Improved High Resolution TOA Estimation for OFDM-WLAN Based ...

IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 2, NO. 2, APRIL 2013

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Improved High Resolution TOA Estimation for OFDM-WLAN Based Indoor Ranging Ziming He, Student Member, IEEE, Yi Ma, Senior Member, IEEE, and Rahim Tafazolli, Senior Member, IEEE

Abstract—This letter presents three novel approaches, namely peak detection, modified maximum peak-to-leaking ratio detection and channel frequency response (CFR) reconstruction, in order to improve the high resolution TOA estimation technique when using OFDM-based WLAN preamble. Computer simulations show that all the proposed approaches outperform the state-of-the-art in the WINNER A1 LOS channel. Moreover, the proposed approaches demonstrate their advantages in WARP2 board based Wi-Fi testbed. Index Terms—High resolution, orthogonal frequency division multiplexing (OFDM), time-of-arrival (TOA).

I. I NTRODUCTION

R

ECENTLY, radio positioning has attracted lots of research interests [1]-[5]. High resolution time-of-arrival (TOA) estimation is a signal processing technique that can yield accurate estimate of fractional timing delay normalized by the sampling period. It is one of key techniques to enable or improve range-based radio positioning particularly for line-ofsight (LOS) environment. Unlike the ultra wideband (UWB) based TOA estimation techniques that can take advantage of a large signal bandwidth (e.g. 500 MHz) [6], the high resolution TOA estimation techniques are particularly useful for radio signals having relatively small bandwidth (e.g. 20 MHz bandwidth for WLAN signals [7]). Existing high resolution TOA estimation techniques are mainly the MUSIC algorithm [8], the SAGE algorithm [9], and the maximum peak-to-leaking ratio (MPLR) approach [10]-[12]. Performance comparison amongst existing approaches was addressed in the literature [10]-[11], and it was shown that the MPLR approach outperforms all the others in terms of both the range estimation accuracy and computational complexity. Moreover, the performance of radio positioning and TOA-based ranging have been extensively analyzed using the Cram´er-Rao bound in [1]-[3] and [13]. The problem arises from our recent implementation of the MPLR approach for WLAN based indoor radio positioning with orthogonal frequency-division multiplexing (OFDM) to be the radio waveform. It is found that the MPLR approach works well when pilot tones are uniformally placed in the frequency domain with equal spacing. However, in the IEEE 802.11 a/g/n standard where the placement of pilot tones does not follow the “uniform and equal spacing” rule, considerable performance degradation can be observed for the Manuscript received November 1, 2012. The associate editor coordinating the review of this letter and approving it for publication was A. Conti. This work was performed in the framework of ICT-248894 WHERE Phase 2, which was partly funded by the European Union. The authors are with the Centre for Communication Systems Research, University of Surrey, Guildford, U.K., GU2 7XH (e-mail: [email protected]). Digital Object Identifier 10.1109/WCL.2012.122612.120802

MPLR approach. The main reason is that the MPLR approach measures the maximum peak-to-leaking ratio of estimated channel impulse response (CIR), which is a function of fractional timing delay. Unfortunately, when the pilot tones are not placed according to the “uniform and equal spacing” rule, the CIR estimation suffers a considerable performance degradation, which results in the performance degradation in the fractional TOA estimation. Major contribution of this work is to improve the MPLR approach when using IEEE 802.11 a/g/n radio waveform for the TOA estimation. We propose three novel approaches named peak detection, modified MPLR, and channel frequency response (CFR) reconstruction. Computer simulations show that all the proposed approaches outperform the MPLR in WINNER A1 LOS channel [14]. Moreover, we perform indoor ranging experiments in an LOS environment, which is recognized as one of important experimental contexts for indoor positioning [5]. The proposed approaches demonstrate advantages in our testbed experiment. II. S YSTEM M ODEL AND P ROBLEM D ESCRIPTION A. System Description Consider an OFDM-WLAN access point (AP) sending data burst containing a preamble. A mobile station is performing the TOA estimation based on the received preamble. As specified by IEEE 802.11 a/g/n, the preamble consists of ten short OFDM symbols mainly for the purpose of coarse timing and frequency synchronization, and two long OFDM symbols for the channel estimation. We assume the coarse timing and frequency synchronization to be good enough (please see detail as follows); and we are now at the stage of performing the fractional timing estimation, which is based on the long OFDM symbols. In order to simplify the presentation, our system description is based on one long OFDM symbols since consideration of two long OFDM symbols is simply count as signal-to-noise ratio (SNR) enhancement. The discrete-time equivalent form of the received long OFDM symbol after removing the cyclic prefix (CP) is expressible as yn = e

j2πεn M

L−1 

αl xnTs −τl + vn , n = 0, 1, ..., M − 1 (1)

l=0

where xn is the time-domain OFDM waveform sampled at the rate of (1/Ts ) (Ts equals to the OFDM symbol duration divided by the number of subcarriers M ); αl is the channel coefficient of the l th path with the propagation delay τl ; L is the total number of propagation path; ε is the residual carrier-frequency-offset after frequency synchronization; vn is

c 2013 IEEE 2162-2337/13$31.00 

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IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 2, NO. 2, APRIL 2013

the additive white Gaussian noise on the n th sample. It is worth noticing that τ0 in (1) is the TOA of the first path. The integer part of (τ0 )/(Ts ), defined by θ = (τ0 )/(Ts ), is the residual coarse timing synchronization error, and the fractional part (i.e.  = (τ0 )/(Ts ) − θ) is the parameter of interest in this letter. Indeed, the overall TOA estimation performance will be limited by the coarse timing synchronization error. On the other hand, an accurate estimation of  can improve the resolution of range estimation subject to perfect samplelevel timing synchronization. This is the major reason that has motivated the research activity towards high resolution TOA estimation for instance in [8]-[12].

(2)

where pm denotes the pilot symbol modulated on the m th subcarrier, v˜m the frequency-domain version of the noise, and ˜ m the CFR with the mathematical form h L−1 

αl e

−j2πmτl M Ts

(3)

l=0

Step 2: Perform M -point inverse discrete Fourier transform 2πmˆ  (IDFT) on (p†m y˜m ej M ), for m = 0, 1, ..., M − 1, to obtain the estimate of CIR M−1 j2πmn 2πmˆ  1  † ˆ n (ˆ ) = pm y˜m ej M e M h M m=0

M−1  j2πm(n+ˆ −τ0 /Ts ) 1  † ˆ n (ˆ M pm pm α0 e )= h M m=0   M−1 L−1  j2πm(n+ˆ −τl /Ts ) 1  † M + αl e pm pm + v¯n (7) M m=0 l=1

Assuming A1) pm = 0, ∀m and |pm | to be constant, we can use the IDFT property to further rewrite (7) into L−1 

(4)

where Γ(x) =

e

j2πm(n+ˆ −τ0 /Ts ) M

=

−τ0 /Ts ) ) sin( 2π(K+1)(n+ˆ M

m=−K m=0

ˆ θ,ˆ

(6)

ˆ 1 θ−1 2 ˆ ˆ) = |h ˆ ˆ(ˆ ˆ )|2 ), and we remind where η(θ, n=0 |hn (ˆ θ )| /( θˆ ˆ s + ˆ. The optimization problem (6) can be easily here τˆ0 = θT solved by exhaustive searching for θˆ = 0, 1, ..., M − 1 and the Newton method for  ∈ (0, 1).

M sin( 2π(n+ˆM−τ0 /Ts ) )

(11)

We define a function G(x) = sin(2π(K + 1)x/M )/ sin(2πx/M ) and can rewrite (7) into

l=0

where v¯n is the corresponding noise. Step 3: Estimate the parameter τ0 through solving the following objective function

(9)

where δ(x) = 1 for x = 0 or otherwise zero; σv2¯ is the variance ˆ ˆ) reaches its of the noise v¯n . It is easy to prove that η(θ, ˆ maximum at (θ + ˆ = τ0 /Ts ) with the largest probability [10]. Unfortunately, the assumption A1 does not always hold in practical communication systems. For instance in IEEE 802.11 a/g/n, the frequency-domain tones with index (−32, ..., −27, 0, 27, ..., 31) carry only zeros [7]. It means that we cannot capture the full CFR, and thus would suffer additional distortion in the CIR estimation; and this distortion would cause considerable performance degradation in the TOA estimation. We can generalize the WLAN pilot configuration by assuming the tones with index (−M/2, ..., −(K + 1), 0, K + 1, ..., M/2 − 1) carrying zeros, where K is an integer. It is straightforward to obtain K 

where the superscript (·) denotes the pseudo inverse. Plugging (2) and (3) into (4) yields   M−1 L−1   j2πm(n+ˆ −τl /Ts ) 1 † ˆ n (ˆ M h pm pm + v¯n (5) ) = αl e M m=0

sin(πx) ejπ(1−1/M)x . M sin(πx/M )

When ˆ = (τ0 )/(Ts ) − θ, it is clear that the term |Γ(n + ˆ − τ0 /Ts )|2 equals to 1 for n = θ, and 0 for n = θ. Hence, in ˆˆ the presence of single dominate path, the term η(θ, ) in (6) approximates to:  |δ(θˆ + ˆ − τ0 /Ts ) + v¯θˆ|2 /σv2¯ , θˆ ≤ θ ˆ ˆ) ≈ (10) η(θ, ˆ θˆ > θ |¯ vθˆ|2 /(σv2¯ + 1/θ),

†

ˆ ˆ) ˆ ˆ} = arg max η(θ, {θ,

αl Γ(n+ˆ −τl /Ts )+¯ vn (8)

l=1

In order to show the difference between our proposed approaches and the state-of-the-art, we provide an introduction of the MPLR approach presented in [10]-[12]. Here, we assume coarse timing synchronization error (i.e. θ) to be smaller than the CP length. The carrier-frequency-offset ε is usually small in the indoor environment, and it would not introduce considerable impact on the TOA estimation. Therefore, we let ε = 0 in (1) to simplify our presentation. The MPLR can be summarized as three major steps: Step 1: Perform M -point discrete Fourier transform (DFT) on yn , for n = 0, 1, ..., M − 1, to obtain the frequency-domain version of yn , i.e.,

˜m = h

In order to clarify the physical essence of MPLR, we rewrite (5) into

ˆ n (ˆ h ) = α0 Γ(n+ˆ −τ0 /Ts )+

B. Introduction of The MPLR Approach

˜ m pm + v˜m , m = 0, 1, ..., M − 1 y˜m = h

C. The New Problem

ˆ n (ˆ h ) = α0 G(n + ˆ − τ0 /Ts ) +

L−1 

αl G(n + ˆ − τl /Ts ) + v¯n

l=1

(12) The term |G(n + ˆ − τ0 /Ts )|2 reaches its maximum, i.e., (K + 1)/(M ), when we have ˆ = (τ0 )/(Ts ) − θ and n = θ. However, |G(n + ˆ − τ0 /Ts )|2 is not zero for n = θ, which causes considerable energy leaking. In this case, the term ˆ ˆ) in (6) approximates to η(θ, ˆ ˆ) = η(θ,

|G(θˆ + ˆ − τ0 /Ts ) + v¯θˆ|2  ˆ θ−1 1 ˆ − τ0 /Ts )|2 + σv2¯ n=0 |G(n +  θˆ

(13)

HE et al.: IMPROVED HIGH RESOLUTION TOA ESTIMATION FOR OFDM-WLAN BASED INDOOR RANGING

ˆ ˆ) to be which considerably reduces the probability for η(θ, ˆ the maximum at the point (θ + ˆ = τ0 /Ts ). III. N EW A PPROACHES AND D ISCUSSION A. The Peak Detection Approach The idea of peak detection is to find the real peak of the first path of arrival and maximize it by searching ˆ . Assuming A2) |αl | |α0 |, for l = 1, 2, ..., L − 1, the peak detection approach can be easily implemented by replacing (6) with 2 ˆ ˆ(ˆ ˆˆ {θ, } = arg max(|h θ )| ) ˆ θ,ˆ

(14)

2 ˆ ˆ(ˆ In the presence of single dominate path, the term |h θ )| 2 ˆ approximates to |G(θ + ˆ − τ0 /Ts ) + v¯θ | , which can reach its maximum for (θˆ + ˆ  = τ0 /Ts ) with the largest probability. On the other hand, the peak detection approach is very sensitive to the multipath distortion.

The idea of Modified MPLR is to combine the merits of peak detection and MPLR. More specifically, it is the MPLR weighted by the corresponding channel gain, i.e., replacing (6) with ⎛ ⎞ 4 ˆ ˆ(ˆ | h  )| ˆˆ ⎠ (15) {θ, } = arg max ⎝  ˆ θ θ−1 ˆ 1 2 ˆ θ,ˆ | h (ˆ  )| n n=0 θˆ Main advantages of the modified MPLR approach are: • It can effectively mitigate the multipath impact when the first path has comparable gain with a stronger path. In order to make this point clear, we assume αl to be the path whose gain is larger than the first path, i.e. α0 . The propagation delay of αl is denoted by τl = (θl + l )Ts . In this case, the peak detection approach would wrongly ˆ n (ˆ ) understand the TOA to be τl since the CIR estimate h 2 2 ˆ ˆ (ˆ ˆ would give the result of |h  )| > | h (ˆ  )| . However, θ1 1 θˆ when the following condition holds

 1 θ−1  )|2 n=0 |hn (ˆ 2 2 2 θ ˆ ˆ ˆ |hθˆ1 (ˆ 1 )| > |hθˆ(ˆ )| > |hθˆ1 (ˆ 1 )|  θ1 −1 1 2  ) 1 n=0 |hn | (ˆ θ1 (16) we can easily justify that the modified MPLR (15) would not miss the first path. • As we have discussed in Sec. II-C, the MPLR approach would miss the first path if there exists a time-domain sample n1 (< θ) such that 1 n1

C. The CFR Reconstruction Approach The key idea here is to reconstruct the CFR on those zero tones so as to mitigate the energy leaking for the CIR estimation. Then, the equation (10) will hold, and the MPLR approach can be employed after the CFR reconstruction. The basic assumptions here are: A3) the timing delay introduces linear phase shifting with respect to the subcarrier index, which is the case when the timing delay is shorter than the CP length; A4) the communication channel is approximately flat for any (M/2 − K + J) adjacent subcarriers (J > 1). We remind that the frequency-domain tones with index (−M/2, −M/2 + 1, ..., −(K + 1)) carry zeros, and their adjacent tones with index (−K, −K + 1, ..., −K + J − 1) ˜ −K+J−1 . ˜ −K , ˜h−K+1 , ..., h carry the CFR information, i.e., h The assumptions A3 and A4 imply ˜ −M/2 | ≈ |h ˜ −M/2+1 | ≈ ... ≈ |h ˜ −K+J−1 | |h

(19)

˜ −K+1 )∗ h ˜ −K+1 ) ≈ ∠((h ˜ −K+2 ) ˜ −K )∗ h φ= ∠((h ∗ ˜ −K+J−2 ) h ˜ −K+J−1 ) (20) ≈ ... ≈ ∠((h

B. The Modified MPLR Approach

2 ˆ ˆ(ˆ |h θ )| <  ˆ θ−1 1 ˆ )|2 n=0 |hn (ˆ θˆ

165

ˆ n1 (ˆ |h )|2 . n1 −1 ˆ )|2 n=0 |hn (ˆ

(17)

This case would happen when there is time-domain energy leaking due to the pilot placement. Using (15), we can find that the modified MPLR approach can effectively overcome this problem when

 1 θ−1 1 θ−1  )|2 )|2 )|2 |hθ (ˆ n=0 |hn (ˆ θ  θ n=0 |hn (ˆ < <  n1 −1 θ −1 2 1 1 1 |hn1 (ˆ )| )|2 )|2 n=0 |hn (ˆ n=0 |hn (ˆ n1 n1 (18)

where ∠a denotes the phase of a, and the superscript (·)∗ denotes the complex conjugate. Then, we can reconstruct the CFR on those zero tones with the following steps: Step 1: Estimate the phase difference between adjacent tones by performing the following averaging φˆ =

1 J −1

−K+J−2 

∠((p†m y˜m )∗ p†m+1 y˜m+1 )

(21)

m=−K

Step 2: Estimate the averaged CFR with the linear phase ¯˜ i.e., shift to be removed (denoted by h), ¯˜ = 1 h J

−K+J−1 

ˆ

(p†m y˜m e−j(m+K)φ )

(22)

m=−K

Step 3: Reconstruct the CFR on the tones with index (−M/2, −M/2 + 1, ..., −(K + 1)) using ¯˜ −j(m+K)φˆ ˆ˜ , h m = he

m=−M/2,−M/2+1,...,−(K+1) .

(23)

Analogously, we can reconstruct the CFR on other zero tones. Once the CFR reconstruction is completed, we can use the MPLR approach in Sec. II-B to perform the TOA estimation. IV. S IMULATIONS AND T ESTBED E XPERIMENT A. Computer Simulations Fig. 1 (a) illustrates the root mean-square-error (RMSE) of TOA based ranging as a function of signal-to-noise ratio (SNR) under WINNER A1 LOS channel [14]. The RMSE is I 1 defined by ( I1 i=1 |(θˆi + ˆi )Ts c − d|2 ) 2 , where c denotes the light speed, d the real distance, i the index of Monte Carlo trial (I = 3000). It is observed that the CFR reconstruction approach offers the best performance, and the peak detection is the second best. Moreover, all the proposed approaches outperform the MPLR for all simulated SNRs. This phenomenon is mainly because the WINNER A1 channel is a multipath channel with one dominate path (i.e. the LOS path), where the approaches designed for multipath mitigation cannot show advantages. Moreover, the LOS path might be weaker than

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IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 2, NO. 2, APRIL 2013

The time difference (t1 − t2 ) was estimated by the Rx, and (t1 − t2 ) was estimated by the RN. The result plotted in Fig. 1 (b) is based on our observation of 1000 snapshots. It is observed that the peak detection approach performs the worst in the experiment. This is a reasonable result since there were many reflectors and moving people around the testbed, which created a complex multipath environment1. Moreover, the other three approaches have comparable performance with each other. Interestingly, the CFR reconstruction approach offers the best performance.

(b)

(a) 1

5 MPLR Peak detection Modified MPLR CFR reconstruction+MPLR

4.5

0.9 0.8 0.7 0.6

CDF

RMSE (m)

4

3.5

0.5 0.4

3 0.3 0.2 2.5 0.1 2

5

10

15

20

25

30

0

V. C ONCLUSION 0

1

2

3

Absolute ranging error (m)

SNR (dB)

Fig. 1. (a) RMSE vs SNR for WINNER A1 LOS channel; (b) CDF curves of absolute ranging error for testbed experiment.

In this letter, we have analyzed a new problem when using WLAN preamble for high resolution TOA estimation. Three new TOA estimation approaches have been proposed to solve the problem. In addition to the theoretical analysis, both simulation and experiment results have been provided to show the advantages of the proposed approaches. R EFERENCES

Fig. 2.

The environment where the testbed evaluation was performed.

non-line-of-sight (NLOS) paths for some channel realizations, for which the CFR reconstruction approach outperforms the peak detection approach. B. Testbed Experiment Moreover, both the proposed approaches and the MPLR were implemented in the WARP2 board based Wi-Fi testbed. The experiment was carried out in one of academic buildings in the University of Surrey, which is depicted in Fig. 2. In the experiment, we used four WARP2 boards (two served as access points (APs) and two as receivers). APs send preambles for the receiver (Rx) to perform the estimation of timedifference-of-arrival (TDOA), which was then translated into the distance difference between AP1-Rx and AP2-Rx. The reason of not estimating TOA is because the local clock between APs and receivers were not synchronized. In order to monitor the clock difference between two APs, we used a reference node (RN), whose distance to the APs was measured using a long ruler. Assuming t1 and t2 to be the time of signal departure from AP1 and AP2, respectively, t1 and t2 to be the time of signal arrival at the Rx correspondingly. The distance difference between AP1-Rx and AP2-Rx can be computed by Δd =

c(t1

− t1 ) −

c(t2

− t2 ) =

c(t1

−

t2 ) −

c(t1 − t2 ) (24)

[1] Y. Shen and M. Z. Win, “On the accuracy of localization systems using wideband antenna arrays,” IEEE Trans. Commun., vol. 58, no. 1, pp. 270–280, Jan. 2010. [2] Y. Shen and M. Z. Win, “Fundamental limits of wideband localization— part I: a general framework,” IEEE Trans. Inf. Theory, vol. 56, no. 10, pp. 4956–4980, Oct. 2010. [3] Y. Shen, S. Mazuelas, and M. Z. Win, “Network navigation: theory and interpretation,” IEEE J. Sel. Areas Commun., vol. 30, no. 9, pp. 1823–1834, Oct. 2012. [4] M. Z. Win, A. Conti, S. Mazuelas, Y. Shen, W. M. Gifford, D. Dardari, and M. Chiani “Network localization and navigation via cooperation,” IEEE Commun. Mag., vol. 49, no. 5, pp. 56–62, May 2011. [5] A. Conti, M. Guerra, D. Dardari, N. Decarli, and M. Z. Win, “Network experimentation for cooperative localization,” IEEE J. Sel. Areas Commun., vol. 30, no. 2, pp. 467–475, Feb. 2012. [6] D. Dardari, A. Conti, U. Ferner, A. Giorgetti, and M. Z. Win, “Ranging with ultrawide bandwidth signals in multipath environments,” Proc. IEEE, vol. 97, no. 2, pp. 404–426, Feb. 2009. [7] IEEE Computer Society, “Wireless LAN medium access control (MAC) and physical layer (PHY) specifications: high-speed physical layer in the 5GHz band,” Dec. 1999. [8] X. Li and K. Pahlavan, “Super-resolution TOA estimation with diversity for indoor geolocation,” IEEE Trans. Wireless Commun., vol. 3, no. 1, pp. 224–234, Jan. 2004. [9] B. H. Fleury, M. Tschudin, R. Heddergou, D. Dahlhaus, and K. I. Pedersen, “Channel parameters estimation in mobile radio environments using SAGE Algorithm,” IEEE J. Sel. Areas Commun., vol. 17, no. 3, pp. 434–449, Mar. 1999. [10] H. Xu, C. C. Chong, I. Guvenc, F. Watanabe, and Y. Liuqing “Highresolution TOA estimation with multi-band OFDM UWB signals,” in Proc. 2008 IEEE Int. Conf. Commun. [11] H. Ni, G. Ren, and Y. Chang, “A TDOA location scheme in OFDM based WLANs,” IEEE Trans. Consumer Electron., vol. 54, no. 3, pp. 1017–1021, June 2008. [12] Z. He, Y. Ma, and R. Tafazolli, “A high accuracy mobile positioning approach in IEEE 802.11a WLANs,” IEICE Trans. Fundamentals, vol. E95-A, no. 10, pp. 1776–1779, Oct. 2012. [13] T. Wang, Y. Shen, S. Mazuelas, and M. Z. Win, “Bounds for OFDM ranging accuracy in multipath channels,” in Proc. 2011 IEEE Int. Conf. Ultra-Wideband. [14] WINNER D5.4 v. 1.4, “Final report on link level and system level channel models.” Available: http://www.ist-winner.org/. 1 One of objectives of this experiment was to test the robustness of considered approaches in a harsh LOS environment as shown in Fig. 2.