A New Fine Tracking Algorithm for Binary Offset Carrier Modulated Signals

In this paper, an analysis of a new synchronization technique for Binary Offset Carrier (BOC) modulated signals will be presented. Goal of the proposed method is to improve the synchronization performances by reducing the synchronization errors due to the characteristic BOC cross-correlation function. The synchronization is generally based on the envelope of the cross-correlation between the received signal and the local replicas. In a classical NRZ modulation this envelope is approximately a triangle whose peak corresponds to the perfect synchronization between the incoming signal and local replicas. In the BOC case, instead, the cross-correlation is given by a set of triangles with positive and negative peaks in which only the central one corresponds to the perfect synchronization. This paper will describe a novel technique characterized by a different choice of the local replica. In this manner the cross-correlation envelope is composed by different triangles with positive and negative peak; this envelope has one and only one zero-crossing that corresponds to the perfect synchronization. In order to demonstrate the effectiveness of the method, a theoretical analysis has been carried on together with computer simulations. In particular, the main properties of the technique, compared with the classical situation, will be presented. INTRODUCTION Due to the modernization of the navigation satellite systems, the interest is recently increased in new spreadspectrum signals and modulations, in order to offer more services to civilian users. To avoid interferences with existing navigation transmissions, and to be compatible with previous systems, new signals must be characterized by precise features, the most important being coexistence with current and already planned signals on the GPS L1 and L2 frequencies, offering more robustness, higher performance, and higher transmission capacity [3]. The choice of the modulation type has to be performed on the basis of different criterions: • Minimization of losses of the satellite signals • Maximization of energy efficiency • Minimization of interferences with the already present transmission systems • Optimization of performances and complexity of the receiver The Binary Offset Carrier (BOC) modulation is the final choice of a long process of analysis, and it is a trade off between the previously pointed out characteristics [1]. A particular power spectral density, which allows the coexistence of different signals in the same bandwidth, is one of the most important characteristics of this new modulation technique. In fact, one of the most desirable characteristic for the new modulations techniques is that it should be as orthogonal as possible to code modulation already present in the L1 and L2 frequencies [2]. The new modulation’s power should be concentrated where the already present spectrum is small. For this purpose a new type of signal, called tri-phase, can be used. In this manner, different services or different signals from the same satellite can be present in the same bandwidth. Unfortunately, a drawback of BOC is related to synchronization problems with respect to classical methods. In fact the correlation with the BOC signal is ambiguous. In order to reduce such errors, a new correlator architecture, obtained by demodulating the received signal with only a local pseudorandom code, is presented. This paper is structured as follows: after this brief introduction, in the first paragraph the BOC modulation is explained, than a theoretical description of the BOC signal is pointed out. In the second part the novel method and its characteristics are described. Finally the experimental results based on a signal simulator able to model the BOC modulation in different carrier-to noise situations are presented followed by the conclusions. BINARY OFFSET CARRIER SIGNAL BOC signal is composed by the product of two different signals. The first one is a classical Pseudo Noise sequence with chip rate Rc and two different values +1 and –1. The second one is a sub-carrier that can be a square signal or a sine signal with frequency Rsc equal or higher than Rc. If a sine-wave is used, instead of a square-wave, the modulation is called Linear Offset Carrier (LOC) [5]. A BOC(n,m), as named in Galileo system, is characterized by n=Rsc/Rca and m=Rc/Rca , where Rca is the frequency of the signal already present in the considered bandwidth. For example, Rca in the GPS C/A code chip rate is equal to 1.023 Mcps. A similar notation, based on the two frequencies of reference, is used in GPS case. The effect of the square sub-carrier on the power spectrum is to split the main lobe of the PN code spectrum into two lobes centered at ± Rsc from the central frequency. Moreover, increasing fs/fc ratio (or equivalently n/m) enlarges the distance between the lateral sides and, in the same manner, power at frequencies around the center of the bandwidth. Two different cases are shown in the following figure (Figure 1). Figure 1 Power Spectrum of two different BOC modulations As it can be seen in Figure 1, BOC modulation can be used without interferences with code modulation already present in the central frequency. Concerning the correlation behaviors, the same modulations are shown in Figure 2. In general, in a classical case, the auto-correlation function of a PN code has a correlation peak. On the contrary, for a BOC signal is visible that multiple peaks (Figure 2), are present [1][10]. They can be useful to improve tracking, but they can be also a potential source of errors. In fact, it is possible that the system locks the synchronization on a lateral (and hence sub-optimal) correlation peak. In Figure 2, an ideal case is shown. In a real receiver the front end filter determines a smoothing of the peaks. Figure 2 Auto-correlation function of two different BOC modulations THEORETICAL BOC MODEL The auto-correlation properties of a BOC modulation can be explained with a theoretical formalization, useful in the following to proof the proposed method. The model shown below is obtained on the basis of the rules of the pseudorandom sequences [4]. Firstly, the transmitted BOC signal can be written as the multiplication between ( ) t x , a continuous PN sequence of length N, and ( ) t sq , a square wave of alternating values +1 or -1