Consistent BCS modulated signals for GNSS applications
2016; Institution of Engineering and Technology; Volume: 11; Issue: 4 Linguagem: Inglês
10.1049/iet-spr.2016.0200
ISSN1751-9683
AutoresMustapha Flissi, Khaled Rouabah, Salim Attia, Djamel Chikouche, Thierry Devers,
Tópico(s)Advanced Frequency and Time Standards
ResumoIET Signal ProcessingVolume 11, Issue 4 p. 415-421 Research ArticleFree Access Consistent BCS modulated signals for GNSS applications Mustapha Flissi, Mustapha Flissi Team of Communication Signals, Geolocation, Parallel Processing and Hardware Implementation, ETA Laboratory, Electronics Department, University of Bordj Bou Arreridj, 34031 El-Anasser, AlgeriaSearch for more papers by this authorKhaled Rouabah, Corresponding Author Khaled Rouabah khaled_rouabah@yahoo.fr Team of Communication Signals, Geolocation, Parallel Processing and Hardware Implementation, ETA Laboratory, Electronics Department, University of Bordj Bou Arreridj, 34031 El-Anasser, AlgeriaSearch for more papers by this authorSalim Attia, Salim Attia Team of Communication Signals, Geolocation, Parallel Processing and Hardware Implementation, ETA Laboratory, Electronics Department, University of Bordj Bou Arreridj, 34031 El-Anasser, AlgeriaSearch for more papers by this authorDjamel Chikouche, Djamel Chikouche LIS Laboratory, Electronics Department, University of Sétif 1, Setif, 19000 Algeria Electronics Department, University of M'sila, M'sila, 28000 AlgeriaSearch for more papers by this authorThierry Devers, Thierry Devers ICMN-CNRS UMR 7374, IUT de Chartres, Université d'Orléans, 21 rue de Loigny la Bataille, 28000 Chartres, FranceSearch for more papers by this author Mustapha Flissi, Mustapha Flissi Team of Communication Signals, Geolocation, Parallel Processing and Hardware Implementation, ETA Laboratory, Electronics Department, University of Bordj Bou Arreridj, 34031 El-Anasser, AlgeriaSearch for more papers by this authorKhaled Rouabah, Corresponding Author Khaled Rouabah khaled_rouabah@yahoo.fr Team of Communication Signals, Geolocation, Parallel Processing and Hardware Implementation, ETA Laboratory, Electronics Department, University of Bordj Bou Arreridj, 34031 El-Anasser, AlgeriaSearch for more papers by this authorSalim Attia, Salim Attia Team of Communication Signals, Geolocation, Parallel Processing and Hardware Implementation, ETA Laboratory, Electronics Department, University of Bordj Bou Arreridj, 34031 El-Anasser, AlgeriaSearch for more papers by this authorDjamel Chikouche, Djamel Chikouche LIS Laboratory, Electronics Department, University of Sétif 1, Setif, 19000 Algeria Electronics Department, University of M'sila, M'sila, 28000 AlgeriaSearch for more papers by this authorThierry Devers, Thierry Devers ICMN-CNRS UMR 7374, IUT de Chartres, Université d'Orléans, 21 rue de Loigny la Bataille, 28000 Chartres, FranceSearch for more papers by this author First published: 01 June 2017 https://doi.org/10.1049/iet-spr.2016.0200Citations: 6AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In this study, the authors propose reliable sequences of binary coded symbol (BCS) modulation, and their characteristics and performances for Global Navigation Satellite System (GNSS) application are described. A BCS sequence vector is formed by eight variable length sub-chips of alternated + 1 and −1 (or −1 and + 1) values. A judicious choice of the sub-chips lengths of the BCS sequence permitted to propose several BCS sequences that provide high performances in terms of multipath mitigation, resistance to the noise and interferences rejection. An overview of the essential characteristics and the resulting autocorrelation functions (ACFs) and power spectral densities of the proposed BCS sequences were introduced. The latter ACFs have a sharp main peak due to the increase in the number of transitions of the BCS sequences within a chip interval, which corresponds to a larger slope of the discrimination function, and consequently a reduced range of search in the delay locked loop with a minimum calculation load. The theoretical and simulation results indicate that the proposed BCS sequences are more consistent compared to the conventional signals adopted by the GNSS navigation systems. 1 Introduction Although the GNSS applications are increasing, the radio frequency (RF) spectrum becomes more and more crowded. The design of new signals in the frequency bands already operable and with a single RF carrier has become often the best solution permitting to maintain lower levels of interferences with existing signals and providing better resistance against multipath (MP) and interferences. Among the several modulations adopted by Galileo and Global Positioning System (GPS) modernisation, we find the basic modulation called binary offset carrier (BOC). Initially the BOC modulation has been designed to ensure the spectral isolation with the binary phase shift keying (BPSK) one that is currently used by GPS due to its symmetric split spectrum [1]. Then it became a serious candidate for future Global Navigation Satellite System (GNSS) modulations since it improves the positioning accuracy and enhances MP rejection [1, 2]. In addition, the BOC modulation can be considered as the basis for all improved navigation modulations such as alternative BOC modulation [3], multiplexed BOC (MBOC) modulation with its both signal implementations: composite BOC (CBOC) and time-mBOC (TMBOC) [4], composite binary coded symbols (CBCSs) modulation [5, 6] and BOC with adjustable width (BOC-AW) modulation or its optimised version OBOC-AW [7]. In particular, the principle of CBCS is to modulate the pseudo random noise (PRN) code by a sub-carrier of frequency fs resulting from the superposition between the BOC modulation and a particular sequence of binary coded symbol (BCS) waveform that has a specific power distribution [5]. In general, the BCS waveform modulates the PRN code by different binary symbols of same length relative to the code chip Tc and coded at a chip rate fc. In the GNSS field, the notation BCS([s], fc) is used, where [s] represents the BCS sequence in one chip. According to this notation, the BPSK(1) (fc = 1 1.023 MHz) modulation can be denoted as BCS([1], 1) and in a similar way BOC(1,1) (fs = 1 1.023 MHz and fc = 1 1.023 MHz) modulation can also be denoted as BCS([1, −1], 1) [6, 8]. A suitable choice of BCS sub-chips sequences can generate new optimised signals and thus improves the spectral properties of GNSS. For example, the sequence: s = [1, −1, 1, −1, 1, −1, 1, −1, 1, 1] has been recognised as a reliable sequence representing what is used for CBOC modulation [5, 9]. In this paper, we propose other more reliable sequences for the GNSS systems. These sequences are two-levels {−1, 1}, with different sub-chips' lengths, selected to allow the optimum control of the spectral properties and correlation characteristics [10]. The judicious choice of the sub-chips' lengths of the proposed sequences gives different BCS signals with alternating sub-chips levels (−1) and (1) or ( + 1) and (−1). The theoretical and simulation results indicate that the proposed BCS sequences are consistent in terms of MP mitigation, code tracking precision and interferences rejection, in particular at 8 and 12 MHz single-side pre-correlation bandwidth. This paper is organised as follows: Section 2 presents the concept of the proposed BCS sequences and provides their spectrums and correlation characteristics. In Section 3, the main performances of these proposed BCS signals are discussed and compared, theoretically and through simulation results, with the existing GPS and Galileo signals. Finally, the conclusions are presented in Section 4. 2 Proposed BCS sequences The spreading signal with the proposed BCS sequences can be expressed as follows: (1)where ck is the ki th chip of the PRN code with frequency fc = n 1.023 MHz and is the proposed subcarrier sequence with , given by (2)where is the sequence length. is the length of the smallest sub-chip and is the length of symbol relative to Tm. The proposed BCS sequences are: , , and . We note that the BCS3 sequence is similar to signal [7]. Fig. 1 shows the waveforms of these subcarriers. Fig. 1Open in figure viewerPowerPoint The proposed BCS waveforms 2.1 Algorithm of generation To obtain the desired sequences, we proceed according to the following simulated steps: Generate any sequence [7]. Calculate the proposed sequence that is given as follows: (3)Here m is a multiple of n. Multiply the so obtained sequence by a PRN code and send the resulting signal through a noiseless MP channel to study the performance. At the receiving end, calculate the MP running average error and compare it to the desired one. Repeat steps (2)–(4) by varying 'm' in (3) until an acceptable MP running average error is obtained (M, in (2), should be an integer). Use the obtained optimised sequence using (2). Other sequences can be obtained by varying the parameters of BOC-AW waveform together with 'm' in (3). 2.2 Proposed sequences ACFs and PSDs As can be seen in [6, 8], the PSD of the different proposed BCS signals with perfect spreading can be expressed as follows: (4)The ACFs and the PSDs of these four proposed BCS waveforms together with BOC(1,1), MBOC (TMBOC and CBOC) and CBCS([1, −1, 1, −1, 1, −1, 1, −1, 1, 1],1) signals are, respectively, illustrated in Figs. 2-7. Fig. 2Open in figure viewerPowerPoint Normalized ACFs of BOC(1,1), BCS1, BCS2, BCS3 (OBOC-AW(1,1,α(2)) and BCS4 Fig. 3Open in figure viewerPowerPoint Normalized ACFs of BCS1, BCS3, TMBOC, CBOC and CBCS Fig. 4Open in figure viewerPowerPoint Normalized ACFs of BCS2, BCS4, TMBOC, CBOC and CBCS Fig. 5Open in figure viewerPowerPoint Normalized PSDs of BOC(1,1), BCS1, BCS2, BCS3 (OBOC-AW(1,1,α(2)) and BCS4 Fig. 6Open in figure viewerPowerPoint Normalized PSDs of BCS1, BCS3, MBOC and CBCS Fig. 7Open in figure viewerPowerPoint Normalized PSDs of BCS2, BCS4, MBOC and CBCS As illustrated in Figs. 2-4, the ACFs of BCS1 and BCS2 waveforms yield sharper peaks [11] followed by BCS3 and BCS4 waveforms with respect to those of the other signals. In other words, this provides an improvement of the code tracking performance, as we are going to see in the last part of this paper. In Figs. 5-7, the PSDs of BCS1 and BCS3 signals present wider side lobes than the other signals. However, BCS1 signal has an additional side lobe around ± 3 MHz compared to BCS3 signal. This shows also that the BCS1 and BCS3 signals have broader principal lobes and higher power on the secondary lobes than the other modulations. The minimum symbol length of the proposed BCS sequences is equal to Tc/84 or Tc/42. In addition, the maximum symbol length is equal to Tc/4 or Tc/4.2. Theoretically, these results mean that the minimum required sampling frequency should satisfy information recovery of Tc/84 length sub-chips. However, in our case, the sequences consist of a combination of PRN code and subcarrier which is not a useful information. Besides, the main goal of the receiver is to keep the correlation function, between the received signal and the locally generated one, with the best possible shape (sharper main peak and weak side peaks) to enable better performances in terms of resistance against multipath and noise. Thus, the sampling frequency needs to accommodate the bandwidth of the desired signal and must provide a resulting sampling bandwidth of 24 MHz that corresponds to the received narrowband L1 navigation signals. If we consider that the sampling process do not act as a second frequency translation stage, the minimum sampling frequency required for acquiring the proposed sequences should be equal to 48 MHz. The 24 MHz bandwidth RF filter will certainly cause a small change in the forms of the proposed sequences, but the most important thing is that the shapes of all correlation functions corresponding to the proposed sequences stay the same as those of infinite bandwidth RF filter case. 3 Theoretical performances comparison In what follows theoretical performances study is realised in terms of code tracking error, root mean square bandwidth (RMSB), spectral separation coefficient (SSC) and robustness against interferences. 3.1 Code tracking error and RMSB The Cramér-Rao lower bound (CRLB) is an important parameter to measure the performance of the code tracking errors estimation. It is given in [1, 12, 13] as follows: (5)where βRMS is the RMSB, BL is the delay locked loop (DLL) bandwidth, C /N0 is the carrier-power-to-noise-density ratio and λ is the correlation loss due to the front-end bandwidth Br, which is defined as (6)where Gs (f) is the signal PSD. In (4), βRMS can be seen as another way of interpreting the CRLB of a signal, which is defined in [1, 14-16] as follows: (7) in (6) is the signal PSD normalised for unit power over the front-end bandwidth Br. In Figs. 8 and 9, using, respectively, 8 and 12 MHz single-side receiver bandwidth with 1 Hz DLL bandwidth, the CRLB of BOC(1,1), TMBOC(6, 1, 4/33)-pilot, CBOC(6, 1, 1/11)-pilot, CBCS(20%) and the proposed BCS signals is compared. As we can see from these two figures, BCS1, BCS2, BCS3 and BCS4 signals have better code-tacking accuracy compared to BOC(1,1), TMBOC(6, 1, 4/33)-Pilot, CBOC(6, 1, 1/11)-pilot and CBCS(20%). For 12 MHz receiver bandwidth (see Fig. 9), BCS1 and BCS2 signals outperform all other signals. Fig. 8Open in figure viewerPowerPoint CRLB of different waveforms for 8 MHz receiving bandwidth Fig. 9Open in figure viewerPowerPoint CRLB of different waveforms for 12 MHz receiving bandwidth Fig. 10 shows the RMSB of the proposed BCS signals in comparison of BOC(1,1), TMBOC(6, 1, 4/33)-pilot, CBOC(6, 1, 1/11)-pilot and CBCS(20%) signals. As we can identify, the RMSBs of BCS2 and BCS4 signals, using 2.5 MHz receiver bandwidth, are larger than those of all other signals. In addition, using 8 MHz receiver bandwidth, all proposed BCS signals have much greater RMSBs than those of all other signals. For example, 2.8 MHz of RMSB is reached at 12 MHz receiver bandwidth with the proposed BCS signals but, for this same value of RMSB, we have 30 MHz receiver bandwidth with TMBOC(6, 1, 4/33)-pilot, CBOC(6, 1, 1/11)-pilot and CBCS(20%) signals. Fig. 10Open in figure viewerPowerPoint RMSBs of the different waveforms 3.2 Spectral separation coefficient The SSC is a fundamental parameter for the design of new GNSS signals to ensure the coexistence of different signals in the same frequency band. It provides a measure of the noise power output from a receiver when certain signals, with given spectra, are incident at its input. The SSC is given in [14-16] by (8)where Br is the receiver bandwidth. Gs (f) and Gi (f) are, respectively, the normalised PSDs of the desired signal and the interfering signal. Tables 1 and 2 show SSCs between the different waveforms. Here, we use GPS signals with 30.69 MHz transmission bandwidth, and Galileo signals with 40.92 MHz transmission bandwidth. In both cases, we consider a double sided receiver bandwidth of 24 MHz. Table 1. SSCs in dB between the different waveforms for the case of GPS signals (30.69 MHz transmitter bandwidth and 24 MHz receiver bandwidth) Signal GPS P(Y) code BPSK(10) GPS C/A code BPSK(1) GPS BOC(1,1) GPS L1C TMBOC(6, 1, 4/33) GPS M code BOC(10, 5) BOC(1, 1) −69.1225 −71.6805 −62.1400 −62.6970 −81.8305 TMBOC(6, 1, 4/33) −69.5099 −74.0651 −62.6095 −63.1355 −81.7975 BCS1 −70.2697 −73.0897 −63.5603 −64.0711 −79.4112 BCS2 −71.7129 −75.0794 −66.1918 −66.6830 −79.8429 BCS3 −70.0312 −72.9698 −63.5033 −64.0107 −82.6908 BCS4 −72.2848 −75.3908 −67.0834 −67.5741 −82.2709 Table 2. SSCs in dB between the different waveforms for the case of Galileo signals (40.92 MHz transmitter bandwidth and 24 MHz receiver bandwidth) Signal Galileo BOC(1, 1) Galileo E1 OS CBOC(6, 1, 1/11) Galileo CBCS(20%) Galileo E1 PRS BOCc(15, 2.5) BOC(1, 1) −62.1627 −62.5736 −63.0689 −103.4062 CBOC(6, 1, 1/11) −62.5409 −62.9355 −63.4399 −102.3610 CBCS(20%) −63.0071 −63.4108 −63.8405 −102.9597 BCS1 −63.6959 −64.0733 −64.5263 −97.1002 BCS2 −66.3866 −66.7497 −67.2054 −97.6666 BCS3 −63.6343 −64.0092 −64.4439 −99.1357 BCS4 −67.2039 −67.5666 −68.0911 −99.3624 As we can recognise from Table 1, the proposed BCS3 and BCS4 signals have better spectral separation with all GPS signals. The same remark can be made concerning the proposed BCS1 and BCS2 signals except with the GPS M code. For example, the SSCs for BCS3 and BCS4 signals in GPS L1C band are, respectively, 1.5 and 5 dB higher than that for BOC(1, 1) using the same code and the same band. However, the SSC for BOC(1,1) signal with GPS M code is 2.5 and 2 dB, respectively, higher than those for BCS1 and BCS2 signals with the same code. From Table 2, we can see that BCS1, BCS2, BCS3 and BCS4 signals have better spectral separation with all Galileo signals except with the Galileo E1 Public Regulated Service (PRS). For example, the SSCs for BCS2 and BCS4 signals with Galileo E1 open service (OS) are, respectively, 3.3 and 4 dB higher than that for CBCS(2%) with the same code. However, the SSC for CBCS(2%) signal with Galileo E1 PRS code is 5.3 and 3.5 dB, respectively, higher than those for BCS2 and BCS4 signals with the same code. 3.3 Robustness against interferences SSCs, which are key parameters to evaluate the isolation of GNSS signals, can give a good overview on the level of degradation of the carrier-to-noise ratio (CNR) caused by the inter-system and intra-system interferences. This degradation, for both inter-system and intra-system interferences, can be given as follows [17-20]: (9) (10)with (11)In (9) and (10), N0 is the power spectral density of white noise, Ix is the intra-system or inter-system interference, Cj is the power of interfering signal j and Nx is the number of interfering signals. We illustrate in Table 3 the intra-system and inter-system degradation of GALILEO signals in comparison with the proposed BCS sequences. Table 4 shows the intra-system and inter-system degradation of GPS signals in compared with the proposed BCS sequences. Here, we use the minimum received power of signals. The PSD of white noise is: N0 = −204 dBW/Hz [20]. Table 3. Intra-system and inter-system degradation of GALILEO signals in compared with the proposed BCS sequences Useful signal Intra-system degradation, dB Inter-system degradation, dB BOC(1,1) 0.2276 0.1469 CBOC(6, 1, 1/11) E1 OS 0.2231 0.1386 CBCS(20%) 0.2143 0.1389 BCS1 0.2261 0.1540 BCS2 0.1567 0.1401 BCS3 0.2126 0.1367 BCS4 0.1281 0. 1303 Table 4. Intra-system and inter-system degradation of GPS signals in compared to the proposed BCS sequences Useful signal Intra-system degradation, dB Inter-system degradation, dB BOC(1,1) 0.1646 0.2204 TMBOC(6, 1, 4/33) L1C 0.2561 0.3099 BCS1 0.2420 0.2794 BCS2 0.1391 0.1587 BCS3 0.2439 0.2805 BCS4 0.1142 0.1283 From Table 3, we can recognise that the proposed BCS2 sequence has a significant lower intra-system degradation compared with the classical CBOC(6, 1, 1/11) E1 OS signal. For BCS3 and BCS4 sequences, there is a lower level of intra-system and intra-system degradation compared with Galileo signals. Table 4 also shows that all the proposed BCS sequences present a very low level of intra-system and inter-system degradation compared with TMBOC (6, 1, 4/33) L1C signal. 4 Simulation results The simulations are conducted to test the efficiency of the proposed waveforms. For this reason, three performances measurement scenarios are considered. For the first one, the performances evaluation is done by calculating the error envelopes and their running average errors [21, 22]. The latter is performed by calculating the absolute values of the error envelopes and their cumulative sum. For this same scenario, four schemes have been simulated. The first one is based on the proposed modulation for its three variants. The second and the third ones are, respectively, based on OBOC-AW and traditional BOC modulations. The last scheme is based on MBOC modulation for its two variants CBOC and TMBOC. Here we consider a (line of sight) LOS and one MP signal. The 24 MHz pre-correlation bandwidth is used to estimate the running average errors for all these schemes. The amplitude of the MP signal is chosen equal to 0.5 and its delay is varied from 0 to 450 m with respect to the LOS. The resulting running average errors calculated from these error envelopes for all the aforementioned schemes are illustrated in Fig. 11. As shown in this figure, the proposed waveform presents better performances for its three variants with respect to what we observe for TMBOC and CBOC. In comparison with CBCS and OBOC-AW, our waveform presents performances that are very close to those of CBCS and better to those of OBOC-AW. Fig. 11Open in figure viewerPowerPoint Running average errors of the different waveforms In the second scenario of performance measuring mechanism, simulations are performed to test the effect of the noise on the performances of the proposed waveform. The results of comparison of standard deviations (STD) in code tracking of all the waveforms presented in scenario (1) are given in Fig. 12. This simulation is performed without MP. As illustrated in this figure, the STDs are plotted against CNR that varies from 30 to 48 dB-Hz. The reduced values of the STDs of the proposed waveform through the range of the CNR confirm its resistance vis-à-vis the noise. Fig. 12Open in figure viewerPowerPoint STDs versus CNR for the different waveforms As shown in this figure, the proposed waveform presents better performances for its three variants with respect to what we observe for TMBOC and CBOC. In compared with CBCS and OBOC-AW, our waveform presents performances that are very close to those of CBCS and better than those of OBOC-AW. In the last scenario of performance measuring mechanism, simulations are performed to compare the true detection probability of the different signals. The results are shown in Fig. 13. In this figure, the probability of true detection of each proposed sequence is compared with those of BOC(1,1), CBCS and MBOC modulation for its two variants CBOC and TMBOC. Here the probability of true detection is plotted versus CNR. We observe that all the traditional waveforms present a degradation of CNR compared to the proposed sequences. The maximum degradation can reach 6 dB-Hz for BOC(1,1) and 2 dB-Hz for CBCS which shows the reduction of the effect of secondary peaks on the proposed sequences. Fig. 13Open in figure viewerPowerPoint True detection probability versus CNR for the different waveforms 5 Conclusion In this paper, four reliable and efficient variants of BCS modulation sequences with eight sub-chips length each have been proposed for GNSS application. They consist of a vector that is formed by alternated + 1 and −1 sub-chips of different time lengths. As illustrated and demonstrated in this contribution, a suitable choice of these sequences sub-chips' lengths provides better performances as compared to classical sequences. This is because the essential characteristics of the proposed BCS sequences such as ACFs and PSDs are optimised. Indeed, all ACFs have a sharp main peak leading to a larger slope of the discrimination function, which reduces the search range of the DLL and thus the calculation load. The simulation results have shown that the proposed optimised BCS sequences present better resistance to noise, MP and interferences reduction due to their DSPs distributions, which present important quantities of power at high frequencies. 6 References 1Betz, J.W.: 'Binary offset carrier modulations for radionavigation', J. Inst. Navig., 2001, 48, pp. 227– 246 2Betz, J.W.: 'The offset carrier modulation for GPS modernization'. 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