KỸ THUẬT BÁM MÃ HIỆU QUẢ DỰA TRÊN CẤU TRÚC ĐA TƯƠNG QUAN CHO TÍN HIỆU BOC PHA COSIN

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[.]

ISSN 1859-1531 - TẠP CHÍ KHOA HỌC VÀ CƠNG NGHỆ ĐẠI HỌC ĐÀ NẴNG, SỐ 11(96).2015, QUYỂN 83 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 Vietnam Maritime University; phamviethung@vimaru.edu.vn Danang 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 xác hệ thống định vị sử dụng vệ tinh (GNSS) chịu ảnh hưởng nhiều trình bám mã thu Bài báo trình bày kỹ thuật bám mã Kỹ thuật hoạt động dựa cấu trúc đa tương quan áp dụng cho tín hiệu định vị sử dụng phương thức điều chế sóng mang dịch nhị phân (BOC) Tuy phương thức mang lại nhiều ưu điểm cho trình đồng tín hiệu tồn nhiều nhược điểm tín hiệu BOC làm xuất nhiều đỉnh tương quan hàm tự tương quan Các đỉnh tương quan phụ làm tăng nguy đồng nhầm Do đó, kỹ thuật đề xuất loại bỏ tượng đồng nhầm Đồng thời, kết mô hiệu giảm ảnh hưởng nhiễu đa đường kỹ thuật 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 xác, MGD 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 correlators instead of 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 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 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 After that, section illustrates the principle of our proposed method The numerical results and discussion are presented in Section Finally, some conclusions are drawn in Section 84 Pham Viet Hung, Tran Hoang Vu 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 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   fTc  GBOCs ( f )  Tc sinc ( fTc ) tan     (1)   fTc    fTc  GBOCc ( f )  Tc sinc ( fTc ) tan  tan         R ( )   G ( f ) H ( f )e j 2 f  df (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 B/2 R( )   G( f )e j 2 f  df (3) B/ The ACFs of ( , ) as well as ( , ) modulated signals are shown in Figure 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 where T = 1/f is code duration (in chips) Figure BPSK, Figure PSDs of BPSK, ( , ) and ( , ) signals The PSDs of two BOC modulated signals are illustrated in Figure 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 = 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] ( , ) and ( , ) normalized ACFs The ACFs of BOCs(n, n) as well as BOCc(n, n) modulated signals are shown in Figure 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] DEMLP ( )  E  L2   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 ISSN 1859-1531 - TẠP CHÍ KHOA HỌC VÀ CÔNG NGHỆ ĐẠI HỌC ĐÀ NẴNG, SỐ 11(96).2015, QUYỂN which the output is given by DDDC ( )    Ei2  L2i  i 1 (5)   i 1   R    i /     R    i /   85 (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 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 ( = ) 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 correlator outputs and is expressed as N DMGD ( )    Ei2  L2i  i 1 N   i 1 (6)  R    / 2   R    / 2  i i where is the number of gates (Early and Late correlators) It is noted that = for NC and = 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 > Therefore, the maximum of gates should be = 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 shows the MGD discriminator function Figure S-curves for NC, DDC and MGD, spacing = 0.1 ℎ ; = [1 − 0.5 − 0.25] ( , ) signal Proposed Multi Gate Delay Structure 3.1 Proposed MGD structure The proposed structure includes 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 D p  MGD ( )    Ei2  L2i  (7) i 1  ()  ()    ()   a1 s(t ) a2  ()    ()    ()    DpMGD ( ) 2 a3 2 Figure The structure of the proposed MGD Without loss of generality, the first weighting coefficient of a1should be chosen as = The structure of the proposed MGD is illustrated in Figure The received GNSS signal is correlated with + 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 wipingoff carrier, the non-coherent integration is implemented Finally, the discriminator function of the proposed MGD is expressed as D p  MGD ( )   i 1  R    / 2   R    / 2  i i (8) 86 Pham Viet Hung, Tran Hoang Vu 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 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 D p  MGD ( )  0, for    1( chip ) (9) D p  MGD ( )  0, for -1    0( chip ) The characteristic of the discriminator function as in Equation (9) depends on the early-late spacing and Scurves 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 with several values of early-late spacing Table The number of oftimum coefficients of MGD Chip spacing = 0.2 = 0.25 = 0.3 = 0.35 Number of pairs of coefficients ( , 35 98 93 92 ) = 0.4 67 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 inphase or out-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 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 Optimum coeffcients of MGD based on MEE Chip spacing = 0.2 = 0.25 = 0.3 = 0.35 = 0.4 -0.1 -0.1 -0.2 0.2 0.2 0.8 0.7 0.5 0.9 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, 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 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 ISSN 1859-1531 - TẠP CHÍ KHOA HỌC VÀ CƠNG NGHỆ ĐẠI HỌC ĐÀ NẴNG, SỐ 11(96).2015, QUYỂN raises the risk of wrong peak selection Finally, as seen in 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 S-curves for NC,DDC, proposed MGD (a=[1 -0.1 0.8]) with = 0.2 ℎ for ( , ) signal Figure S-curves for NC,DDC, proposed MGD (a=[1 -0.1 0.7]) with = 0.25 ℎ for ( , ) signal Figure S-curves for NC,DDC, proposed MGD (a=[1 -0.2 0.5]) with = 0.3 ℎ for ( , ) signal 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 87 multipath signal are 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 MEE for NC,DDC, proposed MGD (a=[1 -0.1 0.8]) with = 0.2 ℎ for ( , ) signal Figure MEE for NC,DDC, proposed MGD (a=[1 -0.1 0.7]) with = 0.25 ℎ for ( , ) signal Figure 10 MEE for NC,DDC, proposed MGD (a=[1 -0.2 0.5]) with = 0.3 ℎ for ( , ) signal 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 88 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 REFERENCES [1] E D Kaplan, and C J Hegarty, Understanding GPS: Principles and Applications: Artech House, 2005 [2] F D Nunes, F M G Sousa, and J M N Leitao, “Gating Functions for Multipath Mitigation in GNSS BOC Signals,” IEEE Transactions on Aerospace and Electronic Systems, vol 43, no 3, pp 951-964, 2007 [3] M Z H Bhuiyan, and E S Lohan, “Advanced Multipath Mitigation Techniques for Satellite – Based Positioning Applications,” International Journal of Navigation and Observation, Hindawi Publishing Corporation, vol 2010, pp 1-15, 2010 [4] A J V Dierendonck, P Fenton, and T Ford, “Theory and Performance of Narrow Correlator Spacing in a GNSS Receiver,” Journal of the Institute of Navigation, vol Vol 39, Fall, 1992 [5] E S Lohan, A Lakhzouri, and M Renfors, “Binary-offset-carrier modulation techniques with applications in satellite navigation [6] [7] [8] [9] [10] [11] [12] systems,” Wireless Communications and Mobile Computing, vol 7, no 6, pp 767-779, 2007 J W Betz, “Binary Offset Carrier Modulations for Radio Navigation,” NAVIGATION: Journal of The Institute of Navigation, vol 48, no 4, pp 227 - 246, 2001 J W Betz, “The Offset Carrier Modulation for GPS Modernization ” Proceedings of the 1999 National Technical Meeting of The Institute of Navigation January 25 - 27, pp 639 - 648 1999 J.-C Juang, and T.-L Kao, “Noncoherent BOC Signal Tracking Based on a Five-Correlator Architecture,” IEEE Transactions on Aerospace and Electronic Systems, vol 48, no 3, pp 1961-1974, 2012 K Borre, D M Akos, N Bertelsen, P Rinder, and S H Jensen, A Software-Defined GPS and Galileo Receiver - A Single-Frequency Approach, Berlin: Birkhäuser, 2007 R Fante, "Unambiguous tracker for GPS binary-offset-carrier signals" H Hurskainen, E Simona Lohan, X Hu, J Raasakka, and J Nurmi, “Multiple gate delay tracking structures for GNSS signals and their evaluation with simulink, systemC, and VHDL,” International Journal of Navigation and Observation, pp 17, 2008 M Irsigler, J A Avila-Rodriguez, and G W Hein, “Criteria for GNSS Multipath Performance Assessment,” Proceedings of the International Technical Meeting of the Institute of Navigation, ION-GNSS 2005, 13-16 September, 2005 (The Board of Editors received the paper on 06/27/2015, its review was completed on 07/22/2015) ... 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... 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,...84 Pham Viet Hung, Tran Hoang Vu The Proposed ProtocolBOC Modulated Signal and Code Delay Tracking Loops 2.1 The characteristics of BOC modulated signals While the