A New Unambiguous BOC(n,n) Signal Tracking Technique*

GALILEO, the major contribution of the European Union to the Global Navigation Satellite System (GNSS), will be both independent and complementary to the current GPS. It is still in its design phase, and while the signals have to be finalized, the main specifications have already been confirmed. The Binary Offset Carrier (BOC) modulation is part of the current GALILEO signal plan. A BOC modulation multiplies a spreading code with a square wave sub-carrier that has a frequency multiple of the code rate. It creates a split spectrum with two main lobes shifted from the center frequency by the frequency of the sub-carrier. This modulated signal induces better tracking in white noise and better inherent multipath mitigation compared to the spreading code alone. However, it also makes acquisition more challenging and tracking potentially ambiguous due to its multiple peak autocorrelation function. As a result, an evaluation of its performance under different conditions and research on advanced tracking techniques are necessary to assess its robustness and advantages before final selection. This paper focuses on a specific BOC signal: the BOC(1,1). Working on a given signal, instead of trying to find a generic solution, offers the possibility to fully exploit this signal’s characteristics to find a more relevant way to improve its performance and cancel its bias threat. A new innovative tracking technique dedicated to BOC(n,n) signals has therefore been developed using a synthesized local correlation function. It completely removes the sidepeak threat and allows clean acquisition and tracking of any BOC(n,n) signal while keeping the same sharp correlation main peak. Consequently, it does not need to check if tracking is done on the main peak. It also offers a good resistance to long-delay multipath. The particular case of BOC(1,1) is taken as an example throughout the paper due to the strong probability that it will be used by the L1 GALILEO civil signal. Both acquisition and tracking are studied and compared with the standard tracking algorithm, first theoretically and then using simulations. INTRODUCTION In the new generation of Global Navigation Satellite Systems (GNSSs), special attention has been made to have efficient and spectrally relevant signals. GALILEO and GPS will share two central frequencies and will both send several signals on the same carriers. Consequently, new signal modulations had to be studied to minimize interand intra-system interference. One modulation emerged due to its split spectrum that spectrally isolates the signal from the currently used Bi-Phased Shift Keying (BPSK) modulation [Godet et al., 2002; Betz, 2002]. This new modulation is known as Binary Offset Carrier (BOC). It multiplies a spreading code with a square wave sub-carrier that has a frequency multiple of the spreading code frequency. This creates a symmetric split spectrum with two main lobes shifted from the carrier frequency by the value of the sub-carrier frequency. The properties of the BOC signals are dependent on the spreading code chip rate, the subcarrier frequency, and the sub-carrier phasing within one PRN code chip. The common notation for BOCmodulated signals in the GNSS field is BOC(fc,fs) where fc represents the code chip rate, and fs is the frequency of the sub-carrier. Both fc and fs are usually noted as a multiple of the reference frequency 1.023 MHz. A summary of all the basic properties and improvements brought by BOC signals compared to BPSK signals is given by Betz (2002). Among others, it is worth noting that for the same chip rate, BOC signals have a lower inherent tracking noise, and better multipath and narrow-band interference Proceedings of The European Navigation Conference GNSS 2004, Rotterdam, 17-19 May 2004 1 mitigation. However, the presence of the sub-carrier introduces several peaks in the range [-1, +1] chip in BOC autocorrelation. Figure 1 shows the autocorrelation of a BPSK signal with a 1.023 MHz spreading code rate and a sine-phased BOC(1,1) with the same spreading code. As observed, BOC autocorrelation presents secondary peaks. The presence of these secondary peaks may cause a serious problem if the receiver locks onto a side peak instead of the main peak. A significant bias of approximately 150 m would then be present in the range measurements, which is unacceptable for navigation applications. Figure 1 – Normalized Autocorrelation for BPSK(1) and sine phased BOC(1,1) Several methods have been proposed to track BOC signals without suffering from any potential tracking bias. Fine and Wilson (1999), Lin et al. (2003), Martin et al. (2003) and Ward (2004) are a few examples. They treat the problem of the BOC tracking ambiguity in a broad sense, trying to find a solution that could be applied to any BOC(n,m) signal. This paper differs from this approach by studying an unambiguous tracking specific to BOC(1,1) signals. The choice of the BOC(1,1) is due the significant possibility that it will be used for the GALILEO civil signal on the E2L1-E1 band. Moreover, there are also discussions to introduce it as a candidate for the GPSIII civil signal on the L1 band [Gibbon, 2004]. This makes the BOC(1,1) signal particularly interesting to study. The research on a single type of BOC signal put forward the desire to exploit fully the particularities of this signal to try to find potentially improved solutions than the ones already known. However, because the structure of a BOC signal depends upon the relation between the spreading code frequency and the subcarrier frequency, a solution for BOC(1,1) signals can be directly extended to any BOC(n,n) signals. The new unambiguous tracking method introduced herein uses the particular correlation between a BOC(n,n) signal and its spreading code (without the subcarrier) to synthesize a single-peak correlation function. It therefore avoids constant checking to ensure that the main peak is being tracked, as necessary on a standard BOC tracking technique. It is important to mention that the new technique presented herein could be extended to other BOC signals, however it may not be optimal for other BOC modulations due to its dedication to BOC(n,n) characteristics. For the sake of simplicity, only BOC(1,1) signals will be studied. The first part of this paper details the BOC(1,1) tracking ambiguity problem to underline the motivation for this research. A new unambiguous synthesized correlation function and its generation are then presented. A new Early-Minus-Late Power (EMLP) discriminator, adapted to the new correlation function, is investigated in the third part and its tracking technique performance is given through extensive simulations thereafter. The inherent multipath mitigation performance of the new tracking technique is then shown. Finally, an unambiguous acquisition scheme using the proposed synthesized correlation is introduced. BOC(1,1) RANGING AMBIGUITY ISSUE Although it is well-known that BOC signals have a tracking ambiguity issue, the understanding and quantification of the threat is a prerequisite to ensure the relevance of the research. Two main sources can lead to a ranging ambiguity when using BOC modulation for ranging: A short loss of lock (due to a low C/N0 for instance) followed by the lock, after a drift of the code tracking, on a secondary peak (an increase of the C/No shortly after the loss of lock) An incorrect acquisition that would acquire on the secondary peak of the autocorrelation function and be followed by ambiguous tracking. As this research is dedicated to the unambiguous tracking of BOC(n,n) signals, the two issues mentioned above that could lead to a range bias, are specifically studied hereafter in the context of the BOC(1,1) signal. Tracking Ambiguity The autocorrelation function of the BOC(1,1) signal with sine phasing, , plotted in Figure 1, can be written as follows: BOC R ( ) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = − 1 2 1 1 2 1 1 2 1 2 1 0 τ τ τ τ tri tri tri RBOC (1) where ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ y x triα is the value in of a triangular function centred in x α with a base width of y and a peak magnitude of 1; τ is the code delay in chips. Assuming that the Delay Lock Loop (DLL) uses an EMLP discriminator, the theoretical expression of the discriminator output is: ( ) [ ] [ ] [ ] 2 2 2 2 BOC BOC BOC BOC BOC EMLP QL IL QE IE V + − + = τ ε (2) Proceedings of The European Navigation Conference GNSS 2004, Rotterdam, 17-19 May 2004 2 Assuming the code tracking error τ ε is smaller than half the Early-Late spacing , and that is smaller than one chip, the EMLP discriminator expression in the central region is given by: s C s C ( ) [ τ τ τ ε ε ε 12 18 4 2 − = s BOC EMLP C A V ] (3) for 2 2 s s C C ≤ ≤ − τ ε where A is the amplitude of the incoming signal. Normalizing the discriminator is mandatory in order to eliminate the dependency of that signal upon the received signal power. The normalization typically used for an EMLP discriminator is: ( ) ( ) [ ] 2 2 BOC BOC BOC BOC QL QE IL IE NORM + + + = (4) As a consequence, the normalized standard BOC(1,1) EMLP discriminator can be expressed as: ( ) ( ) ( ( ) ) NORM C V C V s BOC EMLP s BOC NORM 12 18 3 2 2