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Joint Device Positioning and Clock Synchronizationin 5G Ultra-Dense Networks

Mike Koivisto, Mario Costa, Janis Werner, Kari Heiska, Jukka Talvitie, Kari Leppanen, Visa Koivunen andMikko Valkama

Abstract—In this article, we address the prospects and keyenabling technologies for high-efficiency device localization andtracking in fifth generation (5G) radio access networks. Buildingon the premises of ultra-dense networks (UDNs) as well as onthe adoption of multicarrier waveforms and antenna arrays inthe access nodes (ANs), we first develop extended Kalman filter(EKF) based solutions for efficient joint estimation and trackingof the time of arrival (ToA) and direction of arrival (DoA) ofthe user nodes (UNs) using the uplink (UL) reference signals.Then, a second EKF stage is proposed in order to fuse theindividual DoA/ToA estimates from multiple ANs into a UNlocation estimate. The cascaded EKFs proposed in this articlealso take into account the unavoidable relative clock offsetsbetween UNs and ANs, such that reliable clock synchronizationof the access-link is obtained as a valuable by-product. Theproposed cascaded EKF scheme is then revised and extendedto more general and challenging scenarios where not only theUNs have clock offsets against the network time, but also theANs themselves are not mutually synchronized in time. Finally,comprehensive performance evaluations of the proposed solutionsin realistic 5G network setup, building on the METIS projectbased outdoor Madrid map model together with complete raytracing based propagation modeling, are reported. The obtainedresults clearly demonstrate that by using the developed methods,sub-meter scale positioning and tracking accuracy of movingdevices is indeed technically feasible in future 5G radio accessnetworks, despite the realistic assumptions related to clock offsetsand potentially even under unsynchronized network elements.

Keywords—5G networks, angle-of-arrival, antenna array,direction-of-arrival, extended Kalman filter, line-of-sight, localiza-tion, location-awareness, synchronization, time-of-arrival, tracking,ultra-dense networks

M. Koivisto, J. Werner, J. Talvitie and M. Valkama are with the Departmentof Electronics and Communications Engineering, Tampere University ofTechnology, FI-33101 Tampere, Finland (email: mike.koivisto@tut.fi).

M. Costa, K. Heiska, and K. Leppanen are with Huawei Technologies Oy(Finland) Co., Ltd, Helsinki 00180, Finland.

V. Koivunen is with the Department of Signal Processing and Acoustics,Aalto University, FI-02150 Espoo, Finland.

This work was supported by the Finnish Funding Agency for Technologyand Innovation (Tekes), under the projects “5G Networks andDevice Posi-tioning”, and “Future Small-Cell Networks using Reconfigurable Antennas”.

Preliminary work addressing a limited subset of initial results was presentedat IEEE Global Communications Conference (GLOBECOM), San Diego, CA,USA, December 2015 [1].

Online video material available athttp://www.tut.fi/5G/TWC16/.This work has been submitted to the IEEE for possible publication. Copy-

right may be transferred without notice, after which this version may no longerbe accessible.

I. I NTRODUCTION

5G mobile communication networks are expected to pro-vide major enhancements in terms of, e.g., peak data rates,area capacity, Internet-of-Things (IoT) support and end-to-end latency, compared to the existing radio systems [2]–[4].In addition to such enhanced communication features 5Gnetworks are also expected to enable highly-accurate deviceor UN localization, if designed properly [3], [4]. Comparedtothe existing radio localization approaches, namely enhancedobserved time difference (E-OTD) [5], [6], uplink-time dif-ference of arrival (U-TDoA) [5], observed time difference ofarrival (OTDoA) [7], which all yield positioning accuracy inthe range of few tens of meters, as well as to global positioningsystem (GPS) [8] or WiFi fingerprinting [9] based solutionsin which the accuracy is typically in the order of 3-5 metersat best, the localization accuracy of 5G networks is expectedto be in the order of 1 meter or even below [3], [4], [10].Furthermore, as shown in our preliminary work in [1], thepositioning algorithms/processing can be carried out at thenetwork side, thus implying a highly energy-efficient approachfrom the devices perspective.

Being able to estimate and track as well as predict the devicelocations in the radio network is generally highly beneficialfrom various perspectives. For one, this can enable location-aware communications [11], [12] and thus contribute to im-prove the actual core 5G network communications functional-ities as well as the radio network operation and management.Concrete examples where device location information can becapitalized include network-enabled device-to-device (D2D)communications [13], positioning of a large number of IoTsensors, content prefetching, proactive radio resource man-agement (RRM) and mobility management [12]. Furthermore,centimeter-wave based 5G radio network could also assist andrelax the device discovery problem [14] in millimeter-waveradio access systems. Continuous highly accurate network-based positioning, either 2D or even 3D, is also a centralenabling technology for self-driving cars, intelligent trafficsystems (ITSs) and collision avoidance, drones as well as otherkinds of autonomous vehicles and robots which are envisionedto be part of not only the future factories and other productionfacilities but the overall future society within the next 5-10years [15].

In this article, building on the premise of ultra-dense 5Gnetworks [2]–[4], [16], we develop enabling technical solutionsthat allow for providing the desired high-efficiency devicepositioning in 5G systems. We particularly focus on theconnected vehicles type of scenario, which is identified e.g.

2

in [4], [10] as one key application and target for future 5Gmobile communications, with a minimum of 2000 connectedvehicles per km2 and at least 50 Mbps per-car downlink(DL) rate [4]. In general, UDNs are particularly well suitedfor network-based UN positioning. As a result of the highdensity of ANs, UNs in such networks are likely to havea line-of-sight (LoS) towards multiple ANs for most of thetime even in demanding propagation environments. Such LoSconditions alone are already a very desirable property inpositioning systems [17]. Furthermore, the 5G radio networksare also expected to operate with very short radio frames,the corresponding sub-frames or transmit time intervals (TTIs)being in the order of 0.1-0.5 milliseconds, as described, e.g.,in [18], [19]. These short sub-frames generally include ULpilots that are intended for UL channel estimation and alsoutilized for DL precoder design. In addition, these UL pilotscan be then also exploited for network-centric UN positioningand tracking. More specifically, ANs that are in LoS with aUN can use the UL pilots to estimate the ToA efficiently. Dueto the very broad bandwidth waveforms envisioned in 5G, inthe order of100MHz and beyond [18], [20], the ToAs cangenerally be estimated with a very high accuracy. Since it ismoreover expected that ANs are equipped with antenna arrays,LoS-ANs can also estimate the DoA of the incoming UL pilots.Then, through the fusion of DoA and ToA estimates across oneor more ANs, highly accurate UN location estimates can beobtained, and tracked over time, as it will be demonstrated inthis article.

More specifically, the novelty and technical contributionsof this article are the following. Building on our preliminarywork in [1], we first propose a novel EKF for joint estimationand tracking of DoA and ToA. Such an EKF is the coreprocessing engine at individual ANs. Then, for efficient fusionof the DoA/ToA estimates of multiple ANs into a deviceposition estimate, a second EKF stage is proposed as depictedin Fig. 2. Compared to existing literature, such as [21]–[23],the cascaded EKFs proposed in this article also take intoaccount the unavoidable relative clock offsets among UNs andreceiving ANs, such that it actually provides reliable clockoffset estimates as a by-product. This makes the proposedapproach much more realistic, compared to earlier reportedworks, while being able to estimate the UN clock offsetshas also a high value of its own. Then, as another importantcontribution, we also develop an efficient cascaded EKF solu-tion for scenarios where not only the UNs have clock offsetsagainst the network time, but also the ANs themselves arenot mutually synchronized in time. Such an EKF-based fusionsolution provides an advanced processing engine inside thenetwork where the UN positions, clock offsets and AN clockoffsets are all estimated and tracked.

To the best of authors knowledge, such solutions have notbeen reported earlier in the existing literature. For generality,we note that a maximum likelihood estimator (MLE) for jointUN localization and network synchronization has been pro-posed in [24]. However, such an algorithm is a batch solutionand does not provide sequential estimation of the UN positionand synchronization parameters needed in mobile scenariosand dynamic propagation environments. In practice, both the

UN position and synchronization parameters are time-varying.Moreover, the work in [24] focuses on ToA measurementsonly, thus requiring fusing the measurements from a largeramount of ANs than that needed in our approach. Hence, thisarticle may be understood as a considerable extension of thework in [24] where both ToA and DoA measurements aretaken into account for sequential estimation and tracking ofUN position and network synchronization. A final contributionof this article consists in providing a vast and comprehensiveperformance evaluation of the proposed solutions in realistic5G network setup, building on the METIS project Madridmap model [25]. The network is assumed to be operating at3.5GHz band, and the multiple-input multiple-output (MIMO)channel propagation for the UL pilot transmissions is modeledby means of a ray tracing tool where all essential propagationpaths are emulated. In the performance evaluations, variousparameters such as the AN inter-site distance (ISD) and ULpilot spacing in frequency are varied. The obtained resultsdemonstrate that sub-meter scale positioning accuracy is in-deed technically feasible in future 5G radio access networks,even under the realistic assumptions related to clock offsets.The results also indicate that the proposed EKF based solutionscan provide highly-accurate clock offset estimates not only forthe UNs but also across network elements, which contains highvalue on its own, namely for synchronization of 5G UDNs.

The rest of the article is organized as follows. In Section II,we describe the basic system model, including the assumptionsrelated to the ultra-dense 5G network, antenna array modelsin the ANs and the clock offset models adopted for the UNdevices and network elements. In Section III, we shortly reviewthe basic formulation of EKFs. The proposed solutions forjoint ToA/DoA estimation and tracking in an individual ANas well as for joint UN position and clock offset estimationand tracking in the network across ANs are all describedin Section IV. In Section V, we provide the extension tothe case of unsynchronized network elements, and describethe associated EKF solutions for estimation and tracking ofall essential parameters including the mutual clock offsetsof ANs. Furthermore, the propagation of universal networktime is shortly addressed. In Section VI, we report the resultsof extensive numerical evaluations in realistic 5G networkcontext, while also comparing the results to those obtainedusing earlier prior art. Finally, conclusions are drawn in SectionVII.

II. SYSTEM MODEL

A. 5G Ultra-Dense Networks and Positioning Engine

We consider an UDN where the ANs are equipped with mul-tiantenna transceivers. The ANs are deployed below rooftopsand have a maximum ISD of around50m; see Fig. 1. The UNtransmits periodically UL reference signals in order to allowfor multiuser MIMO (MU-MIMO) schemes based on channelstate information at transmitter (CSIT). The UL referencesignals are assumed to employ a multicarrier waveform suchas orthogonal frequency-division multiplexing (OFDM), inthe form of orthogonal frequency-division multiple access(OFDMA) in a multiuser network. These features are widely

3

Fig. 1. Positioning in5G ultra-dense networks (UDNs). Multiantenna accessnodes (ANs) and multicarrier waveforms make it possible to estimate and trackthe position of the user node (UN) with high-accuracy by relying on uplink(UL) reference signals, used primarily for downlink (DL) precoder calculation.

accepted to be part of5G UDN developments, as discussed,e.g., in [2]–[4], [10], [25], and in this paper we take advantageof such a system in order to provide and enable high-efficiencyUN positioning.

In particular, the multiantenna capabilities of the ANs makeit possible to estimate the DoA of the UL reference signalswhile employing multicarrier waveforms allows one to esti-mate the ToA of such UL pilots. The position of the UN isthen obtained with the proposed EKF by fusing the DoA andToA estimates from multiple ANs, given that such ANs arein LoS condition with the UN. In fact, the LoS probability inUDNs comprised of ANs with a maximum ISD of50m is veryhigh, e.g.,0.8 in the stochastic channel model descibed in [26],[27] and already around 0.95 for an ISD of40m. Note thatthe LoS/non-line-of-sight (NLoS) condition of a UN-AN linkmay be determined based on the Rice factor of the receivedsignal strength, as described, e.g., in [28]. Hence, we assumethat such conditions have been correctly detected.

In this paper, we focus on 2D positioning (xy-plane only)and assume that the locations of the ANs are fully known.However, the extension of the EKFs proposed here to 3Dpositioning is straightforward. We also note that the methodsproposed in this paper can be used for estimating the positionsof the ANs as well, given that a few ANs are surveyed.We further assume two different scenarios for synchronizationwithin a network. First, UNs are assumed to have unsynchro-nized 1 clocks whereas the clocks within ANs are assumedto be synchronized among each other. Second, not only theclock of a UN but also the clocks within ANs are assumed

1We assume that the timing and frequency synchronization needed foravoiding inter-carrier-interference (ICI) and inter-symbol-interference (ISI) hasbeen achieved. Such an assumption is similar to that needed in OFDM basedwireless systems in order to decode the received data symbols.

Fig. 2. Cascaded extended Kalman filters (EKFs) for joint user node (UN)positioning and network clock synchronization. The DoA/ToA EKFs operatein a distributed manner at each access node (AN) while the Pos&Clock/SyncEKFs operate in a central-unit fusing the ToA/DoA measurements of K[n]ANs.

to be unsynchronized. For the sake of simplicity, we makean assumption that the clocks within ANs are phase-lockedin the second scenario, i.e., the clock offsets of the ANsare essentially not varying with respect to the actual time.Completely synchronized as well as phase-locked clocks canbe adjusted using a reference time from, e.g., GPS, or bycommunicating a reference signal from a central-entity of thenetwork to the ANs, but these methods surely increase thesignaling overhead.

B. Channel Model for DoA/ToA Estimation and Tracking

The channel model employed by the proposed EKF forestimating and tracking the DoA/ToA parameters comprises asingle dominant path. It is important to note that a detailedray tracing based channel model is then used in all thenumerical results (see Section VI) for emulating the estimatedchannel frequency responses at the ANs. However, the EKFproposed in this paper fits a single-path model to the estimatedmultipath channel. The motivation for such an approach istwofold. Firstly, the typical Rice factor in UDNs is 10-20 dB[27], [29]. Secondly, the resulting EKF is computationallymore efficient than the approach of estimating and trackingmultiple propagation paths [30]. This method thus allowsfor reduced computing complexity, while still enabling high-accuracy positioning and tracking, as will be shown in theevaluations.

In particular, the EKFs proposed in Sections III-V exploitthe following model for the UL single-input-multiple-output(SIMO) multicarrier-multiantenna channel response estimatedat an AN [31]:

g ≈ B(ϑ, ϕ, τ)γ + n. (1)

Here,B(ϑ, ϕ, τ) ∈ CM×2 andγ ∈ C2×1 denote the polarimet-ric response of the multicarrier-multiantenna AN and the pathweights, respectively. Moreover,n ∈ CM×1 in (1) denotescomplex-circular zero-mean white-Gaussian distributed noisewith varianceσ2

n. The dimension of the multichannel vectorg is given byM = MfMAN, whereMf andMAN denotethe number of subcarriers and antenna elements, respectively.

4

In this paper, planar or conformal antenna arrays can beemployed, and their elements may be placed non-uniformly. Inparticular, the polarimetric array response is given in terms ofthe effective aperture distribution function (EADF) [30]–[32]as

B(ϑ, ϕ, τ) = [GHd(ϕ, ϑ)⊗Gfd(τ),

GV d(ϕ, ϑ) ⊗Gfd(τ)], (2)

where ⊗ denotes the Kronecker product. Here,Gf ∈CMf×Mf denotes the frequency response of the receivers, andGH ∈ CMAN×MaMe andGV ∈ CMAN×MaMe denote theEADF of the multiantenna AN for an horizontal and verticalexcitation, respectively. Also,Ma andMe denote the numberof modes (spatial harmonics) of the array response; see [31,Ch.2], [32] for details. Moreover,d(τ) ∈ CMf×1 denotes aVandermonde structured vector given by

d(τ) = [exp{−π(Mf − 1)f0τ}, . . . , exp{π(Mf − 1)f0τ}]T,

(3)

wheref0 denotes the subcarrier spacing of the adopted mul-ticarrier waveform. Finally, vectord(ϕ, ϑ) ∈ CMaMe×1 isgiven by

d(ϕ, ϑ) = d(ϑ)⊗ d(ϕ), (4)

whered(ϕ) ∈ CMa×1 andd(ϑ) ∈ CMe×1 have a structureidentical to that in (3) by usingπf0τ → ϑ/2, and similarly forϕ. Note that we have assumed identical radio frequency (RF)-chains at the multiantenna AN and a frequency-flat angularresponse. Such assumptions are taken for the sake of clarity,and an extension of the EKF proposed in Section IV-A to non-identical RF-chains as well as frequency-dependent angularresponses is straightforward but computationally more demand-ing. Note also that the model in (2) accommodates widebandsignals and it is identical to that typically used in space-timearray processing [33], [34]. Moreover, the array calibrationdata, represented by the EADF, is assumed to be known orpreviously acquired by means of dedicated measurements inan anechoic chamber [31], [32].

We consider both co-elevationϑ ∈ [0, π] and azimuthϕ ∈[0, 2π) angles even though we focus on 2D positioning. This isdue to the challenge of decoupling the azimuth angle from theelevation angle on the EKF proposed in Section IV-A withoutmaking further assumptions on the employed array geometryor on the height of the UN. It should be also noted that inan OFDM based system the parameterτ as given in (1) (i.e.,after the fast Fourier transform (FFT) operation) denotes thedifference between the actual ToA (wrt. the clock of the AN)of the LoS path and the start of the FFT window [35, Ch.3],[36]. The ToA wrt. the clock of the AN is then found simplyby adding the start-time of the FFT window toτ . However,throughout this paper and for the sake of clarify we will callτ simply the ToA.

C. Clock Models

In the literature, it is generally agreed that the clock offsetρ is a time-varying quantity due to imperfections of the clock

oscillator in the device, see e.g., [36]–[38]. For a measurementperiod∆t, the clock offset is typically expressed in a recursiveform as [38]

ρ[n] = ρ[n− 1] + α[n]∆t (5)

whereα[n] is known as the clock skew. Some authors, e.g., theauthors in [37] assume the clock skew to be constant, whilesome recent research based on measurements suggests thatthe clock skew can also, in fact, be time-dependent, at leastover the large observation period (1.5months) considered in[38]. However, taking the research and measurement resultsin[39], [40] into account, where devices are identified remotelybased on an estimate of the average clock skew, one couldassume that theaverage clock skewis indeed constant. Thisalso matches with the measurement results in [38], wherethe clock skew seems to be fluctuating around a mean value.Nevertheless, the measurements in [38]–[40] were obtainedindoors, i.e., in a temperature controlled environment. How-ever, in practice, environmental effects such as large changesin the ambient temperature affect the clock parameters in thelong term [37]. Therefore, we adopt the more general model[38] of a time-varying clock skew, which also encompassesthe constant clock skew model as a special case.

The clock skew in [38] is modeled as an auto-regressive(AR) process of orderP . While the measurement results in[38] reveal that modeling the clock offset as an AR processresults in large performance gains compared to a constant clockskew model, an increase of the order beyondP = 1 doesnot seem to increase the accuracy of clock offset trackingsignificantly. In this paper, we consequently model the clockskew as an AR model of first order according to

α[n] = βα[n− 1] + η[n] (6)

where |β| ≤ 1 is a constant parameter andη[n] ∼ N (0, σ2η)

is additive white Gaussian noise (AWGN). Furthermore, thejoint DoA/ToA Pos&Clock EKF as well as the joint DoA/ToAPos&Sync EKF proposed in Sections IV-B1 and V, respec-tively, could be extended to AR processes of higher orders.

III. E XTENDED KALMAN FILTER

The state of a noisy linear system can be estimated ef-ficiently using the well known and optimal Kalman filter(KF). However, estimation using the KF is not often possiblesince the models of systems are often non-linear. The EKFis an extension of the linear KF to these non-linear filteringproblems in which the state of a non-linear dynamic systemis estimated iteratively using Taylor-series based first orderlinearization of the models [41, p. 69]. In this section, weshortly review the basic processing model and notations of theEKF, while the actual proposed solutions are formulated in thenext sections.

Let us assume a system where the transition between twoconsecutive statess[n − 1] ∈ Rm and s[n] ∈ Rm can bemodelled with the following linear state equation

s[n] = Fs[n− 1] + u[n], (7)

5

whereF ∈ Rm×m is the state transition matrix andu[n] ∈Rm is the normally distributed zero-mean driving noise with acovariance matrixE

[

u[n]uT[k]]

= δk−nQ[n] ∈ Rm×m whereδi−j is the Kronecker delta function. Here,E[·] denotes theexpectation operator.

Then, different to the linear state model, the measurementmodel for the system of interest is considered to be non-linear.Thus, the measurementsy[n] ∈ Rq at time stepn can bewritten as

y[n] = h(s[n]) +w[n], (8)

where h : Rm → Rq is a non-linear function of thecurrent states[n] andw[n] ∈ Rq is normally distributed zero-mean measurement noise with a covarianceE

[

w[n]wT[k]]

=δk−nR[n] ∈ Rq×q.

In this paper, the same notations are used as in [42], wherea predicted and an updated state estimate of the system attime stepn are denoted bys−[n] and s+[n], respectively.Furthermore, the predicted covariance matrix of the state isdenoted asP−[n] and the updated covariance matrix asP+[n].It is also assumed that the initial distribution of the state,in other words, the mean of the initial states+[0] and itscovariance matrixP+[0] are known or have been previouslyestimated.

At each time-step, the EKF consists of a prediction and anupdate phase. With the above notation, the predicted estimatesof the state and its covariance at time stepn can be written inthe prediction phase as

s−[n] = Fs+[n− 1] (9)

P−[n] = FP+[n− 1]FT +Q[n], (10)

After the prediction phase, thea priori estimate s−[n] isupdated using the latest measurementsy[n] in the followingupdate phase as

K[n] = P−[n]HT[n](H[n]P−[n]HT[n] +R[n])−1 (11)

s+[n] = s−[n] +K[n][

y[n]− h(s−[n])]

(12)

P+[n] = (I−K[n]H[n])P−[n] (13)

where, the Jacobian matrix, denoted asH[n] = ∂h[n]∂s[n] , is

evaluated ats−[n]. The Kalman gainK[n] ∈ Rm×q repre-sents the relative importance of the measurement residual bytransforming the informative part of the measurements intoacorrection term. This term is used to correct thea priori stateestimate [43, p. 62].

The so-called information-form of the EKF is computa-tionally more attractive than the above Kalman-gain form incases where the dimension of the state is smaller than that ofthe measurement vector as well as in dealing with complex-valued data. More precisely, employing the matrix-inversionlemma [44, p. 571] to the update expressions (12) and (13),and including the Kalman gain expression, yields [42, Ch. 6]:

P+[n] = ((P−[n])−1 + J[n])−1 (14)

s+[n] = s−[n] +P+[n]v[n], (15)

where J[n] ∈ Rm×m and v[n] ∈ Rm denote the observedFisher information matrix (FIM) and score-function of (8).

IV. JOINT UN POSITIONING AND UN CLOCK OFFSETESTIMATION

The EKF reviewed in the previous section is a widely usedestimation method for the UN positioning when measurementssuch as the DoAs and ToAs are related to the state througha non-linear model, e.g., [23]. However, the UN positioningis quite often done within the UN device which leads toincreased energy consumption of the device compared to anetwork-centric positioning approach [1]. In this paper, the UNpositioning together with the UN clock offset estimation aredone in a network-centric manner using a cascaded EKF. Thefirst part of the cascaded EKF consists of tracking the DoAsand ToAs of a given UN within each LoS-ANs, whereas thesecond part consists of the joint UN positioning and UN clockoffset estimation, where the DoA/ToA measurements obtainedfrom the first part of the cascaded EKF are used. The structureof the cascaded EKF is illustrated in Fig. 2.

A. DoA/ToA Tracking EKF at ANIn this section, a novel EKF for tracking the DoA and ToA

of the LoS-path at an AN is proposed. It stems from the workin [30]. However, the formulation of the EKF proposed in thispaper is computationally more attractive than that in [30].Inparticular, the goal in [30] is to have an accurate character-ization of the radio channel, and thus all of the significantspecular paths need to be estimated and tracked. However,in our work only a single propagation path corresponding tothe largest power is tracked. In addition to the computationaladvantages, the main motivation for using such a model inthe EKF follows from the fact that the propagation path withlargest power typically corresponds to the LoS path. This iseven more noticeable in UDNs where the AN-UN distanceis typically less than50m, and the Rice-K factor is around10-20 dB [29].

Another difference between the EKF proposed in this sec-tion and the work in [30] consists on the path weights. Inparticular, the EKF in [30] tracks a logarithmic parameteriza-tion of the path weights (magnitude and phase components)thereby increasing the dimension of the state vector, andconsequently the complexity of each iteration of the EKF. ForUN positioning the path weights are nuisance parameters, andit is desirable to formulate the EKF such that the path weightsare not part of the state vector. The EKF proposed in this paperthus tracks the DoA and ToA, only. This is achieved by notingthat the path weights are linear parameters of the model for theUL multicarrier multiantenna channel [31], and by employingthe concentrated log-likelihood function in the derivation ofthe information-form of the EKF [42, Ch.6].

1) EKF: The prediction and update equations of theinformation-form of the EKF for theℓkth AN can now beexpressed as

s−ℓk [n] = Fs+ℓk [n− 1] (16)

P−ℓk[n] = FP+

ℓk[n− 1]FT +Q[n] (17)

P+ℓk[n] =

(

(

P−ℓk[n])−1

+ Jℓk [n])−1

(18)

s+ℓk [n] = s−ℓk [n] +P+ℓk[n]vℓk [n], (19)

6

whereJℓk [n] ∈ R6×6 andvℓk [n] ∈ R6×1 denote the observedFIM and score-function of the state evaluated ats−ℓk [n], re-spectively. They are found by employing the model in SectionII-B for the estimated UL channel, and concentrating thecorresponding log-likelihood function wrt. the path weights.In particular, the observed FIM and score-function are givenby [31], [32], [45]

Jℓk [n] =2

σ2n

ℜ

(

∂r

∂s−T

ℓk[n]

)*∂r

∂s−T

ℓk[n]

, (20)

vℓk [n] =2

σ2n

ℜ

(

∂r

∂s−T

ℓk[n]

)*

r

. (21)

Here,r = Π⊥(s−ℓk [n])gℓk [n] andΠ⊥(s−ℓk [n]) = I−Π(s−ℓk [n])denotes an orthogonal projection matrix onto the nullspaceof B(ϑ, ϕ, τ); see Section II-B. In particular,Π(s−ℓk [n]) =

B(ϑ, ϕ, τ)B†(ϑ, ϕ, τ), where the superscript{·}† denotes theMoore-Penrose pseudo-inverse.

A continuous white noise acceleration model is employedfor the state-evolution [46]. Hence, the state-vector in (16) isgiven by

sℓk [n] = [τℓk [n], ϑℓk [n], ϕℓk [n],∆τℓk [n],∆ϑℓk [n],∆ϕℓk [n]]T,

(22)

where ϕℓk [n] ∈ (0, 2π] and ϑℓk [n] ∈ [0, π] denote theazimuth and elevation arrival-angles at thenth time-instant,respectively. Similarly,τℓk [n] denotes the ToA at theℓkth AN.Finally, the parameters∆τℓk [n], ∆ϑℓk [n], and∆ϕℓk [n] denotethe rate-of-change of the ToA as well as of the arrival-angles,respectively.

The state transition matrixF ∈ R6×6 and the covariancematrix of the state-noiseQ[n] ∈ R

6×6 can be found as follows.Let the continuous-time state-dynamic equation be given by

ds(t)

dt= As(t) + Lw(t), (23)

wherew(t) ∈ R3×1 denotes a white-noise process, andA ∈R6×6 andL ∈ R6×3 are given by

A =

[

03×3 I3×3

03×3 03×3

]

, L =

[

03×3

I3×3

]

. (24)

By defining a power spectral density for the white-noiseprocessQc ∈ R3×3, and using matricesA and L one canobtain the state transition matrixF and covariance matrixof the state noiseQ[n] using the numerical discretizationapproach described in [47, Ch.2].

2) EKF Initialization: Initial estimates of the DoA, ToA, andrespective rate-of-change parameters are needed for initializingthe EKF proposed in the previous section. Here, we describe asimple yet reliable approach for finding such initial estimates.In particular, the initial estimatesϑℓk [0], ϕℓk [0], andτℓk [0] arefound as follows:• Reshape the UL channel vector into a matrix:

Hℓk = mat{gℓk ,Mf ,MAN} (25)

• Multiply Hℓk with the EADF for horizontal and verticalcomponents, and reshape into a 3D matrix:

AH = mat{HℓkGcℓkH

,Mf ,Ma,Me}, (26)

AV = mat{HℓkGcℓkV

,Mf ,Ma,Me} (27)

• Employ the 3D FFT and determine

BH = |FFT3D{AH}|2, (28)

BV = |FFT3D{AV }|2 (29)

• Find the indexes of the largest element of the following3D matrix:BH +BV . They correspond to the estimates(ϑℓk [0], ϕℓk [0], and τℓk [0]).

We note that the initialization method described above is acomputationally efficient implementation of the space-timeconventional beamformer (deterministic MLE for a singlepath), and it stems from the work in [31], [32]. The initializa-tion of the covariance matrix may be achieved by evaluatingthe observed FIM ats+ℓk [0], and usingP+

ℓk[0] = (Jℓk [0])

−1.The rate-of-change parameters may be initialized once two

consecutive estimates of (ϑℓk , ϕℓk , τℓk ) are obtained. For ex-ample, in order to initialize∆τℓk at n = 2 the following canbe used

∆τℓk [2] =τℓk [2]− τℓk [1]

∆t, (30)

(P+ℓk[2])4,4 =

1

(∆t)2(

(P+ℓk[1])1,1 + (P+

ℓk[2])1,1

)

, (31)

where∆t denotes the time-interval between two consecutiveestimates and the notation(A)i,j denotes the entry of matrixA located at theith row andjth column.

B. Positioning and Synchronization EKF at Central Process-ing Unit

Next, a novel algorithm for the simultaneous UN positioningand clock synchronization is presented, following the prelim-inary work by the authors in [1]. Since in practice every UNhas an offset in its internal clock wrt. the ANs’ clocks, it iscrucial to track the clock offset of the UN in order to achievereliable ToA estimates for positioning. Furthermore, differentclock offsets among the ANs should be taken into accountas well, but that topic is covered in more detail in SectionV. In this section, we first present the novel EKF solution,called joint DoA/ToA Pos&Clock EKF, for simultaneous UNpositioning and clock synchronization for the case when ANsare synchronized. Then, a practical and improved initializationmethod for the presented Pos&Clock EKF is also proposed.For notational simplicity, we assume below that only a singleUN is tracked. However, assuming orthogonal UL pilots, theToAs and DoAs of multiple UNs can, in general, be estimatedand tracked, thus facilitating also simultaneous positioning andclock offset estimation and tracking of multiple devices.

7

1) Joint DoA/ToA Pos&Clock EKF: Within the jointDoA/ToA Pos&Clock EKF, the obtained ToA and DoA es-timates from different LoS ANs are used to estimate the UNposition and velocity as well as the clock offset and clockskew of the UN. Thus, a six-dimensional state of the processis defined as

s[n] = [x[n], y[n], vx[n], vy[n], ρ[n], α[n]]T, (32)

where p[n] = [x[n], y[n]]T and v[n] = [vx[n], vy[n]]T are

two-dimensional position and velocity vectors of the UN,respectively. Furthermore, the clock offsetρ[n] and the clockskewα[n] of the UN are assumed to evolve according to theclock models in (5) and (6).

Let us next assume that the velocity of the UN is almostconstant between two consecutive time-steps, being only per-turbed by small random changes (i.e., velocity is followingarandom walk model) [44, p. 459]. Then, stemming from thisassumption and since the clock models for the evolution of theclock offset and skew are linear, a joint linear model for thestate transition can be expressed as

s[n] = Fs[n− 1] +w[n], (33)

where the state transition matrixF ∈ R6×6 is

FUN =

[

I2×2 ∆t · I2×2 02×2

02×2 I2×2 02×2

02×2 02×2 Fc

]

, Fc =

[

1 ∆t0 β

]

. (34)

Here, the process noise is assumed to be zero-mean Gaussiansuch thatw[n] ∼ N (0,Q′) where the discretized blockdiagonal covarianceQ′ ∈ R6×6 is given by

Q′ =

σ2v∆t3

3 · I2×2σ2v∆t2

2 · I2×2 02×1 02×1σ2v∆t2

2 · I2×2 σ2v∆t · I2×2 02×1 02×1

01×2 01×2σ2η∆t3

3

σ2η∆t2

2

01×2 01×2σ2η∆t2

2 σ2η∆t

. (35)

Hereσv andση denote the standard deviation (STD) for thevelocity and clock skew noises, respectively.

The upper left corner of the state transition matrixFUNrepresents the constant movement model of the UN, whereasthe matrixFc describes the clock evolution according to theclock models (5) and (6). Both presented clock models havebeen shown to be suitable for clock tracking in [38] usingpractical measurements. Unfortunately, the authors in [38]do not provide details on the values for the parameterβ asdetermined in their experiments. Although the clock skew isnot necessarily completely stationary, the change in the clockskew is relatively slow compared to the clock offset. Therefore,the authors in [38] argue that the clock skew can be assumedto be quasi-stationary for long time periods. According to thecalculations and observations in [1], we employ the valueβ = 1 throughout the paper. Thus, the clock skew caneventually be considered as a random-walk process as well.

In contrast to the linear state transition model, the mea-surement model for the joint DoA/ToA Pos&ClockEKF isnon-linear. For each time stepn, let us denote the numberof ANs with a LoS condition to the UN asK[n] and the

indices of those ANs asℓ1, ℓ2, . . . , ℓK[n]. For each LoS-ANℓk, the measurement equation consists of the DoA estimateϕℓk [n] = ϕℓk [n] + δϕℓk [n] and the ToA estimateτℓk [n] =τℓk [n] + δτℓk [n], whereδϕℓk [n] andδτℓk [n] denote estimationerrors for the obtained DoA and ToA measurements, respec-tively. Note that the focus is on 2D position estimation, andthus the estimated elevation angles are not employed by thisEKF. The measurements for each AN can thus be combinedinto a joint measurement equation expressed as

yℓk [n] = [ϕℓk [n], τℓk [n]]T = hℓk(s[n]) + uℓk [n], (36)

where uℓk [n] = [δϕℓk [n], δτℓk [n]]T is the zero-mean obser-

vation noise with a covarianceRℓk [n] = E[uℓk [n]uTℓk[n]].

Furthermore,hℓk(s[n]) = [hℓk,1(s[n]), hℓk,2(s[n])]T is the real-

valued and non-linear measurement function that relates themeasurement vectoryℓk [n] to the UN state through

hℓk,1(s[n]) = arctan

(

∆yℓk [n]

∆xℓk [n]

)

(37)

hℓk,2(s[n]) =dℓk [n]

c+ ρ[n], (38)

where∆xℓk [n] = x[n] − xℓk and∆yℓk [n] = y[n] − yℓk aredistances between the ANℓk and the UN inx- andy-direction,respectively. In (38), the two-dimensional distance between the

UN and the AN is denoted asdℓk =√

∆x2ℓk[n] + ∆y2ℓk [n]

and the speed of light is denoted asc. Finally, the completemeasurement equation containing measurementsyℓk from allLoS-ANs at time stepn can be written as

y[n] = h(s[n]) + u[n], (39)

where y = [yTℓ1,yT

ℓ2, . . . ,yT

ℓK[n]]T is the collection of mea-

surements andh = [hTℓ1,hT

ℓ2, . . . ,hT

ℓK[n]]T is the respective

combination of the model functions. Furthermore, the noiseu[n] ∼ N (0,R) with a block diagonal covariance matrixR = blkdiag

([

Rℓ1 ,Rℓ2 , . . . ,RℓK[n]

])

describes the zero-mean measurement errors for allK[n] LoS-ANs.

Let us next assume that the initial states+[0] as well asthe initial covariance matrixP+[0] are known. Furthermore,assuming the linear state transition model and the non-linearmeasurement model as derived in (33) and (39), respectively,the presented EKF equations (9)-(13) can be applied to esti-mate the state of our system. Because of the linear state tran-sition model, the prediction phase of the EKF can be appliedin a straightforward manner within the joint Pos&Clock EKF.However, the Jacobian matrixH used in (11)-(13) needs to beevaluated ats−[n] before applying the subsequent equations ofthe general EKF. It is straightforward to show that after simpledifferentiation the elements of the Jacobian matrixH become

H2k−1,1[n] = [hℓk,1]x (s−[n]) = −

∆yℓk [n]

d2ℓk [n](40)

H2k−1,2[n] = [hℓk,1]y (s−[n]) =

∆xℓk [n]

d2ℓk [n](41)

8

H2k,1[n] = [hℓk,2]x (s−[n]) =

∆xℓk [n]

c dℓk [n](42)

H2k,2[n] = [hℓk,2]y (s−[n]) =

∆yℓk [n]

c dℓk [n](43)

H2k,5 = [hℓk,2]ρ (s−[n]) = 1, (44)

for k = 1, 2, . . . ,K[n] and zero otherwise [1]. In (40)-(43), we denote distances between the AN and the predictedUN position in x- and y-directions as∆xℓk [n] and∆yℓk [n],respectively. Similarly, the notationdℓk [n] denotes the two-dimensional distance between theℓkth AN and the predictedUN position.

At every time stepn, the two-dimensional UN positionestimate is hence obtained asp[n] = [(s+[n])1, (s

+[n])2]T

with an estimated covariance found as the upper-left-most2×2submatrix ofP+[n]. In addition to the UN position estimate,an estimate of the UN clock offset is given through the statevariable(s+[n])5 as a valuable by-product.

2) EKF Initialization: Initialization of the EKF, i.e., thechoice of the means+[0] and the covarianceP+[0] of theinitial Gaussian distribution plays an important role in theperformance of the EKF. In the worst case scenario, poorlychosen initial values for the state and covariance might lead toundesired divergence in the EKF whereas good initial estimatesensure fast convergence. Here, we propose a practical two-phase initialization method for the Pos&Clock EKF in whichno external information is used besides that obtained throughthe normal communication process between the UN and ANs.The proposed initialization method is illustrated in Fig. 3.

In the first phase of initialisation, we determine coarseinitial position and velocity estimates of the UN togetherwith their respective covariances which are used, thereafter,as an input to the next phase of the proposed initializationmethod. In the literature, there are many different methodsthat can be used to determine such initial position estimates.For example, the authors in [48] used received signal strength(RSS) measurements to obtain the position estimates whereasin [23] the authors used DoA and ToA based methods for theUN positioning. The UN could even communicate positionestimates that are obtained by the UN itself using, e.g., globalnavigation satellite system (GNSS), but has the disadvantageof increasing the amount of additional communication betweenthe UN and ANs, and such an external positioning service isnot necessarily always available. In our initialization method,we apply the centroid localization (CL) method [49] buildingon the known positions of the LoS-ANs in order to obtain arough position estimate for the UN. Thus, the initial positionestimate, denoted asp+[0] = [x+[0], y+[0]]T, can be expressedas

p+[0] =

1

K[0]

K[0]∑

k=1

pℓk, (45)

whereK[0] is the total number of LoS-ANs andpℓkdenotes

the known position of the LoS-AN with an indexℓk. Intuitively,(45) can be understood as the mean of the LoS-ANs’ positions,and depending on the location of the UN relative to the LoS-ANs the initial position estimate may be poor. Such coarse

Fig. 3. Initialization of position estimatep+[n] where also a velocity estimatev+[n] is improved as a by-product in the second phase of the initialization

initial position estimate can be improved by using a weightedcentroid localization (WCL) method where the weights can beobtained from e.g., RSS measurements [50].

Unless the positioning method provides an initial estimatealso for the velocity, the EKF can be initialized even witha very coarse estimate. If external information about theenvironment or device itself is available, a reliable estimatefor the velocity can be easily obtained considering, e.g., speedlimits of the area where the obtained initial position estimateis acquired. However, since external information is not usedin our initialization method, the initial velocity estimate of theUN is set to zero without loss of generality. By combiningthe initial position and velocity estimates we can determine areduced initial state estimates+[0] that can be used as an inputfor the next phase of the proposed initialization method.

It is also important that the employed initialization methodprovides not only the state estimate but also an estimate ofthe covariance. In our method, the uncertainty of the initialposition is set to a large value, since the initial position estimateobtained using the CL method might easily be coarse and,therefore, cause divergence in the EKF if a small uncertaintyis used. Since the initial velocity is defined without any fur-ther assumptions, it is consequential to set the correspondingcovariance also to a large value. Hence, by setting the initialcovariance to be reasonably large we do not rely excessivelyon the uncertain initial state.

However, the initial position estimate obtained using theabove initialization procedure may not be accurate enoughto ensure reliable convergence in the presented DoA/ToApositioning and synchronization EKF, especially in the senseof using susceptible ToA measurements in the update phaseof the filtering. Therefore, we chose to execute DoA-onlyEKF, i.e., an EKF where only the DoA measurements aremomentarily used to update the state estimate of the UN [51],in the second phase of the overall initialization procedure.The DoA-only EKF, in which the obtained initial state andcovariance estimate are used as prior information, is carriedout only for pre-definedNI iterations. In addition to moreaccurate position estimate, we can also estimate the UNvelocity v[n] = [vx[n], vy[n]]

T as a by-product in the DoA-only EKF.

The state estimate obtained from the DoA-only EKF afterthe NI iterations can then be used to initialize the jointDoA/ToA Pos&Clock EKF after the state has been extendedwith the initial UN clock parameters. In the beginning, theclock offset can be limited to a fairly low value by simplycommunicating the time from one of the LoS-ANs. Thereafter,the communicated time can be used to set up the clock withinthe UN. Typically, manufacturers report the clock skew of their

9

oscillators in parts per million (ppm). Based on the resultsachieved in the literature, e.g., in [38]–[40] the clock skewof the UN can be initialized toα+[0] = 25 ppm with aSTD of a few tens of ppm [1]. Finally, the extended stateand covariance that contain also the necessary parts for theclock parameters can be used as prior information for theactual DoA/ToA Pos&Clock EKF as well as for the yetmore elaborate DoA/ToA Pos&Sync EKF proposed next inSection V.

V. CASCADED EKFS FORJOINT UN POSITIONING ANDNETWORK CLOCK SYNCHRONIZATION

In the previous section, we assumed that the clock of aUN is unsynchronized with respect to ANs whereas the ANswithin a network are mutually synchronized. In this section,we relax such an assumption, by considering unsynchronizedrather than synchronized ANs. For mathematical tractabilityand presentation simplicity, we assume that the ANs’ clockswithin a network are, however, phase-locked, i.e., the clockoffsets of the ANs are static. It is important to note that thisassumption does not imply the same clock offsets between theANs, leaving thus a clear need for network synchronization.In the following, an EKF for both joint UN positioning andnetwork synchronization is proposed. The issue of propagatinga universal time within a network is also discussed.

A. Positioning and Network Synchronization EKF at CentralUnit

In general, the proposed EKF for simultaneous UN position-ing and network synchronization, denoted as a joint DoA/ToAPos&Sync EKF, is an extension to the previous joint DoA/ToAPos&Clock EKF where also the mutual clock offsets of theLoS-ANs are tracked using the available ToA measurements.An augmented state where also the clock offsets of all LoS-ANs at time stepn are considered can now be expressed as

s[n] = [sTUN[n], ρℓ1 [n], · · · , ρℓK[n]

[n]]T, (46)

wheresTUN[n] = [x[n], y[n], vx[n], vy[n], ρ[n], α[n]] is the same

state vector containing the position and velocity of the UN aswell as the clock parameters of the UN clock as presentedin Section IV-B1. Furthermore, the clock offset of the LoS-AN with an indexℓk wherek ∈ 1, 2, . . . ,K[n] is denoted inthe augmented state asρℓk [n]. Here, all the clock offsets areinterpreted relative to a chosen reference AN clock.

Since the clocks within ANs are assumed to be phase-locked,we can now write the clock offset evolution model for the ANwith an indexℓk as

ρℓk [n] = ρℓk [n− 1] + δρ[n], (47)

whereδρ ∼ N (0, σ2ρ) denotes the zero-mean Gaussian noise

for the clock offset evolution. Using the model (47) for theclock offsets and assuming the same motion model (33), wecan write then a linear transition model for the state (46) withinDoA/ToA Pos&Sync EKF such that

s[n] = F[n]s[n− 1] +w[n], (48)

where w[n] ∼ N (0,Q) denotes the zero-mean distributednoise with the following covariance

Q =

[

Q′ 0K[n]×K[n]

0K[n]×K[n] σ2ρ∆t · IK[n]×K[n]

]

, (49)

whereQ′ is the same covariance as in (35). Furthermore, theaugmented state transition matrixF[n] ∈ R(6+K[n])×(6+K[n])

can be written as

F[n] =

[

FUN 06×K[n]

0K[n]×6 IK[n]×K[n]

]

, (50)

where the matrixFUN ∈ R6×6 represents the same statetransition matrix for the UN state as in (34). The identitymatrix in the lower-right corner of the state transition matrixF[n] represents the assumed clock offset evolution for the ANsas presented in (47).

Next, due to the mutually unsynchronized ANs, the mea-surement equation related to ToA in (38) needs to be revisedaccordingly. Thus, by adding the clock offset of the consideredLoS-AN to the earlier ToA measurement equation in (38), wecan write new measurement equations as

hℓk,1(s[n]) = arctan

(

∆yℓk [n]

∆xk[n]

)

(51)

hℓk,2(s[n]) =dℓk [n]

c+ ρ[n] + ρℓk [n], (52)

whereρℓk [n] denotes the clock offset of the LoS-AN with anindex ℓk. Furthermore, the measurement equations in (52) foreach LoS-AN can be combined into the similar measurementmodel as in (39) such that

y[n] = h(s[n]) + u[n], (53)

whereu[n] ∼ N (0,R) is the measurement noise with covari-anceR = blkdiag

([

Rℓ1 ,Rℓ2 , . . . ,RℓK[n]

])

obtained from theDoA/ToA tracking phase.

In the following, we apply the EKF equations (9)-(13) tothe models (48) and (53) in order to obtain the joint DoA/ToAPos&Sync EKF. Since our measurement model contains nowalso the clock offset parameters for the LoS-ANs, we needto modify the Jacobian matrixH in (40)-(44) by adding thecorresponding elements for each LoS-ANs, namely

H2k,6+k = [hℓk,2]ρℓk(s−[n]) = 1, (54)

wherek ∈ 1, 2, . . . ,K[n], and zeros elsewhere to complete thematrix.

In the beginning of the filtering, e.g., when a UN establishesa connection to the network, we use the same initializationmethod as proposed earlier in Section IV-B2. Thereafter, theUN position and clock offset estimates at time stepn areobtained as[(s+[n])1, (s+[n])2]T and (s+[n])5, respectively,with estimated covariances found as respective elements ofthe matrix P+. Since the proposed DoA/ToA Pos&SyncEKF also tracks now the clock offsets of the LoS-ANs, theestimated clock offsets for each LoS-AN are given through thestate estimates(s+[n])6+k wherek ∈ 1, 2, . . . ,K[n]. These

10

obtained UN and LoS-ANs clock offset estimates can be usedthereafter in network synchronization.

In order to be able to track the offsets of LoS-ANs properlyand define synchronization within an unsynchronized network,we need to choose one of the LoS-ANs as a reference AN.Since the ToA measurements are not used in the earlierproposed initialization phase, the reference AN can be chosento be, e.g., the closest AN to the UN when the initializationphase is completed and the ToA measurements are started to beused in positioning and clock offset tracking. This impliesthatin the initial phase,ρℓ1 [n] = 0, assuming that the ANℓ1 refersto the reference AN. Thus, synchronization can be achievedwithin the network wrt. the reference AN by communicatingthe clock offset estimates for the LoS-ANs and the UN.

B. Propagation of Universal Network Time

In the case of tracking only one UN at the time, synchro-nization of the network is done with respect to the referencetime obtained from a chosen reference AN. However, when weapply the proposed method for multiple UNs simultaneouslywe have to consider how to treat clock offset estimates thathave different time references [52], [53]. In general, it isrealistic to assume that there are a large number of UNsconnected to a network, and thus tracked, simultaneously.Therefore, we can obtain clock offset estimates for numerousANs within a network using the proposed method such that theclock offsets for each AN have been estimated using differentreference times. If this information is stored and available in acentral unit, the relative offsets of these ANs can be estimatedeasily and the network can be thereafter synchronized wrt. anyof these ANs.

However, storing the clock offset information increases thecomputational load and the use of memory capacity in thecentral node of a network and, therefore, alternative approacheshow to utilize the estimated clock offsets can be considered.As an alternative approach, the same relative offset informationcould be used also as a prior information for the clock offsetestimation in the case of new UNs. If this information isavailable in the beginning of tracking a new UN, it wouldmost probably speed up convergence in the proposed EKF andeven improve the clock offset estimate of the UN. Furtheraspects related to establishing and propagating a universalnetwork time is an interesting and important topic for ourfuture research.

VI. N UMERICAL EVALUATIONS AND ANALYSIS

In this section, comprehensive numerical evaluations arecarried out to illustrate and quantify the achievable devicepositioning performance using the proposed methods. Theevaluations are carried out in an urban outdoor environment,adopting the METIS Madrid grid model [25], while thedeployed UDN is assumed to be operating at the 3.5 GHzband. We specifically focus on the connected car use case[2], [4], [10] where cars are driving through a city withvelocities in the order of50 km h−1. In all our evaluations, wedeploy comprehensive map and ray tracing based propagationmodeling [26] such that the modeling of the incoming UL

50 m

Fig. 4. Madrid map with example access node (AN) deployment (bluetriangles) and user node (UN) trajectory (red path).

reference signals in different ANs is as realistic as possibleand explicitly connected to the environment and map. Furtherdetails of the environment and evaluation methodologies aregiven below. In general, the performances of the proposed jointDoA/ToA Pos&Clock and Pos&Sync EKFs, as well as theDoA-only based EKF implemented for reference, are evaluatedand reported.

A. Simulation and Evaluation Environment

In the following, a detailed description of the employedsimulation environment is presented. First, the structureandproperties of the Madrid grid environmental model [25] thatstems from the METIS guidelines are described with anessential accuracy. After that, details of the used ray tracingchannel model are discussed and finally a realistic motionmodel for the UN is presented.

1) Madrid map:Outdoor environment has a huge impact notonly on constraining the UN movement but also on wirelesscommunications, especially, when modelling the radio signalpropagation within a network. The Madrid map, which refersto the METIS Madrid grid environmental model, is consideredas a compromise between the existing models like Manhattangrid and the need of characterising dense urban environmentsin a more realistic manner [25]. For evaluating and visualizingthe positioning performance, we used a two-dimensional layoutof the Madrid map as illustrated in Fig. 4.

In the connected car application, we model only the nec-essary parts of the Madrid map based on the METIS guide-lines [25], i.e., the indoor model as well as minor details likebus stops and metro entrances are ignored during the process.The majority of the Madrid map is covered with square andrectangle shaped building blocks as represented in Fig. 4 withdark gray color. Square blocks have both dimensions equal to120m whereas length and width of the other building blocksare120m and30m, respectively. The height of the buildings

11

Fig. 5. Illustration of the 3D array geometry employed at theANs. Cylindricalarrays comprising10 dual-polarized 3GPP patch-elements are used. The arrayelements are placed along two circles each of which comprising 5 patch-elements.

range from28m to 52.5m. In addition to the buildings, themap contains also a park with the same dimensions as squareshaped buildings, and it is located almost in the middle ofthe map. The rest of the map is determined to be roads andsidewalks, but for the sake of simplicity, sidewalks are notillustrated in Fig. 4. In general, these3m wide sidewalks aresurrounding every building in the map, but in our visualizationsthey are represented as a part of the roads. Road lanes are3m wide and they are accompanied by3m wide parkinglanes, except the vertical lanes in the widest Gran Via roadon the right side of the park. Thus, the normal roads are18m wide in our evaluations and visualization containing alsothe sidewalks. Special Grand Via road consists of three lanesin both directions, where the lanes in different directionsareseparated by6m wide sidewalk. The parallel road on the rightside of Gran Via road is called Calle Preciados and it is definedas a21m sidewalk in the METIS guidelines [25]. Despite thefact that the sidewalks are illustrated as a part of the roadsinFig. 4, we do not allow vehicles to move on these sidewalks.

2) Channel and antenna models:We employ the ray tracingas well as the geometry-based stochastic channel modelsdescribed in [27], [29]. In particular, the ray tracing channelmodel is employed in order to model the propagation of the ULreference signals that are exploited by the proposed EKFs forUN positioning as realistically as possible. In particular, theemployed ray tracing implementation takes into account the3D model of the Madrid grid when calculating the reflectedand diffracted paths between the UN and ANs. The diffractedpaths are given according to the Berg’s model [29]. Moreover,the antennas composing the arrays at the ANs are assumedto observe the same directional channel, and thus a single-reference point at the AN’s location is used in calculatingthe ray tracing channels. The effect of random scatterers isalso modeled according to the METIS guidelines [29] with adensity of0.01 scatterers/m2.

The geometry-based stochastic channel model (GSCM) [27],[29] is used in this paper in order to model uncoordinatedinterference. In particular, the interferers are randomlyplacedon a disk-shaped area ranging between200m and500m awayfrom the ANs receiving the UL reference signals. A densityof 1000 interferers/km2 is used and their placement follows aPoisson point process. The channels among the interferers’andmultiantenna ANs are calculated according to the GSCM, andused to calculate a spatially correlated covariance matrixat

0 10 20 30 40 50 60 70Time [s]

-1.5

-1

-0.5

0

0.5

1

1.5

Acceleration[m

/s2]

Fig. 6. Acceleration profile for the example UN trajectory shown in Fig. 4.

the receiving ANs. This is done for all subcarriers modulatedby the UL reference signals. Such a covariance matrix is thenused to correlate a zero-mean complex-circular white-Gaussiandistributed vector for each UL transmission. This approachofmodeling uncoordinated interference is similar to that in [54].

The multiantenna transceivers at the ANs are assumed tohave a cylindrical geometry; see Fig. 5. In particular, thecylindrical arrays are comprised of10 dual-polarized patch-elements, and thus20 output ports. The beampatterns of thepatch-elements are taken from [27]. The patch-elements areplaced along two circles, each with an inter-element distanceof λ/2. The vertical separation between the two circles isalso λ/2. Moreover, the circles have a relative rotation/shiftof 2π/10. Note that the EADF given in Section II is foundand calculated for this antenna array. Finally, the UN employsa vertically-oriented dipole while the interferers are equippedwith randomly-oriented dipoles.

3) UN motion model: In order to demonstrate that theproposed system is capable of positioning UNs with realistictime-varying velocities as well as time-varying accelerations,we assume that the UNs are moving in vehicles on trajectoriessuch as the one depicted in Fig. 4. On straightforward sectionsof the trajectory, the vehicle is assumed to accelerate up toamaximum velocity ofvm = 50 km h−1, whereas all turns areperformed with a constant velocity ofvt = 20 km h−1. Thetime-varying acceleration fromvt to vm and the time-varyingdeceleration fromvm to vt are modelled according to poly-nomial models stemming from real-life traffic data describedin [55]. The polynomial model in [55] makes it possible tocreate acceleration profiles with varying characteristics. In thiswork, we generate profiles that follow from the estimationof acceleration time and distance as described in [55]. Theresulting acceleration profile for one UN route depicted inFig. 4 and velocitiesvm = 50 km h−1 and vt = 20 km h−1

is shown in Fig. 6.4) 5G Radio Interface Numerology and System Aspects:

The 5G UDN is assumed to deploy OFDMA based radioaccess with 75 kHz subcarrier spacing, 100 MHz carrier band-width and 1280 active subcarriers. This is practically 5 timesup-clocked radio interface numerology, compared to 3GPPLTE/LTE-Advanced, and is very similar to those described,e.g., [19], [56]. The corresponding radio frame structure incor-porates subframes of length0.2ms, which include 14 OFDMsymbols. This is also the basic time resolution for UL referencesignals. In the upcoming evaluations, both continuous and

12

DoA ToA0

1

2

3

4

5

6

7

8

9RMSE

[◦]

0

0.5

1

1.5

RMSE

[ns]

96 MHz BW and ANs with an ISD of ∼25 m19.2 MHz BW and ANs with an ISD of ∼25 m96 MHz BW and ANs with an ISD of ∼50 m19.2 MHz BW and ANs with an ISD of ∼50 mSecond LoS-ANs

Fig. 7. The average RMSEs for the estimated DoA and ToA at the closestLoS-ANs (colored bars) and the second LoS-ANs (gray bars) along differentrandom routes through the Madrid map.

sparse UL reference signal subcarrier allocations are deployed,for comparison purposes, while the UN transmit power isalways 0 dBm. In both reference signal cases, 256 pilot subcar-riers are allocated to a given UN which are either continuous(19.2 MHz) or sparse over the whole carrier passband widthof 96 MHz. Also, two different ISDs of50m and25m in theUDN design are experimented.

In the evaluations, we assume that the UL reference signalsof all the UNs within a given AN coordination area areorthogonal, through proper time and frequency multiplexing.However, also co-channel interference from uncoordinatedUNs is modeled as explained in Section VI-A2. Assuminga typical noise figure of 5 dB, the signal-to-interference-and-noise ratio (SINR) at the AN receiver ranges between 5 dBto 40 dB, depending on the locations of the target UN andinterfering UNs on the map.

In general, all the EKFs are updated only once per100ms,to facilitate realistic communication of the ToA and DoAmeasurements from involved ANs to the central processingunit. Furthermore, in the positioning EKF, onlyK[n] = 2closest LoS-ANs are fused for simplicity.

B. DoA and ToA Estimation

In order to evaluate first the accuracy of the DoA and ToAtracking using the proposed DoA/ToA EKF, the RMSEs forboth estimates are illustrated in Fig. 7, averaged across mul-tiple random routes through the Madrid map. Each colouredbar represents a different network configuration used in theevaluations for the LoS-ANs that are the closest to the UNwhereas bars with a gray colour represent the respective resultsfor the second closest LoS-ANs. All the depicted results areobtained by averaging over multiple different routes.

Pos&Clock EKF Pos&Sync EKF DoA-only EKF0

0.5

1

1.5

2

2.5

3

RMSE

[m]

96 MHz BW and ANs with an ISD of ∼25 m19.2 MHz BW and ANs with an ISD of ∼25 m96 MHz BW and ANs with an ISD of ∼50 m19.2 MHz BW and ANs with an ISD of ∼50 m

Fig. 8. Positioning RMSEs for all tracking methods and with differentsimulation numerologies, along different random routes through the Madridmap.

As expected, the ToA estimation and tracking is moreaccurate when the UL beacons are transmitted using the wider96 MHz bandwidth and a sparse subset of subcarriers thanusing the narrower 19.2 MHz bandwidth due to enhanced time-domain resolution. Decreasing the ISD leads to better ToAestimates due to higher average SINRs at the ANs, especiallywhen using the narrow bandwidth while the difference is notso significant in the case of the 96 MHz bandwidth.

The accuracy of the DoA estimates, in turn, is generallyvery high. In general, since the variance of the azimuth angleestimation is always smaller, the more coplanar geometrybetween the TX and RX we have, the average accuracy of theDoA estimates do not substantially vary between the differentISDs, or between the closest and second closest ANs. This isindeed because the geometry of more far away UNs is morefavorable for azimuth angle estimation. In general, one canconclude that excellent ToA and DoA estimation and trackingaccuracy can be obtained using the proposed EKF.

C. Positioning, Clock and Network Synchronization

Next, the performance of the proposed DoA/ToAPos&Clock and Pos&Sync EKFs is evaluated by trackingUNs moving through the earlier described Madrid map withrandomly drawn trajectories. Each generated route starts froman endpoint of a road on the map with some pre-determinedinitial velocity. Thereafter, the motion of the UN is definedaccording to the presented motion model. The routes aredefined to end when the UN crosses 6 intersections on themap. For the sake of simplicity, the UN is moving in themiddle of the lane. In all the evaluations, the update periodof the positioning and synchronization related EKFs at thecentral processing unit is only every 500th radio sub-frame,i.e., only every 100ms. This reflects a realistic situation such

13

Pos&Clock EKF Pos&Sync EKF LoS-ANs0

2

4

6

8

10

12

14RMSE

[ns]

96 MHz BW and ANs with an ISD of ∼25 m19.2 MHz BW and ANs with an ISD of ∼25 m96 MHz BW and ANs with an ISD of ∼50 m19.2 MHz BW and ANs with an ISD of ∼50 m

Fig. 9. The average RMSEs for the UN clock offset estimates along differentrandom routes through the Madrid map, with synchronous (left) and unsyn-chronous (middle) ANs. Also shown are the respective RMSEs for the LoS-ANs mutual clock offset estimates (right).

that the DoA and ToA measurements of individual ANs canbe realistically communicated to and fused at the central unit.

Before the actual evaluations, in case of unsynchronizedANs, we initialize the clock offsets of all unsynchronized ANswithin a network according toρℓk [0] ∼ N (0, σ2

ρ,0) with σρ,0 =100µm as motivated in Section IV-B2. Whenever a new UN isplaced on the map, we initialize the UN position estimatep[0]using the CL method within the proposed initialization process.In our evaluations, covariance of the initialized positionesti-mate is defined as a diagonal matrixσ2

p,0·I2×2 whereσp,0 is setto large using the distance between the initial position estimateand current LoS-ANs. Furthermore, we set the initial velocityaccording to[vx[0], vy[0]]

T ∼ N (0, σ2v,0 ·I2×2) with quite large

STD of σv,0 = 5m s−1 based on the earlier discussion inSection IV-B2. The initial estimates that we have determinedfor the UN so far are then used as a prior for the DoA-onlyEKF within the proposed initialization method. The DoA-onlyEKF is executed forNI = 20 iterations to initialize the moreelaborate EKFs, in terms of position and velocity. Thereafter,we need to initialize also the necessary clock parameters inorder to use the actual DoA/ToA Pos&Clock and Pos&SyncEKFs. As motivated in Section IV-B2, we set the clock offsetand skew for the UNs according toρ[0] ∼ N (0, σ2

ρ,0) whereσρ,0 = 100µs, andα[0] ∼ N (µα,0, σ

2α,0) where µα,0 =

25ppm andσα,0 = 30ppm, respectively. In addition to settingthe initial clock parameters, we also choose the reference ANto be the closest LoS-AN to the UN before we start to usethe final DoA/ToA Pos&Clock and Pos&Sync EKFs for thepositioning and network synchronization purposes. The samevalues are also used for the initialization of the DoA-only EKFthat is used as a comparison method for the proposed moreelaborate EKFs.

Furthermore, we set the STD of the clock skew drivingnoise in the clock model (6) toση = 6.3 · 10−8 based onthe measurement results in [38]. However, the STD of theclock skew within the EKF is increased toση = 10−4 sinceit leads to a much better overall performance especially whenthe clock offset and clock skew estimates are very inaccurate,e.g., in the initial offset tracking phase. Since we assume thatthe UN is moving in a vehicle in an urban environment, weset the STD of UN velocity toσv = 3.5m s−1.

Position and clock offset tracking performance of the pro-posed cascaded DoA/ToA Pos&Clock and Pos&Sync EKFs incomparison to the DoA-only EKF is illustrated in Figures 8-9, where each color represents a different simulation setupused in the evaluations. In contrast to the classical DoA-onlyEKF, the root-mean-squared errors (RMSEs) obtained usingthe DoA/ToA Pos&Clock and Pos&Sync EKFs are partitionedaccording to network synchronization assumptions. Further-more, we also analyse the accuracy of the UN clock offsetestimates in both synchronized and phase-locked networks.Forthe sake of simplicity, we fuse the DoA and ToA estimatesat each EKF update period of100ms only from two closestLoS-ANs. The first 10 EKF iterations (1 second in real time)after the initialization procedure are excluded in the RMSEcalculations, to avoid any dominating impact of the initialestimates on the tracking results.

Based on the obtained positioning results that are illustratedin Fig. 8 the proposed Pos&Clock and Pos&Sync EKFssignificantly outperform the earlier proposed DoA-only EKFinall considered evaluation scenarios. In particular, an impressivesub-meter positioning accuracy, set as one core requirement forfuture 5G networks in [10], is achieved by the both proposedmethods in all test scenarios, and they even attain positioningaccuracy below0.5m in RMSE sense with the 96 MHzbandwidth and ISD of around25m. An unfavourable andknown feature of the DoA-only EKF is that its performancedegrades when the geometry of the two LoS-ANs and theUN resembles a line. Since the proposed Pos&Clock andPos&Sync EKFs use also the ToA estimates for ranging, theydo not suffer from such disadvantageous geometries.

In the case of a synchronized network, the Pos&Clock EKFachieves highly accurate synchronization between the unsyn-chronized UN and network with an RMSE below2ns in everytest scenario as illustrated in Fig. 9. Since the presented ToAestimation errors in Fig. 7 are between0.1ns and1.5ns, thesepropagate very well to the achievable clock offset trackinginthe fusion EKF. Interestingly the high initial clock offsetSTDof 100µs is, in general, improved by 5 orders of magnitude.

Investigating next the achievable clock-offset estimationaccuracy with unsynchronized ANs in Fig. 9 (Pos&SyncEKF), we can clearly observe that overall the performanceis somewhat worse than in the corresponding synchronouscase. Furthermore, network densification from ISD of50mdown to25m actually degrades the UN clock offset estimationaccuracy to some extent. These observations can be explainedwith the assumed motion model and how the clock offsets ofthe LoS-ANs are initialized within the EKF. When the UNis moving at the velocity of50 km h−1, each LoS-AN alongthe route, with ISD of25m, is in LoS condition with the UN

14

only 1.8 s and, therefore, we can obtain only 18 DoA/ToAmeasurements in total from each LoS-AN due to assumedupdate period of100ms. Therefore, the Pos&Sync EKF canbe executed a lower number of iterations for a given LoS-ANpair, compared to the network with50m ISD. This, in turn,means that the initial more coarse clock offset estimates oftheindividual LoS-ANs have relatively higher weight, throughthemeasurement equation (52), to the UN clock offset estimate inthe network with ISD of25m. However, even in the presenceof unsynchronized network elements, UN clock offset can beestimated with an accuracy of around5 ns to10ns, as depictedin Fig. 9. Furthermore, the results in Fig. 9 (LoS-ANs) alsodemonstrate that highly accurate estimates of the mutual clockoffsets of the ANs can be obtained using the proposed cascadedPos&Sync EKF.

The behaviour and performance of both the joint DoA/ToAPos&Sync EKF and the DoA-only EKF in trackingwith different simulation configurations are further visu-alized through the videos that can be found on-line athttp://www.tut.fi/5G/TWC16/.

VII. C ONCLUSION

In this article, we addressed high-efficiency device position-ing and clock synchronization in 5G radio access networks.First, a novel EKF solution was proposed to estimate and trackthe DoAs and ToAs of different devices in individual ANs,using UL reference signals, and building on the assumptionof multicarrier waveforms and antenna arrays. Then, a secondnovel EKF solution was proposed, to fuse the DoA and ToAestimates from one or more LoS-ANs into a device positionestimate, such that also the unavoidable clock offsets betweenthe devices and the network, as well as the mutual clock offsetsbetween the network elements, are all taken into account.Hence, the overall solution is a cascaded EKF structure, whichcan provide not only high-efficiency device positioning butalso valuable clock synchronization as a by-product. Then,comprehensive performance evaluations were carried out andreported in 5G UDN context, with realistic movement modelson the so-called Madrid grid incorporating also full ray trac-ing based propagation modeling. The obtained results clearlyindicate and demonstrate that sub-meter scale positioningandtracking accuracy of moving devices can be achieved usingthe proposed cascaded DoA/ToA EKF solutions. Moreover,network synchronization in the nano-second level can also beachieved by employing the proposed EKF based scheme. Ourfuture work will focus on extending the processing solutionsto 3D positioning, as well as exploiting the high-efficiencypositioning information in mobility management and location-based beamforming in 5G networks.

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