ISSN 1859 1531 TẠP CHÍ KHOA HỌC VÀ CÔNG NGHỆ ĐẠI HỌC ĐÀ NẴNG, SỐ 11(96) 2015, QUYỂN 2 83 AN EFFICIENT CODE TRACKING TECHNIQUE BASED ON MULTI GATE DELAY STRUCTURE FOR COSINE PHASED BOC SIGNALS KỸ THUẬT[.]
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AN EFFICIENT CODE TRACKING TECHNIQUE BASED ON MULTI-GATE
DELAY STRUCTURE FOR COSINE PHASED BOC SIGNALS
KỸ THUẬT BÁM MÃ HIỆU QUẢ DỰA TRÊN CẤU TRÚC ĐA TƯƠNG QUAN
CHO TÍN HIỆU BOC PHA COSIN Pham Viet Hung1, Tran Hoang Vu2
1 Vietnam Maritime University; phamviethung@vimaru.edu.vn
2Danang College of Technology; tranhoangvu_university@yahoo.com.vn
Abstract - The accuracy of code tracking plays an important role in
signal processing of Global Navigation Satellite System (GNSS)
receivers In this paper, a novel method of code tracking is proposed It is
based on using seven correlators as multiple gate delay structure This
method can be applied to new navigation signals which adopt a new
type of modulation called binary offset carrier (BOC) Some variants of
BOC have been developed for new navigation signals These new types
of modulation provide some advantages in signal synchronization
However, there are some challenges since there are some side peaks in
auto correlation function of signals These side peaks could raise a risk of
wrong peak selection called ambiguity problem The proposed method in
this paper also removes the ambiguity in code tracking The simulation
results show the good performance of this method in code tracking as
well as multipath mitigation
Tóm tắt - Độ chính xác của hệ thống định vị sử dụng vệ tinh (GNSS) chịu ảnh hưởng khá nhiều bởi quá trình bám mã trong bộ thu Bài báo này sẽ trình bày kỹ thuật bám mã mới Kỹ thuật này hoạt động dựa trên cấu trúc đa tương quan và có thể được áp dụng cho các tín hiệu định vị mới sử dụng phương thức điều chế sóng mang dịch nhị phân (BOC) Tuy phương thức này mang lại nhiều ưu điểm cho quá trình đồng bộ tín hiệu nhưng cũng tồn tại nhiều nhược điểm do tín hiệu BOC làm xuất hiện nhiều đỉnh tương quan ở trong hàm tự tương quan Các đỉnh tương quan phụ này làm tăng nguy cơ đồng bộ nhầm Do đó, kỹ thuật được
đề xuất sẽ loại bỏ hiện tượng đồng bộ nhầm Đồng thời, các kết quả mô phỏng cũng chỉ ra hiệu năng giảm ảnh hưởng của nhiễu
đa đường của kỹ thuật này cũng rất tốt
Key words - BOC signal, multipath mitigation technique, side
peaks cancellation, unambiguous tracking, MGD
Từ khóa - Tín hiệu BOC, kỹ thuật giảm nhiễu đa đường, triệt đỉnh phụ, bám chính xác, MGD
1 Introduction
Recently, the Global navigation satellite systems (GNSS)
play an important role in most sectors of life The navigation
services have been used in aviation, marine navigation,
environment surveying and disaster warning system
However, the performance of GNSS suffers from some error
sources such as ionosphere delay, tropospheric delay,
ephemeris error, receiver noise and multipath While other
errors could be removed by differential technology [1],
multipath is still the main error since its impact is dependent
on the location of each receiver The influence of multipath
on GNSS performance should be mitigated by multipath
mitigation techniques in order to improve the accuracy of
signal synchronization Multipath mitigation techniques
could be classed as three approaches [2]: pre-receiver
techniques applied before the GNSS signals entering the
antenna; receiver signal processing techniques applied in
code and carrier phase tracking loops and post-processing
techniques used after the pseudo-range have been achieved
The approach in this paper focuses on the second class This
approach is correlation-based technique This category of
multipath mitigation technique is used in most commercial
GNSS receivers [3] In typical GNSS receivers, the tracking
loops include phase lock loop (PLL) for carrier phase
tracking and delay lock loop (DLL) for code delay tracking
The conventional DLL uses 03 correlators named Early (E),
Prompt (P) and Late (L) with early-late spacing as one chip
to create a discriminator function based on Early-Minus-Late
(EML) form However, this classical DLL fails to mitigate
multipath impact Therefore, many EML-based multipath
mitigation techniques have been proposed in literature in
recent years One of the first method for enhancing multipath
mitigation, called Narrow Correlator (NC), is proposed in [4] based on the narrowing the early-late spacing to 0.1chips However, the correlator spacing depends on the frontend filter bandwidth, thus, it could not be reduced too much Another approach called Double Delta Correlator (DDC) based on using 5 correlators instead of 3 correlators as NC The multipath mitigating performance of DDC is better than
NC for medium-to-long multipath delays Some variants of DDC are High Resolution Correlator (HRC), Strobe Correlator (SC) and Pulse Aperture Correlator (PAC) Another method which could be a generalization of DDC is Multi Gate Delay (MGD) In MGD, there are more than 3 correlators used to create the discriminator function The performance of MGD may be worse than DDC and NC However, it could eliminate the risk of wrong peak selection when applied to binary offset carrier (BOC) modulated signals
In this paper, a new method of code tracking is proposed in order to improve the code tracking performance of MGD applied to cosine phased BOC signals The structure of the proposed method based on 7 correlators and the weight coefficients of each correlator are being adjusted in order to get the unambiguous tracking Moreover, the performance in multipath mitigation is also improved according to some criteria such as multipath error envelope (MEE)
The rest of the paper is organized as follows The characteristics of BOC modulated signals is described in Section 2 After that, section 3 illustrates the principle of our proposed method The numerical results and discussion are presented in Section 4 Finally, some conclusions are drawn in Section 5
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2 The Proposed ProtocolBOC Modulated Signal and
Code Delay Tracking Loops
2.1 The characteristics of BOC modulated signals
While the traditional navigation signal, GPS L1 C/A,
uses binary phase shift keying (BPSK) as its modulation
[1], many new navigation signals such as Galileo E1, GPS
L1C use new type modulation of BOC in order to co-exist
with each other signal on the same carrier frequency
According to [5], the baseband BOC modulated signal is
the result of multiplied the pseudorandom noise (PRN)
code with a rectangular subcarrier of frequency f
Typically, the BOC modulated signals is denoted as
BOC(m, n), in which m = f /f and n = f /f where
f is code rate and f = 1.023MHz is the reference
frequency Depending on the initial phase of subcarrier,
the BOC(m, n) modulated signal could be sine-phased
BOC(m, n) (BOCs(m, n)) or cosine-phased BOC(m, n)
(BOCc(m, n)) if the initial phase of subcarrier is 0 radian
or π/2 radian, respectively
Two important characteristics of BOC(m, n)
modulated signals could be considered are power spectral
density (PSD) and autocorrelation function (ACF)
Firstly, as in [6] the PSD of BOCs(n, n) as well as
BOCc(n, n) modulated signals could be express as
( ) sinc ( ) tan
2
c
fT
(1)
where T = 1/f is code duration (in chips)
The PSDs of two BOC modulated signals are
illustrated in Figure 1 along with the PSD of BPSK signal
(GPS L1 C/A) As seen in the figure, the subcarrier splits
the spectrum of the signal into two parts and move the
main energy component away from carrier frequency It is
also noted that total of main lobes and sidelobes between
two main lobes is equal to N = 2 where N is defined
as modulation order [7]
Secondly, another characteristic of BOC modulated
signal is the ACF Generally, the filtered ACF is related to
the PSD by [8]
2
where ( ) is the transfer function of the GNSS receiver frontend filter In case the frontend filter is ideal with bandwidth of , the filtered ACF should be
/ 2
2
/ 2
B
j f B
The ACFs of ( , ) as well as ( , ) modulated signals are shown in Figure 2 As shown in the figure, besides the main lobe, the ACF of BOC modulated signal also introduces some side lobes The number of the side lobes depends on the modulation order of and the initial phase of subcarrier The side lobes of the ACF will raise the risk of false lock in code tracking because the tracking loop may lock on one of the side lobes instead of the main lobe This phenomenon is called ambiguous problem
The ACFs of BOCs(n, n) as well as BOCc(n, n) modulated signals are shown in Figure 2 As shown in the figure, besides the main lobe, the ACF of BOC modulated signal also introduces some side lobes The number of the side lobes depends on the modulation order of N and the initial phase of subcarrier The side lobes of the ACF will raise the risk of false lock in code tracking because the tracking loop may lock on one of the side lobes instead of the main lobe This phenomenon is called ambiguous problem
2.2 Delay tracking loops in GNSS receivers
Typically, in GNSS receiver, the code delay tracking loop is based on feedback delay lock loop (DLL) [3], which is an implementation of maximum likehood Estimation (MLE) of time delay of PRN code of a navigation signal of a visible satellite The zero crossings
of discriminator function (S-curve) defines the path delay
of received navigation signal There are several variants of discriminator function as in [9] Among them, the most common type is Early-Minus-Late-Power (EMLP) which discriminator output is expressed as [9]
2 2
EMLP
D E L R R (4) Where , denote the output of Early ( ) and Late ( ) correlator, respectively and is early-late spacing (in chips) Another type of discriminator function is DDC, in
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2
1
2
1
( )
i
i
(5)
where are weighting factors with = 1;
= −0.5; , are the outputs of Early and Late
correlators, respectively; are spacing between the ℎ
early and the ℎ late correlator ( = 2 )
As a generality, multiple gate delay (MGD) has been
proposed as a novel structure for discriminator for the first
time in [10] In MGD structure, the discriminator function
includes more than 3 correlator outputs and is expressed as
1
1
( )
N
i
N
i
(6)
where is the number of gates (Early and Late correlators)
It is noted that = 1 for NC and = 2 for DDC
The MGD structure could eliminate the ambiguity
problem in code tracking of BOC signals However, as in
[11], the increase in the number of gates could not
provide the significant improvement of code tracking in
multipath environment for > 3 Therefore, the
maximum of gates should be = 3 Although the MGD
structure shows the capability of ambiguous cancellation,
its performance in multipath mitigation is not very good
in comparison to NC and DDC since there is no best way
of choosing the weighting factors
Figure 3 shows the MGD discriminator function
(S-curve) along with NC and DDC in multipath-free environment As seen in this figure, without multipath signal, the discriminator functions have got zero crossings
at zero delay Moreover, in three cases, there are some false lock points of code tracking loops It raises the risk of ambiguous tracking and causes code tracking errors
Figure 3 S-curves for NC, DDC and MGD, spacing
= 0.1 ℎ ; = [1 − 0.5 − 0.25] ( , ) signal
3 Proposed Multi Gate Delay Structure
3.1 Proposed MGD structure
The proposed structure includes 3 pairs of Early and Late correlators ( = 3) The early-late spacing between the ℎ early and the ℎ late correlator is given by
= , where , is early-late spacing (in chips) of the first early and late correlator The characteristic of the proposed MGD is expressed as the discriminator function, which is given by
3
1
( )
i
( )
s t
2
2
2
2
2
2 1
3
( )
( )
( )
( )
( )
( )
Figure 4 The structure of the proposed MGD
Without loss of generality, the first weighting
coefficient of a1should be chosen as = 1 The structure
of the proposed MGD is illustrated in Figure 4 The
received GNSS signal is correlated with 2 + 1 replicas
of the locally generated BOC signal After that, they are
integrated coherently In order to robust signal power
against noise as well as to remove the impact of wiping-off carrier, the non-coherent integration is implemented Finally, the discriminator function of the proposed MGD is expressed as
3
1
i
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In Equation (8), there are two weighting coefficients
of , being adjusted to achieve the best ones according
to the early-late spacing and other criteria
3.2 The coefficients for unambiguous code tracking and
multipath mitigation
Firstly, the weighting coefficients are adjusted in order
to get the discriminator function in which there is no false
lock point It means that the main peak of ACF is still
tracked even if the initial tracking error is larger than chip
period Although the power of side peaks in ACF is
significant in comparison to the one of the main peak, the
code tracking loops which is based on the proposed MGD
structure is unambiguous Then, among the achieved set
of weighting coefficients, which set provides the best
multipath mitigation is found out The risk of wrong peak
selection is eliminated The range of values of weighting
coefficient is between −1 and 1 with the step of 0.1 This
range of values is sufficient to compare with other
structures (NC, DDC) It is noted that the wider range is
also used for coefficient optimization but finally, the
achieved weighting factors are in the assumed range
In the first phase, the channel model only includes the
LOS signal As seen in Figure 3, in order to get the
unambiguous discriminator function, the following
characteristic has been obtained: in both side of correct
zero crossing point, the discriminator function must not
change the sign It means that
p MGD
p MGD
(9)
The characteristic of the discriminator function as in
Equation (9) depends on the early-late spacing and
S-curves of each pair of correlators since the discriminator
function of MGD is the sum of three discriminator
functions of − , − − Therefore, in
order to get discriminator function of MGD, there is at
least one discriminator function of − , −
− changing the sign in different ranges of
code delays in comparison with the rest of discriminator
functions For the shape of ACF, if there is at least one of
pairs of correlators located outside the main lobe, the
weighting coefficients could be found in order to get
unambiguous discriminator function For the proposed
MGD structure with = 3, the weighting coefficients for
unambiguous discriminator function is found out if the
early – late spacing of is not smaller than 0.2 ℎ
With the range of coefficient values of [−1; 1] with
the step of 0.1, for the first phase of optimization, the
number of pairs of optimized coefficients is shown in
Table 1 with several values of early-late spacing
Table 1 The number of oftimum coefficients of MGD
Chip spacing Number of pairs of coefficients ( , )
In the second phase, among the resulting set of coefficients achieved in the first phase, the finally optimized coefficients should be found in order to provide the best multipath mitigation In order to assess the performance of code tracking delay loop of GNSS receivers in multipath environment, the typical criterion is multipath error envelope (MEE) [12] In MEE, there are only two paths of receiving GNSS signals entering the antenna of receivers, one line-of-sight (LOS) signal and one multipath signal The multipath signal is either in-phase or out-in-phase in comparison to LOS signal Moreover, the multipath signal should be delay-invariant
It means that for all delays amplitude, phase of multipath signal are constant Using MEE, the multipath mitigation
of delay tracking structure is good if there are small average errors, small worst errors in MEE and small maximum multipath delay after that MEE reaches zero The values of optimum coefficients are shown in Table 2 with several values of early-late spacing
From these tables, it can be seen that the weighting coefficients could be chosen in order to get the minimum multipath errors as well as providing an unambiguous discriminator function
Table 2 Optimum coeffcients of MGD based on MEE
Chip spacing
4 Simulation results and discussion Simulations have been carried out in closely spaced multipath scenarios for infinite front-end bandwidth The channel model used in the simulation is the static channel with the amplitudes and phases fixed within the simulation interval
4.1 The discriminator function of the proposed MGD structure
For verifying the characteristic of the discriminator functions (S-curve), the received GNSS signal only includes
a single LOS component Figure 5, 6, 7 illustrate the shapes
of discriminator functions with NC, DDC and the proposed MGD for ( , ) signal As seen in the figures, there is only one zero crossing point for the proposed MGD This zero crossing point is located at zero code delay (in case of multipath – free) It means that the tracking loop could lock
at the main peak of ACF Therefore, the ambiguity problem
is resolved In the same cases, the NC and DDC create more than one crossing point The more the number of side peaks, the more the number of false lock point For ( , ) signal, there are 4 side peaks in ACF of signal (as seen in Figure 2) Moreover, when the number of side peaks rises, the ratio between the power of the main peak of ACF and the power of the first side peaks is reduced Therefore, it
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these figures, the linear region in S-curves of the proposed
method changes a little in comparison with two other
methods of NC and DDC The linear region in the respone
of discriminator function is very important It shows the
accurate response of the discriminator to the changing of
input error
Figure 5 S-curves for NC,DDC, proposed MGD
Figure 6 S-curves for NC,DDC, proposed MGD
Figure 7 S-curves for NC,DDC, proposed MGD
4.2 The performance of multipath mitigation
As mentioned above, MEE criteria can be used for
assessing the multipath mitigation performance in code
tracking loop The amplitudes of LOS signal and
multipath signal are 1 and 0.5, respectively The MEE are shown in Figure 8, 9, 10 for some values of chip spacing and the optimized values of coefficients (as seen in 0) As shown in the figures, the performance of the proposed MGD in multipath mitigation is still good as the performance of NC and DDC structures
Figure 8 MEE for NC,DDC, proposed MGD
Figure 9 MEE for NC,DDC, proposed MGD
Figure 10 MEE for NC,DDC, proposed MGD
5 Conclusions
In this paper, an unambiguous BOC tracking technique based on MGD structure is presented The weighting coefficients of the proposed structure are optimized in two
Trang 688 Pham Viet Hung, Tran Hoang Vu steps in order to get an unambiguous discriminator function
and to achieve the best multipath mitigation Moreover, the
proposed method is also compared to NC and DDC
Although the multipath mitigation performance of the
proposed method is worse than DDC, this method achieves
an unambiguous BOC tracking
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(The Board of Editors received the paper on 06/27/2015, its review was completed on 07/22/2015)