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**Combining Secondary Code Correlations for Fast GNSS Signal Acquisition**

*Jérôme Leclère, René Jr Landry, LASSENA, École de Technologie Supérieure (ÉTS), Montreal, Canada*

**Location:** Cypress

Although bringing some notable advantages, the secondary codes present in modern GNSS signals are challenging for the acquisition process. Indeed, there is now a potential transition between each period of the primary code, which complicates the correlation over the primary code; and if high sensitivity is required the acquisition should synchronize with the secondary code as well. This adds a third dimension to the acquisition search space, in addition to the primary code delay and to the Doppler frequency.

Several methods have already been proposed to increase the coherent integration time when there is a secondary code. Basically, they can be classified in two categories: 1. those with long coherent integration times, which requires to synchronize with the secondary code and implies a significant computational burden. 2. Those with a very short coherent integration time, testing all the possible combinations for the secondary code. Since the number of combinations grows exponentially, the coherent integration time stays limited in this case.

Therefore, there is no current effective solution for intermediate coherent integration time, to enable a higher sensitivity while keeping the complexity reasonable. In this paper, we propose a method to address this problem. The idea is to combine secondary code correlation results to reduce the number of secondary code delays to test and thus reduce the complexity, in exchange of a loss in the signal-to-noise ratio (SNR) compared to the full secondary code correlation. What is interesting, it’s that since the length of the secondary codes is relatively short (e.g. 20 chips for the L5 pilot signal, 25 chips for E1 pilot signal), these combinations can be performed in an optimal way, to minimize the SNR loss and to maximize the complexity reduction. The goal of this paper is thus to present the different ways of performing these combinations.

The paper first presents the complexity of the secondary code correlation when the coherent integration is perform over 1 to 4 periods of the primary code, i.e. 1 to 4 chips of the secondary code, and when the coherent integration is performed over one period of the secondary code. Then, it introduces the principle of combining secondary codes correlation results, the impact on the SNR, and how it reduces the complexity. Then, the paper discusses the constraints associated with the possible combinations, and their impact on the performance. Two parameters are particularly important: the delay between the correlation results combined, and the pattern of the combinations.

For example, the L5 secondary code of the pilot channel is 20 chips long, therefore we may combine the results for the delays 0, 5, 10 and 15 ; 1, 6, 11 and 16 ; 2, 7, 12 and 17 ; 3, 8, 13 and 18 ; 4, 9, 14 and 19. In this case the delay between the correlation results combined is 5. In the paper, we discuss the cases where the delay is a divisor of the secondary code length, where the delay is coprime to the secondary code length, or where it is neutral (i.e. neither a divisor nor a coprime), because each case provides different performance.

Continuing on the previous example, the combination of the correlation results can be done in different ways using additions and subtractions : 0+5+10+15, 0–5+10–15, 0–5+10–15, or something less regular such as 0–5+10+15. When the pattern of these combinations is made of consecutives + + or + –, the complexity is decreased as the square of the number of results combined. For other patterns, the complexity is decreased by a lower factor, and when there is no pattern there is no additional complexity reduction rather than the reduction of the number of delays.

Finally, some combinations provide the same maximum peak whatever the incoming secondary code delay, and some not.

All these constraints are thus studied to determine which ones are interesting and which ones are not.

In conclusion, the idea of combining correlation results for different secondary code results reduces the complexity in exchange of a loss. The goal is that the reduction of the complexity is higher than the loss. For example, with the L5 signal, it is shown that it is possible to combine two correlations results to reduce the complexity by at least 4, for an equivalent integration time of 12 ms instead of 20 ms, i.e. a reduction by a factor of 1.6. All the possible combinations are studied and compared to determine the best ones for the L5 and E1 pilot signal.

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