estimation and tracking of lte signals time of arrival in

Estimation and Tracking of LTE Signals Time ofArrival in a Mobile Multipath Environment

Marco Driusso, Fulvio BabichUniversity of Trieste, [email protected]

[email protected]

Fabian Knutti, Mischa SabathyHochschule fur Technik Rapperswil, Switzerland

[email protected]@hsr.ch

Chris Marshallu-blox UK Ltd, United Kingdom

[email protected]

Abstract—This paper proposes an algorithm for the estimationand tracking of the direct path (DP) time of arrival (TOA) ofthe signals received from 4G long term evolution (LTE) cellularbase stations (BSs) in a mobile multipath environment. This isimportant for TOA-based ranging measurements, which may beexploited for positioning applications. A sub-space approach isused for the estimation of the multipath time of arrival, anda state-space approach is exploited for tracking the direct path.The developed framework is applied to real LTE signals collectedusing a portable experimental setup during a car drive in thetown of Rapperswil, Switzerland. The pseudoranges derived fromthe tracking of the DP TOA are then compared to the rangesfrom the considered LTE base stations calculated using GPS,demonstrating the effectiveness of the proposed approach.

Index Terms—Time of arrival estimation, Direct path tracking,LTE, ESPRIT, Kalman filter, SDR.

I. INTRODUCTION

Recently, the downlink signals of cellular mobile systemshave been considered as an alternative to the poor performanceof global navigation satellite systems (GNSSs) in challengingpropagation environments [1]. Areas characterized by limitedsky view and distortion caused by multipath, such as urbancanyons and indoors, where it is difficult for clean GNSSsignals to be received, are usually well covered by the cellularsystems, which therefore may be exploited for ranging. Fromthis point of view, the third generation partnership projectlong term evolution (3GPP LTE) standard is a communicationsystem of particular interest because of its availability, signalstrength, signal bandwidth [2], and because it is based onorthogonal frequency division multiplexing (OFDM) [3]. Al-though the LTE signal power is generally sufficient in the chal-lenging areas described above, multipath still dominates thepropagation environment. Therefore, specific signal processingtechniques are needed to perform time of arrival (TOA) basedrange measurements that do not suffer bias due to multipathand non-line-of-sight (NLOS) propagation. Moreover, trackingof the estimated direct path (DP) TOA is needed, since theenvironment as well as the receiver position vary with time.Accordingly, the recent literature presents several works onthese subjects. The authors of [4] propose a cross-correlationbased TOA estimator with NLOS mitigation together witha particle filter for performing indoor positioning with LTEsignals generated ad-hoc using prototyping hardware. In [5],super-resolution algorithms and frequency diversity techniques

are employed for indoor static ranging measurements usingwideband sounding signals. State-space approach algorithmsspecifically designed for channel sounding may also be em-ployed, such as [6]–[8], but they require specific and too com-plex hardware for real time consumer product implementation.

This paper proposes an estimation and tracking algorithmfor the DP TOA of LTE signals in multipath mobile channels.Similarly to [9], the TOA estimation is performed using theestimation of signal parameters via rotational invariance tech-niques (ESPRIT) exploiting opportunistically the LTE OFDMpilot tones. A state-space approach similar to [7] is thenadopted for tracking, and a novel measurement noise covari-ance estimation is performed, using the ESPRIT performancebound of [10]. To explore and validate the developed algo-rithm, real LTE data gathered with the portable setup of [11]during a car drive on a route around the town of Rapperswil(Switzerland) is processed with the proposed framework. Theresults obtained are then compared with ranges from theconsidered LTE base stations (BSs) calculated using GPS, toassess the effectiveness of the suggested approach.

The remainder of the paper is organized as follows. SectionII describes the exploited LTE downlink signals. Section IIIdescribes the portable experimental setup used for collectingthe data. Section IV explains the proposed algorithm. SectionV reviews the obtained estimation and tracking results andSection VI summarizes the most relevant conclusions.

II. EXPLOITED LTE SIGNALS

LTE offers two downlink signals that are indicated for rangemeasurements, i.e., the positioning reference signal (PRS) andthe cell-specific reference signal (CRS). The PRS is specif-ically designed for the acquisition of multiple simultaneousrange measurements and is transmitted in dedicated timeintervals [12]. However, operators generally tend to avoidits transmission in order to save bandwidth for user data.On the other hand, although the CRS is primarily designedfor channel estimation and coherent data demodulation, itmay be opportunistically exploited for range measurements,particularly because it is always transmitted [11]. Hence, thiswork considers the CRS as the reference signal for TOAestimation and pseudorange evaluation.

The LTE downlink physical layer is organized in 10 mslong radio frames. Each radio frame corresponds to 10 sub-

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Signal Processing Theory and Methods

Table ILIST OF POSSIBLE DOWNLINK BANDWIDTH CONFIGURATIONS

B 1.4MHz 3MHz 5MHz 10MHz 15MHz 20MHzNDL

RB 6 15 25 50 75 100Nsc 72 180 300 600 900 1200Ntot 12 30 50 100 150 200

frames, each made of 2 slots (20 slots per frame, 0.5 mseach). Each slot is composed of NDL

symb OFDM symbols inthe time domain. In the frequency domain (FD), each OFDMsymbol corresponds to Nsc =NRB

sc NDLRB sub-carriers, spaced of

∆f = 15 kHz when the normal cyclic prefix configuration isadopted (for which NDL

symb = 7 and NRBsc = 12). The basic

resource unit of LTE, corresponding to the kth sub-carrier ofa certain OFDM symbol in a slot, is referred to as resourceelement (RE). REs are grouped in resource blocks (RBs), eachcorresponding to NRB

sc adjacent sub-carriers in the FD, for theduration of one slot. The number of total sub-carriers used ineach OFDM symbol (and ultimately the LTE signal bandwidthB) is determined by the number NDL

RB of RBs per slot. Thereare 6 possible configurations, which are summarized in TableI. Finally, LTE is capable of transmitting signals from differentantennas, which are identified with the concept of antenna portby using the index p [12].

The CRS is defined as a QPSK modulated length-31 Goldsequence, mapped to the REs with the diamond pattern definedin [12, p.78]. When a configuration with 2 antenna portsis adopted, a CRS transmission occurs twice per slot: eachtime, a different CRS is transmitted from each antenna porton the same OFDM symbol in non-overlapping sub-carriers.Since the CRS pilot tones occupies one sub-carrier everysix through all the available bandwidth (with a spacing of∆fCRS = 6∆f = 90 kHz), the total number of transmittedpilot tones is Ntot = Nsc/6 per antenna port. As specifiedin [12, p.77], the mapping to REs of CRSs transmitted fromdifferent BS sectors (identified with N cell

ID ∈ {0, . . . , 503})differs by a FD shift of k0 =mod(N cell

ID , 6).

III. EXPERIMENTAL SETUP FOR MEASUREMENTS

A live data set has been recorded which was then processedwith the methods described herein. The live data gatheringsetup consisted of two universal radio peripheral (USRP) N210software defined radios (SDR), which used the high precision10 MHz reference clock of a GPS-locked Rubidium frequencystandard. Two USRP N210 SDRs were required since twoLTE operators were available on different frequency downlinkchannels. A conventional personal computer (PC) acted as sys-tem controller and data recording unit. The PC recorded GPStime and position stamped live data and guaranteed coherentsampling between the two USRP N210 devices. The coherentand absolute GPS timed sampling provided the possibility tocompare the different LTE signals of the two LTE operators. Toreduce the large amount of sampling data (25 MSPS for eachUSRP N210), a block-wise storage method was implemented,storing 10 ms of consecutive samples every second. For the

Patch Antenna- Built-in LNA

Wide Band Antenna- Magnetic Mount- Gain: 3dBi peak

u-blox EVK-6N- GPS/GNSS Evaluation Kit

SRS FS725- Rubidium Frequency Standard

- Accuracy: ±5× 10−11

USRP N210- Daughterboard: WBX 50-2200MHz RX/TX

- Sampling Rate: 25MSPS

USRP N210- Daughterboard: WBX 50-2200MHz RX/TX

- Sampling Rate: 25MSPS

PC- Data Recording Software

1PPS

UBX & NMEAmessages

1PPS

10MHz Ref

Ethernet1Gbps

Ethernet1Gbps

Figure 1. Live data gathering setup, which is all powered by a 12V/85Ahbattery with a DC to AC converter.

705 706231

232

1

2

3

4

5

6

1

2

3

X-coordinate CH1903 (Grid 1km)

Y-coordinateCH19

03(G

rid1k

m)

GPS Track

Operator 1

Operator 2

Figure 2. Live data gathering route and considered LTE BSs.

post-processing, the data was down-sampled from 25 MSPSto 15.36 MSPS. Fig. 1 shows a detailed overview of the livedata gathering setup, which for this experiment was installedin a van. The data was gathered in the area of RapperswilSG, Switzerland. The chosen route led through urban, sub-urban and open-field areas as the GPS track of route in Fig. 2shows. These different sections are well suited for gainingknowledge about the performance of the DP TOA trackingmethod in various common scenarios. This route resulted in a20 minute drive at speeds between 0 and 50 km/h. The entirecaptured data was then searched for signals from availableBSs by means of an exhaustive search against a list ofthe cell identities of all the BSs visible in the Rapperswiltest area. After obtaining the coarse symbol timing of allavailable BSs, the 10 ms chunks where a BS was receivedwith sufficient quality were marked for each BS. One OFDMsymbol containing the CRS, without cyclic prefix, was thensaved from every block of raw data for every available BS forfurther processing. The recorded data contained signals from atotal of 9 BSs, 6 BSs from operator 1 and 3 BSs from operator


277Signal Processing


2, using a downlink transmission bandwidth of 15 MHz and10 MHz, respectively. Figure 2 shows the location of the BSs[11] except for one distant BS which is located across the lakein south-southeasterly direction and one BS located on a hillto the north. All BSs were found to be using a configurationwith 2 antenna ports.

IV. PROPOSED ALGORITHM

The sampled data was processed according to the algorithmdescribed in the following sections, which for conveniencewill be referred to as EKAT, i.e., ESPRIT and Kalman filterfor time of Arrival Tracking. Let rit[n], n = 0, . . . , Nfft−1,be the samples of the OFDM symbol containing the CRScoming from the ith detected cell ID, and collected at thediscrete time index t. An Nfft-point DFT is used to evaluatethe content of the sub-carriers of rit[n] as Rit[k]=DFT{rit[n]}.The knowledge of the particular symbol and slot indexes towhich rit[n] pertains, acquired during the coarse timing phasedescribed above, is used to identify the actual CRS pilot tonesSi,pt [k], k ∈ Ci,pt , contained in rit[n] for each antenna port p.The set Ci,pt ={k0+k∆fCRS, k=0, · · · , Ntot−1} is constitutedby the Ntot indexes of the sub-carriers occupied by a CRS tonefor the considered OFDM symbol and antenna port. Usingthis information, a noisy sampling of the channel frequencyresponse (CFR) encountered by the considered CRS duringits propagation can be easily obtained using the least squaresestimator as Hi,p

t [k] = Rit[k0 + k∆fCRS]/Si,pt [k0 + k∆fCRS],k = 0, · · · , Ntot−1, where the noise variance is assumed tobe σ2. Since the CRS tones are equally spaced, Hi,p

t [k] is auniform sampling of the CFR, with spacing ∆fCRS.

A. Multipath TOA estimation

As explained in [5], super resolution algorithms (SRAs)can be employed for the estimation of the TOA τ0, . . . , τL−1

of a multipath channel h(t) =∑L−1l=0 hlδ(τ − τl), by using

a uniform sampling of the corresponding CFR H(f) =∑L−1l=0 hle

−j2πτlf . In this case, starting from the noisy CFRsampling Hi,p

t [k], a SRA is used to estimate the multipathTOA of the propagation channel encountered by the con-sidered CRS. Out of the available SRAs, an ESPRIT-basedapproach similar to [9] was chosen, as it allows a smallercomputational complexity compared to other SRAs [13].

EKAT starts by arranging the samples Hi,pt [k] in M -length

overlapping snapshots xi,pt [m], that constitute the data matrixXi,pt as:

Xi,pt = 1√

N

[xi,pt [0], · · · ,xi,pt [N − 1]

]∈ CM×N , (1)

xi,pt [m] =[Hi,pt [m], · · · , Hi,p

t [m+M − 1]]T ∈ CM , (2)

where N = Ntot−M + 1, M is a design parameter of theSRA, and (·)T denotes the transpose operator. In the following,the indexes t, i, p will be omitted for notational simplicity.The data matrix X is related to the estimate of the cross-correlation matrix of x as Rx =X·XH∈CM×M , where (·)H

is the Hermitian transpose operator. Hence, the eigenvaluesλ1 ≥ · · · ≥ λM of Rx can be calculated taking the square

of the singular values of X, obtained with a singular valuedecomposition (SVD) as X = U ·Σ ·VH. The matrices U ∈CM×M and V ∈ CN×N are unitary, and Σ ∈ CM×N is adiagonal matrix with the singular values σ1 ≥ · · · ≥ σM in themain diagonal, where (σj)

2 = λj . Using the eigenvalues λj ofRx, the minimum descriptive length criterion can be appliedfor the estimation of the number L of multipath componentsin the considered CFR, by using the metric [5], [9]:

MDL(k)=−N(M−k) log

{∏M−1i=k λ

1/(M−k)i

1M−k

∑M−1i=k λi

}+ p(k), (3)

where p(k) = 12k(2M−k) logN . Then, L is estimated as L=

arg mink∈{0,...,M−1}MDL(k). Once the number of multipathcomponents has been estimated, the actual ESPRIT algorithmis applied. This consists in selecting the first L singular vectorsof X, which are equal to the L eigenvectors of Rx correspond-ing to the L biggest eigenvalues. These are stored in the matrixUs=U·[IL0L×(M−L)]

T∈CM×L, where IP is the P ×P eyematrix and 0P×Q is a P × Q all-zero matrix. Afterwards,Us is decomposed in Us,1 = [IM−10M−1] ·Us ∈ CM−1×L

and Us,2 = [0M−1IM−1] ·Us ∈CM−1×L, where 0P is a P -length all-zero column vector. The ESPRIT rotational matrixis evaluated as Ψ = (UH

s,1·Us,1)−1·UHs,1·Us,2 ∈ CL×L, where

(·)−1 denotes the inverse of a matrix. The multipath TOA arefinally calculated using the L eigenvalues {ψl}L−1

l=0 of Ψ as:

τl = − 12π∆fCRS

arg {ψl} , l = 0, · · · , L− 1, (4)

where arg{·} denotes the argument of a complex number.Since arg{ψl}∈ [−π, π], ∀l, then the adopted SRA is capableof estimating a TOA in the interval [− 1

2∆fCRS, 1

2∆fCRS] =

[−5.55µs, 5.55µs] around the instant of measure t.By using the described procedure, a set of Li,p(t) multipath

TOA Υi,p(t) = {τ i,pl (t), l = 0, · · · , Li,p(t) − 1}, can beestimated for the CRS coming from the antenna port p of theith sector in the measurement sample at time t. The estimationof the multipath TOA is necessary for separating the delayedpaths from the DP, which is then tracked for positioningpurposes with the procedure described in the following.

B. State-space model

A state-space approach similar to the one of [7] is used inEKAT for the tracking of the DP TOA. Consider a specific BSsector identified by the index i. The real DP TOA τ i0(t) of theCRS coming from i at time t, and its rate of change ∆τ i0(t),are modeled as the unknown state of a dynamic discrete-timelinear system, which is estimated using a Kalman filter (KF)on the basis of the TOA measurements acquired as describedin Section IV-A. Hence, the state-space vector of such systemis defined as ζi(t) = [τ i0(t),∆τ i0(t)]T ∈ R2 (in the followingthe superscript i will be omitted). Then, a novel aspect ofthe proposed approach is to combine the measurements of thetwo antenna ports by defining the entries of the measurementvector zE(t) = [z0

E(t), z1E(t)]T ∈R2 as the two measurements

of the DP TOA acquired with ESPRIT at time t from antennaports p = 0 and p = 1, respectively. This is justified by the




fact that usually when only 2 antenna ports are present, thesediffer only in the polarization, and not in the antenna position,resulting in the same distance (and hence the same DP TOA)at the receiver. The discrete-time equations that model theevolution of ζ(t) are then:

ζ(t) = F·ζ(t− 1) + q(t− 1), (5)zE(t) = H·ζ(t) + r(t), (6)

where:F =

[1 10 1

]and H =

[1 01 0

]. (7)

In (5)-(6), the process noise vector q(t) ∈ R2 and themeasurement noise vector r(t) ∈ R2 have zero-mean whiteGaussian distributed entries with covariance matrices givenby Q(t)=E[q(t)qT(t)] and R(t)=E[r(t)rT(t)], respectively.According to [6], the process noise covariance is equal to:

Q(t) = Q = q

[13

12

12 1

], ∀t, (8)

where q may be set empirically during the KF tuning. Finally,EKAT relies on a time variant measurement noise covariancematrix R(t), which is selected at every t as will be explainedin Section IV-D.

C. Kalman filtering for tracking

The Kalman filtering for the estimation of the state ζ(t)pertaining to the ith BS sector follows the approach of [14]and consists of the following set of recursive equations:

ζ−(t) = F·ζ(t−1), (9)

P−(t) = F·P(t−1)·FT + Q, (10)

W(t) = P−(t)·HT ·[R(t) + H·P−(t)·HT]−1

, (11)

ζ(t) = ζ−(t) + W(t)·

[zE(t)−H·ζ−(t)

], (12)

P(t) =[I2 −W(t)·H

]·P−(t), (13)

where ζ−(t), P−(t), ζ(t), P(t) and W(t) correspond to the

predicted state, the predicted state covariance, the estimatedstate, the estimated state covariance, and the KF gain, respec-tively. The calculation of the first estimated state ζ(t0) and thecorresponding covariance P(t0) is performed according to thetwo step initialization procedure of [14, p.247], by exploitingthe measurements zE(t0), zE(t0−1). During initialization, theentries zpE(t), p∈{0, 1} of the measurement vector zE(t) areselected from the results Υi,p(t) of the ESPRIT multipath TOAestimation as zpE(t)= τ i,p0 (t), t∈{t0−1, t0}. Conversely, afterinitialization (i.e., for t > t0), zpE(t) is selected from Υi,p(t)according to the following strategy:

zpE(t) =

min{Ξi,p(t)} n[Ξi,p(t)] > 0

τ i,p0 (t) n[Ξi,p(t)] = 0, Li,p(t) > 0

zpE(t− 1) Li,p(t) = 0

[1 0]·ζ−(t) sparse missing measure

, (14)

where: Ξi,p(t) = {τ ∈Υi,p(t) : cT |τ− ζ0(t − 1)| < vmax}; n[·]

denotes the cardinality of a set; c is the speed of light; T is the

interval between two measurements (T = 1 s in the proposedsetup); vmax is a design parameter representing the maximumallowed speed for the receiver; and ζ0(t) is the first componentof the estimated state ζ(t) = [ζ0(t), ζ1(t)]T, representing thetracked DP TOA at time t.

The measurement selection strategy of (14) is needed fordealing with the following three problems. Firstly, the ESPRITmultipath TOA estimation may produce outliers with TOAmuch earlier than the real DP TOA, and these are discardedaccording to a maximum allowed receiver speed vmax, bycomparing the estimated TOA in Υi,p(t) with the previousDP TOA estimation ζ0(t− 1). Secondly, it may happen that,in a particular measurement, despite a particular cell ID beingdetected, the MDL criterion fails to find multipath componentsin the considered signal, producing Li,p(t) = 0. In this case,the value of the previous measurement is used. Thirdly, theCRS from a particular cell may not be detected continuouslythrough the measurement period. It may in practice happenthat at a certain t the receiver suffers of a deep fade orshadowing, resulting in a sparse missing measure, which issubstituted with the measurement prediction H · ζ−(t). On theother hand, when the CRS is not received for more than Dmaxconsecutive measurements (e.g., when the BS is too far forbeing detected), the tracking is stopped and the KF restartedat the next available measurement.

D. Measurement noise covariance estimationThe analysis of [10] evaluated the error variance of the

ESPRIT algorithm when used to estimate the directions ofarrival of narrowband waveforms on a linear uniform array.Using a similar approach, the variance of the estimation errorεl relative to the lth estimated TOA has been quantified in thepresented framework. However, the procedure of [10] is basedon the knowledge of the real number of multipath componentsL and on the SVD of the exact data matrix X, which is builtin the same way as (1)-(2), except that the real values ofthe channel samples H[k] are used instead of the LS noisyestimations H[k]. Clearly, this is not feasible in real scenarios,since these quantities are unknown. Hence, EKAT relies on theuse of the noisy data matrix X and of the estimated value L.Monte Carlo simulations, not reported for lack of space, wereperformed to assess the effectiveness of this approach, and theyshowed a substantial agreement between the values of Var(εl)calculated using X and the ones obtained using X, providedthat the noise variance σ2 determines a signal-to-noise ratiocorresponding to an above-threshold estimation.

To estimate the measurement noise variance, consider, inaddition to the matrices defined in Section IV-A, the ma-trices Uo = U · [0(M−L)×LIM−L]T ∈ CM×(M−L), Uo,1 =[IM−10M−1] ·Uo and Uo,2 = [0M−1IM−1] ·Uo, whereUo,1,Uo,2∈C(M−1)×(M−L). Then, the error variance relativeto the estimation of τl can be approximated by:

Var (εl)' C2σ2

2

∥∥vlU†s,1(Uo,2 − ψlUo,1

)∥∥2∥∥Σ−1

Lul∥∥2, (15)

where: C2 = 1/(2π∆fCRS)2; σ2 is an estimate of the varianceof the noise affecting the CFR samples H[k]; ‖ · ‖ denotes the




Table IICONSIDERED SECTORS AND RANGING PERFORMANCE COMPARISON

Op. BS N cellID i ε I [m] ε I

0.5 [m] ε I0.95 [m] ε E [m] εE

0.5 [m] εE0.95 [m]

1

1 84 1 30.02 12.54 56.61 20.98 11.18 48.9686 2 106.67 9.97 73.19 17.47 9.87 35.54

2183 3 94.22 18.03 156.60 76.84 9.09 40.47184 4 132.14 17.35 110.17 17.59 8.71 44.40185 5 112.78 14.14 127.09 16.91 7.19 23.60

372 6 180.26 28.20 249.57 34.89 15.54 36.5573 7 336.10 15.74 1038.79 123.19 9.86 181.6174 8 209.93 27.18 230.83 114.25 17.72 58.32

5 36 9 149.24 20.15 123.30 22.65 15.33 48.5938 10 48.71 8.07 127.29 9.22 5.82 15.94

21

51 11 78.18 27.20 131.72 29.96 20.39 48.8752 12 98.31 23.32 228.41 30.29 18.90 53.1353 13 61.15 21.92 107.53 20.66 15.36 37.10

2321 14 56.95 16.44 121.72 24.42 14.58 34.00322 15 17.65 3.10 27.08 18.86 2.26 27.89323 16 100.44 28.48 270.68 35.08 14.63 79.58

norm of a vector; U†s,1 =(UHs,1·Us,1)−1·UH

s,1; ΣL∈CL×L isthe sub-matrix obtained taking the upper-left L× L block of√N ·Σ; and ul, vl, ψl are respectively the left eigenvector,

the right eigenvector and the corresponding eigenvalue of Ψ.In the proposed framework, σ2 is obtained using the approachof [15], by exploiting the M − L smaller eigenvalues of Rx:

σ2 = 1M−L

∑Mj=L+1 λj . (16)

The error variances Var(εl) are evaluated using (15) for eachmultipath TOA estimate τ i,pl (t)∈Υi,p(t) obtained at t for theCRS of sector i, antenna port p. Then, the measurement noisecovariance matrix is chosen as R(t) = diag{[R0(t), R1(t)]}∈R2×2, where the value of Rp(t), p ∈ {0, 1}, is determined inaccordance to the choice of (14), i.e.:

Rp(t)=

Var (εl′) n[Ξi,p(t)] > 0

γ0 ·Var (ε0) n[Ξi,p(t)] = 0, Li,p(t) > 0

γ1 ·Rp(t− 1) Li,p(t) = 0

γ2 ·Rp(t− 1) sparse missing measure

. (17)

In (17), l′ is the index for τl′ =min{Ξi,p(t)}, and γ1, γ2, γ0>1increase the unreliability when using a previous measurement,a predicted measurement, and a measurement implying areceiver speed higher than vmax, respectively.

V. RESULTS

The EKAT algorithm explained in Section IV was appliedto the data collected with the setup of Section III. All thedetected signals were considered, except the ones having cellID pertaining to BS 4 and 6 of operator 1, and to BS 3 ofoperator 2, since too weak or too few measurements wereavailable for these sectors. The considered cell IDs and thecorresponding indexes i are listed in Table II. For all themeasurements in which each sector i was detected, EKATwas applied, obtaining a sequence of estimated states ζ

i(t), of

which the first component ζi0(t) identifies the tracked DP TOAfor every t. Hence, ρi(t) = c· ζi0(t) represents the pseudorange

100 101 1020

0.2

0.4

0.6

0.8

1

ε [m]

P(|e

rror|<ε)

Op. 1, BS1, NcellID =86






Figure 3. Cumulative density functions of the absolute ranging error for theEKAT algorithm (thick lines) and IDFT-based estimator of [11] (thin lines).

measured from the BS of sector i at time t. The algorithm wasrun using the following parameters: Dmax = 5, M = 0.48Ntot,q=5 · 10−19, vmax =70 m/s, γ0 =γ1 =100, γ2 =10.

Since the receiver does not have the same time reference asthe transmitting LTE BSs, a bias ∆i was removed from ρi(t) inorder to obtain a proper range measure. Moreover, although thereceiver clock is locked to a frequency standard, the transmitterclock still exhibits a drift δi, which was corrected together withthe bias. The bias and drift over the period of the experimentwere estimated using the same approach of [11]. Finally, theestimated range was evaluated as di(t) = ρi(t)−∆i−δit.

As a reference, the TOA estimator of [11] is taken as abenchmark. This is based on selecting the DP TOA as the timecorresponding to the highest peak of the discrete time channelimpulse response that can be obtained as IDFT{Hi,p

t [k]}. Thesame bias ∆i and drift δi corrections were applied to thepseudoranges obtained with the benchmark estimator.

Table II compares the ranging performance of EKAT (indi-cated with E) with that of the IDFT-based benchmark estimator(indicated with I). The ranging error was evaluated for allt as the difference between the tracked range di(t) and thecorresponding GPS range. The used performance figures arethe root mean square error (RMSE), denoted as ε x, x∈{E, I},and the error probability abscissa, defined as the value ε xp suchthat P (|error|< ε xp ) = p, x ∈ {E, I}. As can be seen, EKAToutperforms the benchmark for all sectors except N cell

ID =322,which however was found to point to north, meaning that aDP reception was never possible on this test route.

In Figure 3, a more detailed investigation compares theranging error cumulative density functions (CDFs) obtainedwith EKAT and with the IDFT-based algorithm for a selectedcell ID of each considered BS. Again, EKAT always obtains abetter curve compared to the corresponding benchmark result.

Finally, consider Figures 4a-4b, where the results of theDP TOA estimation and tracking algorithm are presentedfor sector i = 12 (operator 2, BS 1, N cell

ID = 52) andi = 4 (operator 1, BS 2, N cell

ID = 184), respectively, overselected illustrative time intervals. The upper plots depict theranges obtained correcting bias and drift on the pseudoranges




400

500

600

700

rangesµ12,p

l(t)[m

]

(p = 0) l = 0 l = 1 l = 2 l = 3

(p = 1) l = 0 l = 1 l = 2 l = 3

2250 2300 2350 2400 2450 2500400

500

600

700

measurement index t

tracked

range[m

]

GPS range IDFT TOA est d12(t), EKAT

(a)

0

200

400

600

rangesµ4,p

l(t)[m

]

(p = 0)(p = 1)

l = 0 l = 0

l = 1 l = 1

l = 2 l = 2

l = 3 l = 3

2060 2080 2100 2120 2140 2160 2180 2200 2220

0

200

400

600

measurement index t

trackedrange

[m]

GPS range

IDFT TOA est

d4(t), EKAT

(b)Figure 4. Results obtained applying EKAT to the collected data from (a)operator 2, BS1, N cell

ID =52, and (b) operator 1, BS2, N cellID =184.

c · τ i,pl (t), i.e. µi,pl (t) = c · τ i,pl (t)−∆i−δit. For both antennaports p ∈ {0, 1}, points corresponding to the first 4 detectedpaths are plotted, i.e., l ∈ {0, · · · , 3}. The lower plots showthe tracked range di(t) and the corresponding ranges obtainedwith the benchmark estimator. As a reference, the GPS range isalso shown. Figure 4a highlights how the benchmark algorithmis biased by multipath (measurement indexes around 2250 and2500) and, conversely, how the proposed approach is capableof reducing its detrimental effects. Figure 4b shows again theeffectiveness of EKAT against multipath effects (measurementindexes around 2100 and 2190), and its robustness againstmultipath TOA estimation outliers (which are visible in thebottom of the upper plot in Figure 4b).

VI. CONCLUSIONS

A TOA-based ranging system has been demonstrated foruse for positioning, which exploits real LTE downlink signalsfor performing distance measurements under practical mobileconditions. A portable measurement setup characterized by

high clock precision has been developed, and used to collectsamples from multiple newly-deployed LTE base stations’downlink signals, in a test scenario representative of a varietyof typical severe propagation environments.

The acquired data was processed with an appropriatelydesigned DP TOA estimation and tracking algorithm namedEKAT, which comprises an ESPRIT SRA for separatingmultipath TOA, together with a KF for tracking the DP. Ameasurement selection strategy was proposed for dealing withthe impairments of data collected in a real environment, andadditional information was incorporated by using the signalsfrom the multiple LTE transmit antenna ports. A measurementnoise covariance estimation method was employed for quan-tifying in the KF the reliability of the TOA estimates. Theresults of all the tests showed that EKAT is effective despitethe detrimental effects of multipath, achieving an improvedRMSE between 9 m and 123 m, and reaching a precisionbetween 2 m and 20 m in 50% of cases, depending on thebase station and propagation environment encountered.

REFERENCES

[1] R. Zekavat and R. M. Buehrer, Handbook of Position Location: Theory,Practice and Advances. John Wiley & Sons, Sep. 2011.

[2] C. Gentner, S. Sand, and A. Dammann, “OFDM indoor positioningbased on TDOAs: Performance analysis and experimental results,” inInt. Conf. on Localization and GNSS, Jun. 2012, pp. 1–7.

[3] M. Driusso, M. Comisso, F. Babich, and C. Marshall, “PerformanceAnalysis of Time of Arrival Estimation on OFDM Signals,” IEEE SignalProcess. Lett., vol. 22, no. 7, pp. 983–987, Jul. 2015.

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[7] T. Jost, W. Wang, U. Fiebig, and F. Perez-Fontan, “Detection and Track-ing of Mobile Propagation Channel Paths,” IEEE Trans. on AntennasPropag., vol. 60, no. 10, pp. 4875–4883, Oct. 2012.

[8] C. Gentner and T. Jost, “Indoor positioning using time difference ofarrival between multipath components,” in Int. Conf. Indoor Positioningand Indoor Navigation, Oct. 2013, pp. 1–10.

[9] B. Yang, K. Letaief, R. Cheng, and Z. Cao, “Channel estimation forOFDM transmission in multipath fading channels based on parametricchannel modeling,” IEEE Trans. Commun., vol. 49, no. 3, pp. 467–479,Mar. 2001.

[10] F. Li, R. Vaccaro, and D. Tufts, “Performance analysis of the state-spacerealization (TAM) and ESPRIT algorithms for DOA estimation,” IEEETrans. Antennas Propag., vol. 39, no. 3, pp. 418–423, Mar. 1991.

[11] F. Knutti, M. Sabathy, M. Driusso, H. Mathis, and C. Marshall, “Posi-tioning Using LTE Signals,” in Europ. Navigation Conf., Apr. 2015.

[12] 3GPP TS 36.211, Evolved Universal Terrestrial Radio Access (E-UTRA); Physical channels and modulation (Release 11), 3rd GenerationPartnership Project, V11.0.0, 2012.

[13] Y. Liu, Z. Tan, H. Hu, L. Cimini, and G. Li, “Channel Estimation forOFDM,” IEEE Commun. Surveys Tuts., vol. 16, no. 4, pp. 1891–1908,Fourth quarter 2014.

[14] Y. Bar-Shalom, X. R. Li, and T. Kirubarajan, Estimation with Appli-cations to Tracking and Navigation: Theory Algorithms and Software.John Wiley & Sons, Apr. 2001.

[15] X. Xu, Y. Jing, and X. Yu, “Subspace-based noise variance and SNRestimation for OFDM systems,” in IEEE Wireless Commun. NetworkingConf., vol. 1, Mar. 2005, pp. 23–26.




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