Wireless Pers Commun DOI 10.1007/s11277-015-2762-y

High Resolution TOA Estimation Based on Compressed Sensing Wenhui Xiong1 • Chang Liu2 • Su Hu1 Shaoqian Li1

•

 Springer Science+Business Media New York 2015

Abstract This paper proposes a novel time of arrival (TOA) estimation method which achieves the sub-chip resolution. In this proposed method, the sparsity of the wireless channel is utilized to adopt the emerging technique of compressive sensing (CS) for accurate TOA estimation. The received signal is first processed to make the sensing matrix satisfy the restrict isometry property requirement of CS framework; then the signal samples with the amplified noise are removed to improve the recovery performance; finally, the dantzig selector method is used to recover the sparse channel for TOA estimation. Keywords

TOA estimation  Compressed sensing  Dantzig selector

1 Introduction Location estimation is an important research area in communication and signal processing communities. In addition to the conventional navigation applications, the location information enables communication facilities to adaptively allocate the radio and computational resources according to the users’ need and spatial distribution.

& Wenhui Xiong [email protected] Chang Liu [email protected] Su Hu [email protected] Shaoqian Li [email protected] 1

The National Lab. of Communication of University of Electronic Science and Technology of China, Chengdu, Sichuan, China

2

Huawei Technologies Co., Ltd, Shenzen, Guangdong, China

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The location estimation techniques can be categorized as power based (range free) and range based techniques. The power based positioning relies on the empirical received signal strength indication (RSSI) map to estimate the use’s location. To successfully implement the power based technique, one needs to build accurate RSSI map which requires extensive amount of manpower. Though the algorithm proposed by [1] is able to reduce the workload of building the RSSI map, certain amount of survey is still needed for the initial RSSI map building. Instead of relying on the RSSI map, the range based positioning techniques use the ranges between user and the anchor nodes to determine the user’s location. The range estimation is achieved by the time of arrival (TOA) of the anchor nodes’ transmitted signal. The signal used for TOA estimation can be ultra wide band (UWB) signal or spread spectrum signal, e.g., global positioning system (GPS) signal [2]. The UWB signal is able to provide high TOA estimation accuracy for its wide bandwidth [3–7]. However, due to its wide bandwidth, high sampling rate is needed to implement the coherent detection scheme for UWB signal [3]. Usually, the threshold based method is often used for UWB signal’s TOA estimation [4] (and reference therein). In [6] and [7] the authors employed the Compressed Sensing (CS) theory to process the low sampling rate UWB signal for TOA estimation. The spread spectrum signal is widely used for range estimation e.g., [2] since it provides good tradeoff between estimation accuracy and the processing complexity. Conventionally, the TOA of the spread spectrum signal is estimated using the correlation based method, i.e., the sliding match filter [2]. However, the multipath environment makes the conventional correlation based method inaccurate for positioning purpose. Specifically, when the separation of the paths is less than one chip (symbol) time, the conventional correlator fails to separate them. The maximum likelihood (ML) [8], a form of superresolution scheme, was proposed to achieve the sub-chip accuracy with performance.The ML scheme’s performance is close to the Cramer–Rao lower bound (CRLB). However, this method is computationally expensive since it performs an exhaustive search on all possible path locations. Other super-resolution methods, originally used in array signal processing, such as multiple signal classification (MUSIC) [9] and estimation of signal parameters via rotation invariance technique (ESPRIT) [10], were used for TOA estimation [9, 10]. These methods, similar to the ML method, are computationally expensive. In addition to high computational complexity, these methods, i.e., MUSIC and ESPRIT, often need information regarding the total number of channel taps and the approximate locations of the channel taps. Since the wireless channel is sparse [11], i.e., most channel taps are of zero or close to zero amplitudes, we can use the CS framework for TOA estimation. CS was originally proposed to find the sparse solution for under-determined systems. In [12], the application of CS for channel impulse response estimation was studied with chip level resolution. However the chip level resolution is far from sufficient for positioning purpose especially for narrow bandwidth signals (e.g., 1.023 MHz). In this paper, we study a CS based subchip resolution TOA estimation method, and propose a novel de-noising scheme to improve the estimation accuracy. The rest of this paper is organized as follows, Sect. 2 provides the system model used in this study; Sect. 3; reviews the CS framework; Sect. 4 illustrates the TOA estimation procedure, followed by the numerical simulations in Sect. 5 and conclusion in Sect. 6.

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2 System Model In this section, we provide the system model used in this work, i.e., the transmitted signal, data processing block diagram and the received signal model.

2.1 Transmitted Signal In this work, we use the spread spectrum signal for TOA estimation. The spread spectrum signal is widely used for range estimation, such as GPS, for its good auto/cross correlation properties. Following the GPS signal structure, we use the short spreading code, which has short code period(e.g., 1 ms for GPS). The transmitted signal in one code period can be expressed as sðtÞ ¼

N1 pffiffiffiffiffiffi X c½nwðt  nTc Þ PT

ð1Þ

n¼0

where PT is power of the transmitted signal, c½n 2 ½1; 1 is the nth chip of the spread sequence, N is the length of the spreading sequence, Tc is the chip duration, and wðtÞ is the chip pulse waveform. Without loss of generality, we assume wðtÞ ¼ sincðpt=Tc Þ The channel to be estimated is assumed to be a semi-static frequency selective channel, i.e., the channel is time-invariant for the observation period. Hence, we model the channel as hðtÞ ¼

P1 X

ap dðt  sp Þ

ð2Þ

p¼0

where ap and sp are the complex gain and delay of the pth path, and P is the total number of paths. To ease the representation, we assume the delays of each channel tap are monotonically increasing, i.e., s0 \s2    \sP1 . With the channel model given by (2), the received signal is yðtÞ ¼

P1 X

ap sðt  sp Þ þ N ðtÞ

ð3Þ

p¼0

where N ðtÞ is the Additive White Gaussian Noise (AWGN) with double sided power spectrum density of N0 =2.

2.2 Receiver Block The block diagram of the receiver is shown in Fig. 1, where the received signal is first sampled with the sampling frequency of fs ¼ M=Tc , i.e., M times of the chip rate. The

Fig. 1 Estimator block diagram

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discrete samples of the received signal y½n are then processed to make the system satisfy the restrict isometry property (RIP) requirement (to be presented in Sect. 3). The discrete reference signal s½n is then used to remove the received signal samples that are contaminated by the amplified noise. Finally the remaining samples are processed under the CS framework for TOA estimation. The discrete received signal can be expressed as the discrete convolution of the digitized transmitted signal, s½n and the channel, h½n, i.e., y½n ¼

L1 X

s½n  lh½l þ N ½n

ð4Þ

l¼0

where L is the effective number of channel taps. The value of L is determined by the ratio between the maximum delay and the sampling rate, i.e., L ¼ dMsP1 =Tc e.1 In the discrete model given by (4), the ith entry of h½n can be interpreted as the effective channel tap resulted from the sampling of the physical channel paths that arrive in the delay bin of iT  Tc iTc Tc c M  2M ; M þ 2M . The conventional correlation based TOA estimator correlates the received signal with the known reference signal. Oftentimes, the peak position of the correlator output is declared as the TOA of received signal. Since, the resolution of the autocorrelation of the signal (spread spectrum signal in our case) is directly proportional to signal bandwidth, oversampling does not improve the TOA estimation accuracy for these conventional correlator based schemes, i.e., only the channel delays that are separated by at least Tc can be distinguished by the correlator. Figure 2 shows an example of TOA estimation using the conventional correlator. This example shows the effect of the closely located channel taps on the correlator output. The channel is a 2-tap channel with equal tap gain and the tap separation of Tc =2. The received signal is oversampled by a factor of 4. As shown in this example, even with the delay bin smaller than the tap separation, the conventional correlator is not able to distinguish these channel taps. Using the correlator peak as the estimated TOA results in an error of Tc =4, which is a distance error of approximately 73 m for 1:023 MHz chip rate (GPS signal chip rate). This simple example illustrates the fundamental limitation of the conventional correlator based TOA estimator. In this work, we utilize the emerging CS technique to estimate the closely spaced channel taps, i.e., tap separation less than one chip duration.

2.3 Received Signal Model Since the short code is used, i.e., the spreading code repeats every N chip, the received signal r½n can be modeled as the result of the circular convolution of the transmitted signal and the channel, y½n ¼ es ½n  h½n þ N ½n

ð5Þ

where es ½n is the circular expansion of s½n. To estimate the TOA, K ¼ MN samples (K  L in most cases) are used by the receiver. The resulted K-length received signal, denoted as y, can be expressed in matrix form as

1

dxe is the ceil of x.

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Fig. 2 Example correlator output for a two-tap channel with equal tap gain and tap separation of Tc =2

First Tap Response Second Tap Response Correlator Output Channel Impulse Response

0.7

Correlator Output

0.6 0.5 0.4 0.3 0.2 0.1

0 −0.1 −0.2 −4

−2

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Tc/4

2

s1

sK

6s 6 2 y¼6 6 .. 4 .

s1 ...

sK

sK1

3 2 3 n1 h1 6 6 7 7    s3 76 h2 7 6 n2 7 7 6 7 6 7 .. 7 .. 76 .. 7 þ 6 .. 7 ¼ Sh þ N . . 54 . 5 4 . 5 hK nK    s1    s2

32

ð6Þ

The measurement conducted by [11] shows that the wireless channel is sparse, i.e., h is characterized by a sparse vector with only a small number of nonzero entries. Thus, we can adopt the CS framework to estimate (recover) the sparse vector h from the received noisy samples.

3 Compressive Sensing Overview The overview of the CS is given in this section to make this paper self-contained. The theory of CS is first introduced in 2004 [13, 14]. It states that the n-dimensional sparse signal can be reconstructed from the m-dimensional observation vector, with m  n. Suppose the n-dimensional signal vector f 2 Rn is expressed as f ¼ Wb ¼

n1 X

bi wi

ð7Þ

i¼0

where W ¼ ½w1 ; w2 ; . . .; wn  is the basis of the signal f . If there are at most S nonzero elements in vector b ¼ ½b0 ; b1    bn T , i.e., kbk0  S, the signal f is said to be S-sparse on W. Usually, the measurement vector y is obtained by the measuring operation that can be expressed as y ¼ Uf ¼ UWb ¼ Ab

ð8Þ

where U is a m n measurement matrix. In CS literature, the matrix A ¼ UW is called the sensing matrix. It is shown in [13] that with certain restrictions on A, the S-sparse vector b can be recovered, and consequently rebuild the original signal f . The conditions that a

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column-normalized matrix A should satisfy are for CS framework are often stated in the context of the RIP by two key parameters, i.e., the restricted isometry constant of order dS , and the restricted orthogonality constant hS;S0 . Suppose we have the sensing matrix A ¼ ½a1 ; a2 ; . . .; an  2 Rm n . Denote the index set by G ¼ f1; 2; . . .; ng and T G with cardinality jTj  S. For any set T, let AT be the submatrix of A with column indexed by i 2 T. The restricted isometry constant of order S (1  S  n) of A, denoted by dS , is defined as the smallest quantity that obeys ð1  dS Þkbk22  kAT bk22  ð1 þ dS Þkbk22

ð9Þ

for any real vectors b 2 RjTj . For a matrix A 2 Rm n , the restricted orthogonality constant hS;S0 , that satisfies S þ S0  n, is defined as the smallest quantity such that the inequality jhAT b; AT 0 b0 ij  hS;S0  kbk2 kb0 k2

ð10Þ

holds for all disjoint sets of T; T 0 G with cardinality jTj  S and jT 0 j  S0 and any real 0 vectors b 2 RjTj ; b0 2 RjT j . To recover the sparse signal b from noisy measurement y ¼ Ab þ N , many algorithms have been proposed, e.g., [15–18]. Among them the Dantzig Selector (DS) [18] shows good performance against noise with bounded recovery error. The DS algorithm is a convex optimization problem that minimize the l1 norm of b [18] pffiffiffiffiffiffiffiffiffiffiffiffiffi ð11Þ b^ ¼ argmin kbk1 subject to kAH rk1  r 2 log n b2Rn

where r ¼ y  Ab is the residual signal, and r2 is the noise power. It has been shown in [18] that if the restricted isometry constant and restricted orthogonal constant of the sensing matrix A obeys d2S þ hS;2S \1

ð12Þ

then with overwhelming probability, the recovery error is bounded by kb^  bk22  C02  S  2 log n  r2

ð13Þ

In (13) S is the sparsity of b, and C0 ¼ 4=ð1  d2S  hS;2S Þ.

4 Signal Processing for TOA Estimation The system model shown in (6) can be solved using the L2 minimization based method, e.g., least square (LS) or support vector machine (SVM) [19]. By using L2 norm as the objective function, these methods fail to find the sparse solution that fits the actual physical channel. Alternatively, the Bayesian type of method, e.g., relevance vector machine (RVM) can also be used to estimate h in (6). However, the result of RVM is sensitive to the model selection, i.e., the distribution of h. In this paper, we use the the CS framework to find the sparse solution for (6) which does not rely on the prior knowledge of h, and is guaranteed to generate sparse solution. For the signal model given by (6), we can interpret the matrix S as the sensing matrix, and h as the unknown that needs to be estimated. Thus, the methods used in CS literature can be applied to this system model to find the sparse channel response h.

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4.1 Processing for Compressive Sensing To guarantee the recovery of sparse signals, different restrictions are required on the sensing matrix, i.e., small restricted isometry constant is needed for sensing matrix S. This can be interpreted as small column correlation for sensing matrix S, i.e., small value of dS in (9). However, the sensing matrix given by (6) has large column correlation since each column is obtained by circular shifting the first column in S. To apply the DS recovery algorithm, we need to process the sensing matrix S so that the RIP requirement (small dS ) is met. Thanks to the property of the circular matrix, we can factorize the sensing matrix S via DFT as S ¼ U H RU

ð14Þ

where U is the DFT matrix, and R ¼ diagfvð1Þ;    ; vðKÞg is the diagonal matrix with vector v being the DFT of the first column of matrix S, i.e., vðiÞ ¼

K X

sm ej2pim=K

ð15Þ

m¼1

By left mulitplying R1 U on both side of (6), a new system model is obtained y0 ¼ Uh þ N

0

ð16Þ

0

where y0 ¼ R1 Uy and N ¼ R1 UN . Since the columns of DFT matrix U are orthogonal to each other, i.e., hui ; uj i ¼ dij , we have dS ¼ 0 for any value of S, and the RIP condition is met.

4.2 De-noising Scheme As shown in (16), the effective sensing matrix is the unitary matrix U. However, the multiplication of R1 U to (6) leads to noise enhancement. Specifically, the vector v is the DFT of the transmitted waveform, which has spectral nulls. By multiplying its inverse, the noise samples at the spectral nulls will be amplified. Figure 3 shows an example of this noise enhancement effect. In this figure, the amplitude of vector b where bðiÞ ¼ j1=vðiÞj; i ¼ 1; 2; . . .; K is shown. As shown in the figure, the noise amplification is serious (up to 15.4 dB), which leads to a severe degradation of the recovery performance. 20

Fig. 3 Amplitude of the vector of bðiÞ ¼ j1=vðiÞj; i ¼ 1; 2; . . .; K for m-sequence of length 31 and M¼4 Magnitude in dB

15

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−5

−10

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40

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i

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In [3], a kurtosis-based scheme is proposed to mitigate the noise-amplification. The scheme is based on the fact that the kurtosis of a given distribution has a definite value. Therefore, the kurtosis calculated from the received samples that follows a given distribution should not severely deviate from its theoretical kurtosis. Thus, the abnormal samples, e.g, samples with amplified noise, that cause the ‘‘sampled kurtosis’’ severely deviate from theoretical kurtosis can be removed. However, the kurtosis-based scheme examines the abnormal samples only from the statistical distribution point of view, and only a few extremely amplified noise samples can be recognized. For the AWGN noise samples that are amplified by the vector b, the sampled kurtosis falls into the 3r range of the theoretic value once two extreme samples are removed. The remaining amplified noise samples still cause the recovery algorithm perform poorly. The effective sensing system shown in (16) is obtained by left multiplying R1 U. Thus, the variance of the noise samples in the effective sensing is scaled by the vector b, i.e., the variance of the ith sample of N is bðiÞN0 =2, so that the ith noise sample will be amplified when bðiÞ [ 1. Thus, with the values of the scaling vector b known, we can remove the entries of y that is corrupted by the amplified noise, and keep only the the entries that are corrupted only by the noise with reduced noise power, i.e., the samples with bðiÞ\1. The signal model after this de-noising process can be represented as 0

y0J ¼ U J h þ N J

ð17Þ

In (17), J is the indices set defined as J ¼ fi 2 f1; 2; . . .; KgjbðiÞ  1g, and U J is the 0 submatrix generated by taking the rows of U indexed by J, and similarly, N J is the noise samples indexed by J.

4.3 RIP Condition After De-Noising As stated in [18], the RIP requirement shown in (12) must be satisfied for DS algorithm to work. In this section, we show that (12) is satisfied with high probability after de-noising. The submatrix UJ in (17), is constructed by taking rows of the unitary DFT matrix. It is shown in [20] that if jJj  OðS  log4 KÞ

ð18Þ

where K is the DFT size, then with overwhelming probability the inequality d3S þ 3d4S  2 holds. By using the monotonically increasing property of isometry constant d,we have d3S  d4S . Thus, we have 4d3S  d3S þ 3d4S  2

ð19Þ

The restricted isometry constant and restricted orthogonality constant have the following property [21] hS;S0  dSþS0 0

ð20Þ

By letting S ¼ 2S in (20), and adding the positive constant d3S on both sides of (20), we have

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High Resolution TOA Estimation Based on Compressed Sensing

d3S þ hS;2S  2d3S

ð21Þ

Using the monotonically increasing property of the restrict isometry constant again, we have d2S þ hS;2S  2d3S . Thus, with (19), it is ready to show d2S þ hS;2S  1. Therefore, the RIP condition for DS recovery shown in (12) is satisfied with overwhelming probability after de-nosing.

5 Numerical Results In this section we present the performance of the proposed TOA estimation scheme. In this simulation, an m sequence of N ¼ 31 is used as the spreading code of the transmitted spread spectrum sequence signal.

5.1 Channel Response Estimation First, the effectiveness of our proposed scheme is shown in Fig. 4. The channel is a 2-tap channel with equal tap gain (one realization of the fading channel), and tap separation of Tc=2. In this simulation, the received signal is oversampled by a factor of 4, i.e., M ¼ 4, and the signal to noise power ratio (SNR) is 10 dB. As shown in Fig. 4, our proposed scheme successfully recovers the sparse channel impulse response h, while the LS method gives the non-sparse estimation,i.e., h^ with more than 2 non-zero entries. The error norms, defined as kh^  hk2 , of our proposed scheme is 0:3336, which is within the error bound of 0:7172 calculated from (13) for C0 ¼ 4.

5.2 TOA Estimation As shown in the previous example, the DS method is able to give a sparse channel estimation. However, due to the noise, the channel recovered by DS algorithm may have more nonzero entries than the true channel does. The bogus nonzero entries, usually with small amplitudes, make the TOA estimation unreliable if the first nonzero taps from h^ is

Recovery From CS

Amplitudes of channel taps

1

true channel response CS estimated response

0.5 0 −0.5

5

5.5

6

6.5

7

7.5

8

8.5

9

9.5

10

Delay in times of symbol duration

Amplitudes of channel taps

Fig. 4 Sparse recovery comparison of CS and LS for two-tap channel with equal tap gain and tap separation of Tc =2 at SNR ¼ 10 dB

Recovery From LS

1.5

true channel response LS estimated response

1 0.5 0 −0.5 −1

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used directly. To address this issue, we can use the following two methods to determine the ^ TOA from the estimated channel impulse response h: • Amplitude Based Method The tap with the maximum amplitude in h^ is assumed to be the first channel tap. The amplitude based method assumes that the first tap has the largest amplitude, which may not always be the case in reality. • Signal Energy Based Method First, we sort the elements of h^ in descending order of ^ is estimated as the smallest number of magnitude. Then the sparsity of the channel, S, channel taps that account for most of the energy. For example, S^ is the smallest number ^ S that satisfies (22). The S-sparse channel, h^D , is obtained by keeping the S^ largest entries of h^ and set the others to zero. Finally, the smallest delay in h^D is adopted as our estimated TOA. S^ X

^ 2  0:95khk ^ 2 khðiÞk 2

ð22Þ

i¼0

Our scheme is compared with correlator peak detection and the modified phase-only correlator (MPOC) proposed in [3]. In the simulation, the received signal is sampled at the rate of 4=Tc . The channel is a time invariant 4-tap channel with exponential power delay profile (PDP), i.e., the average power of the lth tap is given by PðlÞ ¼ X0 expðglÞ, where g is the decay factor, l is the tap index and X0 is the average power of the first tap.2 The separation of the first 2 taps is set to be 1=4 chip, i.e., s1  s0 ¼ 1=4Tc . The delays of other 2 taps are uniformly distributed in ðs1 ; sP1 Þ and the amplitude of each tap follows independent Rayleigh distribution. The performances of different TOA estimation methods are compared in terms of the mean and standard deviation of the TOA estimation error as le ¼

NS 1 X js^0 ðiÞ  s0 j NS i¼1

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u NS u1 X re ¼ t ks^0 ðiÞ  s0  le k2 NS i¼1

ð23Þ

ð24Þ

where NS is the number of simulation runs. The TOA estimation performance is shown in Figs. 5 and 6 to compare the mean and standard deviation of TOA error for all schemes. Figure 5 shows that the correlator peak based scheme has the worst mean TOA error performance followed by our proposed scheme with amplitude criteria and MPOC. Our proposed scheme with the energy criteria has the best TOA error performance in terms of mean error. The mean TOA estimation error of our proposed scheme with energy criteria is asymptotically to zero as the SNR increases. The standard deviation of different TOA estimation schemes are shown in Fig. 6. When the SNR is moderate, e.g., greater than 0 dB, our proposed schemes have similar estimation error standard deviation as correlator based scheme and MPOC. When the SNR is greater than 6 dB, our proposed scheme with the energy criteria decreases rapidly as the SNR increases. 2

The total average power of the channel is normalized to be unity.

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High Resolution TOA Estimation Based on Compressed Sensing 0.2 CS energy based CS amplitude based Correlation peak detection MPOC

0.18 0.16 0.14

c

0.12 e

μ /T

Fig. 5 Mean error comparison of different TOA estimation methods. The channel is a fourtap channel with exponential PDP (g ¼ 0:25), Rayleigh distributed tap amplitude, and the separation of the first two taps is Tc =4

0.1 0.08 0.06 0.04 0.02 0 −5

0

5

10

15

20

SNR in dB

0.25

CS energy based CS amplitude based Correlation peak detection MPOC

0.2

c

0.15 e

σ /T

Fig. 6 Standard deviation of the TOA error comparison of different TOA estimation methods. The channel is a fourtap channel with exponential PDP (g ¼ 0:25), Rayleigh distributed tap amplitude, and the separation of the first two taps is Tc =4

0.1

0.05

0 −5

0

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SNR in dsB

6 Conclusion In this work we proposes a novel scheme to estimate the TOA of the signal by exploiting the sparsity of the wireless channel. To apply the results of the CS framework, we extend the work of [12] to sub-chip level resolution by making the sensing matrix satisfies RIP, and using a novel de-noising scheme to improve the recovery accuracy of the DS. Simulation results show that the proposed scheme is able to achieve a sub-chip resolution for TOA estimation. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant: 61101093, 61101090) and Fundamental Research Funds for the Central Universities (ZYGX2013J113).

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Wenhui Xiong received the B.S. and M.S. degrees from the University of Electronic Science and Technology of China (UESTC) in 1999 and 2002 respectively, and the Ph.D. degree from Ohio University Athen, Ohio, in 2007, all in electrical engineering. He was with the at corporate R&D group, Qualcomm inc. from 2006 to 2009, where he worked on mobile positioning for CDMA network and Femtocell. In November 2009, he joined the National key Laboratory of Communication at the University of Electronic Science and Technology of China (UESTC), where he worked as associate professor. His research interest includes wireless communication and signal processing.

Chang Liu received the B.S. in communication engineering from Kunming University of Science and Technology in 2009, and M. S. degrees in electronics and communication engineering from the University of Electronics Science and Technology of China in 2013. His research interest was the compressed sensing and its application in communication and signal processing. In 2013 he was employed by the Huawei Technologies Co., Ltd. working as an algorithm developing engineer.

Su Hu was born in Guangan, Sichuan, People’s Republic of China in 1983. He received his Ph.D. degree from University of Electronic Science and Technology of China, Chengdu, China, in 2010. Currently, he is an associate professor of UESTC. As a visiting scholar, he worked in Positioning and Wireless Technology Center (PWTC), Nanyang Technological University, Singapore from 2011 to 2012. His researches focus on OFDM, cooperative communication and signal processing.

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W. Xiong et al. Shaoqian Li received the BEng degree from University of Electronic Science and Technology of Xi’an, China, in 1982 and the MEng. degree from University of Electronic Science and Technology of China (UESTC), Sichuan, in 1984. Since July 1984, he has been a Faculty Member with the Institute of Communication and Information Engineering, UESTC, China, where he is a Professor, since 1997, and Ph.D. supervisor, since 2000. He is also the director of National Key Lab of Communication in UESTC and is a Member of Telecommunication Subject with National High Technology R & D Program of China (863 Program). His main fields of research interest include mobile communications systems (3G, Beyond 3G), wireless communication (CDMA, OFDM, MIMO and etc.), integrate circuit in communication systems and radio/spatial resource management.

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