Access the full text.
Sign up today, get DeepDyve free for 14 days.
Hindawi Publishing Corporation International Journal of Navigation and Observation Volume 2008, Article ID 246703, 14 pages doi:10.1155/2008/246703 Research Article Design of Short Synchronization Codes for Use in Future GNSS System 1 1 2 1 Surendran K. Shanmugam, Cecile ´ Mongredien, ´ John Nielsen, and Ger ´ ard Lachapelle Department of Geomatics Engineering, University of Calgary, AB, Canada T2N 1N4 Department of Electrical and Computer Engineering, University of Calgary, AB, Canada T2N 1N4 Correspondence should be addressed to Surendran K. Shanmugam, suren@geomatics.ucalgary.ca Received 4 August 2007; Accepted 7 February 2008 Recommended by Olivier Julien The proliﬁc growth in civilian GNSS market initiated the modernization of GPS and the GLONASS systems in addition to the potential deployment of Galileo and Compass GNSS system. The modernization eﬀorts include numerous signal structure innovations to ensure better performances over legacy GNSS system. The adoption of secondary short synchronization codes is one among these innovations that play an important role in spectral separation, bit synchronization, and narrowband interference protection. In this paper, we present a short synchronization code design based on the optimization of judiciously selected performance criteria. The new synchronization codes were obtained for lengths up to 30 bits through exhaustive search and are characterized by optimal periodic correlation. More importantly, the presence of better synchronization codes over standardized GPS and Galileo codes corroborates the beneﬁts and the need for short synchronization code design. Copyright © 2008 Surendran K. Shanmugam et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION modernized signals encompass key innovations such as data- less channel, improved navigation data message format, The legacy global positioning system (GPS) has performed secondary spreading code structure, and new modulations well beyond initial expectations in the past but faces schemes [6]. More speciﬁcally, both GPS and Galileo systems stern impediments in the view point of new civilian GPS utilize secondary short synchronization codes to accomplish applications. Several initiatives were launched during the last decade to satisfy the demands of these new civilian (i) data symbol synchronization, applications. Consequently, these eﬀorts led to the birth (ii) spectral separation, of second-generation global navigation satellite systems (GNSSs). These eﬀorts include the modernization of legacy (iii) narrowband interference protection. GPS and the restoration of Russian global navigation satellite system (GLONASS). The Galileo system, a major European For instance, the use of short 10-bit and 20-bit Neuman- initiative, is well positioned to beneﬁt from the three decades Hofman (NH) codes, in GPS L5 signals, readily alleviates the of GPS and GLONASS experience [1]. More recently, the issue of data symbol synchronization. Besides, the diﬀerent GNSS community has witnessed yet another highpoint with code period of NH10 and NH20 codes in the data and pilot the launch of ﬁrst medium earth orbit (MEO) satellite of channels readily provides the necessary spectral separation. Chinese Compass GNSS system [2]. The secondary synchronization code further enhances the A major milestone in the modernization initiative is correlation suppression performance of the primary pseu- the inclusion of new civilian signals that will provide dorandom noise (PRN) code. Finally, it spreads the spectral the beneﬁts of frequency diversity besides accuracy and lines of primary PRN I5/Q5 codes thereby reducing the eﬀect availability improvements [3–5]. These new civilian signals of narrowband interference by another 13 dB [4]. The Galileo include numerous structural innovations that will provide system also utilizes short secondary synchronization codes the foremost beneﬁt to the civilian GNSS community. The of various lengths to facilitate the aforementioned tasks [7]. 2 International Journal of Navigation and Observation Table 1: Secondary code assignment in GPS and Galileo systems. GPS Galileo Signal type Code name Code length Signal type code name Code length L5-Data NH10 10 E5a-Data CS20 20 L5-Pilot NH20 20 E5a-Pilot CS100 100 1−50 L1C-Pilot OC1800 1800 E1c CS25 25 1−210 E5b-Data CS4 4 E5b-Pilot CS100 100 51−1001 E6c CS100 100 1−50 GPS L5 NH20 code acquisition Galileo E1c CS25 code acquisition 1 1 0.8 0.8 5.5dB 4.8dB 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0 5 10 15 0 5 10 15 20 Time (ms) Time (ms) (a) (b) Figure 1: Superposition of secondary code correlation outputs for various Doppler oﬀsets. (LHS) GPS L5 NH20 code (RHS) Galileo E1c CS25 code. Table 1 lists the secondary code assignments and their lengths of Doppler uncertainties is discussed in [9]. The isolation in GPS and Galileo systems. of the main correlation peak to that of secondary peaks The secondary synchronization codes are predominantly can degrade from the nominal 14 dB to 4.8 dB level under memory codes except for the L1C, wherein the overlay worst case Doppler scenarios [10]. Under these conditions, codes were obtained through truncated m-sequences (1– the NH code acquisition of weak GPS L5 signals becomes 63) and gold sequences (64–210) [8]. There exists a trade- more diﬃcult in the presence of other strong GPS L5 oﬀ between memory codes and codes that are obtained signals. The existence of better synchronization codes over from linear feedback shift register (LFSR) implementation. standardized NH20 code was later reported in [10], which While the LFSR-based codes are appealing in the view point is based on the 20-bit synchronization code originally of hardware implementation, they only exist for speciﬁc proposed in [11]. Under speciﬁc Doppler conditions, the lengths. The use of truncation technique can alleviate this new 20-bit code (known as the Merten’s code) showed an issue at the expense of inferior correlation properties. On the improvement of around 2 dB over the standardized NH20 other hand, memory codes can be obtained for any speciﬁc code in terms of correlation suppression [10]. However, the lengths with optimal correlation characteristics. However, performance improvement achieved by the Merten’s code exhaustive search of optimal synchronization code becomes corresponds to a speciﬁc Doppler scenario and thus does not more diﬃcult with increasing code lengths. reﬂect the actual performance improvement under Doppler A limitation arising due to the usage of short synchro- uncertainty. Interestingly, the importance of spreading code nization codes is the degradation in correlation suppression selection for the Galileo GNSS system and the corresponding especially in the presence of frequency errors. For instance, measures was identiﬁed in [12]. Besides, it is also desirable the vulnerability of NH20 code acquisition in the presence to develop optimal synchronization codes that oﬀer better Normalized correlation output Normalized correlation output Surendran K. Shanmugam et al. 3 resistance to residual Doppler errors. In this paper, we be improved with longer length codes, judicial selection of introduce relative performance measures such as peak-to- synchronization codes can oﬀer better correlation suppres- side lobe ratio (PSLR) and integrated side lobe ratio (ISLR) sion for the same code length. For example, in [10], the related to the design of periodic binary codes that are authors reported a correlation suppression gain of around utilized in GNSS system. More importantly, new optimal 2 dB for Merten’s code over standard NH20 code under secondary synchronization codes were obtained using these speciﬁc Doppler scenario. The LHS plot in Figure 2 shows performance measures through exhaustive search for lengths the superposition of the Merten’s 20-bit synchronization up to 30 bits. The merits of the proposed synchronization code (M20) correlation outputs for the same Doppler codes are also compared with standardized codes using setting as in Figure 1. The RHS plot shows the correlation the same performance measures. Besides, the association suppression performance for the standardized NH20 and the of the optimal synchronization codes with the systematic M20codefor variousresidualDoppler’s.The Dopplerwas codes such as Golay complementary codes is also estab- searched between 0 to 250 Hz in steps of 25 Hz. lished. Numerical simulations were used to demonstrate the The RHS plot in Figure 2 readily shows the 2 dB improve- superior acquisition performance of the proposed short syn- ment accomplished by the M20 code over the standardized chronization codes over standardized codes under Doppler NH20 code for the residual Doppler of 12 Hz. In other uncertainties in terms of PSLR measure. words, the M20 code can tolerate another 10 Hz of residual The remainder of this paper is organized as follows. In Doppler for the same PSLR of 4.8 dB achieved by the NH20 Section 2, the advantage of optimal synchronization codes is code. The M20 code resulted in an average performance further established in the view point of GPS L5 NH code improvement of around 1.7 dB over the NH20 code for the acquisition. More speciﬁcally, we show the inadequacy of range of residual Doppler’s. The performance improvement NH20 code in comparison to Merten’s 20-bit code under in M20 code can readily be accredited to its better correlation diﬀerent Doppler conditions. The relevant performance characteristic. For instance, the periodic correlation of the measures pertaining to optimal binary periodic synchro- diﬀerent synchronization codes of length 20 (see Table 2)is nization code are introduced in Section 3. The binary- summarized below code search strategy and the various code construction R ={10,−2, 2,−2,−2, 2,−2,−2, 2,−2}, NH10 methods are detailed in Section 4. Besides, the merits of new synchronization codes are compared with the standardized R ={20, 0, 0, 0, 0, 0,−4, 0, 4, 0,−4, 0, 4, 0,−4, 0, 0, 0, 0, 0}, NH20 codes. Acquisition performance analysis is then carried out R ={20, 0, 0, 0, 0, 0, 4, 0,−4, 0,−4, 0,−4, 0, 4, 0, 0, 0, 0, 0}, CS20 in Section 5. The ﬁnal concluding remarks are made in Section 6. R ={20, 0, 0, 0, 0,−4, 0,−4, 0, 0, 0, 0, 0,−4, 0,−4, 0, 0, 0, 0}. M20 (1) 2. NEED FOR IMPROVED SYNCHRONIZATION CODES The periodic correlation output of the M20 code, R ,has M20 An issue with short synchronization codes is limited correla- lesser number of out-of-phase correlation when compared tion suppression performance due to their short code length. to both NH20 and CS20 codes. Accordingly, one can expect For instance, the correlation suppression performance of itscodeacquisition performancetobesuperiorevenin NH20 code can be degraded by as much as 8 dB from the the presence of residual Doppler. It is worth emphasizing nominal 14 dB in the presence of Doppler uncertainty [9]. In here that the NH10 and NH20 codes were not obtained [10], the authors reported a degradation of 9.2 dB for NH20 from exhaustive search, whereas the M20 code was obtained code under speciﬁc Doppler scenarios. To further illustrate through exhaustive search [11]. The very existence of the this, the GPS L5 NH20 code and Galileo E1c CS25 code NH20, M20, and CS20 corroborates the presence of multiple correlation outputs for diﬀerent Doppler bins are plotted in solutions for the code design problem. Besides, the search Figure 1. The acquisition criterion in Figure 1 was obtained for periodic code is expected to yield multiple solutions following the analysis reported in [10]. For instance, the due to the existence of equivalence classes [13]. Hence, it is residual Doppler during the acquisition of NH20 and CS25 necessary to obtain the binary codes that satisfy the optimal code was set to 12 Hz; and this residual Doppler was searched correlation characteristics and select the best possible code between 0 and 250 Hz in steps of 25 Hz. judiciously using relevant performance measures. In Figure 1, we can readily observe the degradation in correlation main peak isolation for NH20 from the nominal 3. OPTIMAL SYNCHRONIZATION 14 dB to 4.8 dB as reported earlier in [10]. On the other CODE—FIGURE OF MERITS hand, the Galileo E1c CS25 code degraded from the nominal 18.4 dB down to 5.5 dB. The additional 3 dB degradation Better synchronization code can be obtained by optimizing in CS25 code acquisition can be attributed to the longer the corresponding correlation characteristics of the individ- coherent integration time (i.e., 25 millie seconds rather than ualcodes.Asweare dealing with binary codesofshort 20 millie seconds) and nonzero out-of-phase correlation in period, the optimization of correlation characteristics can be the original CS25 code. Accordingly, the acquisition of weak achieved in an exhaustive fashion. It is however, necessary GPS L5 signals or Galileo E1c signals can be hindered in the to derive performance measure or measures that readily presence of strong GPS L5 and Galileo E1c signals from other embody the correlation characteristics of a binary code satellites. While the correlation suppression performance can [12]. The two important performance measures pertaining 4 International Journal of Navigation and Observation Table 2: Optimal binary synchronization code search result. Code length Number of codes PSLR (dB) ISLR (dB) Code length Number of codes PSLR (dB) ISLR (dB) 48(1) ∞∞ 18 6,047 (168) 19.1 2.4 5 10 (1) 14 3.2 19 75 (2) 22.6 10 6 47 (8) 9.5 0.9 20 5,079 (45) 14 3.1 7 28 (2) 16.9 4.1 21 1,259 (30) 16.9 4.2 8 32 (2) 6 2 22 15,839 (360) 20.8 2.9 9 108 (8) 9.5 1.7 23 91 (2) 27.3 12 10 360 (16) 14 1.4 24 1,535 (32) 15.6 9 11 44 (4) 20.8 6.1 25 7,000 (260) 18.4 4.3 12 96 (4) 9.5 4.5 26 31,615 (608) 22.3 3.4 13 104 (4) 22.3 7.1 27 775 (144) 19.1 4.9 14 1,791 (128) 16.9 1.9 28 23,743 (424) 16.9 4.1 15 59 (4) 23.5 8 29 3,247 (56) 19.7 4.6 16 255 (16) 12 2.7 30 35,039 (584) 23.5 3.9 17 2,175 (64) 15.1 2.3 to optimal synchronization codes are the peak-to-side lobe the mutual interference experienced by the individual codes ratio (PSLR) [14] and the integrated side lobe ratio (ISLR) from other codes. Minimizing the magnitude of cross- [15]. Besides, the synchronization codes are also expected to correlation readily limits the eﬀect of mutual interference be balanced for desirable spectral characteristics. To deﬁne between any two codes. The mean square correlation (MSC) PSLR and ISLR, we ﬁrst express the periodic auto-correlation measure embodies this mutual correlation and can be of the binary code of length N (i.e., x = [x , x ,... , x ]), at utilized during multiobjective synchronization code opti- 0 1 N−1 shift i,as mization. For any two codes x (k)and x (k)oflength N p q pertaining to the code set comprising of M unique codes, the N−1 mutual correlation or the MSC is given by R(i) = x(k)x(k − i mod N ), i = 0, 1, 2,... , N − 1, k=0 N−1 (2) MSC(p, q) = 2 R (i) , p= q,(6) p,q / i=0 where x(k) ∈{+1,−1} and mod is the modulo operation. The PSLR for the binary code x(k) with the periodic auto- where R (i) is the periodic cross-correlation between the p,q codes x (k)and x (k), and is given by correlation, R(i), is given by p q N−1 R(i = 0) PSLR(x) = , i = 0, 1, 2,... , N − 1. (3) R (i) = x (k)x (k − i mod N ), i = 0, 1, 2,... , N − 1. p,q p q max R(i= 0) k=0 (7) Maximizing the PSLR measure minimizes the out-of-phase correlation that eventually aids in reducing false acquisition. The aforementioned mean square correlation is closely On the other side, ISLR measures the ratio of auto- related to the well-known total squared correlation measure correlation main lobe (or peak) energy to its side lobe energy utilized in CDMA spread code optimization [16]. [15]. The ISLR of a binary code is deﬁned as 4. OPTIMUM CODE SEARCH RESULTS ISLR(x) = , i = 0, 1, 2,... , N − 1. (4) N−1 2 R(i) i=1 For short code length, the synchronization code optimiza- tion can be accomplished through exhaustive search of Maximizing the ISLR measure readily limits the eﬀect of out- binary codes with optimal correlation characteristics. The of-phase correlation from all shifts. It will be emphasized developed exhaustive search technique utilized fast Fourier here that the maximization of ISLR often maximizes the transform (FFT)-based block processing and matrix manip- PSLR measure. Finally, the balanced property of a binary ulations to speed up the search process. Both PSLR and code is related to the mean value of the code and is given ISLR were utilized for the objective maximization. Optimal by synchronization codes for lengths up to 30 were obtained N−1 through exhaustive search. Interestingly, the search process μ(x) = x(k). (5) yielded large number of codes that were optimal based k=0 on the aforementioned performance measures. Table 2 lists For binary code sets design, as in the case of OC1800 in the number of codes alongside the unique solutions within GPS and CS100 in Galileo, it is also desirable to minimize braces, the PSLR and ISLR values, respectively. Surendran K. Shanmugam et al. 5 M20 code acquisition Correlation suppression performance 0.8 6.85 dB 0.6 0.4 0.2 0 2 0 5 10 15 20 25 0 5 10 15 Time (ms) Residual doppler (Hz) NH20 CS20 M20 (a) (b) Figure 2: (LHS) superposition of secondary code correlation outputs for various Doppler oﬀsets for M20 code (RHS) PSLR performance as a function of residual Doppler. The large number of codes arise from existence of the expressed below equivalence classes due to the shift invariance property of 0or4or − 4 N mod 4 = 0, the periodic codes [13]. For example, the code x(k), its 1or − 3 N mod 4 = 1, negated version, its time reversed, or its shifted version R(i) = i= 0. (10) will be characterized by similar PSLR and ISLR measures. ⎪ 2or − 2 N mod 4 = 2, To obtain unique solutions, the search technique discarded ⎩ −1or3 N mod 4 = 3, codes if their maximum cross-correlation is equal to the code From (1)and (9), we see that both NH10 and M20 possess length. Accordingly, any two codes x (k)and x (k) satisfy the p q optimal periodic correlation. Besides, the Galileo CS25 code following cross-correlation constraint are considered unique: was also optimal as it satisﬁed the periodic correlation expressed in (10). On the other hand, both NH20 and max R (i) <N , i = 0, 1, 2,... , N − 1. (8) CS20 are not optimal in the view point of (9), but can be p,q considered optimal in terms of PSLR measure. The inferior periodic correlation of NH20 does not come as a surprise Besides, the codes are time-reversed and hence were tested as the original NH codes were not obtained by exhaustive for (8). While the balance property (i.e., μ(x)) was not search [19]. It should be noted here that all the secondary included during the code selection, its signiﬁcance will be codes utilized in GPS and Galileo system are not balanced emphasized during the acquisition performance analysis. (i.e., sum of individual code phases is not equal to zero) and In Table 2, the binary codes whose lengths are similar to thus (9) cannot be applied in a strict sense, but indicates the the standardized codes are highlighted in bold. In [17], conditions for optimality. Numerical analysis later conﬁrmed the authors theoretically established the optimal periodic the fact that even unbalanced binary code is characterized by correlation of a balanced binary code as periodic correlation as predicted in (9). All the binary codes obtained through exhaustive search indeed satisﬁed the periodic correlation as expressed in 0or − 4 N mod 4 = 0, (10) and thereby asserting the optimality of the developed R(i) = i= 0. (9) 2or − 2 N mod 4 = 2, binary codes. The optimal 10-bit and 25-bit code obtained through exhaustive search resulted in similar PSLR and ISLR performance measures to that of NH10 and CS25 The periodic correlation of optimal binary code for both codes in accordance to (10). On the other hand, the 20- odd and even lengths was further established in [18], and is bit code obtained via exhaustive search resulted in better Normalized correlation output PSLR (dB) 6 International Journal of Navigation and Observation ISLR performance even as the PSLR performance was the also optimal. Consequently, the 45 optimal binary codes of same. Moreover, the new 20-bit code had similar correlation length 20 (see Table 2) were tested for Golay complementary characteristics as that of M20 code introduced earlier. condition. Surprisingly, 75% (32 out of 45 codes) of the 20- In Table 2, we can also observe that odd-length codes bit optimal binary codes satisﬁed the Golay complementary generally yielded better PSLR and ISLR performance. More condition. A corollary of this conjecture indicates the speciﬁcally, the binary codes for lengths N = 5, 7, 11, 13, 15 possibility of constructing optimal codes of length N from showed similar PSLR and better ISLR, even when compared Golay complementary pairs of length N/2. The construction to twice their code lengths (i.e., N = 10, 14, 22, 26, 30). of binary codes by multiplexing Golay complementary pairs The high PSLR and ISLR values observed for code lengths readily guarantees that every alternate shift will result in zero N = 5, 7, 11, 13, 15, 23 can readily be attributed to their ideal correlation due to the complementary correlation output correlation characteristics as expressed in (10). However, it of individual Golay codes. Interestingly, the aforementioned is recognized that the choice of secondary code length in property of the Golay codes was utilized for signal acquisition GNSS system can be inﬂuenced by other parameters besides in ultrasonic operations [23]. To further verify this corollary, correlation characteristics alone. we constructed a binary code from Golay complementary Further analysis of the optimal binary code of length 20 pairs of length 20 (hex values “CD87F” and “CE5AA”). The revealed the existence of close association of optimal binary resulting binary code of length 40 (hex value “F0F6916EEE”) codes to that of the well-known Golay complementary pairs demonstrated optimal periodic correlation as predicted by [20]. The Golay complementary pairs have been extensively (9). Thus, it is possible to construct optimal binary codes utilized in a number of applications ranging from radar of larger lengths by utilizing the aforementioned association signal processing [21] and communication [22] to multislit between optimal codes and the Golay complementary codes. spectrometry [20]. Two binary codes x (k)and x (k)are said Besides, the highly regular structure of binary Golay com- a b to be Golay complementary pair, if they satisfy the following plementary codes readily allows for an eﬃcient construction constraint: [24]. Motivated by the aforementioned observation, we con- 2N , i = 0, structed synchronization codes of length N = 100 from R (i) = R (i)+ R (i) = (11) G a b 0, i= 0, optimal codes of lengths 10, 20, and 25. The speciﬁc choice of code length was dictated by the fact that the desired code length 100 was divisible by 10, 20, and 25. The ﬁnal code where R (i)and R (i) are the periodic correlation of x (k) a b a length of 100 was obtained by manipulating the individual and x (k), respectively. R (i) is the periodic correlation b G codes of length 10, 20, and 25 with the augmentation codes function of the Golay complementary pair. Besides, the individual codes in a Golay complementary pair are referred of length 10, 5 and 4. Let x (k)and x (k) be the primary p s and the augmentation code of length N and N .Thus, we as Golay codes. The periodic correlation in (11) immediately p s have N = N N ,where N = 100, N ={10, 5, 4},and asserts the advantage of Golay complementary codes in the s p s view point of code design. For example, the NH10 code and N ={10, 20, 25} in our case. The ﬁnal binary code, x(k), of length N can be obtained as follows: the ﬁrst-half of the NH20 code are Golay complementary pair as shown in Figure 3. Hence, there exists a possibility N −1 N −1 N N of utilizing this underlying structure to accomplish better x(k) = x (m)x (n)g k − m − n , s p acquisition abilities. Unfortunately, the NH10 code and N N (13) s p m=0 n=0 second half of NH20 code are not Golay complementary k = 0, 1, 2,... , N − 1, pairs. Motivated by this observation, the optimal binary codes where g (k) is the rectangular pulse function and is given by of length 20 obtained via exhaustive search were tested for 10 ≤ ΔT< T , Golay complementary pair. Interestingly, many binary codes g (k + ΔT ) = (14) 0 elsewhere, of length 20 obtained through exhaustive search (i.e., S20 in Table 3) satisﬁed the Golay complementary condition. For where T is the basic bit duration over which the x is b k G10 G10 example, the Golay complementary pairs and a b constant. For example, the 100-bit code, x(k)(hexvalue can be constructed from the even and odd samples of S20 “C7F526E3FA9371FD49A7015B2”), was obtained from the (hex value “05D39” and “FA2C6” also give rise to Golay primary code, x (k) (hex value “380AD90”), and the aug- pairs) listed in Table 3, and the corresponding Golay codes mentation code, x (k) (hex value “1”). In Table 2,wesaw are given by that there exists 7,000 codes of length 25 with 260 unique solutions but we only need 100 unique codes. Thus, we G10 = [−1, 1,−1, 1,−1,−1,−1,−1, 1, 1], utilized the following constraints on the PSLR and ISLR (12) measures to limit the number of codes: G10 = [1,−1,−1, 1, 1,−1, 1, 1, 1, 1]. PSLR ≥ 21.9dB, (15) G10 More importantly, the individual Golay codes and ISLR ≥ 3dB. G10 were also optimal having periodic correlation in accordance to (9). Moreover, the Golay codes of length The PSLR and ISLR thresholds in (15) were duly obtained N/2 obtained from an optimal code of length N were from the average PSLR and ISLR measures of the Galileo Surendran K. Shanmugam et al. 7 Table 3: Secondary synchronization code—performance measures (μ(x), PSLR, and ISLR are deﬁned in (5), (3), and (4), resp.). Secondary code performance Standard codes Proposed codes Code identiﬁer Code length |μ(x)| PSLR (dB) ISLR (dB) Code identiﬁer Code length |μ(x)| PSLR (dB) ISLR (dB) CS4 4 0.5 ∞∞ S4 4 0.5 ∞∞ NH10 10 0.2 14 1.5 S10 10 0 14 1.5 NH20 20 0.2 14 4 S20 20 0 14 4 CS20 20 0.2 14 4 S20 20 0.1 14 4.9 CS25 25 0.2 18.4 6.3 S20 20 0.2 14 4 M4 4 0.5 ∞∞ S25 25 0.2 18.4 6.3 M10 10 0.4 14 1.5 S25 25 0.2 18.4 6.3 M20 20 0.1 14 4.9 M25 25 0.2 18.4 6.3 code acquisition, wherein the primary code is assumed to be acquired within half chip duration alongside residual Doppler. The secondary code is acquired by correlating the primary code correlation outputs with the locally generated secondary code samples. The residual Doppler was assumed to be within ±250 Hz. During the secondary code acquisi- tion, the residual Doppler was also searched within ±250 Hz in steps of 25 Hz. The Galileo CS4 code is already established as the optimal code and will not be dealt during the acquisition perfor- mance analysis. Table 3 lists the μ(x), the PLSR, and the ISLR measures of the standardized Merten’s and the proposed codes of various lengths. While the 20-bit synchronization −5 codes achieved similar PSLR measure as that of 10-bit codes, −5 −4 −3 −2 −1 012 3 4 their ISLR performances were much better than that of 10- Delay bit codes. In Table 3, it can be noticed that there are 3 NH10 code diﬀerent sets of S20 code (S20 ,S20 ,and S20 ) and two 1 2 3 NH20 (ﬁrst-half ) sets of S25 code (S25 and S25 ). While these diﬀerent 1 2 Combined codes are optimal in terms of correlation characteristics, Figure 3: Correlation output of Golay complementary codes their correlation characteristics diﬀered in the presence of (NH10 and ﬁrst half of NH20). the residual Doppler with some outperforming the other codes. In Table 3, we see that the designed codes were not only optimal in terms of PSLR and ISLR measures, they were also more balanced. The advantage of the M20 and G100 code set [25]. Finally, the cross-correlation constraint S20 over the NH20 and CS20 codes is readily asserted by expressed in (8) was also utilized to obtain unique solutions. 2 the higher ISLR values. Interestingly, the other 20-bit codes Consequently, a total number of 105 unique codes were S20 and S20 demonstrated better acquisition performance 1 3 obtained in this fashion which satisﬁed the aforementioned in comparison to M20 and S20 codes despite being inferior conditions. The hexadecimal representations of the individ- in ISLR measure. In the case of CS100 and S100 codes, ual codes are listed in Table 6. It is worth noting here that not the autocorrelation and cross-correlation protection were a single Galileo G100 code as well as the proposed 100-bit evaluated using a number of measures. The PSLR measure codes satisﬁed the optimal periodic correlation based on (9). based on the auto-correlation was same for both CS100 and The following section establishes the merits and limitations S100 codes despite being suboptimal in the view point of of the proposed binary synchronization codes in comparison (9). The cross-correlation PSLR (CPSLR) measure was also to the standardized secondary synchronization codes. obtained for CS100 and S100 codes. The CPSLR measures the ratio between the auto-correlation main peak of code 5. ACQUISITION PERFORMANCE ANALYSIS (R(i)) to the maximum of the cross-correlation peak (R (i)) p,q and it is given by Having obtained the optimal binary codes of various lengths, we now turn our focus on the evaluation of the proposed codes in comparison to the standardized codes utilized in R(i = 0) GPS and Galileo system. In this paper, the structure proposed CPSLR = . (16) in Tran and Hegarty [26] was adopted for the secondary max R (i= 0) p,q / Correlation output 8 International Journal of Navigation and Observation Table 4: Galileo CS100 and proposed S100 codes performance. Secondary code performance CPSLR (dB) ISLR (dB) MSC (dB) CS100 S100 CS100 S100 CS100 S100 Max 14.9 14 6.6 5.9 43.5 43.6 Min 6 2.9 3.7 5.1 42.6 42.8 Mean 11.2 9.1 4.9 5.6 43 43.1 Std. Dev 1.2 2.4 0.6 0.3 0.1 0.2 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 44.55 5.56 6.5 46 8 10 12 14 ISLR (dB) CPSLR (dB) CS100 codes CS100 codes S100 codes S100 codes (a) (b) Figure 4: PSLR and ISLR performance of Galileo CS100 and the proposed S100 codes. Table 5: Hexadecimal representation GPS/Galileo and proposed secondary codes (highlighted colour in bold represents equivalence). Code identiﬁer Code length Number of hex symbols Number of zero padding Hex value CS4 4 1 0 E NH10 10 3 2 F28 NH20 20 5 0 FB2B1 CS20 20 5 0 842E9 CS25 25 7 3 380AD90 M4 4 1 0 D M10 10 3 2 CBC M20 20 5 0 FA2C6 M25 25 7 3 E3FA930 S4 4 1 0 B S10 10 3 2 3B0, 3C8 S20 20 5 0 14B37, 14B37 S20 20 5 0 05D39, 6345F S20 20 5 0 315B0, 640E5 S25 25 7 3 21228F8, DFB45C0 S25 25 7 3 AD04C18 CDF CDF Surendran K. Shanmugam et al. 9 5.5 4.5 3.5 0 100 200 300 0 1000 2000 3000 4000 5000 Code index Code index Proposed codes CS20 code Proposed codes NH20 code M20 code NH10 code M10 code (a) (b) Figure 5: PSLR performance in the presence of residual Doppler (LHS) 10-bit code (RHS) 20-bit code. 10-bit code acquisition performance 20-bit code acquisition performance 5.5 8 5 7 4.5 6 4 5 3.5 4 3 3 2.5 2 0 5 10 15 20 25 0 5 10 15 20 25 Residual doppler (Hz) Residual doppler (Hz) NH10 code NH20 code S20 code M10 code CS20 code S20 code S10 code M20 code S20 code (a) (b) Figure 6: Eﬀect of residual Doppler on secondary code acquisition (LHS) 10-bit code (RHS) 20-bit code. Table 4 lists the maximum, minimum, mean, and the the proposed S100 codes were appealing in the view point standard deviation of CPSLR, ISLR, and MSC measures for of ISLR. The MSC performance of both the codes was the Galileo CS100 and the proposed S100 codes. While the similar. The distribution of the CPSLR and ISLR measures standardized CS100 code is attractive in terms of CPSLR, of the CS100 and S100 codes is plotted in Figure 4 for better PSLR (dB) PSLR (dB) PSLR (dB) PSLR (dB) 10 International Journal of Navigation and Observation Table 6: Hexadecimal representation of proposed S100 codes. Hexadecimal values of S100 codes Code length = 100, no. of hex. symbols = 25, no. of zero padding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comparison. In Figure 4, we see that the standard CS100 are better then the standardized codes in terms of PSLR codes achieved 1 dB improvement over proposed S100 codes measure. However, a question may arise on the speciﬁc for 50% of the times in terms of CPSLR. On the other Doppler setting and whether that could inﬂuence the PSLR hand, the proposed codes showed an 0.9 dB improvement performance. Further analysis did conﬁrm this conjecture over standard CS100 codes for 50% of the times in terms due to the existence of codes that were superior for certain of ISLR. The CPSLR degradation observed in proposed S100 Doppler scenarios. codes is inherent to its construction. Alternatively, one can Thus, the average of the PSLR over a range of Doppler utilize evolutionary techniques for the multiple-objective (namely from 0 Hz to 25 Hz) was utilized as the selection code optimization encountered in CS100 code design [27]. criterion for code selection. Under the new average PSLR In the preceding section, we inferred the existence of measure, the codes that accomplished superior correlation multiple solutions due to the code periodicity and Table 2 suppression are listed in Table 5. The S10 and S20 codes listed the number of codes that accomplished the optimal achieved the overall best performance in terms of aver- correlation characteristics as predicted by (10). To further age PSLR taken over a range of Doppler’s. It should be arrange them, the individual codes were utilized for code emphasized here that both these codes were balanced and acquisition and their corresponding PSLR measure was thus asserting the signiﬁcance of the balanced property obtained in the presence of residual frequency error. For introduced earlier. Figure 6 shows the PSLR performance of example, the PSLR of the 10-bit and the 20-bit codes in the standard, Merten’s and the proposed 10-bit and 20-bit the presence of 12 Hz residual error is plotted in Figure 5. synchronization codes during two-dimensional acquisition In the case of 20-bit synchronization code, the ISLR mea- in the absence of background noise. The residual Doppler sure was relaxed to 4 dB so as to include the remaining was searched between 0 Hz and 250 Hz in steps of 25 Hz as synchronization codes. Accordingly, we evaluated the PSLR reported in [10]. performance of all the 20-bit codes (5079 codes as listed The LHS plot in Figure 6 readily aﬃrms the limitation of in Table 2) obtained via exhaustive search. Figure 5 readily standard NH10 code and the advantage of utilizing the M10 conﬁrms the existence of optimal synchronization codes that and the proposed S10 code. Later it will be shown that the Surendran K. Shanmugam et al. 11 10-bit code acquisition performance 20-bit code acquisition performance 14 14 10 8 6 2 010 20 30 010 20 30 Frequency oﬀset (Hz) Frequency oﬀset (Hz) NH10 code NH20 code S20 code M10 code CS20 code S20 code S10 code M20 code S20 code (a) (b) Figure 7: PSLR performance in the presence of frequency oﬀset (LHS) 10-bit code (RHS) 20-bit code. Eﬀect of residual doppler in 2-D acquisition Eﬀect of frequency oﬀset on PSLR 10 20 −2 0 102030 0 5 10 15 20 25 Frequency oﬀset (Hz) Doppler (Hz) CS25 code CS25 code S25 code S25 code 1 1 M25 code S25 code M25 code S25 code 2 2 (a) (b) Figure 8: 25-bit code performance. (LHS) eﬀect of residual Doppler on secondary code acquisition (RHS) PSLR performance as a function of frequency oﬀset. proposed S10 code correlation can be better than that of M10 and the proposed S20 code resulted in same performance code in the presence of frequency oﬀset. Amongst the 20-bit as they belong to the same equivalence class. The S20 code codes, the Galileo CS20 code had the worst performance in demonstrated similar performance as that of the NH20 code. accordance to result shown in Figure 5. Both the M20 code Finally, the proposed S20 code showed the best performance PSLR (dB) PSLR (dB) PSLR (dB) PSLR (dB) 12 International Journal of Navigation and Observation Eﬀect of residual doppler on 2-D acquisition Eﬀect of frequency oﬀset on PSLR 8 15 0 0 024 6 024 6 Doppler (Hz) Frequency oﬀset (Hz) Galileo CS100 code Galileo CS100 code Proposed S100 code Proposed S100 code (a) (b) Figure 9: 100-bit code performance. (LHS) eﬀect of residual Doppler on secondary code acquisition (RHS) PSLR performance as a function of frequency oﬀset. in terms of PSLR under Doppler conditions. The S20 code Interestingly, the codes S25 and S25 were complementary 1 1 2 although suboptimal in terms of ISLR still performed better in their PSLR performance as shown in Figure 8.However, owing to its balanced property. the code S25 can be considered optimal for not only The correlation performance degradation in NH20 code achieving better PSLR performance (around 2 dB) in the as afunctionoffrequency oﬀset was analyzed in [10]. To presence of residual Doppler, it also retained similar PSLR further validate this initial observation and also to compare performance to that of standard CS25 code for a wide range the correlation suppression performance of the proposed of frequency oﬀsets. codes, numerical simulations were carried out. Figure 7 Finally, the code acquisition performance of the standard shows the PSLR performance for both 10-bit and 20-bit CS100 and the proposed S100 codes was also evaluated in a synchronization codes as a function of frequency oﬀset. For similar manner. The residual Doppler range was reduced to the 10-bit code, one can readily notice the advantage of the 7.5 Hz so as to reﬂect the longer coherent integration utilized proposed S10 code over the M10 and NH10 codes. In the in acquiring these codes. Figure 9 shows the average PSLR case of 20-bit code, the standard NH20 and the CS20 codes performance of the standard and the proposed codes. The performed better in comparison to the M20, S20 ,and S20 standard CS100 code demonstrated better performance in 1 2 codes. On the other hand, the S20 resulted in the overall regards to the proposed S100 codes under both settings. The best performance and readily showed a PSLR gain of around proposed code despite being characterized by better ISLR 2.5 dB over standard NH20 and CS20 codes. However, the measure was still limited by its construction method from S20 is still attractive as it yielded the best PSLR performance code of short length. Nevertheless, it readily corroborates as shown in Figures 6 and 7. The aforementioned analysis for the use of alternative solutions for the multiple code design a similar setting was carried out for the 25-bit code, which problem. included the CS25, M25, and the proposed S25 and S25 1 2 codes. Note that the M25 and CS25 codes are essentially 6. CONCLUSIONS similar and are expected to perform similar. Figure 8 shows the eﬀect of residual Doppler on secondary code acquisition The design of secondary synchronization code for GNSS and the PSLR performance as a function of frequency oﬀset. system is important due to its role in acquisition and The standard CS25 code and that of M25 code were tracking. A limitation arising due to the usage of short exactly same as far as frequency oﬀset is concerned. However, secondary code is the apparent degradation in correlation the standard CS25 resulted in better PSLR performance as isolation especially in the presence of residual frequency shown in LHS plot of Figure 8. On the other hand, both the errors. This paper introduced the various performance mea- proposed codes demonstrated superior PSLR performance. sures that can be utilized for secondary synchronization code Average PSLR (dB) Average PSLR (dB) Surendran K. Shanmugam et al. 13 optimization. Consequently, these performance measures [9] L. Ries, C. Macabiau, Q. Nouvel, et al., “A software receiver for GPS-IIF L5 signal,” in Proceedings of the International were utilized to obtain optimal codes of various lengths via Technical Meeting of the Satellite Division of the Institute of exhaustive search. This paper also established the association Navigation (ION GPS ’02), pp. 1540–1553, Portland, Ore, between the optimal codes and the systematic codes such USA, September 2002. as Golay complementary codes. The proposed secondary [10] C. Macabiau, L. Ries, F. Bastide, and J.-L. Issler, “GPS synchronization codes of lengths 10, 20, and 25 obtained L5 receiver implementation Issues,” in Proceedings of the in this fashion readily demonstrated superior correlation International Technical Meeting of the Institute of Navigation isolation performance in the presence of residual frequency (ION GPS ’03), pp. 153–164, Portland, Ore, USA, September errors. The developed S100 codes although appealing in terms of ISLR measure demonstrated inferior acquisition [11] S. Mertens, “Exhaustive search for low-autocorrelation binary performance over standardized CS100 codes. Truncation of sequences,” Journal of Physics A, vol. 29, no. 18, pp. L473–L481, LFSR codes or code design using genetic algorithms can 1996. produce code sets with better correlation characteristics. [12] F. Soualle, M. Soellner, S. Wallner, et al., “Spreading code selection criteria for the future GNSS Galileo,” in Proceedings The signiﬁcance of the correlation isolation improvement of the European Navigation Conference (ENC GNSS ’05), p. 10, demonstrated by the new synchronization codes in terms of Munich, Germany, July 2005. probability of false alarm and detection is currently being [13] C. Tellambura, M. G. Parker, Y. J. Guo, S. J. Shepherd, and S. investigated. Finally, judicious design of short synchroniza- K. Barton, “Optimal sequences for channel estimation using tion codes can oﬀer optimal correlation suppression and discrete Fourier transform techniques,” IEEE Transactions on eﬃcient signal generation. Communications, vol. 47, no. 2, pp. 230–238, 1999. [14] D. V. Sarwate and M. B. Pursley, “Crosscorrelation properties Example 1. The NH10 Code represented by the hexadecimal of pseudorandom and related sequences,” Proceedings of the value “F28” is obtained as follows: IEEE, vol. 68, no. 5, pp. 593–619, 1980. [15] M. Golay, “The merit factor of long low autocorrelation binary sequences (Corresp.),” IEEE Transactions on Information The- F −→ 1111, ory, vol. 28, no. 3, pp. 543–549, 1982. 2 −→ 0010, (17) [16] M. Rupf and J. L. Massey, “Optimum sequence multisets for 8 −→ 1000. synchronous code-division multiple-access channels,” IEEE Transactions on Information Theory, vol. 40, no. 4, pp. 1261– 1266, 1994. Hence, “F28”−→ 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0. The last two [17] A. Lempel, M. Cohn, and W. L. Eastman, “A class of balanced digits highlighted in bold are discarded, and the zero symbols binary sequences with optimal autocorrelation properties,” are mapped in to −1. (i.e., 0 →−1). IEEE Transactions on Information Theory,vol. 23, no.1,pp. 38–42, 1977. [18] D. Jungnickel and A. Pott, “Perfect and almost perfect REFERENCES sequences,” Discrete Applied Mathematics, vol. 95, no. 1–3, pp. 331–359, 1999. [1] G. W. Hein, J. Godet, J. L. Issler, et al., “Status of Galileo [19] F. Neuman and L. Hofman, “New pulse sequences with frequency and signal design,” in Proceedings of the 15th desirable correlation properties,” in Proceedings of the IEEE International Technical Meeting of the Satellite Division of the National Telemetry Conference (NTC ’71), pp. 272–282, Wash- Institute of Navigation (ION GPS ’02), pp. 266–277, Portland, ington, DC, USA, April 1971. Ore, USA, September 2002. [20] M. Golay, “Complementary series,” IEEE Transactions on [2] T. Grelier, J. Dantepal, A. Delatour, A. Ghion, and L. Ries, Information Theory, vol. 7, no. 2, pp. 82–87, 1961. “Initial observations and analysis of compass MEO satellite [21] H. Urkowitz, “Complementary-sequence pulse radar with signals,” Inside GNSS, pp. 39–43, June 2007. matched ﬁltering following doppler ﬁltering,” US patent 5151702, September 1992. [3] R. D. Fontana, W. Cheung, and T. Stansell, “The modernized L2 civil signal,” GPS World, pp. 28–34, September 2001. [22] H. Minn, V. K. Bhargava, and K. B. Letaief, “A robust timing and frequency synchronization for OFDM systems,” IEEE [4] A. J. van Dierendonck and C. Hegarty, “The new L5 civil GPS Transactions on Wireless Communications,vol. 2, no.4,pp. signal,” GPS World, vol. 11, no. 9, pp. 64–71, 2000. 822–839, 2003. [5] B. C. Barker, K. A. Rehborn, J. W. Betz, et al., “Overview of the [23] V. Diaz, J. Urena, M. Mazo, J. J. Garcia, E. Bueno, and GPS M code signal,” in Proceedings of the National Technical A. Hernandez, “Using Golay complementary sequences for Meeting of the Institute of Navigation (ION NTM ’00), pp. 542– multi-mode ultrasonicoperation,” in Proceedings of the 7th 549, Anaheim, Calif, USA, January 2000. IEEE International Conference on Emerging Technologies and [6] S. Pullen and P. Enge, “A civil user perspective on near- Factory Automation (ETFA ’99), vol. 1, pp. 599–604, Barcelona, term and long-term GPS modernization,” in Proceedings of the Spain, October 1999. GPS/GNSS Symposium, p. 11, Tokyo, Japan, November 2004. [24] S. Z. Budisin, “Eﬃcient pulse compressor for Golay comple- [7] Galileo SIS ICD, “Galileo Open Service: Signal In Space mentary sequences,” Electronics Letters, vol. 27, no. 3, pp. 219– Interface Control Document,” August 2006. 220, 1991. [8] J. J. Rushanan, “The spreading and overlay codes for the L1C [25] European Space Agency, “Galileo Open Service: Signal In signal,” in Proceedings of the National Technical Meeting of Space Interface Control Document,” Interface control docu- the Institute of Navigation (ION NTM ’07), pp. 539–547, San ment, European Union, May 2006, http://www.galileoic.org/ Diego, Calif, USA, January 2007. la/ﬁles/Galileo%20OS%20SIS%20ICD%20230506.pdf. 14 International Journal of Navigation and Observation [26] M. Tran and C. Hegarty, “Receiver algorithms for the new civil GPS signals,” in Proceedings of the National Technical Meeting of the Institute of Navigation (ION NTM ’02), pp. 778–789, San Diego, Calif, USA, January 2002. [27] S. K. Shanmugam and H. Leung, “Chaotic binary sequences for eﬃcient wireless multipath channel estimation,” in Pro- ceedings of the 60th IEEE Vehicular Technology Conference (VTC ’04), vol. 60, pp. 1202–1205, Los Angeles, Calif, USA, September 2004. International Journal of Rotating Machinery International Journal of Journal of The Scientific Journal of Distributed Engineering World Journal Sensors Sensor Networks Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Volume 2014 Journal of Control Science and Engineering Advances in Civil Engineering Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Submit your manuscripts at http://www.hindawi.com Journal of Journal of Electrical and Computer Robotics Engineering Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 VLSI Design Advances in OptoElectronics International Journal of Modelling & Aerospace International Journal of Simulation Navigation and in Engineering Engineering Observation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2010 Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com http://www.hindawi.com Volume 2014 International Journal of Active and Passive International Journal of Antennas and Advances in Chemical Engineering Propagation Electronic Components Shock and Vibration Acoustics and Vibration Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014
International Journal of Navigation and Observation – Hindawi Publishing Corporation
Published: May 6, 2008
You can share this free article with as many people as you like with the url below! We hope you enjoy this feature!
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.