- Email: [email protected]
A novel TOA estimation method with effective NLOS error reduction
THE JOURNAL OF CHINA UNIVERSITIES OF POSTS AND TELECOMMUNICATIONS Volume 15, Issue 1, March 2008
ZHANG Yi-heng, CUI Qi-mei, LI Yu-xiang, ZHANG Ping
A novel TOA estimation method with effective NLOS error
reduction CLC number TN911
Document A
Abstract It is well known that non-line-of-sight (NLOS) error has been the major factor impeding the enhancement of accuracy for time of arrival (TOA) estimation and wireless positioning. This article proposes a novel method of TOA estimation effectively reducing the NLOS error by 60%, comparing with the traditional timing and synchronization method. By constructing the orthogonal training sequences, this method converts the traditional TOA estimation to the detection of the first arrival path (FAP) in the NLOS multipath environment, and then estimates the TOA by the round-trip transmission (RTT) technology. Both theoretical analysis and numerical simulations prove that the method proposed in this article achieves better performance than the traditional methods. Keywords TOA estimation, NLOS error, B3G
1 lntroductlon In the future B3G wireless telecommunication system, the services based on location will be widely deployed, and the location estimation of mobile terminal is expected to become a basic function of the network. Most of the current location estimation algorithms are based on the TOA or time difference of arrival (TDOA), and TDOA can be derived by the difference of two TOAs. Therefore, the TOA estimation is the basic stage to locate the mobile terminals and the accuracy of TOA estimation will directly affect the accuracy of location estimation algorithms. The maximum search method, as one the traditional TOA estimation method, utilizes the synchronization procedure and picks out the maximum peak of the correlation function. In the narrow bandwidth system, the maximum search method suffers large TOA estimation error due to the low resolution of the multipath and NLOS propagation. It has been proved by Received date: 2007-05-25 WANG Yi-heng (!.::), CUI Qi-mei, LI Yu-xiang, ZHANG Ping Key Laboratory of Universal Wireless Communications, Beijing University of Posts and Telecommunications, Ministry of Education, Wireless Technology Innovation Institute (WTI), Beijing 100876, China E-mail: [email protected]
Article ID 1005-8885 (2008) 01-0032-06
measurements that the NLOS error can be as large as several hundred meters. NLOS error has been the major error source impeding the enhancement of location accuracy [ 11. To resolve the above-mentioned problems, several highresolution algorithms have been studied: 1) Forwardhackward linear prediction (FBLP) algorithm PI; 2) Singular value decomposition (SVD) or eigendecomposition methods [3]; 3)Methods based on subspace theory, such as roots multiple signals classification (roots-MUSIC) [4]; 4)Methods based on the minimum variance (MV) and normalized minimum variance (NMV) of the power delay profile [S]. Although these high-resolution algorithms achieve accurate TOA estimation in the NLOS and multipath environment, the computational complexity is too high to be implemented in the practical applications. As the development of wireless location research, beyond 3G (B3G) technology will be deployed in the near future. Both in the B3G time division duplex (TDD) and frequency division duplex (FDD) system, bandwidth is up to 20 MHz [6]. Consequently, the decreasing chip period significantly enhances the multipath resolution. Based on the high resolution of multipath in the B3G system, this article proposes a TOA estimation method effectively reducing the NLOS error, meanwhile, the computational complexity is far less than that of FBLP and MUSIC algorithms. Numerical simulations show that, comparing with the traditional maximum search method by timing and synchronization, TOA estimation method proposed in this article can reduce the NLOS error by 6070%. The novel TOA estimation method is proposed based on the TDD system structure, however, it is easy to extend our TOA estimation method to the FDD system.
2 TOA estlmatlon based on FAP 2.1 R l l measurement procedure
Measuring the RTT is a common method to estimate the
No. 1
ZHANG Yi-heng, et al.: A novel TOA estimation method with effective NLOS error reduction
TOA [7]. BS sends a training sequence to the MT, then the MT receives it and sends a training sequence back to MT after the predetermined time delay. The synchronization procedure in the TDD frame can be used to accomplish the RTT measurement, as shown in Fig. 1. D I is the downlink propagation delay and D , is the uplink propagation delay: TR= D I +D2 + 0
(1)
3
where TR denotes the duration time of RTT.
DownLink
Processed
I
I
Fig. 1 RTT measurement in the TDD system
Because TR is far less than the coherent time of wireless channel, and both uplink and downlink in the TDD system use the same frequency band, it can be concluded that the channel condition does not change much between D I and D , :
To = D I = D3 where TOA is denoted by To.
in this article is called orthogonal autocorrelation sequencefirst arrival path detection (OAS-FAP). Comparing with the algorithms proposed by Winter, Josep Vidal and Rene Jativa, OAS-FAP method involves lower complexity. Meanwhile, this method reserves the advantage of high accuracy for TOA estimation. Traditional training sequences are constructed by pseudonoise (PN) sequences. However, the constant amplitude zero autocorrelation (CAZAC) codes are adopted to construct the training sequences for the following advantages: 1) CAZAC codes have zero autocorrelation after cyclic shift. On the contrast, PN sequence's autocorrelation is not zero, then interference is induced when detecting the multipaths. 2) OFDM symbols constructed by CAZAC sequences have a lower PAPR than PN sequences, which makes CAZAC codes suitable for OFDM system, which is adopted in B3G 2.3
lime *
(2)
Substituting Eiq.(2). into Eq. (1) gives: (3)
33
Fundamental propertiesof CAZAC codes
Chu. D proposed the modified CAZAC codes in Ref. [9] with the perfect autocorrelation properties. The perfect autocorrelation properties mean that autocorrelation function of CAZAC is zero everywhere, except at the multiple periods where it has a single maximum. This characteristic is referred to as zero autocorrelation (ZAC). At the same time, the periodic Fourier transform of ZAC codes yields a constant amplitude line spectrum, called CA feature. The length of CAZAC codes can be any integer. Let the code length denoted by Nand CAZAC code denoted by C, : Pnk(k+I)
When N is an odd number: 2.2 TOA estlmatlon algorithms
ck = e ' 7
When N is even number: .Pnk'
Traditional RTT measurements by synchronization method illustrated in Fig. 1 ignore the contribution of multipath. In fact, the synchronization procedure only detects the most powerful path and neglects the other paths. Unfortunately, the most powerful path in the NLOS environment always carries very large NLOS error. Meanwhile, the FAP carrying the least NLOS error has experienced deep fading. Therefore, the traditional synchronization method is unsuitable for accurate TOA estimation. FAP detection method is one of the promising ways to reduce the NLOS error. Winter, Josep Vidal and Rene Jativa had articulated this idea in Refs. [3, 5, 81. However, their high-resolution methods involve very high computational complexity, because these algorithms are based on SVD, root-MUSIC algorithms, or MV and NMV algorithms. In this article, a method with lower complexity is proposed to measure the RTT through the detection of FAP by orthogonal autocorrelation sequences. The method proposed
ck= e ' N
(4)
where k = O , 1, 2,..., N - 1 ,
( P is prime to I?);
P and N
determine the initial phase of CAZAC codes. The autocorrelation function of C, ,denoted by R(i), is formulated as: N -I
R(0) = C C k C l k=O
N-i-l
N-I
C C,C,'+,_,; i = l , 2,...,N-1
CkC,'+i+
R(i)= k =O
k=N-i
It can be proved that [ 121: R(0)= N R ( i ) = 0; i = 1, 2,...,N - 1 2.4 Algorithm of OASFAP
OAS-FAP algorithm aims to decompose the multipath and select the f i s t arrival path to calculate the RTT duration time and TOA. In the NLOS environment, the first arrival paths always experience deeper fading, as shown in Fig. 2.
34
The Journal of CHUPT
I
Power
2008
Obviously, T, determines the maximum multipath resolution. The autocorrelation function can be defined as:
Maximum search
t
Substituting Eqs. (7)-(11) into Eq. (12):
-
I
I
TSSyr~ehmnilamn
-
I
I
)
Delay
The impulse response of the multipath channel can be mathematically modeled as L -taps delay line: L
h(t; z) = C h l ( t , z)e'J2@cp'(')' 60- zdt))
(6)
/=I
According to the autocorrelation properties of CAZAC codes, when z = j N + Dl and D, E r : 1 ztN-l y ( z ) = hf e* + n ( k ) ~ ' (k z) (14)
c k=z
when z f j N + D , :
where hl(t,z), zr(t)andq(t) are the attenuation, propagation delay, and phase corresponding to path 1, respectively. According to Clark's model, the stochastic variable hr(t,z) follows the Rayleigh distribution and q ( t ) follows the uniform distribution from 0 to 2 s . The OFDM symbols without CP transmitted at the BS can be constructed: S , ( k )= C ( k ); k = 0, 1,...,N - 1 (7)
where j = O , 1,..., M -1. It can be inferred from Eqs. (14) and (15) that the stochastic variable y ( z ) follows complex normal distribution. When z=jN+D,
when z
f
and D,E
r
, denote y ( z ) as y,(z) , and
j N + Dl , denoted as y,(z). The following can be
where N is denoted as the OFDM sampling number (without CP). After inserting CP at the beginning of the OFDM symbols, the complete OFDM symbol can be formulated as: S , ( k ) = C [ ( k + Q > ] , , , ; k = O , 1,...,N + Q - 1 where N - Q is the length of CP.
(8)
The synchronization data can be constructed by repeating the OFDM symbols M times: S(k)=S2(k)mad(N+Q) ; k = O , 1, 2,..., ( N + Q ) M -1
(9)
The corresponding complex base band signal is denoted as Since it is assumed that the RTT duration time is far less than the coherent time of the channel, parameters in Eq. (6) can be deemed as constants. Therefore, the received signal r ( t )at the MT can be formulated as: s(t).
8
4 0.6 CI
R
L
r ( t )= c 4epls ( t - z,) + n(t)
The multipath delay D/ can be estimated by searching the peak values of the Iy(z)I , as shown in Fig. 3.
(10)
/=I
3
"1 0.2 0
500
where n ( t ) is complex AWGN, the variances of both real part and imaginary part of n ( t ) is denoted as 0; . After sampling at the receiver, the discrete form of r ( t ) :
L
1000 1500 2000 2500 3000 3500 Delaylchips
Fig. 3 Autocorrelation function
where k =0, 1, 2,... ,T, is the chip period and Dl is the discrete multipath delay denoted as Dl = IT,] . All the
In the NLOS environment, the first arrival path experiences deep fading, making the FAP detection difficult. Thus, to reduce the erroneous detections due to low SNR of FAP, M OFDM symbols consisting CAZAC codes in time domain can be combined to judge the peaks of ly(z)(. Redefining the
discrete multipath delays can be included in the set r = { 4, D2 ,...,Dl } , and the TOA of FAP can be denoted as min(r).
autocorrelation function R ( z ) : 1 M-l z = 0, 1,...,N - 1 R ( z ) = - y( j N t z ) N j=o
L
r ( k ) = x4 e"lS(k - 4 )+ n ( k )
(11)
1=1
c
(17)
No. 1
ZHANG Yi-heng, et al.: A novel TOA estimation method with effective NLOS error reduction
When z = Dl :
When z # Dl :
Stochastic variable R( z )
follows
complex
normal
35
the blocking effect of the dense urban buildings, the probability of LOS propagation is very low. Therefore, the NLOS propagation is considered in the following simulation. The sampling number of OFDM symbol without CP is 1 024, and the length of the CP is 216. So, the length of a complete OFDM symbol is 1 240 and the length of corresponding CAZAC codes is 1 024. The bandwidth is 20 MHz, which means the chip period is 0.05 ps ,
distribution. R ( z ) is denoted as R,(z) when z = D, , R ( z ) is denoted as &(z) when z
#
3.2
DI , so:
~[&(z)]=hce"
E[Ro(z)]= 0
(20)
Comparing Eqs. (16) and (20). the variance of R ( z ) is 1/M of y(z). 2.5 Evaluation of decision threshold
It can be derived from Eqs. (18) and (19) that if IR(z)l3T ,
z is judged as one of the delay values and if IR(z)l< T , z is not deemed as the delay value. The basic principle of the evaluation for the decision threshold T is to minimize the erroneous judgment probability P, . Neglecting the parameter z, let
R =IR(z)I
, so:
Error performance
To verify the performance of OAS-FAP algorithm, simulations have been carried out to compare with certain other highresolution TOA estimation algorithms. The root-mean- square (RMS) error of TOA estimation has been chosen as the criteria for comparison. Four algorithms to estimate the RTT are compared: 1) OAS-FAP algorithm proposed by this article; 2) Traditional maximum search method by synchronization; 3) Forward-backward-linear-prediction (FBLP) algorithm based on SVD; 4) Roots-MUSIC algorithm. Figure 4 depicts the RMS error in meters for the abovementioned four algorithms. The results indicate clearly that the OAS-FAP algorithm achieves better error performance than the other algorithms.
t OAS-FAP
where p ( * ) is the probability density function (PDF) of
+Maximum seach
randomvariable R , P, = P ( z = D [ ) , P o = P { z # D l } .
+FBLP +- Roots-MUSIC
-
_-
p[TIz=D11- Po p[TIz#DiI P
(21)
It can be inferred from Eqs. (19) and (20) that conditional probability density p ( R I z f D l )follows Rayleigh distribution and conditional probability density p ( k I z = D l ) follows Rice distribution.
8 Slmulatlon and ovaluatlon 3.1 Slmulatlon envlronment
Numerical Analysis is based on the geometrically based single bounce macrocell (GBSBM) [ 101 channel model. GBSBM channel model assumes all the electromagnetic waves transmitted between MT and BS propagating on the same horizontal plane, and assumes that each NLOS propagation path experiences only one reflection. Because of
I
I
I
0
15
30
SNWdB
Fig. 4 Simulation result of error performance
It can also be inferred from Fig. 5 that the OAS-FAP algorithm achieves good performance even at the poor SNR environment. The RMS error of the OAS-FAP is about 30 meters when SNR is 0 dB, while the RMS error of the traditional maximum search method is above 100 meters. So it can be concluded that the OAS-FAP algorithm proposed in this article reduces the TOA estimation error by 60%-70%. The RMS error performances of both OAS-FAP and traditional algorithms converge to the floor level, and the floor level depends on the radii of the local scattering area. This
36
The Journal of CHUPT
phenomenon reveals the intrinsic error source of the TOA algorithms based on first arrival path: the larger the local scattering area is, larger NLOS error will occur. Two local scattering area radius, 200 m and 350 m, are assumed in the simulation and the simulation results demonstrated in Fig. 5. tOAS-FAP/I
+Maximum searchiRadii:200 m OAS-FAP/Radii:350 m 4- Maximum search/Radii:350 m
E --I
2008
4 Concluslons This article proposes a novel TOA estimation method based on the B3G TDD system structure. The basic steps of the method include: First, the FAP is detected in downlink and uplink by orthogonal training sequences; Second, the RTT duration time is calculated and the TOA estimation is acquired. Since the FAP carries least NLOS error compared to other multipaths, the method proposed can achieve very high accuracy for TOA estimation. The numerical simulations prove that, comparing with the traditional maximum search method by synchroniz- ation, this novel method can reduce the NLOS error by 60%-70%. Meanwhile, the low computational complexity makes OAS-FAP method more suitable for practical applications.
SNKIdB
Fig. 5 TOA estimation performance comparison
3.3 Complexlty analysts
A comparison of the computational complexity of the above mentioned four algorithms is made: OAS-FAP, maximum search by synchronization, FBLP based on SVD and roots MUSIC algorithm. The following parametric definitions are made: N the length of training sequence; Dmax: the maximum multipath delay in chips; A: the linear prediction matrix for FBLP algorithm; R:the correlation matrix for roots-MUSIC algorithm; L the order of the forwardhackward linear prediction filter; M. the number of frequency sampling for discrete Fourier transform (DFT) . These parameters have the following relationship [2-4]: M >Dmax; M = 2k, where k is the minimum natural number satisfy the above inequation; L=3M/4. Both singular value decomposition and eigendecomposition involve heavy burden for computation, especially when the dimension of the matrix is large. It can be concluded from Table 1 that the computational complexity of OAS-FAP is far less than that of FBLP and roots-MUSIC algorithms, which makes OAS-FAP method more applicable in the practical environment.
Acknowledgements This work is supported by the National Natural Science Foundation of China (60496312), Program for New Century Excellent Talents in University (NCET-05-0116), and the Hi-Tech Research and Development Program of China (2006AAOIZ260), the Fund for Foreign Scholars in University Research and Teaching Programs (B07005).
References 1. Caffery J Jr, Stuber G L. Subscriber location in CDMA cellular
2.
3.
4.
5.
Table 1 Computation complexity comparison Algorithm name
Computational complexity /Operation N multiplication
Maximum search
N 2a ~ r f i t i ~ n ..
OAS-FAP
N multiplication N 2addition
Roots MUSIC
Eigendecomposition of R polynomial root exbact (length f.)
Parameter
I
6. N=l 024 M=5 12 k384
7.
networks. IEEE Transactions on Vehicular Technology, 1998, 47(2): 406-416 Fertig L B, McClellan J H. Instantaneous frequency estimation using linear prediction with comparisons to the DESAs. IEEE Signal Processing Letters, 1996, 3: 54-56 Winter J, Wengerter C. High resolution estimation of the time of arrival for GSM location. Proceedings of 51st IEEE Vehicular Technology Conference (VTC' 2000-Spring): Vol 2, May 15-18, 2000, Tokyo, Japan. Piscataway, NJ, USA: IEEE, 2000: 1343-1 347 Rao B D, Hari V S. Performance analysis of root-MUSIC. IEEE Transactions on Acoustics, Speech and Signal Processing, 1989, 37(12): 1939-1949 Vidal J, Jativa R. First arriving path detection for subscriber location in mobile communication systems. Proceedings of 2002 IEEE International Conference on Acoustics, Speech and Processing (ICASSP' 02): Vol3, May 13-17.2002, Orlando, Fli, USA. Piscataway, NJ, USA: IEEE, 2002: 2733-2736 Zhang Ping, Tao Xiao-feng, Zhang Jian-hua, et al. A vision from the future: beyond 3G TDD. IEEE Communications Magazine, 2005,43(1): 38-44 Dongwoo K, Young N, Suckchel Y,et al. A simple asynchronous U W B position location algorithm based on single round-trip transmission. The 8th International Conference on Advanced Communication Technology (ICACT 2006), Feb. 2006, Phoenix
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ZHANG Yi-hens!. et al.: A novel TOA estimation method with effective NLOS error reduction
Park Korea: 2006: 4 8. Vidal J, Najar M, Jativa R. High resolution time-of-arrival detection for wireless positioning systems. Proceedings of 56th IEEE Vehicular Technology Conference (VTC’2002-Fall): Vol4, Sep 24-28, 2004, Vancouver Canada. Piscataway, NJ, USA: IEEE, 2002: 2283-2287 9. Chu D. Polyphase codes with good periodic correlation properties. IEEE Transactions on Information Theory, 1972, 18(4): 531-532 10. Petrus P, Reed J H, Rappaport T S. Geometrically based statistical channel model for macrocellular mobile environments. Proceedings of IEEE Global Telecommunications Conference (GLOBECOM’ 96): Vol 2, Nov 18-22, 1996, London, UK. Piscataway, NJ, USA: IEEE, 1996: 1197-1201
Biographies: ZHANG Yi-heng, Ph. D. Candidate from Wireless Technologies Innovation Institute and Key Laboratory of Universal Wireless Communication, Ministry of Education in Beijing University of Posts and Telecommunications, interested in the research on advanced radio transmission technologies in 4G mobile communication systems. CUI Qi-mei, lecturer from Wireless Technologies Innovation Institute and Key Laboratory of Universal Wireless Communication, Ministry of Education in Beijing University of Posts and Telecommunications. She received her Ph. D. degree in Telecommunication engineering from Beijing University of Posts and Telecommunication
37
in 2006. Her research covers ultra-wideband (UWB), wireless location and MIMO techniques. She has applied 6 patents and published more than 20 papers and achieved the first-class prize for science and technology of China Institute of Communications in 2006. LI Yu-xiang, master Candidate from Wireless Technologies Innovation Instituteand Key Laboratory of Universal Wireless Communication, Ministry of Education in Beijing University of Posts and Telecommunications, interested in the research on advanced radio transmission technologies in mobile communication systems. ZHANG Ping, Ph. D., professor from Wireless Technologies Innovation Institute and Key Laboratory of Universal Wireless Communication, Ministry of Education in Beijing University of Posts and Telecommunications, interested in the research on key techniques of the Beyond 3G systems, especially in the multiple access technique, modulation and channel coding, etc.
ZHANG Yi-heng, CUI Qi-mei, LI Yu-xiang, ZHANG Ping
A novel TOA estimation method with effective NLOS error
reduction CLC number TN911
Document A
Abstract It is well known that non-line-of-sight (NLOS) error has been the major factor impeding the enhancement of accuracy for time of arrival (TOA) estimation and wireless positioning. This article proposes a novel method of TOA estimation effectively reducing the NLOS error by 60%, comparing with the traditional timing and synchronization method. By constructing the orthogonal training sequences, this method converts the traditional TOA estimation to the detection of the first arrival path (FAP) in the NLOS multipath environment, and then estimates the TOA by the round-trip transmission (RTT) technology. Both theoretical analysis and numerical simulations prove that the method proposed in this article achieves better performance than the traditional methods. Keywords TOA estimation, NLOS error, B3G
1 lntroductlon In the future B3G wireless telecommunication system, the services based on location will be widely deployed, and the location estimation of mobile terminal is expected to become a basic function of the network. Most of the current location estimation algorithms are based on the TOA or time difference of arrival (TDOA), and TDOA can be derived by the difference of two TOAs. Therefore, the TOA estimation is the basic stage to locate the mobile terminals and the accuracy of TOA estimation will directly affect the accuracy of location estimation algorithms. The maximum search method, as one the traditional TOA estimation method, utilizes the synchronization procedure and picks out the maximum peak of the correlation function. In the narrow bandwidth system, the maximum search method suffers large TOA estimation error due to the low resolution of the multipath and NLOS propagation. It has been proved by Received date: 2007-05-25 WANG Yi-heng (!.::), CUI Qi-mei, LI Yu-xiang, ZHANG Ping Key Laboratory of Universal Wireless Communications, Beijing University of Posts and Telecommunications, Ministry of Education, Wireless Technology Innovation Institute (WTI), Beijing 100876, China E-mail: [email protected]
Article ID 1005-8885 (2008) 01-0032-06
measurements that the NLOS error can be as large as several hundred meters. NLOS error has been the major error source impeding the enhancement of location accuracy [ 11. To resolve the above-mentioned problems, several highresolution algorithms have been studied: 1) Forwardhackward linear prediction (FBLP) algorithm PI; 2) Singular value decomposition (SVD) or eigendecomposition methods [3]; 3)Methods based on subspace theory, such as roots multiple signals classification (roots-MUSIC) [4]; 4)Methods based on the minimum variance (MV) and normalized minimum variance (NMV) of the power delay profile [S]. Although these high-resolution algorithms achieve accurate TOA estimation in the NLOS and multipath environment, the computational complexity is too high to be implemented in the practical applications. As the development of wireless location research, beyond 3G (B3G) technology will be deployed in the near future. Both in the B3G time division duplex (TDD) and frequency division duplex (FDD) system, bandwidth is up to 20 MHz [6]. Consequently, the decreasing chip period significantly enhances the multipath resolution. Based on the high resolution of multipath in the B3G system, this article proposes a TOA estimation method effectively reducing the NLOS error, meanwhile, the computational complexity is far less than that of FBLP and MUSIC algorithms. Numerical simulations show that, comparing with the traditional maximum search method by timing and synchronization, TOA estimation method proposed in this article can reduce the NLOS error by 6070%. The novel TOA estimation method is proposed based on the TDD system structure, however, it is easy to extend our TOA estimation method to the FDD system.
2 TOA estlmatlon based on FAP 2.1 R l l measurement procedure
Measuring the RTT is a common method to estimate the
No. 1
ZHANG Yi-heng, et al.: A novel TOA estimation method with effective NLOS error reduction
TOA [7]. BS sends a training sequence to the MT, then the MT receives it and sends a training sequence back to MT after the predetermined time delay. The synchronization procedure in the TDD frame can be used to accomplish the RTT measurement, as shown in Fig. 1. D I is the downlink propagation delay and D , is the uplink propagation delay: TR= D I +D2 + 0
(1)
3
where TR denotes the duration time of RTT.
DownLink
Processed
I
I
Fig. 1 RTT measurement in the TDD system
Because TR is far less than the coherent time of wireless channel, and both uplink and downlink in the TDD system use the same frequency band, it can be concluded that the channel condition does not change much between D I and D , :
To = D I = D3 where TOA is denoted by To.
in this article is called orthogonal autocorrelation sequencefirst arrival path detection (OAS-FAP). Comparing with the algorithms proposed by Winter, Josep Vidal and Rene Jativa, OAS-FAP method involves lower complexity. Meanwhile, this method reserves the advantage of high accuracy for TOA estimation. Traditional training sequences are constructed by pseudonoise (PN) sequences. However, the constant amplitude zero autocorrelation (CAZAC) codes are adopted to construct the training sequences for the following advantages: 1) CAZAC codes have zero autocorrelation after cyclic shift. On the contrast, PN sequence's autocorrelation is not zero, then interference is induced when detecting the multipaths. 2) OFDM symbols constructed by CAZAC sequences have a lower PAPR than PN sequences, which makes CAZAC codes suitable for OFDM system, which is adopted in B3G 2.3
lime *
(2)
Substituting Eiq.(2). into Eq. (1) gives: (3)
33
Fundamental propertiesof CAZAC codes
Chu. D proposed the modified CAZAC codes in Ref. [9] with the perfect autocorrelation properties. The perfect autocorrelation properties mean that autocorrelation function of CAZAC is zero everywhere, except at the multiple periods where it has a single maximum. This characteristic is referred to as zero autocorrelation (ZAC). At the same time, the periodic Fourier transform of ZAC codes yields a constant amplitude line spectrum, called CA feature. The length of CAZAC codes can be any integer. Let the code length denoted by Nand CAZAC code denoted by C, : Pnk(k+I)
When N is an odd number: 2.2 TOA estlmatlon algorithms
ck = e ' 7
When N is even number: .Pnk'
Traditional RTT measurements by synchronization method illustrated in Fig. 1 ignore the contribution of multipath. In fact, the synchronization procedure only detects the most powerful path and neglects the other paths. Unfortunately, the most powerful path in the NLOS environment always carries very large NLOS error. Meanwhile, the FAP carrying the least NLOS error has experienced deep fading. Therefore, the traditional synchronization method is unsuitable for accurate TOA estimation. FAP detection method is one of the promising ways to reduce the NLOS error. Winter, Josep Vidal and Rene Jativa had articulated this idea in Refs. [3, 5, 81. However, their high-resolution methods involve very high computational complexity, because these algorithms are based on SVD, root-MUSIC algorithms, or MV and NMV algorithms. In this article, a method with lower complexity is proposed to measure the RTT through the detection of FAP by orthogonal autocorrelation sequences. The method proposed
ck= e ' N
(4)
where k = O , 1, 2,..., N - 1 ,
( P is prime to I?);
P and N
determine the initial phase of CAZAC codes. The autocorrelation function of C, ,denoted by R(i), is formulated as: N -I
R(0) = C C k C l k=O
N-i-l
N-I
C C,C,'+,_,; i = l , 2,...,N-1
CkC,'+i+
R(i)= k =O
k=N-i
It can be proved that [ 121: R(0)= N R ( i ) = 0; i = 1, 2,...,N - 1 2.4 Algorithm of OASFAP
OAS-FAP algorithm aims to decompose the multipath and select the f i s t arrival path to calculate the RTT duration time and TOA. In the NLOS environment, the first arrival paths always experience deeper fading, as shown in Fig. 2.
34
The Journal of CHUPT
I
Power
2008
Obviously, T, determines the maximum multipath resolution. The autocorrelation function can be defined as:
Maximum search
t
Substituting Eqs. (7)-(11) into Eq. (12):
-
I
I
TSSyr~ehmnilamn
-
I
I
)
Delay
The impulse response of the multipath channel can be mathematically modeled as L -taps delay line: L
h(t; z) = C h l ( t , z)e'J2@cp'(')' 60- zdt))
(6)
/=I
According to the autocorrelation properties of CAZAC codes, when z = j N + Dl and D, E r : 1 ztN-l y ( z ) = hf e* + n ( k ) ~ ' (k z) (14)
c k=z
when z f j N + D , :
where hl(t,z), zr(t)andq(t) are the attenuation, propagation delay, and phase corresponding to path 1, respectively. According to Clark's model, the stochastic variable hr(t,z) follows the Rayleigh distribution and q ( t ) follows the uniform distribution from 0 to 2 s . The OFDM symbols without CP transmitted at the BS can be constructed: S , ( k )= C ( k ); k = 0, 1,...,N - 1 (7)
where j = O , 1,..., M -1. It can be inferred from Eqs. (14) and (15) that the stochastic variable y ( z ) follows complex normal distribution. When z=jN+D,
when z
f
and D,E
r
, denote y ( z ) as y,(z) , and
j N + Dl , denoted as y,(z). The following can be
where N is denoted as the OFDM sampling number (without CP). After inserting CP at the beginning of the OFDM symbols, the complete OFDM symbol can be formulated as: S , ( k ) = C [ ( k + Q > ] , , , ; k = O , 1,...,N + Q - 1 where N - Q is the length of CP.
(8)
The synchronization data can be constructed by repeating the OFDM symbols M times: S(k)=S2(k)mad(N+Q) ; k = O , 1, 2,..., ( N + Q ) M -1
(9)
The corresponding complex base band signal is denoted as Since it is assumed that the RTT duration time is far less than the coherent time of the channel, parameters in Eq. (6) can be deemed as constants. Therefore, the received signal r ( t )at the MT can be formulated as: s(t).
8
4 0.6 CI
R
L
r ( t )= c 4epls ( t - z,) + n(t)
The multipath delay D/ can be estimated by searching the peak values of the Iy(z)I , as shown in Fig. 3.
(10)
/=I
3
"1 0.2 0
500
where n ( t ) is complex AWGN, the variances of both real part and imaginary part of n ( t ) is denoted as 0; . After sampling at the receiver, the discrete form of r ( t ) :
L
1000 1500 2000 2500 3000 3500 Delaylchips
Fig. 3 Autocorrelation function
where k =0, 1, 2,... ,T, is the chip period and Dl is the discrete multipath delay denoted as Dl = IT,] . All the
In the NLOS environment, the first arrival path experiences deep fading, making the FAP detection difficult. Thus, to reduce the erroneous detections due to low SNR of FAP, M OFDM symbols consisting CAZAC codes in time domain can be combined to judge the peaks of ly(z)(. Redefining the
discrete multipath delays can be included in the set r = { 4, D2 ,...,Dl } , and the TOA of FAP can be denoted as min(r).
autocorrelation function R ( z ) : 1 M-l z = 0, 1,...,N - 1 R ( z ) = - y( j N t z ) N j=o
L
r ( k ) = x4 e"lS(k - 4 )+ n ( k )
(11)
1=1
c
(17)
No. 1
ZHANG Yi-heng, et al.: A novel TOA estimation method with effective NLOS error reduction
When z = Dl :
When z # Dl :
Stochastic variable R( z )
follows
complex
normal
35
the blocking effect of the dense urban buildings, the probability of LOS propagation is very low. Therefore, the NLOS propagation is considered in the following simulation. The sampling number of OFDM symbol without CP is 1 024, and the length of the CP is 216. So, the length of a complete OFDM symbol is 1 240 and the length of corresponding CAZAC codes is 1 024. The bandwidth is 20 MHz, which means the chip period is 0.05 ps ,
distribution. R ( z ) is denoted as R,(z) when z = D, , R ( z ) is denoted as &(z) when z
#
3.2
DI , so:
~[&(z)]=hce"
E[Ro(z)]= 0
(20)
Comparing Eqs. (16) and (20). the variance of R ( z ) is 1/M of y(z). 2.5 Evaluation of decision threshold
It can be derived from Eqs. (18) and (19) that if IR(z)l3T ,
z is judged as one of the delay values and if IR(z)l< T , z is not deemed as the delay value. The basic principle of the evaluation for the decision threshold T is to minimize the erroneous judgment probability P, . Neglecting the parameter z, let
R =IR(z)I
, so:
Error performance
To verify the performance of OAS-FAP algorithm, simulations have been carried out to compare with certain other highresolution TOA estimation algorithms. The root-mean- square (RMS) error of TOA estimation has been chosen as the criteria for comparison. Four algorithms to estimate the RTT are compared: 1) OAS-FAP algorithm proposed by this article; 2) Traditional maximum search method by synchronization; 3) Forward-backward-linear-prediction (FBLP) algorithm based on SVD; 4) Roots-MUSIC algorithm. Figure 4 depicts the RMS error in meters for the abovementioned four algorithms. The results indicate clearly that the OAS-FAP algorithm achieves better error performance than the other algorithms.
t OAS-FAP
where p ( * ) is the probability density function (PDF) of
+Maximum seach
randomvariable R , P, = P ( z = D [ ) , P o = P { z # D l } .
+FBLP +- Roots-MUSIC
-
_-
p[TIz=D11- Po p[TIz#DiI P
(21)
It can be inferred from Eqs. (19) and (20) that conditional probability density p ( R I z f D l )follows Rayleigh distribution and conditional probability density p ( k I z = D l ) follows Rice distribution.
8 Slmulatlon and ovaluatlon 3.1 Slmulatlon envlronment
Numerical Analysis is based on the geometrically based single bounce macrocell (GBSBM) [ 101 channel model. GBSBM channel model assumes all the electromagnetic waves transmitted between MT and BS propagating on the same horizontal plane, and assumes that each NLOS propagation path experiences only one reflection. Because of
I
I
I
0
15
30
SNWdB
Fig. 4 Simulation result of error performance
It can also be inferred from Fig. 5 that the OAS-FAP algorithm achieves good performance even at the poor SNR environment. The RMS error of the OAS-FAP is about 30 meters when SNR is 0 dB, while the RMS error of the traditional maximum search method is above 100 meters. So it can be concluded that the OAS-FAP algorithm proposed in this article reduces the TOA estimation error by 60%-70%. The RMS error performances of both OAS-FAP and traditional algorithms converge to the floor level, and the floor level depends on the radii of the local scattering area. This
36
The Journal of CHUPT
phenomenon reveals the intrinsic error source of the TOA algorithms based on first arrival path: the larger the local scattering area is, larger NLOS error will occur. Two local scattering area radius, 200 m and 350 m, are assumed in the simulation and the simulation results demonstrated in Fig. 5. tOAS-FAP/I
+Maximum searchiRadii:200 m OAS-FAP/Radii:350 m 4- Maximum search/Radii:350 m
E --I
2008
4 Concluslons This article proposes a novel TOA estimation method based on the B3G TDD system structure. The basic steps of the method include: First, the FAP is detected in downlink and uplink by orthogonal training sequences; Second, the RTT duration time is calculated and the TOA estimation is acquired. Since the FAP carries least NLOS error compared to other multipaths, the method proposed can achieve very high accuracy for TOA estimation. The numerical simulations prove that, comparing with the traditional maximum search method by synchroniz- ation, this novel method can reduce the NLOS error by 60%-70%. Meanwhile, the low computational complexity makes OAS-FAP method more suitable for practical applications.
SNKIdB
Fig. 5 TOA estimation performance comparison
3.3 Complexlty analysts
A comparison of the computational complexity of the above mentioned four algorithms is made: OAS-FAP, maximum search by synchronization, FBLP based on SVD and roots MUSIC algorithm. The following parametric definitions are made: N the length of training sequence; Dmax: the maximum multipath delay in chips; A: the linear prediction matrix for FBLP algorithm; R:the correlation matrix for roots-MUSIC algorithm; L the order of the forwardhackward linear prediction filter; M. the number of frequency sampling for discrete Fourier transform (DFT) . These parameters have the following relationship [2-4]: M >Dmax; M = 2k, where k is the minimum natural number satisfy the above inequation; L=3M/4. Both singular value decomposition and eigendecomposition involve heavy burden for computation, especially when the dimension of the matrix is large. It can be concluded from Table 1 that the computational complexity of OAS-FAP is far less than that of FBLP and roots-MUSIC algorithms, which makes OAS-FAP method more applicable in the practical environment.
Acknowledgements This work is supported by the National Natural Science Foundation of China (60496312), Program for New Century Excellent Talents in University (NCET-05-0116), and the Hi-Tech Research and Development Program of China (2006AAOIZ260), the Fund for Foreign Scholars in University Research and Teaching Programs (B07005).
References 1. Caffery J Jr, Stuber G L. Subscriber location in CDMA cellular
2.
3.
4.
5.
Table 1 Computation complexity comparison Algorithm name
Computational complexity /Operation N multiplication
Maximum search
N 2a ~ r f i t i ~ n ..
OAS-FAP
N multiplication N 2addition
Roots MUSIC
Eigendecomposition of R polynomial root exbact (length f.)
Parameter
I
6. N=l 024 M=5 12 k384
7.
networks. IEEE Transactions on Vehicular Technology, 1998, 47(2): 406-416 Fertig L B, McClellan J H. Instantaneous frequency estimation using linear prediction with comparisons to the DESAs. IEEE Signal Processing Letters, 1996, 3: 54-56 Winter J, Wengerter C. High resolution estimation of the time of arrival for GSM location. Proceedings of 51st IEEE Vehicular Technology Conference (VTC' 2000-Spring): Vol 2, May 15-18, 2000, Tokyo, Japan. Piscataway, NJ, USA: IEEE, 2000: 1343-1 347 Rao B D, Hari V S. Performance analysis of root-MUSIC. IEEE Transactions on Acoustics, Speech and Signal Processing, 1989, 37(12): 1939-1949 Vidal J, Jativa R. First arriving path detection for subscriber location in mobile communication systems. Proceedings of 2002 IEEE International Conference on Acoustics, Speech and Processing (ICASSP' 02): Vol3, May 13-17.2002, Orlando, Fli, USA. Piscataway, NJ, USA: IEEE, 2002: 2733-2736 Zhang Ping, Tao Xiao-feng, Zhang Jian-hua, et al. A vision from the future: beyond 3G TDD. IEEE Communications Magazine, 2005,43(1): 38-44 Dongwoo K, Young N, Suckchel Y,et al. A simple asynchronous U W B position location algorithm based on single round-trip transmission. The 8th International Conference on Advanced Communication Technology (ICACT 2006), Feb. 2006, Phoenix
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ZHANG Yi-hens!. et al.: A novel TOA estimation method with effective NLOS error reduction
Park Korea: 2006: 4 8. Vidal J, Najar M, Jativa R. High resolution time-of-arrival detection for wireless positioning systems. Proceedings of 56th IEEE Vehicular Technology Conference (VTC’2002-Fall): Vol4, Sep 24-28, 2004, Vancouver Canada. Piscataway, NJ, USA: IEEE, 2002: 2283-2287 9. Chu D. Polyphase codes with good periodic correlation properties. IEEE Transactions on Information Theory, 1972, 18(4): 531-532 10. Petrus P, Reed J H, Rappaport T S. Geometrically based statistical channel model for macrocellular mobile environments. Proceedings of IEEE Global Telecommunications Conference (GLOBECOM’ 96): Vol 2, Nov 18-22, 1996, London, UK. Piscataway, NJ, USA: IEEE, 1996: 1197-1201
Biographies: ZHANG Yi-heng, Ph. D. Candidate from Wireless Technologies Innovation Institute and Key Laboratory of Universal Wireless Communication, Ministry of Education in Beijing University of Posts and Telecommunications, interested in the research on advanced radio transmission technologies in 4G mobile communication systems. CUI Qi-mei, lecturer from Wireless Technologies Innovation Institute and Key Laboratory of Universal Wireless Communication, Ministry of Education in Beijing University of Posts and Telecommunications. She received her Ph. D. degree in Telecommunication engineering from Beijing University of Posts and Telecommunication
37
in 2006. Her research covers ultra-wideband (UWB), wireless location and MIMO techniques. She has applied 6 patents and published more than 20 papers and achieved the first-class prize for science and technology of China Institute of Communications in 2006. LI Yu-xiang, master Candidate from Wireless Technologies Innovation Instituteand Key Laboratory of Universal Wireless Communication, Ministry of Education in Beijing University of Posts and Telecommunications, interested in the research on advanced radio transmission technologies in mobile communication systems. ZHANG Ping, Ph. D., professor from Wireless Technologies Innovation Institute and Key Laboratory of Universal Wireless Communication, Ministry of Education in Beijing University of Posts and Telecommunications, interested in the research on key techniques of the Beyond 3G systems, especially in the multiple access technique, modulation and channel coding, etc.