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

Transcription

1 9th Internationa Symposium on Image and Signa Processing and Anaysis (ISPA 05) September 7-9, 05, Zagreb, Croatia Estimation and Tracking of LTE Signas Time of Arriva in a Mobie Mutipath Environment Marco Driusso, Fuvio Babich University of Trieste, Itay marco.driusso@phd.units.it babich@units.it Fabian Knutti, Mischa Sabathy Hochschue für Technik Rapperswi, Switzerand fabian.knutti@hsr.ch mischa.sabathy@hsr.ch Chris Marsha u-box UK Ltd, United Kingdom chris.marsha@u-box.com Abstract This paper proposes an agorithm for the estimation and tracking of the direct path (DP) time of arriva (TOA) of the signas received from 4G ong term evoution (LTE) ceuar base stations (BSs) in a mobie mutipath environment. This is important for TOA-based ranging measurements, which may be expoited for positioning appications. A sub-space approach is used for the estimation of the mutipath time of arriva, and a state-space approach is expoited for tracking the direct path. The deveoped framework is appied to rea LTE signas coected using a portabe experimenta setup during a car drive in the town of Rapperswi, Switzerand. The pseudoranges derived from the tracking of the DP TOA are then compared to the ranges from the considered LTE base stations cacuated using GPS, demonstrating the effectiveness of the proposed approach. Index Terms Time of arriva estimation, Direct path tracking, LTE, ESPRIT, Kaman fiter, SDR. I. INTRODUCTION Recenty, the downink signas of ceuar mobie systems have been considered as an aternative to the poor performance of goba navigation sateite systems (GNSSs) in chaenging propagation environments []. Areas characterized by imited sky view and distortion caused by mutipath, such as urban canyons and indoors, where it is difficut for cean GNSS signas to be received, are usuay we covered by the ceuar systems, which therefore may be expoited for ranging. From this point of view, the third generation partnership project ong term evoution (3GPP LTE) standard is a communication system of particuar interest because of its avaiabiity, signa strength, signa bandwidth [], and because it is based on orthogona frequency division mutipexing (OFDM) [3]. Athough the LTE signa power is generay sufficient in the chaenging areas described above, mutipath sti dominates the propagation environment. Therefore, specific signa processing techniques are needed to perform time of arriva (TOA) based range measurements that do not suffer bias due to mutipath and non-ine-of-sight (NLOS) propagation. Moreover, tracking of the estimated direct path (DP) TOA is needed, since the environment as we as the receiver position vary with time. Accordingy, the recent iterature presents severa works on these subjects. The authors of [4] propose a cross-correation based TOA estimator with NLOS mitigation together with a partice fiter for performing indoor positioning with LTE signas generated ad-hoc using prototyping hardware. In [5], super-resoution agorithms and frequency diversity techniques are empoyed for indoor static ranging measurements using wideband sounding signas. State-space approach agorithms specificay designed for channe sounding may aso be empoyed, such as [6] [8], but they require specific and too compex hardware for rea time consumer product impementation. This paper proposes an estimation and tracking agorithm for the DP TOA of LTE signas in mutipath mobie channes. Simiary to [9], the TOA estimation is performed using the estimation of signa parameters via rotationa invariance techniques (ESPRIT) expoiting opportunisticay the LTE OFDM piot tones. A state-space approach simiar to [7] is then adopted for tracking, and a nove measurement noise covariance estimation is performed, using the ESPRIT performance bound of [0]. To expore and vaidate the deveoped agorithm, rea LTE data gathered with the portabe setup of [] during a car drive on a route around the town of Rapperswi (Switzerand) is processed with the proposed framework. The resuts obtained are then compared with ranges from the considered LTE base stations (BSs) cacuated using GPS, to assess the effectiveness of the suggested approach. The remainder of the paper is organized as foows. Section II describes the expoited LTE downink signas. Section III describes the portabe experimenta setup used for coecting the data. Section IV expains the proposed agorithm. Section V reviews the obtained estimation and tracking resuts and Section VI summarizes the most reevant concusions. II. EXPLOITED LTE SIGNALS LTE offers two downink signas that are indicated for range measurements, i.e., the positioning reference signa (PRS) and the ce-specific reference signa (CRS). The PRS is specificay designed for the acquisition of mutipe simutaneous range measurements and is transmitted in dedicated time intervas []. However, operators generay tend to avoid its transmission in order to save bandwidth for user data. On the other hand, athough the CRS is primariy designed for channe estimation and coherent data demoduation, it may be opportunisticay expoited for range measurements, particuary because it is aways transmitted []. Hence, this work considers the CRS as the reference signa for TOA estimation and pseudorange evauation. The LTE downink physica ayer is organized in 0 ms ong radio frames. Each radio frame corresponds to 0 sub /5/$3.00 c 05 IEEE 76 Signa Processing Signa Processing Theory and Methods

2 9th Internationa Symposium on Image and Signa Processing and Anaysis (ISPA 05) September 7-9, 05, Zagreb, Croatia Tabe I LIST OF POSSIBLE DOWNLINK BANDWIDTH CONFIGURATIONS B.4MHz 3MHz 5MHz 0MHz 5MHz 0MHz NRB DL N sc N tot frames, each made of sots (0 sots per frame, 0.5 ms each). Each sot is composed of Nsymb DL OFDM symbos in the time domain. In the frequency domain (FD), each OFDM symbo corresponds to N sc =Nsc RB NRB DL sub-carriers, spaced of f = 5 khz when the norma cycic prefix configuration is adopted (for which Nsymb DL RB = 7 and Nsc = ). The basic resource unit of LTE, corresponding to the k th sub-carrier of a certain OFDM symbo in a sot, is referred to as resource eement (RE). REs are grouped in resource bocks (RBs), each corresponding to Nsc RB adjacent sub-carriers in the FD, for the duration of one sot. The number of tota sub-carriers used in each OFDM symbo (and utimatey the LTE signa bandwidth B) is determined by the number NRB DL of RBs per sot. There are 6 possibe configurations, which are summarized in Tabe I. Finay, LTE is capabe of transmitting signas from different antennas, which are identified with the concept of antenna port by using the index p []. The CRS is defined as a QPSK moduated ength-3 God sequence, mapped to the REs with the diamond pattern defined in [, p.78]. When a configuration with antenna ports is adopted, a CRS transmission occurs twice per sot: each time, a different CRS is transmitted from each antenna port on the same OFDM symbo in non-overapping sub-carriers. Since the CRS piot tones occupies one sub-carrier every six through a the avaiabe bandwidth (with a spacing of f CRS = 6 f = 90 khz), the tota number of transmitted piot tones is N tot = N sc /6 per antenna port. As specified in [, p.77], the mapping to REs of CRSs transmitted from different BS sectors (identified with NID ce {0,..., 503}) differs by a FD shift of k 0 =mod(nid ce, 6). III. EXPERIMENTAL SETUP FOR MEASUREMENTS A ive data set has been recorded which was then processed with the methods described herein. The ive data gathering setup consisted of two universa radio periphera (USRP) N0 software defined radios (SDR), which used the high precision 0 MHz reference cock of a GPS-ocked Rubidium frequency standard. Two USRP N0 SDRs were required since two LTE operators were avaiabe on different frequency downink channes. A conventiona persona computer (PC) acted as system controer and data recording unit. The PC recorded GPS time and position stamped ive data and guaranteed coherent samping between the two USRP N0 devices. The coherent and absoute GPS timed samping provided the possibiity to compare the different LTE signas of the two LTE operators. To reduce the arge amount of samping data (5 MSPS for each USRP N0), a bock-wise storage method was impemented, storing 0 ms of consecutive sampes every second. For the UBX & NMEA messages 0MHz Ref PPS Patch Antenna - Buit-in LNA u-box EVK-6N - GPS/GNSS Evauation Kit PPS Wide Band Antenna - Magnetic Mount - Gain: 3dBi peak SRS FS75 - Rubidium Frequency Standard - Accuracy: ±5 0 USRP N0 - Daughterboard: WBX 50-00MHz RX/TX - Samping Rate: 5MSPS USRP N0 - Daughterboard: WBX 50-00MHz RX/TX - Samping Rate: 5MSPS PC - Data Recording Software Ethernet Gbps Ethernet Gbps Figure. Live data gathering setup, which is a powered by a V/85Ah battery with a DC to AC converter. Y-coordinate CH903 (Grid km) 3 3 GPS Track Operator Operator X-coordinate CH903 (Grid km) Figure. Live data gathering route and considered LTE BSs. post-processing, the data was down-samped from 5 MSPS to 5.36 MSPS. Fig. shows a detaied overview of the ive data gathering setup, which for this experiment was instaed in a van. The data was gathered in the area of Rapperswi SG, Switzerand. The chosen route ed through urban, suburban and open-fied areas as the GPS track of route in Fig. shows. These different sections are we suited for gaining knowedge about the performance of the DP TOA tracking method in various common scenarios. This route resuted in a 0 minute drive at speeds between 0 and 50 km/h. The entire captured data was then searched for signas from avaiabe BSs by means of an exhaustive search against a ist of the ce identities of a the BSs visibe in the Rapperswi test area. After obtaining the coarse symbo timing of a avaiabe BSs, the 0 ms chunks where a BS was received with sufficient quaity were marked for each BS. One OFDM symbo containing the CRS, without cycic prefix, was then saved from every bock of raw data for every avaiabe BS for further processing. The recorded data contained signas from a tota of 9 BSs, 6 BSs from operator and 3 BSs from operator Signa Processing Signa Processing Theory and Methods

3 9th Internationa Symposium on Image and Signa Processing and Anaysis (ISPA 05) September 7-9, 05, Zagreb, Croatia, using a downink transmission bandwidth of 5 MHz and 0 MHz, respectivey. Figure shows the ocation of the BSs [] except for one distant BS which is ocated across the ake in south-southeastery direction and one BS ocated on a hi to the north. A BSs were found to be using a configuration with antenna ports. IV. PROPOSED ALGORITHM The samped data was processed according to the agorithm described in the foowing sections, which for convenience wi be referred to as EKAT, i.e., ESPRIT and Kaman fiter for time of Arriva Tracking. Let rt[n], i n = 0,..., N fft, be the sampes of the OFDM symbo containing the CRS coming from the i th detected ce ID, and coected at the discrete time index t. An N fft -point DFT is used to evauate the content of the sub-carriers of rt[n] i as Rt[k]=DFT{r i t[n]}. i The knowedge of the particuar symbo and sot indexes to which rt[n] i pertains, acquired during the coarse timing phase described above, is used to identify the actua CRS piot tones S i,p t [k], k C i,p t, contained in rt[n] i for each antenna port p. The set C i,p t ={k 0 +k f CRS, k =0,, N tot } is constituted by the N tot indexes of the sub-carriers occupied by a CRS tone for the considered OFDM symbo and antenna port. Using this information, a noisy samping of the channe frequency response (CFR) encountered by the considered CRS during its propagation can be easiy obtained using the east squares estimator as Ĥi,p t [k] = Rt[k i 0 + k f CRS ]/S i,p t [k 0 + k f CRS ], k = 0,, N tot, where the noise variance is assumed to be σ. Since the CRS tones are equay spaced, Ĥ i,p t [k] is a uniform samping of the CFR, with spacing f CRS. A. Mutipath TOA estimation As expained in [5], super resoution agorithms (SRAs) can be empoyed for the estimation of the TOA τ 0,..., τ L of a mutipath channe h(t) = L =0 h δ(τ τ ), by using a uniform samping of the corresponding CFR H(f) = L =0 h e jπτf. In this case, starting from the noisy CFR samping Ĥi,p t [k], a SRA is used to estimate the mutipath TOA of the propagation channe encountered by the considered CRS. Out of the avaiabe SRAs, an ESPRIT-based approach simiar to [9] was chosen, as it aows a smaer computationa compexity compared to other SRAs [3]. EKAT starts by arranging the sampes Ĥi,p t [k] in M-ength overapping snapshots x i,p t [m], that constitute the data matrix as: X i,p t x i,p t X i,p t = N [ x i,p t [0],, x i,p t [N ] ] C M N, () [m] = [ Ĥ i,p t [m],, Ĥi,p t [m + M ] ] T C M, () where N = N tot M +, M is a design parameter of the SRA, and ( ) T denotes the transpose operator. In the foowing, the indexes t, i, p wi be omitted for notationa simpicity. The data matrix X is reated to the estimate of the crosscorreation matrix of x as ˆR x =X X H C M M, where ( ) H is the Hermitian transpose operator. Hence, the eigenvaues λ λ M of ˆR x can be cacuated taking the square of the singuar vaues of X, obtained with a singuar vaue decomposition (SVD) as X = U Σ V H. The matrices U C M M and V C N N are unitary, and Σ C M N is a diagona matrix with the singuar vaues σ σ M in the main diagona, where (σ j ) = λ j. Using the eigenvaues λ j of ˆR x, the minimum descriptive ength criterion can be appied for the estimation of the number L of mutipath components in the considered CFR, by using the metric [5], [9]: MDL(k)= N(M k) og { M i=k λ/(m k) i M M k i=k λ i } + p(k), (3) where p(k) = k(m k) og N. Then, L is estimated as ˆL= arg min k {0,...,M } MDL(k). Once the number of mutipath components has been estimated, the actua ESPRIT agorithm is appied. This consists in seecting the first ˆL singuar vectors of X, which are equa to the ˆL eigenvectors of ˆR x corresponding to the ˆL biggest eigenvaues. These are stored in the matrix U s =U [I ˆL0 ˆL (M ˆL) ] T C M ˆL, where I P is the P P eye matrix and 0 P Q is a P Q a-zero matrix. Afterwards, M ˆL U s is decomposed in U s, = [I M 0 M ] U s C and U s, = [0 M I M ] U s C M ˆL, where 0 P is a P - ength a-zero coumn vector. The ESPRIT rotationa matrix is evauated as Ψ = (U H s, U s, ) UH s, U s, C ˆL ˆL, where ( ) denotes the inverse of a matrix. The mutipath TOA are finay cacuated using the ˆL eigenvaues {ψ } ˆL =0 of Ψ as: ˆτ = π f CRS arg {ψ }, = 0,, ˆL, (4) where arg{ } denotes the argument of a compex number. Since arg{ψ } [ π, π],, then the adopted SRA is capabe of estimating a TOA in the interva [ f CRS, f CRS ] = [ 5.55 µs, 5.55 µs] around the instant of measure t. By using the described procedure, a set of ˆL i,p (t) mutipath TOA Υ i,p (t) = {ˆτ i,p (t), = 0,, ˆL i,p (t) }, can be estimated for the CRS coming from the antenna port p of the i th sector in the measurement sampe at time t. The estimation of the mutipath TOA is necessary for separating the deayed paths from the DP, which is then tracked for positioning purposes with the procedure described in the foowing. B. State-space mode A state-space approach simiar to the one of [7] is used in EKAT for the tracking of the DP TOA. Consider a specific BS sector identified by the index i. The rea DP TOA τ i 0(t) of the CRS coming from i at time t, and its rate of change τ i 0(t), are modeed as the unknown state of a dynamic discrete-time inear system, which is estimated using a Kaman fiter (KF) on the basis of the TOA measurements acquired as described in Section IV-A. Hence, the state-space vector of such system is defined as ζ i (t) = [τ i 0(t), τ i 0(t)] T R (in the foowing the superscript i wi be omitted). Then, a nove aspect of the proposed approach is to combine the measurements of the two antenna ports by defining the entries of the measurement vector z E (t) = [z 0 E (t), z E (t)]t R as the two measurements of the DP TOA acquired with ESPRIT at time t from antenna ports p = 0 and p =, respectivey. This is justified by the 78 Signa Processing Signa Processing Theory and Methods

4 9th Internationa Symposium on Image and Signa Processing and Anaysis (ISPA 05) September 7-9, 05, Zagreb, Croatia fact that usuay when ony antenna ports are present, these differ ony in the poarization, and not in the antenna position, resuting in the same distance (and hence the same DP TOA) at the receiver. The discrete-time equations that mode the evoution of ζ(t) are then: where: ζ(t) = F ζ(t ) + q(t ), (5) z E (t) = H ζ(t) + r(t), (6) F = [ ] 0 and H = Q(t) = Q = q [ 3 [ ] 0. (7) 0 In (5)-(6), the process noise vector q(t) R and the measurement noise vector r(t) R have zero-mean white Gaussian distributed entries with covariance matrices given by Q(t)=E[q(t)q T (t)] and R(t)=E[r(t)r T (t)], respectivey. According to [6], the process noise covariance is equa to: ], t, (8) where q may be set empiricay during the KF tuning. Finay, EKAT reies on a time variant measurement noise covariance matrix R(t), which is seected at every t as wi be expained in Section IV-D. C. Kaman fitering for tracking The Kaman fitering for the estimation of the state ζ(t) pertaining to the i th BS sector foows the approach of [4] and consists of the foowing set of recursive equations: ˆζ (t) = F ˆζ(t ), (9) ˆP (t) = F ˆP(t ) F T + Q, (0) W(t) = ˆP (t) H T [R(t) + H ˆP (t) H T], () ˆζ(t) = ˆζ (t) + W(t) [z E (t) H ˆζ (t) ], () ˆP(t) = [ I W(t) H ] ˆP (t), (3) where ˆζ (t), ˆP (t), ˆζ(t), ˆP(t) and W(t) correspond to the predicted state, the predicted state covariance, the estimated state, the estimated state covariance, and the KF gain, respectivey. The cacuation of the first estimated state ˆζ(t 0 ) and the corresponding covariance ˆP(t 0 ) is performed according to the two step initiaization procedure of [4, p.47], by expoiting the measurements z E (t 0 ), z E (t 0 ). During initiaization, the entries z p E (t), p {0, } of the measurement vector z E(t) are seected from the resuts Υ i,p (t) of the ESPRIT mutipath TOA estimation as z p i,p E (t) = ˆτ 0 (t), t {t 0, t 0 }. Conversey, after initiaization (i.e., for t > t 0 ), z p E (t) is seected from Υi,p (t) according to the foowing strategy: min{ξ i,p (t)} n[ξ i,p (t)] > 0 z p E (t) = ˆτ i,p 0 (t) n[ξi,p (t)] = 0, ˆL i,p (t) > 0 z p E (t ), (4) ˆLi,p (t) = 0 [ 0] ˆζ (t) sparse missing measure where: Ξ i,p (t) = {τ Υ i,p (t) : c T τ ˆζ 0 (t ) < v max }; n[ ] denotes the cardinaity of a set; c is the speed of ight; T is the interva between two measurements (T = s in the proposed setup); v max is a design parameter representing the maximum aowed speed for the receiver; and ˆζ 0 (t) is the first component of the estimated state ˆζ(t) = [ˆζ 0 (t), ˆζ (t)] T, representing the tracked DP TOA at time t. The measurement seection strategy of (4) is needed for deaing with the foowing three probems. Firsty, the ESPRIT mutipath TOA estimation may produce outiers with TOA much earier than the rea DP TOA, and these are discarded according to a maximum aowed receiver speed v max, by comparing the estimated TOA in Υ i,p (t) with the previous DP TOA estimation ˆζ 0 (t ). Secondy, it may happen that, in a particuar measurement, despite a particuar ce ID being detected, the MDL criterion fais to find mutipath components in the considered signa, producing ˆL i,p (t) = 0. In this case, the vaue of the previous measurement is used. Thirdy, the CRS from a particuar ce may not be detected continuousy through the measurement period. It may in practice happen that at a certain t the receiver suffers of a deep fade or shadowing, resuting in a sparse missing measure, which is substituted with the measurement prediction H ˆζ (t). On the other hand, when the CRS is not received for more than D max consecutive measurements (e.g., when the BS is too far for being detected), the tracking is stopped and the KF restarted at the next avaiabe measurement. D. Measurement noise covariance estimation The anaysis of [0] evauated the error variance of the ESPRIT agorithm when used to estimate the directions of arriva of narrowband waveforms on a inear uniform array. Using a simiar approach, the variance of the estimation error ɛ reative to the th estimated TOA has been quantified in the presented framework. However, the procedure of [0] is based on the knowedge of the rea number of mutipath components L and on the SVD of the exact data matrix X, which is buit in the same way as ()-(), except that the rea vaues of the channe sampes H[k] are used instead of the LS noisy estimations Ĥ[k]. Ceary, this is not feasibe in rea scenarios, since these quantities are unknown. Hence, EKAT reies on the use of the noisy data matrix X and of the estimated vaue ˆL. Monte Caro simuations, not reported for ack of space, were performed to assess the effectiveness of this approach, and they showed a substantia agreement between the vaues of Var(ɛ ) cacuated using X and the ones obtained using X, provided that the noise variance σ determines a signa-to-noise ratio corresponding to an above-threshod estimation. To estimate the measurement noise variance, consider, in addition to the matrices defined in Section IV-A, the matrices U o = U [0 (M ˆL) ˆLI M ˆL] T C M (M ˆL), U o, = [I M 0 M ] U o and U o, = [0 M I M ] U o, where U o,, U o, C (M ) (M ˆL). Then, the error variance reative to the estimation of τ can be approximated by: Var (ɛ ) C ˆσ v U ) s,( Uo, ψ U o, Σ ˆL u, (5) where: C = /(π f CRS ) ; ˆσ is an estimate of the variance of the noise affecting the CFR sampes Ĥ[k]; denotes the 79 Signa Processing Signa Processing Theory and Methods

5 9th Internationa Symposium on Image and Signa Processing and Anaysis (ISPA 05) September 7-9, 05, Zagreb, Croatia Tabe II CONSIDERED SECTORS AND RANGING PERFORMANCE COMPARISON Op. BS NID ce i ε I [m] ε0.5 I [m] ε 0.95 I [m] ε E [m] ε0.5 E [m] ε 0.95 E [m] norm of a vector; U s, =(UH s, U s, ) UH s,; Σ ˆL C ˆL ˆL is the sub-matrix obtained taking the upper-eft ˆL ˆL bock of N Σ; and u, v, ψ are respectivey the eft eigenvector, the right eigenvector and the corresponding eigenvaue of Ψ. In the proposed framework, ˆσ is obtained using the approach of [5], by expoiting the M ˆL smaer eigenvaues of ˆR x : ˆσ = M ˆL M j= ˆL+ λ j. (6) The error variances Var(ɛ ) are evauated using (5) for each mutipath TOA estimate ˆτ i,p (t) Υ i,p (t) obtained at t for the CRS of sector i, antenna port p. Then, the measurement noise covariance matrix is chosen as R(t) = diag{[r 0 (t), R (t)]} R, where the vaue of R p (t), p {0, }, is determined in accordance to the choice of (4), i.e.: Var (ɛ ) n[ξ i,p (t)] > 0 R p γ 0 Var (ɛ 0 ) n[ξ i,p (t)] = 0, (t)= ˆL i,p (t) > 0 γ R p. (7) (t ) ˆLi,p (t) = 0 γ R p (t ) sparse missing measure In (7), is the index for τ =min{ξ i,p (t)}, and γ, γ, γ 0 > increase the unreiabiity when using a previous measurement, a predicted measurement, and a measurement impying a receiver speed higher than v max, respectivey. V. RESULTS The EKAT agorithm expained in Section IV was appied to the data coected with the setup of Section III. A the detected signas were considered, except the ones having ce ID pertaining to BS 4 and 6 of operator, and to BS 3 of operator, since too weak or too few measurements were avaiabe for these sectors. The considered ce IDs and the corresponding indexes i are isted in Tabe II. For a the measurements in which each sector i was detected, EKAT was appied, obtaining a sequence of estimated states ˆζ i (t), of which the first component ˆζ i 0(t) identifies the tracked DP TOA for every t. Hence, ˆρ i (t) = c ˆζ i 0(t) represents the pseudorange P ( error <ε) Op., BS, N ce ID =86 Op., BS, N ce ID =84 Op., BS3, N ce ID =7 Op., BS5, N ce ID =38 Op., BS, N ce ID =5 Op., BS, N ce ID = ε [m] Figure 3. Cumuative density functions of the absoute ranging error for the EKAT agorithm (thick ines) and IDFT-based estimator of [] (thin ines). measured from the BS of sector i at time t. The agorithm was run using the foowing parameters: D max = 5, M = 0.48N tot, q =5 0 9, v max =70 m/s, γ 0 =γ =00, γ =0. Since the receiver does not have the same time reference as the transmitting LTE BSs, a bias i was removed from ˆρ i (t) in order to obtain a proper range measure. Moreover, athough the receiver cock is ocked to a frequency standard, the transmitter cock sti exhibits a drift δ i, which was corrected together with the bias. The bias and drift over the period of the experiment were estimated using the same approach of []. Finay, the estimated range was evauated as ˆd i (t) = ˆρ i (t) i δ i t. As a reference, the TOA estimator of [] is taken as a benchmark. This is based on seecting the DP TOA as the time corresponding to the highest peak of the discrete time channe impuse response that can be obtained as IDFT{Ĥi,p t [k]}. The same bias i and drift δ i corrections were appied to the pseudoranges obtained with the benchmark estimator. Tabe II compares the ranging performance of EKAT (indicated with E) with that of the IDFT-based benchmark estimator (indicated with I). The ranging error was evauated for a t as the difference between the tracked range ˆd i (t) and the corresponding GPS range. The used performance figures are the root mean square error (RMSE), denoted as ε x, x {E, I}, and the error probabiity abscissa, defined as the vaue εp x such that P ( error < εp x ) = p, x {E, I}. As can be seen, EKAT outperforms the benchmark for a sectors except NID ce =3, which however was found to point to north, meaning that a DP reception was never possibe on this test route. In Figure 3, a more detaied investigation compares the ranging error cumuative density functions (CDFs) obtained with EKAT and with the IDFT-based agorithm for a seected ce ID of each considered BS. Again, EKAT aways obtains a better curve compared to the corresponding benchmark resut. Finay, consider Figures 4a-4b, where the resuts of the DP TOA estimation and tracking agorithm are presented for sector i = (operator, BS, NID ce = 5) and i = 4 (operator, BS, NID ce = 84), respectivey, over seected iustrative time intervas. The upper pots depict the ranges obtained correcting bias and drift on the pseudoranges 80 Signa Processing Signa Processing Theory and Methods

6 9th Internationa Symposium on Image and Signa Processing and Anaysis (ISPA 05) September 7-9, 05, Zagreb, Croatia ranges ˆµ,p (t) [m] tracked range [m] ranges ˆµ 4,p (t) [m] tracked range [m] (p = 0) = 0 = = = 3 (p = ) = 0 = = = 3 GPS range IDFT TOA est ˆd(t), EKAT measurement index t (a) (p = 0)(p = ) = 0 = 0 = = = = = 3 = 3 GPS range IDFT TOA est ˆd 4(t), EKAT measurement index t (b) Figure 4. Resuts obtained appying EKAT to the coected data from (a) operator, BS, NID ce =5, and (b) operator, BS, N ce ID =84. c ˆτ i,p (t), i.e. ˆµ i,p (t) = c ˆτ i,p (t) i δ i t. For both antenna ports p {0, }, points corresponding to the first 4 detected paths are potted, i.e., {0,, 3}. The ower pots show the tracked range ˆd i (t) and the corresponding ranges obtained with the benchmark estimator. As a reference, the GPS range is aso shown. Figure 4a highights how the benchmark agorithm is biased by mutipath (measurement indexes around 50 and 500) and, conversey, how the proposed approach is capabe of reducing its detrimenta effects. Figure 4b shows again the effectiveness of EKAT against mutipath effects (measurement indexes around 00 and 90), and its robustness against mutipath TOA estimation outiers (which are visibe in the bottom of the upper pot in Figure 4b). VI. CONCLUSIONS A TOA-based ranging system has been demonstrated for use for positioning, which expoits rea LTE downink signas for performing distance measurements under practica mobie conditions. A portabe measurement setup characterized by high cock precision has been deveoped, and used to coect sampes from mutipe newy-depoyed LTE base stations downink signas, in a test scenario representative of a variety of typica severe propagation environments. The acquired data was processed with an appropriatey designed DP TOA estimation and tracking agorithm named EKAT, which comprises an ESPRIT SRA for separating mutipath TOA, together with a KF for tracking the DP. A measurement seection strategy was proposed for deaing with the impairments of data coected in a rea environment, and additiona information was incorporated by using the signas from the mutipe LTE transmit antenna ports. A measurement noise covariance estimation method was empoyed for quantifying in the KF the reiabiity of the TOA estimates. The resuts of a the tests showed that EKAT is effective despite the detrimenta effects of mutipath, achieving an improved RMSE between 9 m and 3 m, and reaching a precision between m and 0 m in 50% of cases, depending on the base station and propagation environment encountered. REFERENCES [] R. Zekavat and R. M. Buehrer, Handbook of Position Location: Theory, Practice and Advances. John Wiey & Sons, Sep. 0. [] C. Gentner, S. Sand, and A. 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