On Time-of-Arrival Estimation in NB-IoT Systems

Transcription

1 On Time-of-Arrival Estimation in NB-IoT Systems Sha Hu, Xuhong Li, an Frerik Rusek Department of Electrical an Information Technology, Lun University, Lun, Sween arxiv:7.383v [cs.it Nov 7 Abstract We consier time-of-arrival (ToA) estimation of a first arrival-path for a evice working in narrowban Internetof-Things (NB-IoT) systems. Due to a limite 8 KHz banwith use in NB-IoT, the time-omain auto-correlation function (ACF) of transmitte NB positioning reference signal (NPRS) has a wie main lobe. Without consiering that, the performance of ToA estimation can be egrae for two reasons. Firstly, uner multiplepath channel environments, the NPRS corresponing to ifferent receive paths are superimpose on each other, an so are the cross-correlations corresponing to them. Seconly, the measure peak-to-average-power-ratio (PAPR) use for etecting the presence of NPRS is inaccurate. Therefore, in this paper we propose a space-alternating generalize expectation-maximization (SAGE) base metho to jointly estimate the number of channel taps, the channel coefficients an the corresponing elays in NB-IoT systems, with consiering the imperfect ACF of NPRS. Such a propose metho only uses the time-omain cross-correlations between the receive signal an the transmitte NPRS, an has a low complexity. We show through simulations that, the ToA estimation of the propose metho performs close to the maximum likelihoo (ML) estimation for a single-path channel, an significantly outperforms a traitional ToA estimator that uses signal-to-noise (SNR) or power threshols base estimation. I. INTRODUCTION Observe-time-ifference-of-arrival (OTDOA) is a ownlink positioning metho aopte in long-term-evolution (LTE) [, which relies on time-of-arrival (ToA) estimates from at least three base-stations. The 3r Generation Partnership Project (3GPP) has eicate a significant effort to enhance positioning support for newly feature narrowban Internetof-Things (NB-IoT) systems [, [3. The NB positioningreference-signal (NPRS) is transmitte to enhance positioning measurements at receivers to ensure sufficiently high signal quality an etection probability, which is istribute in time an frequency resources over a subframe, an a number of consecutive positioning subframes can be allocate with a certain perioicity. In a subframe where NPRS is present, no ata but only control signalings are transmitte to reuce interference such as epicte in Fig.. In NB-IoT systems, the quarature phase-shift keying (QPSK) moulate NPRS symbols are generate an mappe to one physical resource block (PRB) (8 KHz) [. A number of consecutive NPRS subframes can be configure an transmitte perioically in every raio frame (ms), an the perio of one positioning occasion can be configure to more than a secon. The minimum unit of ToA use in LTE is T s =/3.7 µs, which correspons to a istance-resolution about meters (m). To successfully position an NB-IoT evice, ToA for at least three base-stations nee to be etecte. With more etecte base-stations, the positioning resolution can be further improve. One an two PBCH antenna ports R R R... R R l= l=6l= l=6 n s is even n s is o PRS subframe R... Fig.. An NPRS pattern in one PRB with normal cyclic-prefix (CP) in LTE. The NPRS transmitte on antenna port 6 is labele as, while the normal cell-specific reference signal (CRS) sent on antenna port is labele as R. A rich literature exists for ToA estimation which can be consiere as channel estimation problem, an investigations have been carrie out for ultra wieban (UWB) an OFDM systems such as in [4, [5. For NB-IoT system, ToA estimation becomes more challenging ue to a limite number of NPRS symbols transmitte in a banwith 8 KHz, even though the channels are assume constant over one subframe ue to low mobility of NB-IoT evices. As shown in [6, it is ifficult to istinguish two arriving paths with a timeelay ifference less than an inverse of the signal banwith [6. Uner multiple-path environments, the imperfect NPRS auto-correlation functions (ACF) corresponing to ifferent receive paths are superimpose on each other, an egraes the ToA estimation performance. Further, even uner a singlepath channel such as AWGN, the measure peak-to-averagepower-ratio (PAPR) use for etecting ToA is inaccurate without consiering the wie lobe of the ACF. Subspace fitting algorithms such as multiple signal classification (MUSIC) [7 an estimation of signal parameters via rotational invariance techniques (ESPRIT) [5 can be efficient in estimating the ToA with superimpose signals. But the computational complexities are relative high an Fourier transformations are neee to transfer the receive signal into frequency omain. In [4, the authors propose a lowcomplexity extension of the sliing correlator for channel an ToA estimations base on maximum likelihoo (ML) principle, in the presence of pulse overlap for impulse-raio UWB system. However, the authors assume that, the number of channel taps are known an no overlap between three or more consecutive paths, which may not apply in NB-IoT systems. Traitionally, there are also threshol-base algorithms R R

2 for ToA estimation utilizing such as measure signal-to-noise (SNR) an power [8 [. In [, the authors propose an iterative algorithm for ToA estimation base on the ACF, which iteratively cancels the peaks from the obtaine crosscorrelations. However, as the peaks are incorrect cause by overlapping of ACFs corresponing to ifferent channel taps, it oes not improve the performance of ToA estimation for NB-IoT systems [. In this paper, we consier ToA estimation in NB-IoT systems where only one PRB is use for ata-transmission. As the ML function epens on the unknown number of channel taps, the channel coefficients an the elays, the optimal estimation has prohibitive complexity. Therefore, we propose a space-alternating generalize expectation-maximization (SAGE) base metho to jointly estimate these parameters an the ToA, with consiering the ACF of the time-omain NPRS signal. The propose algorithm is base on the time-omain cross-correlations of the receive signal an the transmitte NPRS signal which yiels a low computational cost, an mainly comprises two steps running iteratively: The first step uses the SAGE algorithm to estimate the channel coefficients an the corresponing elays for a given number of channel taps; While the secon step uses heuristic approaches to remove the invali channel taps. We show through simulations results that, the propose ToA estimation metho works well both for a single-path channel such as AWGN an multi-path faing channels, which is ifficult for traitional threshol base ToA estimators to achieve. A. Receive Signal Moel II. PROBLEM FORMULATION In the consiere single-input-single-output (SISO) NB-IoT system, we assume a sampling-rate F s with a typical value.9 MHz. Denote the true elay of the ith channel tap as τ i, which is measure in number of samples as i = τ i Fs. () Then, the superimpose receive samples y[n with a total length D for all L taps can be moele as L y[n = h i s[n i + w[n, () i= where s[n is the time-omain NPRS signal (incluing CP) transmitte in one subframe with a total length S, an h i are complex-value channel coefficients that are assume constant over one subframe. The noise w[n is moele as AWGN with a zero-mean an variance σ, an the SNR is efine as SNR=σ s /σ, (3) where σ s is the average power of transmitte s[n. Traitionally, in orer to etect the ToA, i.e.,, a crosscorrelation between the receive samples y[n an the NPRS s [ n is implemente with a correlator, which yiels +S R[ = y[ks [k = k= L h i γ( i ) + w[, (4) i= Amplitue Amplitue Delay [T s Delay [T s Fig.. The amplitue of time-omain ACFs of PRS in one subframe with PRB an PRB at sampling rate 3.7 MHz, respectively. where γ() is the normalize ACF of s[n with elay, an w[ is the noise term after correlation which is colore. An NPRS signal is claime to exist if a following conition max { R[ } PAPR >η D, (5) R[ D = is satisfie, where D is the length of R[ that correspons to a possible maximum time-elay. With (5) satisfie, a threshol base metho [4, [ estimates the ToA accoring to = argmin max R[ { R[ } > η. (6) In (5) an (6), η an η are preefine threshols that can be ajuste for ifferent scenarios. There are several rawbacks of estimating ToA applying (5) an (6) in NB-IoT systems. Firstly, when channel coefficients h i are unkown, the non-coherent aition in (5) of R[ is inferior to a coherent aition that compensates the channel impacts [. Seconly, since the ACF of the NPRS has a wie lobe in NB-IoT systems, it shoul be consiere in the PAPR evaluation in (5). Thirly, the estimate in (6) can be inaccurate uner the case that max { R[ } is attaine with the correct ToA such as uner a sing-path channel channel. Lastly, the threshol in (6) nees to be tune for ifferent channels types, which is however, unknown to the receivers. In Fig. the amplitue of normalize time-omain ACF of the NPRS transmitte in PRBs an only one PRB at sampling rate 3.7 MHz are shown. As what can be clearly seen that, with only one PRB use, the ACF has a wie lobe. Hence, the ACFs corresponing to ifferent channel taps in R[ can be superimpose with each other. We illustrate such an phenomenon through an example below. Example. Consier a customize two-path channel with constant coefficients h = [.4, an elays τ = [, 6T s. The noiseless cross-correlation R[ is shown in Fig. 3.

3 3 Amplitue Delay [T s Fig. 3. The superimpose cross-correlations in Example, with the correct ToA at, but the maximum of R() is achieve at = 38, ue to the strong impact from a secon path. B. Formulation of ToA Estimation Denote the elay vector = [,,, L an the channel vector h = [h, h,, h L. From (), the ML estimator is (, h, L) = arg min,h,l N n= L y[n h i s[n i, (7) i= Directly optimizing (7) for all possible values of the unknown parameters can yiel a prohibitive complexity. Therefore, we next solve (7) in a suboptimal manner with an objective of goo performance for all types of channel an a low computational cost. III. PROPOSED TOA ESTIMATION METHOD The propose ToA estimation metho to solve (7) mainly comprises two steps. In a first step, we assume L is known an estimate h an n using SAGE algorithm [3. Then, in a secon step, heuristic approaches are use to refine L an removing invali channel taps. These two steps are running iteratively until L converges. As shown in Table, an initial value of L can be set to 9, 5 an for R[ evaluate at 3.7 MHz,.9 MHz an 4 KHz, respectively, which is sufficiently large to cope with the largest elays for the liste faing channels. A. Step : SAGE Iteration with a Given L We first present the SAGE base algorithm which is summarize in Algorithm. If there is no priori information about the channel elays an coefficients, we can sort R[ an set an initial to the locations of the L largest values, an an initial channel estimate as h l =R[ l, l<l. (8) Let an h be the estimate elays an channel coefficients in a previous iteration. Then, in a next SAGE iteration, the elay of the l-th tap can be upate as l = arg max R l [, (9) where R l [ is the cross-correlation that removes the other estimate NPRS, which equals with +S R l [ = ỹ l [ks [k. () k= ỹ l [n = y[n Inserting () into () yiels R l [ = R[ L i=,i l L i=,i l With (), the noise power is estimate as σ = D D = h i s[n i. () h i γ( i ). () R l [ h l γ( l ). (3) Then, l is upate as in (9), an finally the channel coefficient h l is upate as h l = E E k= E followe by an LMMSE filtering h l = γ (k) R l [ l + k, (4) h l + σ / h l. (5) The variable E is yet to be optimize, which epens on the property of the ACF shown in Fig.. In principle, for a singlepath channel, it is beneficial to set E to a large value to enoise the estimate h l. However, for multiple-path channel, a large E can also egrae the accuracies of estimate h l, ue to potential interferences from the other channel taps. Therefore, it is a trae-off between these two ifferent channel types. The processes (9)-(5) are implemente successively for each of the L channel taps. In such a way, solving problem (7) is transfere to solve a following problem (, h, L) arg min,h,l D = L R[ h i γ( i ), (6) i= which is suboptimal (ue to the colore noise in (4)), but simplifies the original problem in two aspects: Firstly, the length D of correlations R[ is in general much shorter then the length N of NPRS s[k, hence, the number of complex multiplications are reuce. Seconly, only one crosscorrelation process is neee to compute R[ in solving (6). To summarize, the SAGE algorithm in the first main step runs iteratively with three sub-steps: First, the ACFs corresponing to the other channel taps are remove from the cross-correlations. Secon, h l an l are upate base on the upate R l [ successively for all taps. Lastly, the reconstructe signal h l γ( ñ l ) with refine estimates are then remove from R[ before moving on to the processes of the next path.

4 4 TABLE I DELAY PROFILE IN NUMBER OF SAMPLES AND RELATIVE POWER IN DB AT DIFFERENT SAMPLING-RATE. Channel Type 3.7 MHz.9 MHz 4 KHz EPA EVA ETU [,,, 3, 6, 3 samples [, samples sample [, -., -., -3., -8., -7., -.8 B [., -5.7 B B [,, 5,,,, 33, 53, 77 samples [,,, 3, 5 samples [, sample [, -.5, -.4, -3.6, -.6, -9., -7., -., -6.9 B [, -.3, -.9, -5.9, -.8 B [, -3. B [,, 4, 6, 7, 5, 49, 7, 54 samples [,, 3, 4, samples [, sample [-., -., -.,,,, -3., -5., -7. B [, -6.4, -9.4, -.4, -3.4 B [, -4.9 B Algorithm SAGE base Channel Estimation Require: Normalize auto-correlation γ(), cross-correlation R[, tap-length L an SAGE iteration number M. : If no initial inputs an h available: Sort R[ an set an initial to be the locations of the L largest values, an the channel estimate h l =R[ l for all l<l. : for l =,,, L o L 3: R[ = R[ h l γ( l ) i= 4: en for 5: if L = then 6: Break 7: else 8: for m =,,, M o 9: for l =,,, L o : R[ = R[ + hl γ( l ) : σ = D D R[ = : l = arg max R[ 3: hl = E E k= E γ (k) R l [ l + k 4: hl = h l + σ / h l 5: R[ = R[ hl γ( l ) 6: en for 7: en for 8: en if 9: Output estimate h, an σ. B. Step : Refinement of L With the estimate h an, we next propose heuristic methos to etect L an remove invali channel taps, which comprises two steps an is summarize in Algorithm. We first consier the case that only one-path is presente, i.e., L =, then from (7), the ML estimates [4 of channel elay an coefficient are peak = arg max R[, (7) h peak = R[ peak. (8) These two estimates plays an key role in fining possible invali paths. Algorithm Propose ToA estimator for NB-IoT Require: An initial input L. : Run Algorithm with L=L, an output h, an σ. : With input h an, output refine h an after removing invali paths satisfying (9). 3: With input h an ñ, output further refine h, an L after removing invali paths satisfying (). 4: while L < L o 5: Set L =L. 6: Repeat Step with initial inputs an h. 7: Repeat Step an Step 3. 8: en while 9: If conition () is satisfie, set L =, = peak, an h =h peak ; Otherwise, go to the next step. : Output a final ToA estimate. The first heuristic step is to remove channel taps that are far away from the peak position peak. That is, if h l peak > max (9) is satisfie, h l is classifie as an invali path an remove from h, an is upate accoringly. Then, L is also upate as the number of remaining taps. The variable max is the maximum time-ifference that is allowe. The rationale behin this step is that, the first-path shoul not be too far away from the position where a peak is foun, especially at low SNRs. For instance, as seen from Table, the largest time-ifference between all channel taps for three faing channels are below at sampling rate.9 MHz, an max can be set to in this case. The secon heuristic step is to recursively remove the channel taps with power less than a fraction of the total channel power. That is, if h l < η 3 ( l<l h l ), () hols, then the l-th path is remove from h an so is the elay ñ l in ñ, an L is also upate as L. Such a process is repeate until the conition () is violate for all remaining taps. The threshol η 3 is a also pre-efine an yet to be optimize, which can be set to, for instance,..

5 5 C. The Propose ToA Estimation Metho Base on the introuce two steps, the propose ToA estimation metho is then summarize in Algorithm, which starts with a sufficient large L an run Algorithm to generate initial estimates of h an. Then, the estimates are refine by removing the channel taps that satisfy conitions (9) an (). If the number of channel taps afterwars is less than the initial value, using the upate L an refine estimates h, as initializations to run Algorithm again, followe by removing the invali paths an the refinement of L. These two steps run iteratively until L converges. With the last outputs h, an σ, there is one more step to improving the ToA estimation for a single-path an AWGN channels. That is, if the output noise power σ is higher than the noise power estimate with peak an h peak in (7) an (8), i.e., σ D D = R[ hpeak γ( peak ) () then we claim that there is only one path exist an set the ToA estimate to peak. This is ue to the sub-optimality of the propose algorithm, which may converge to a local optimum especially when the true conition is that only a single-path is present. IV. NUMERICAL RESULTS In this section, we provie numerical results to show the performance of the propose ToA estimator. Without loss of generality, we assume a sampling frequency of.9 MHz for ToA estimation with a sample time 6T s, ue to low-en analog evices use in NB-IoT receivers. We make no attempt to optimize the parameters an set E = 4 in (4), max = in (9) an η 3 =. in (). The true value of ToA is set to 5 samples. The number of SAGE iterations in Algorithm is set to M = 8 with an initial L = 5 for all test cases. For comparison, we also set η =.5 in (6) for a traitional threshol base ToA estimator as in [. A. PAPR Improvement for False-Alarm Probability First we show the PAPR improvements with consiering the impact of NPRS ACF uner AWGN channel. We evaluate at sampling rate.9 MHz an 4 KHz, respectively. The PAPR is measure in (5) for both methos, while for the propose metho, R[ in the enominator is replace by R l [ in () that removes the ACF centere at the peak position. As can be seen from Fig. 4, when there is no NPRS presente, the CDFs of the PAPR are almost the same for both methos at ifferent sampling rates. However, when NPRS is presente, the CDFs of PAPR are further pushe to right of the propose metho compare to the traitional metho. That means, the falsealarm probability of etecting NPRS is improve by removing the impact of the ACF in the propose metho. B. Convergence of the SAGE Algorithm Next we show the convergence spee of the propose SAGE Algorithm uner ETU-3Hz channel at SNR 5 B. We show the estimate noise power σ that are average over channel CDF Propose MHz Propose 4 KHz Traitional MHz Traitional 4 KHz PAPR measure without NPRS 5 5 PAPR Fig. 4. The PAPR improvements with consiering the ACF of NPRS uner AWGN channel at SNR -4 B. Estimate noise power B 5 B B SAGE iter. Fig. 5. Convergence of Algorithm in the first running uner ETU-3Hz channel. Each curve is average over channel realizations. realizations. As can be seen in Fig. 5, the algorithm converges fast in aroun 8 SAGE iterations. We also show an example of Rl [ with removing the ACFs corresponing to each of the etecte channel path in Fig. 6 with the propose metho. The peak of R[ is attaine at peak = 53 while the true value is 5. With the propose algorithm, the ToA can be correctly etecte with four channel taps etecte at elays [5, 5, 53, 54 an estimate channel coefficients h=[ i, i, i, i. In this case, the fifth channel tap is unetecte ue to its low power. As it can be seen that, with removing each of the four etecte path component successively, the amplitue of R l [ ecreases an acts like a noise floor at last. C. ToA Detection Performance Last we show the ToA etection performance with the propose ToA estimation metho uner ifferent channels. We measure both the exact etection probability, an the etection probability that the estimate errors are less than 3 samples. In Fig. 7, the etection probabilities of the propose metho are compare to the ML estimator uner AWGN channel, where the ML estimator utilizes the priori information that only one channel tap exists an the ML estimates are in (7) an (8), while the propose metho oes not use such a priori information. As can be seen, the propose metho performs close to the ML in both cases.

6 6 Amplitue Original superimpose correlation function Remove the first etecte path Remove the secon etecte path Remove the thir etecte path Remove the fourth etecte path P [% EPA-3Hz, propose metho, samples ETU-3Hz, propose metho, samples EPA-3Hz, propose metho ETU-3Hz, propose metho ETU-3Hz, traitional metho, samples EPA-3Hz, traitional metho, samples Delay [6T s Fig. 6. The amplitue of the correlation R[ with removing the four etecte paths uner ETU-3Hz Channel at SNR 5 B. P [% Propose SAGE base ToA etection Propose SAGE base ToA etection, samples ML ToA etection ML ToA etection, samples SNR [B Fig. 7. ToA etection performance uner ETU-3Hz channel. In Fig. 8, the etection probabilities of the propose metho are compare to the traitional estimator uner faing channels. As can be seen, the traitional threshol base metho performs quite poor uner both EPA-3Hz an ETU-3Hz channels even with tolerable estimate errors less than 3 sample. With tolerable estimate errors less than 3 sample, even at SNR -5B, the etection probability using the propose ToA estimation metho is above 75% an 9% uner ETU-3Hz an EPA-3Hz channels, respectively. The performance uner EPA-3Hz channel is better ue to the fact that, as seen from Table, at sampling rate.9 MHz, EPA channel egraes to a single path channel (since the power of the secon path is negligible), while ETU-3Hz channel comprises 5 taps that make it is more ifficult for ToA estimation. V. SUMMARY We have consiere time-of-arrival (ToA) estimation in narrowban Internet-of-Things (NB-IoT) systems an propose a low-complexity space-alternating generalize expectationmaximization (SAGE) base metho for joint estimating the number of channel taps, the channel coefficients an the elays. Due to a limite banwith 8 KHz an the number of NPRS symbols use, the time-omain auto-correlation function (ACF) of the NB positioning reference signal (NPRS) is not perfect an has a wie lobe. By taking this impairment into account, in a first step of the propose ToA estimation metho, the SAGE algorithm is utilize to ecompose the superimpose correlations corresponing to ifferent channel taps an generate estimates for channel coefficients an the SNR [B Fig. 8. ToA etection performance uner EPA-3Hz an ETU-3Hz Channel. corresponing elays. Then in a secon step, the estimate channel taps an number of taps are refine by removing invali paths. These two steps run iteratively until the number of estimate channel taps is converge. We show through simulation results that, the propose ToA estimation metho performs close to the maximum likelihoo (ML) estimator for a single-path channel, an outperforms a traitional threshol base ToA estimator without consiering the impacts of multiple-path channel an the ACF of NPRS in NB-IoT systems. REFERENCES [ S. Fischer, Observe time ifference of arrival (OTDOA) positioning in 3GPP LTE, Qualcomm White Paper, Qualcomm Technologies Inc., Jun. 4. [ 3GPP TS 36., Evolve Universal Terrestrial Raio Access (E- UTRA): Physical channels an moulation, Release 4, Dec. 6. [3 3GPP TSG RAN WG, R-683, WF on simulation assumption for NB-IoT positioning, Gothenburg, Sween, -7 Aug. 6. [4 F. Vanhaverbeke, Y. L. Guan an M. Moeneclaey, Optimal channel an time-of-arrival estimation for IR-UWB in the presence of pulse overlap, IEEE Int. Conf. on Commun., (ICC), Cape Town, South Africa, May,, pp. -5. [5 V. Prabhu an D. Jalihal, An improve ESPRIT base time-of-arrival estimation algorithm for vehicular OFDM systems, IEEE Veh. Tech. Conf. (VTC), Barcelona, Spain, Apr. 9, pp. -4. [6 M. Takeshi an T. Hitoshi, Superresolution of Mltipath elay profiles measure by PN correlation metho, IEEE Trans. Antennas an Propagation, vol. 4, no. 5, pp. 5-59, May, 99. [7 X. Li an K. Pahlavan, Super-resolution TOA estimation with iversity for inoor geolocation, IEEE Trans. Wireless Commun., vol. 3, no., pp. 4-34, Jan. 4. [8 J. Liu an S. Feng, RSTD performance for small banwith of OTDOA positioning in 3GPP LTE, IEEE Veh. Tech. Conf. (VTC), Las Vegas, NV, USA, Jan. 4, pp. -5. [9 W. Xu, M. Huang, C. Zhu, an A. Dammann, Maximum likelihoo TOA an OTDOA estimation with first arriving path etection for 3GPP LTE system, Trans. Emerging Tel. Tech., Aug. 4. [ H. Ryén, et al., Baseline performance of LTE positioning in 3GPP 3D MIMO inoor user scenarios, International Conference on Location an GNSS (ICL-GNSS), Gothenburg, Sween, Jun. 5. [ H. Ryén, A. A. Zaii, S. M. Razavi, F. Gunnarsson, an I. Siomin, Enhance time of arrival estimation an quantization for positioning in LTE networks, IEEE International Symposium on Personal, Inoor an Mobile Raio Communications (PIMRC), Sep. 6. [ Sha Hu, Axel Berg, Xuhong Li, Frerik Rusek, Improving the performance of OTDOA base positioning in NB-IoT systems, accepte in IEEE Global Commun. Conf. (GLOBECOM), Singapore, 4-8 Dec. 7. [3 S. Hu, G. Wu, B. E. Priyanto, F. Rusek, S. Kant, an J. Chen, Iterative interference cancellation metho, Patent US43693 A, file on Aug. 4. [4 S. M. Kay, Funamentals of statistical signal processing, volume I: Estimation theory, Prentice Hall signal processing series, 993.