyquist

sampling is applicable for energy detectors, but limits on the

other hand the ranging performance [5]. The IEEE 802.15.4a

standard has a large number of selectable system parameters,

which are important for the achievable ranging performance

[6]. Their impact is studied in a signal-to-noise (SNR) analysis

for a coherent receiver and an energy detector. The influence

of the preamble parameters is also studied with respect to

the maximal allowed transmit power according to the FCC

[7] and EC [8] regulations. A detailed analysis about the

FCC regulations for specific signaling schemes can be found

in [9]. In this work, these concepts have been adopted to

the preamble design of IEEE 802.15.4a. A detailed analysis

shows the best preamble parameter setting for maximal al-

lowed transmit energy. Furthermore, the different frequency

Hilbert∑

w(t)∣∣ . ∣∣ Ranging

e−ωct ci

1T

××

Fig. 1: Coherent receiver architecture

(.)2∫TI

1TI

×

ci ∑w(t) Ranging

Fig. 2: Energy Detector

channels are discussed to optimize the system performance.

The performance is analyzed based on the maximal operating

distance, which is based on a link budget calculation according

to [10].

The rest of the paper is organized as follows: Section II

gives an overview of the introduced receiver architectures,

while Section III presents the signal model of the IEEE

802.15.4a standard, the received signal and the two receiver

architectures. The SNR analysis and the performance metric

definition is given in Section IV. The FCC and EC regulations

are discussed in Section V and the link budget is introduced

in Section VI. This is followed by performance results and a

short conclusion in Sections VII and VIII.

II. RECEIVER SYSTEM MODELS

This section shows the system models of the coherent

receiver and the energy detector.

A. Coherent Receiver

Fig. 1 shows the coherent receiver. The signal is received

by a UWB antenna and is filtered by transmit pulse shape

w(t). Thus, a matched filtering to the pulse shape is applied.

The signal is converted to discrete complex baseband using

the Hilbert transform, the carrier frequency ωc and Nyquist

sampling with 1/T . Next, the channel response is obtained by

code despreading, and the ranging algorithm is applied on the

magnitude of the complex baseband signal. A similar receiver

structure can be found in [11] and [12].

This receiver architecture suffers from the high sampling

rates according to the Nyquist theorem. Another disadvantage

978-1-4244-7157-7/10/$26.00 ©2010 IEEE 10

TABLE I: Preamble characteristicNs L Npr Tchip [ns] Tpr [µs] PRF [MHz] MRF [MHz] ERF [MHz] N1ms

31 16 16 2.0032 15.897 31.2 16.1 0.256 100631 16 64 2.0032 63.590 31.2 16.1 1.024 100631 16 256 2.0032 254.358 31.2 16.1 4.096 100631 16 1024 2.0032 1017.436 31.2 16.1 16.1 100631 16 4096 2.0032 4069.744 31.2 16.1 16.1 1006

31 64 16 2.0032 63.590 7.8 4.03 0.256 25131 64 64 2.0032 254.359 7.8 4.03 1.024 25131 64 256 2.0032 1017.433 7.8 4.03 4.03 25131 64 1024 2.0032 4069.744 7.8 4.03 4.03 25131 64 4096 2.0032 16278.974 7.8 4.03 4.03 251

127 4 16 2.0032 16.282 124.8 62.89 1.024 982127 4 64 2.0032 65.128 124.8 62.89 4.096 982127 4 256 2.0032 260.512 124.8 62.89 16.384 982127 4 1024 2.0032 1042.051 124.8 62.89 62.89 982127 4 4096 2.0032 4168.205 124.8 62.89 62.89 982

of this concept is the required synchronization of the carrier

frequency and the phase, which can harm the performance.

The energy detector is able to cope with these two problems,

thus a low complexity solution can be obtained.

B. Energy Detector

The energy detector works as shown in Fig. 2. The signal is

again received by a UWB antenna and filtered by a bandpass

filter, which is implemented as a filter matched to the pulse

shape. Next, the signal is squared and integrated for short time

periods TI , which also defines the sampling period. The length

of TI causes a mean absolute error (MAE) of at least TI/4[5], which limits TI to a few ns. The signal is correlated and

despread with the corresponding despreading code ci. This

delivers the channel response, where the ranging algorithm is

applied.

III. SIGNAL MODEL

The following notations are used: Column vectors are

denoted by boldface symbols and estimated values are marked

by hats.

A. IEEE 802.15.4a Preamble and Received Signal

The most important signal part for ranging is the preamble,

thus this section gives a short overview on the design of the

preamble. The IEEE 802.15.4a preamble sequence cs has a

length Ns of 31 or 127 [1]. It consists of ternary elements

∈ {−1, 0, 1}. The spread preamble code vector csp is created

as

csp = 1Npr⊗ cs ⊗ δL = c ⊗ δL (1)

where ⊗ denotes the Kronecker product, δL is the spreading

sequence of the preamble, which is defined as a unit vector

with a one at the first position and length L. 1Nprdenotes a

vector of ones with length of the preamble sequence repetitions

Npr and c is the periodically extended preamble code. The

transmitted signal s(t) is defined as

s(t) =ℜ{√

Ep

M−1∑m=0

cmw(t − mLTchip)ejωct

}

=√

Ep

M−1∑m=0

cm w(t − mLTchip)

(2)

where Ep is the energy per pulse, cm is the m-th element of c,

w(t) is the energy normalized pulse shape, M is the number

of code elements in the preamble, ωc is the carrier frequency,

Tchip is the chip duration, and w(t) is the up-converted pulse

assuming the carrier and the pulse are phase synchronous.

Table I shows the timing characteristics of the preamble,

where Tpr is the total duration of the preamble, PRF is

the peak pulse repetition frequency, MRF is the mean pulse

repetition frequency and N1ms is the number of preamble

sequences within 1 ms. ERF is the effective pulse repetition

frequency according to the regulations (see Section V).

The transmitted signal (2) is sent over a multipath channel

with channel impulse response hc(t), where also the effects of

the antenna are contained for simplicity. Furthermore, hc(t) is

assumed to be constant during Tpr. Thus, the analog received

signal

ra(t) = s(t) ∗ hc(t) + ν(t) (3)

where ν(t) is modeled as additive white Gaussian noise and

∗ is the convolution. Next, the received signal enters the two

receiver architectures, as described in the next sections.

B. Coherent Receiver

First the signal is pulse matched filtered by w(−t), where

w(t) = w(−t) due to symmetry. It follows

rf (t) = s(t) ∗ hc(t) ∗ w(t) + ν(t) ∗ w(t) (4)

Next, the negative frequencies are canceled by a Hilbert

filter hhilb(t) and the complex baseband signal is obtained

by down-converting the signal with the estimated carrier

11

frequency ωc. The resulting baseband signal is given by

r[n] =(rf (t) ∗ hhilb(t)) e−j(ωct+ϕ)

=M−1∑m=0

cmh(nT − mLTchip)ej[ωc−ωc]nT + νl[n](5)

where h(t) is an equivalent channel response incorporating

the channel hc(t), the unknown carrier phase ϕ, the pulse√Epw(t) and the downconverted matched filter w(t). The

noise νl[n] is the band limited input noise νl[n] = ν[n] ∗w[n]in complex baseband. The carrier frequency is assumed to be

known in this analysis. Thus, (5) simplifies to

r[n] =M−1∑m=0

cmh[n − mLNchip] + νl[n] (6)

where h[n]=h(nT ). The number of samples within a chip

is defined by Nchip=Tchip/T . Assuming synchronization, the

estimation of the despread channel response h[n] is given by

h[n] =Npr−1∑

q=0

Ns−1∑m=0

cm r[n + (m + qNs)LNchip]

=M1h[n] +M−1∑m=0

cmνl[n + mLNchip]

(7)

where the despreading is first performed sequence-wise (∑

m)

and then over the sequence repetitions (∑

q). c2m = 1 for

the non-zero coded elements, it follows that∑

q and∑

m

is simple the number of non-zero code elements in the

preamble M1 = Ns+12 Npr. In other words, M1 is the number

of transmitted pulses.

C. Energy Detector

The signal model of the energy detector after squaring,

integration and sampling is given by

x[n] =

(n+1)TI∫nTI

(M−1∑m=0

cmg(t − mLTchip) + νf (t)

)2

dt (8)

where νf (t) is the passband filtered noise and the channel

response g(t)=√

Epφw(t) ∗ hc(t + mLTchip) and φw(t) is the

autocorrelation function of w(t). Thus, the estimated channel

response y[n] is obtained by despreading x[n],

y[n] =Npr−1∑

q=0

Ns−1∑i=0

ci x[n + iLNchip + q Ns LNchip]

=Npr−1∑

q=0

Ns−1∑i=0

ci

(n+1)TI+iTchip+qTs∫nTI+iTchip+qTs

(M−1∑m=0

cmg(t−mLTchip)

)2

dt

+2Npr−1∑

q=0

Ns−1∑i=0

ci

(n+1)TI+iTchip+qTs∫nTI+iTchip+qTs

M−1∑m=0

cmg(t−mLTchip)νf (t)dt

+Npr−1∑

q=0

Ns−1∑i=0

ci

(n+1)TI+iTchip+qTs∫nTI+iTchip+qTs

ν2f (t) dt

= yss[n] + ysν [n] + yνν [n](9)

where Nchip = Tchip/TI , is the number of samples in a

code frame, and the sequence duration Ts = NsLTchip. The

code despreading is performed sequence wise with∑

q and∑i with the despreading code ci. In contrast to the coherent

receiver the non-coherent receiver uses a different despreading

code than the spreading code, which shows also perfect

circular correlation properties for the squared sequences. The

despreading code c is created by squaring c and setting all

zeros to −1 [2]. As observable, the output of the energy

detector is dependent on a signal-by-signal yss[n], a linear

signal-by-noise ysν [n] and a quadratic noise-by-noise yνν [n]term.

IV. SNR ANALYSIS AND MAXIMAL OPERATING RANGE

ESTIMATION

The goal of a ranging system is to find the LOS component

in the channel response, due to the fact that a detection

of a multipath component may lead to very large ranging

errors. The LOS-SNR (LSNR) correlates very well with the

ranging performance [11]. This section shows the relation

between receiver input SNR, the energy of the despread LOS

component over the noise spectral density ELOS/N0, and the

receiver output SNR, written as LSNR. ELOS = M1E(1)LOS,

where E(1)LOS is the received energy for the LOS component

for a single pulse.

A. Coherent Receiver

If only the LOS component is taken into account, h[n] sim-

plifies to hLOS[n]=√

E(1)LOSw[n]∗w[n]ejϕ. Thus, (7) simplifies

to

hLOS[n] =M1

√E

(1)LOSφw [n]ejϕ

+Npr−1∑

q=0

Ns−1∑m=0

cmνl[n + (m + qNs)LNchip]

=ys[n] + yν [n]

(10)

where φw[n] is the autocorrelation of w[n], ys[n] is the signal

part and yν [n] is the noise part of the receiver output signal.

12

1) Expected value of hLOS[n]: The expected value of

hLOS[n] is given by

E{hLOS[n]

}= M1

√E

(1)LOSφw[n]ejϕ (11)

2) Expected value of |ys[n]|2: The expected value of the

signal power is given by

E{|ys[n]|2

}= E

(1)LOSM

21 φ2

w[n] = ELOSM1φ2w[n] (12)

3) Variance of hLOS[n]: The variance of hLOS[n] is defined

by the variance of the noise component in (10) and is given

by E{|yν [n]|2

}due to the zero mean noise process. Thus, it

follows

E{|yν [n]|2

}=

Npr−1∑q=0

Npr−1∑q′=0

Ns−1∑m=0

Ns−1∑m′=0

cmcm′

×νl[n+(m + qNs)LNchip]ν∗

l [n+(m′+q′Ns)LNchip] .(13)

The noise νl is uncorrelated for a spacing of LNchip, thus

it follows m′ = m, q′ = q and (13) simplifies to

E{|yν [n]|2

}= N0

M−1∑m=0

c2mφw[0] = N0M1φw [0] (14)

where φw[0] is the equivalent bandwidth of the matched

filter.

B. Energy Detector

The statistical analysis of the energy detector for ranging

in IEEE 802.15.4a has been derived in [6]. Here only the

final equations for the LOS component without inter-pulse-

interference are shown.

1) Signal-by-Signal Term yss[n]: The signal-by-signal term

is given by

yss[n] = E(1)LOSM1

(n+1)TI∫nTI

φ2w(t)dt (15)

2) Signal-by-Noise Term ysν [n]: The variance of the signal-

by-noise term is given by

var{ysν [n]} = E(1)LOS(Ns + 1)NprN0

(n+1)TI∫nTI

φ2w(t)dt (16)

where it is shown that this term depends on the pulse shape

and the received signal energy ELOS. Note, this term does not

occur in the coherent receiver and degrades the performance

of the energy detector.

0 10 20 30 40 50 60 70−10

0

10

20

30

40

50

60

ELOS

/N0 [dB]

LS

NR

[dB

]

ED: Npr

=16, ND=992

ED: Npr

=64, ND=3968

ED: Npr

=256, ND=15872

ED: Npr

=1024, ND=63488

ED: Npr

=4096, ND=253951

CR: all Npr

Working Point ED

Working Point CR

Fig. 3: Relation between input SNR ELOS/N0 and out-

put SNR LSNR with respect to the noise dimensionality

ND = Ns Npr TI WRRC for the energy detector ED and the

coherent receiver CR. The static parameters are Ns = 31,

TI = 2.0032 ns, and WRRC = 1 GHz.

3) Noise-by-Noise Term yνν [n]: The variance of the noise-

by-noise term is given by

var{yνν [n]} =N2

0

2MTIWRRC (17)

where WRRC is an equivalent bandwidth defined as

WRRC =∫ Tw

−Twφ2

w(µ)dµ. A comparison to the coherent re-

ceiver (see (14)) shows that this variance scales with M instead

of M1, which means that approx. two times more noise occurs

due to the despreading method and is further proportional to

N20 .

C. Input-to-Output SNR Relation

The Input-to-Output SNR relation is given for the coherent

receiver, using (14) and (12), by

LSNRCR =|ys[nLOS]|2E{|yν [n]|2} =

ELOSφw [0]N0

=ELOS

N0(18)

as φw[0] is energy normalized, where nLOS is the sample

containing the LOS component at φw[0]. The energy detector

relation is obtained from (15)-(17) and is given by

LSNRED = 10 log2(

ELOS

N0

)2

4ELOS

N0+ NsNprTIWRRC

(19)

The first term of the denominator corresponds to the linear

and the second to the quadratic noise term. The quadratic

noise term depends on the receiver parameters, which can be

combined to the noise dimensionality ND=Ns Npr TI WRRC

[4].

Fig. 3 shows the relation of the detector input SNR

ELOS/N0 and the output LSNR based on (18) and (19). The

specific curves for the energy detector ED are obtained by

13

increasing ND by factors of 4, where the depicted curves corre-

sponds to Npr=[16, 64, 256, 1024, 4096], Ns = 31, TI = 2 ns,

and WRRC = 1 GHz, . Note, Npr = 256 is not intended in

the standard, but is shown for visibility in this analysis. The

curves are separated if the quadratic noise term dominates and

they merge if the linear noise term is dominant. Increasing

ELOS/N0 by 6 dB leads to LSNR +12 dB in the quadratic part

and to +6 dB in the linear one. The horizontal line illustrates

the LSNR at the working point LSNRWP = 12 dB for the

energy detector (cf. [6]), where 80% of the range estimations

are within 1 m. The coherent receiver shows a working point

LSNRWP = 9 dB (cf. [11]). Both working points are evaluated

by extensive simulations. It can be seen for the energy detector,

that 3 dB more ELOS/N0 is required when the number of

sequences is increased by a factor of 4. Note, the linear noise

term is negligible at this working point. A detailed analysis of

the energy detector for IEEE 802.15.4a can be found in [6].

As observeable from (18), LSNR for the coherent receiver is

independent of the number of the pulses. It depends only on

the transmitted energy. In other words, it does not matter if

this energy is transmitted in one pulse or in a sequence of

pulses. The coherent receiver shows a gain of ≥ 11 dB in the

working point in comparison to the non-coherent receiver.

D. Maximal Operating Distance Estimation

As N0 is constant in the scenario, ELOS/N0 is modeled

by the well-known pathloss model for the maximal operating

distance dmax. Thus

ELOS

N0(dmax)dB =

ELOS

N0(d0)dB − 10n log

(dmax

d0

)(20)

where n is the pathloss exponent and d0 is a reference distance.

The maximal operating distance for the coherent receiver is

obtained from (18) and (20):

dmax =

(ELOS

N0(1)

ELOS

N0(dmax)

)1/n

=

(ELOS

N0(1)

LSNRWP

)1/n

(21)

where the reference distance is assumed to be 1 m. It follows

for the energy detector

dmax =(

ELOSN0

(1)

LSNRWP+√

LSNRWP (LSNRWP+ND/2)

)1/n

(22)

using (19) in (20).

E. Maximal Allowed Pathloss PLmax

A more general look at achieveable range is given by the

maximal allowed pathloss, which is independent of the channel

model, fading margins or implementation losses. It follows

from the pathloss model

ELOS

N0(dmax)dB =

ELOS

N0(d0)dB − PLmax,dB (23)

where ELOS is the energy of the received LOS component

at 1 m, which does not take fading margins or implementation

losses into account (see Table II). Thus, PLmax for the coherent

receiver at 1 m is given by

PLmax,dB =ELOS

N0(1)dB − LSNRWP,dB (24)

using (18) and (23). For the energy detector, using (19) and

and (23), it follows

PLmax,dB =ELOS

N0(1)dB

−10 log(

LSNRWP +√

LSNRWP (LSNRWP + ND/2))

.

(25)

ELOS/N0(1) and ELOS/N0(1) are defined by the transmitted

preamble energy Epr (see Section V) and the link budget (see

Section VI).

V. FCC REGULATIONS

In this section the maximal allowed transmit power is

calculated w.r.t. the FCC regulations [7]. In principle, the same

regulations have been adopted by the EC in Europe for the

band between 6 − 8.5 GHz [8]. In the band between 3.1 and

4.8 GHz the EC requires detect and avoid (DAA) or low duty

cycle (LDC) mitigation additionally, which does not influence

this analysis. This analysis is done in accordance to [9].

The FCC constraints essentially consist of an average and

a peak power limit. In any band of bandwidth Bav = 1 MHz,

the average transmit power is limited to P FCCav = −41.3 dBm

by averaging over an integration window Tav = 1 ms. The

peak power within the bandwidth Bpk = 50 MHz is restricted

to P FCCpk = 0 dBm. Both peak and average transmit power are

defined by the equivalent isotropically radiated power (EIRP).

The 802.15.4a preamble is a sequence of non-uniformly

spaced pulses whose polarities are chosen pseudo-randomly

by the codes. According to [9], its average and peak power is

determined by ERF and PRF respectively and the pulse energy

spectral density Ep,av|V (f0)|2 for the average power limit is

given by

Ep,av|V (f0)|2 =

TavPFCCav

2BavERF ≤ 1/Tav

P FCCav

2BavERFERF ≥ 1/Tav

(26)

where V (f0) is the spectrum of the UWB pulse at the center

frequency f0. ERF is defined as

ERF =

{MRF

Tpr

Tav= M

TavTpr < Tav

MRF Tpr ≥ Tav

(27)

where (Ns +1)/2 is the number of code elements 6=0. ERF

is the compressed MRF due to stretching the preamble over

the averaging time Tav = 1 ms (FCC), or for greater Tav it

is MRF. The mean power limit is limited by the number of

pulses within one 1 ms (N1ms) (see Table I). The peak power

14

102

103

104

105

106

107

108

109

10−23

10−22

10−21

10−20

10−19

10−18

10−17

10−16

Effective Repetion Frequency (ERF) [Hz]

Ep

|V2(f

0)|

[J/H

z]

FCC: Avg

FCC: Peak

PL−ERF: Ns=31,L=16

PL−ERF: Ns=31,L=64

PL−ERF: Ns=127,L=4

Active Power Contstraint

Fig. 4: Pulse Power Spectral Density

limit is defined by the PRF, due to sequenced pulses within

the observation window 1/Bpk = 20 ns at the long preamble

codes. The peak power limit is obtained by

Ep,p|V (f0)|2 =

P FCCpk

9B2pk

PRF ≤ (3/2)Bpk

P FCCpk

4PRF2 PRF ≥ (3/2)Bpk

and ∃f ′ ∈ [−Bpk/2, Bpk/2]

(28)

The maximal FCC compliant pulse energy spectral density

(ESD) with respect to peak and average power are shown

in Fig. 4. To find the active ESD for a specific preamble,

the smaller value between ESDpk at PRF and ESDAv at ERF

is considered. It is observable that only the short preamble

sequences with Ns = 31 with a spreading of L = 16 and

L = 64 are peak power limited, where ERF = 0.256 MHz

(see also Table I). As PRF is constant for these values the

markers are set at ERF of the peak power limit.

Assuming a pulse with rectangular spectrum, the energy per

pulse Ep=2BEp|V (f0)|2, where B is the pulse bandwidth.

Thus, the achieveable preamble energy can be calculated as

shown in Fig. 5. The long preamble codes with Ns = 127are always restricted by the average power limit, thus in-

creasing Npr up to 1024 does not lead to a preamble energy

improvement due to Tpr ≤ 1 ms. Npr = 4096 leads to an

improvement, due to Tpr > 4 ms, which means the preamble

is more than 4 times longer than Tav. At Npr = 16, the long

preamble sequences lead to an advantage of approximately

5 dB in comparison to the short sequences. The short preamble

codes with spreading 64 imply a 4 times longer preamble in

contrast to the others, thus a gain of 6 dB can be achieved.

VI. LINK BUDGET

As mentioned before, ELOS/N0(1) is the input SNR of the

receiver at 1 m, which depends on the link budget. Table II

101

102

103

104

−50

−48

−46

−44

−42

−40

−38

−36

−34

−32

Npr

Pre

am

ble

Energ

y [dB

mW

s]

N

s=31,L=16

Ns=31,L=64

Ns=127,L=4

Tpr

≤ 1ms

Tpr

>1ms

Fig. 5: Achievable preamble energies. The dotted line shows

the boundary for the mean power limit, which limits preambles

with a length ≤ 1 ms.

TABLE II: Link BudgetParameter Values

Pulse Ep (incl. GTX ) −116.38 dBWsPreamble Epr −74.31 dBWs

Free space loss @ 1 meter −45.5 dBReceiver antenna gain GRX 0 dBi

Received LOS component energyELOS −119.81 dBWs

Noise Spectral Density N0 −198, 93 dBW/HzImplementation Loss 4 dB

Fading Margin 3 dB

ELOS/N0(1) 72.12 dB

shows an example link budget calculation for 802.15.4a chan-

nel 3 using Npr = 1024, Ns = 31, L = 16, fc = 4.4928 GHz,

and a bandwidth of 499.2 MHz. In that case the average power

limit of the FCC regulations applies and Ep is calculated from

(26), where also the antenna gain is included. Ep is limited for

1006 sequences due to averaging over 1 ms (see Table I). The

preamble energy Epr = EpM1, the free space loss L at 1 m is

given by 45.5 dB using Friis’ equation [10] and the receiver

antenna gain GRX is defined by 0 dBi. These values yield

the received preamble energy without multipath components,

meaning the energy of the line of sight component ELOS.

Assuming the input structure of the receiver is linear, the

noise spectral density is given by N0 = kT0F [10], where the

Boltzmann constant k = 1.38 10−23 Joule/Kelvin [J/K], the

temperature of the environment T0 = 293 K, and the noise

figure of the receiver input structure F = 5 dB (cf. [13]).

Implementation losses of 4 dB1 and a LOS fading margin of

3 dB are assumed. Thus, ELOS/N0(1) is achieved and can be

used to calculate the maximal operating range according to

(20) and (22).

1This value was provided by DecaWave (www.decawave.com)

15

65 70 75 80 85 90 95 100

102

103

104

ELOS

/N0(d

0) [dB]

Max. O

pera

ting D

ista

nce [m

]

ED: N

s=31, L=16

ED: Ns=31, L=64

ED: Ns=127, L=4

CR: Ns=31, L=16

CR: Ns=31, L=64

CR: Ns=127 L=4

65 70 75 80 85 90 95 100

45

50

55

60

65

70

75

80

85

90

Max. A

llow

ed P

ath

loss [dB

]

Fig. 6: Code sequence analysis on the maximal operating

distance and the maximal allowed pathloss. Fig. 5illustrates the mapping of Npr to the different energy levels.

VII. RESULTS

The maximal operating distance and the maximal acceptable

pathloss are analyzed in this section. The maximal operating

distance is based on the free space link budget, because

only the LOS component is analyzed in this paper. The

maximal acceptable pathloss is shown as a more general

value, which allows the implementer to analyze the effect

of specific channel models, e.g. NLOS scenarios, or specific

system parameters, e.g. lower noise figures.

A. Effect on Codes

Fig. 6 shows the maximal operating distance dmax and

the maximal allowed pathloss PLmax with respect to the

preamble sequences. As expected from Section V the best

performance is achieved by the short preamble with long

spreading (L = 64) due to the highest transmitted energy,

where a maximal operating distance of approximately 430 m

(PLmax≈60 dB) is achieved for the energy detector. The

performance of the short preamble sequences with L = 16 is

up to 220 m (PLmax≈53 dB). As observable, the increasing

of Npr does not necessarily lead to a better performance

because of the non-coherent combining loss. Thus, a per-

formance degradation is seen at around Elos/N0(d0)≈79 dB

for increasing numbers of transmitted pulses due to constant

transmitted energy. This effect also harms the performance

of the long preamble codes significantly and leads to the

lowest achieveable performance. The performance with short

preamble sequences and spreading L = 16 is best at Npr = 64and with the long preamble sequences at Npr = 16. In

contrast to the energy detector, the coherent receiver is only

dependent on ELOS/N0, thus only the allowed transmit energy

per preamble limits the performance. It achieves for the

short preamble code with L = 64 the maximal distance of

≈6000 m (PLmax≈82 dB), where the other two codes achieve

approx. the half maximal operating distance with ≈3000 m

(PLmax≈76 dB).

0 5 10 15 20 25 30 35 40−10

−5

0

5

10

15

20

25

30

ELOS

/N0 [dB]

LS

NR

[dB

]

Ch 3: fc ≈ 4.5, B ≈ 0.5

Ch 4: fc ≈ 4, B ≈ 1.33

Ch 7: fc ≈ 6.5, B ≈ 1.1

Ch 9: fc ≈ 8, B ≈ 0.5

Ch11: fc ≈ 8, B ≈ 1.33

Ch15: fc ≈ 9.5, B ≈ 1.35

CR all channels

Working Point ED

Working Point CR

Fig. 7: Relation between input SNR ELOS/N0 and output SNR

LSNR for the short preamble codes with a spreading L = 64and Npr = 16 with respect to the IEEE 802.15.4a channels.

Note, the channel parameters in the legend are in GHz

The IEEE 802.15.4a standard defines also different channels

with specific bandwidths and carrier frequencies, which also

influences the achieveable operating range. Thus, an analysis

for the specific channels is given in the next section.

B. Effect on Channels

The IEEE 802.15.4a standard defines 16 channels in three

frequency bands, namely the Sub-Giga-Hertz (<1 GHz),

the Low-Band (3.2 − 4.8 GHz) and the High-Band (5.9 −10.3 GHz). The channel bandwidths B range from 499.2 to

1354.97 MHz. As mentioned in Section V, keep in mind that

the EC allows only the usage of the frequency bands 3.1−4.8and 6 − 8.5 GHz for UWB, where for LDC the signals have

to be shorter than 5 ms. Thus, the short preamble symbol with

spreading L = 64 and Npr = 4096 is not allowed for LDC

transmission. As it is well-known, that the carrier frequency fc

shows an influence on the received signal strength according

to Friis’ equation and a larger bandwidth leads to a higher

allowed transmit power (see Section V). Thus, 6 channels

are analyzed in this paper with their effect on the maximal

received signal strength. The short preamble codes with a

spreading of L = 64 are used for this analysis.

Fig. 7 shows the relation between input and output SNR for

the specific channels, where the variations occur due to the

different pulse and low-pass filter bandwidths. It is observable

that the channels with the large bandwidths need up to 1.5 dB

more Ep/N0 in the working point to achieve the same LSNR.

As seen from (18), the coherent receiver is again independent

of the channel bandwidths.

Fig. 8 shows the allowed preamble energies for the specific

channels. The large bandwidths of the preambles delivers a

gain of up to 4 dB, which is sufficient to compensate the

SNR loss of the energy detector (see Fig. 7). This is also seen

from (19), where the equivalent bandwidth WRRC influences

LSNR linearly and the additional energy improves the SNR

16

101

102

103

104

−50

−48

−46

−44

−42

−40

−38

−36

−34

−32

−30

Npr

Pre

am

ble

En

erg

y [

dB

mW

s]

Ch 3: f

c ≈ 4.5, B ≈ 0.5

Ch 4: fc ≈ 4, B ≈ 1.33

Ch 7: fc ≈ 6.5, B ≈ 1.1

Ch 9: fc ≈ 8, B ≈ 0.5

Ch11: fc ≈ 8, B ≈ 1.33

Ch15: fc ≈ 9.5, B ≈ 1.35

Fig. 8: Allowed preamble energy for the specific

IEEE802.15.4a channels.

quadratically in the working point. Thus, a gain of up to 2.5 dB

can be achieved. For the coherent receiver the additional

energy will directly improve the performance.

Fig. 9 shows the maximal operating distance and the

maximal allowed pathloss for the specific channels. The best

performance is achieved by Channel 4, which shows a low

carrier frequency fc ≈ 4 GHz and a large bandwidth of

B ≈ 1.33 GHz. It reaches a dmax ≈ 10620 m (PLmax ≈ 88 dB)

for the coherent receiver and dmax ≈ 620 m for the energy

detector (PLmax ≈ 63 dB). The mandatory Ch 3 of the low

band shows a significantly better performance in comparison

to the mandatory channel in the high band Ch 9 due to much

lower fc. It can be seen that a shift in the carrier frequency

leads to a change of ELOS/N0 but it does not change the

relation of input and output SNR. A shift of the bandwidth

changes the relation between them for the energy detector

(change of ND), which is observable for Ch 9 and Ch 11.

Even the higher bandwidth of the high frequency channels are

not able to compensate the higher free space losses. Again

the characteristic of the coherent receiver only depends on

ELOS/N0.

VIII. CONCLUSIONS

A coherent matched filter and an energy detector are studied

in detail for ranging in IEEE 802.15.4a, in the sense of

allowed transmission energy and maximal operating distance.

The FCC/EC regulations are studied with the 802.15.4a-

defined preamble sequences and frequency channels. The

effects of the pulse repetition frequency and the bandwidth

are analyzed. The maximal operating distance of the energy

detector strongly depends on the system parameters, where the

coherent receiver is independent. The energy detector suffers

from non-coherent combining losses and achieves maximal

operating distances of several hundred meters, while the co-

herent receiver can achieve maximal distances up to several

thousand meters in free space. Furthermore, the maximal

allowed pathloss is shown as performance metric in a more

general sense. It is shown that the preamble sequences with

a length of 127 do not lead to a better performance. The

preamble sequences with a spreading factor of 64 lead to the

best performance due to additional allowed transmit energy.

This leads to a trade off between complexity and performance

in the sense of the used preamble length and further receiver

complexity. The performance of the channels from the low

frequency band show better performance due to the lower

pathloss, which is also not compensateable by the expanded

channel bandwidths in the high band.

ACKNOWLEDGMENT

The authors would like to warmly thank G. Kubin, TU Graz,

and M. Pistauer, CISC Semiconductor GmbH, for their support

in the project. The project was funded by the Federal Ministry

for Transport, Innovation and Technology (BMVIT) and the

Austrian Research Promotion Agency (FFG).

REFERENCES

[1] IEEE Working Group 802.15.4a, Wireless Medium Access Control(MAC) and Physical Layer (PHY) Specifications for Low-Rate Wireless

Personal Area Networks (WPANs), tech. rep. IEEE 2007[2] Y.S. Kwok, F. Chin, and X. Peng; Ranging Mechanism, Preamble Gener-ation, and Performance with IEEE802.15.4a Low-Rate Low-Power UWB

Systems, Ultra-Wideband, ICU2006, IEEE Int. Conf. on, Pages:525-530[3] M. Weisenhorn and W. Hirt; Robust Noncoherent Receiver ExploitingUWB Channel Properties, Ultra Wideband Systems, 2004. Joint withConference on Ultrawideband Systems and Technologies. Joint UWBST& IWUWBS. 2004 International Workshop on Page(s): 156-160

[4] K. Witrisal, G. Leus, G.J.M. Janssen, M. Pausini, F. Troesch, T.Zasowski, and J. Romme Noncoherent ultra-wideband systems, IEEESignal Processing Mag., July 2009

[5] I. Guvenc and Z. Sahinoglu, Threshold-based TOA estimation forimpulse radio UWB systems, Ultra-Wideband, ICU2005, IEEE Inter-national Conference on, Pages: 420-425

[6] T. Gigl, J. Preishuber-Pfluegl, and K. Witrisal, Statistical Analysis of aUWB Energy Detector for Ranging in IEEE 802.15.4a, Ultra-Wideband,ICU2009, IEEE International Conference on, In press

[7] FCC, Revision of part 15 of the commission’s rules regarding ultra-wideband transmission systems, First Report and Order, ET-Docket 98-153, FCC 02-28, adoped/released Feb.23, 2004/Apr. 22, 2002

[8] European Commission; Commission Decision of 21 April 2009: Onallowing the use of the radio spectrum for equipment using UWB

technology, Official Journal of the European Union L 105/9, 2009[9] F. Troesch, Novel Low Duty Cycle Schemes From Ultra Wide Band toUltra Low Power, PhD-Thesis, ETH Zurich

[10] L.W. Couch, Digital and Analog Communication Systems, SeventhEdition, Pearson Prentice Hall, 2007

[11] T. Gigl, J. Preishuber-Pfluegl, D. Arntiz, K. Witrisal ExperimentalCharacterization of Ranging in IEEE 802.15.4a using a Coherent

Reference Receiver, in IEEE Intern. Symp. on Personal, Indoor, andMobile Radio Communications, PIMRC, Tokyo, Japan, September 2009.

[12] I. Guvenc, Z. Sahinoglu, P.V.Orlik, TOA Estimation for IR-UWB SystemsWith Different Transceiver Types, IEEE Transactions on MircrowaveTheory and Techniques, Vol.54, No.4, 2006

[13] G. Fischer, O. Klymenko, D. Martynenko, Time-of-Arrival Measure-ment Extension to a Non-Coherent Impulse Radio UWB Transceiver,Workshop on Positioning, Navigation and Communication 2008, WPNC2008.

17

65 70 75 80 85 90 95 100

102

103

104

ELOS

/N0(d

0) [dB]

Ma

x.

Ope

rating

Dis

tan

ce

[m

]

ED: Ch 3: f

c ≈ 4.5, B ≈ 0.5

CR: Ch 3: fc ≈ 4.5, B ≈ 0.5

ED: Ch 4: fc ≈ 4, B ≈ 1.33

CR: Ch 4: fc ≈ 4, B ≈ 1.33

ED: Ch 7: fc ≈ 6.5, B ≈ 1.1

CR: Ch 7: fc ≈ 6.5, B ≈ 1.1

ED: Ch 9: fc ≈ 8, B ≈ 0.5

CR: Ch 9: fc ≈ 8, B ≈ 0.5

ED: Ch11: fc ≈ 8, B ≈ 1.33

CR: Ch11: fc ≈ 8, B ≈ 1.33

ED: Ch15: fc ≈ 9.5, B ≈ 1.35

CR: Ch15: fc ≈ 9.5, B ≈ 1.35

65 70 75 80 85 90 95 100

45

50

55

60

65

70

75

80

85

90

Ma

x.

Allo

we

d P

ath

loss [d

B]

Fig. 9: Maximal operating distance and maximal allowed pathloss for the specific IEEE 802.15.4a channels. The dashed lines

show the characteristic for a channel with B = 499.2 MHz with the ND of Fig. 6.

18