We will now analyse the effect of code search step size with the |VE2+P2| method, see Figure 7. The worst case correlation values for the |VE2+P2| method are close to that of BPSK worst case values and swings around it. For 0.5 step size we incur only about 1 dB loss compared to BPSK worst case. A keen observation of the |VE2+P2| worst case loss curve shows us an interesting phenomenon. The curve shows flattened response at three places. The middle one is worth closely observing. From 0.5 to around 0.8 step size, the correlation loss remains at 0.67. This means that even at 0.8 step size we will incur only a loss of 3.5 dB and this loss is less than even the BPSK worst case at 0.8 step size.
To understand the advantage in terms of number of cell searches we again consider a one millisecond pre-detection integration period. With 0.8 step size, we need only 10230*(1/0.8) = 12788 cells in the first step and around 36 cells (assuming 3 chip ambiguity and 1/12 chip step) in the second step. This is a huge reduction in the number of cells to search for the acquisition (which requires 0.1 chip step for the same loss with Direct AltBOC). When compared to the 0.5 chip stepping case which requires 20460 cell searches, we obtain an improvement of about 37%.
**System description**
In this section we describe the acquisition engine architecture to realize the Direct AltBOC acquisition and the |VE2+P2| methods. Figure 8 shows the Direct AltBOC acquisition architecture. is the code search step size used for stepping the energy search. As discussed earlier this value is typically 0.083 chips. Once the decision is made, the control is handed over directly to the tracking process.
Figure 9 shows the architecture with addition of VE and P correlation values when the sampling frequency is such that it enables us to provide the required code delay D between the samples used for the addition. This is the case with sampling frequency of 122.76 MHz which can be used to realize the required D = 0.167 chips (every alternate sample). Observe that the architecture does not use any additional correlators compared to the previous approach. Also note that can be as large as 0.8 as discussed earlier.
**Probability of detection and mean acquisition time evaluation**
Figure 10 shows the average probability of detection for BPSK and AltBOC. Note that the difference between AltBOC =0.5 and the BPSK =0.5 reduces to around 2.2 dB in this case.
Figures 11 and 12 provide the theoretical and simulated average probability of detection and corresponding mean acquisition time for the |VE2+P2| method with both =0.5 and 0.8 scenarios. We can see that the average probability of detection for the |VE2+P2| method is worse by 0.4 dB compared to the BPSK case and the |VE2+P2| method outperforms the Direct AltBOC approach by about 2.2 dB. Also, observe that the mean acquisition time for the |VE2+P2| method with =0.8 chip step performs better than the BPSK case with =0.5 at a given C/N0.
Legends for Figures 11 and 12: i. BPSK theoretical, ii. AltBOC =0.5 theoretical, iii. |VE2+P2| =0.5 theoretical, iv. |VE2+P2| =0.8 theoretical, v. BPSK simulation, vi. AltBOC =0.5 simulation, vii. |VE2+P2| =0.5 simulation, viii. |VE2+P2| =0.8 simulation.
**Conclusion**
In this paper we discussed the complexity and problems with the Galileo E5 signal acquisition and revisited different strategies which address these problems. We analysed the probability of detection and the mean acquisition time for these strategies especially concentrating on the |VE2+P2| method along with the acquisition engine architecture.
For the same probability of detection, compared to the Direct AltBOC approach, the |VE2+P2| method results in an improvement in C/N0 of about 2.2 dB in the average scenario and about 5.3 dB in the worst case scenario. In addition an interesting observation shows that the correlation loss in the |VE2+P2| method remains constant for chip step sizes from 0.5 to 0.8 which, when exploited, reduces the mean acquisition time by 37%. We conclude that |VE2+P2| method is a good candidate for implementation in Galileo E5 receivers.
**Acknowledgements**
The authors would like to acknowledge that this research work has been carried out under the Australian Research Council (ARC) project DP0556848.
**References**
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