Abstract
Nowadays, civil Global Navigation Satellite System (GNSS) signals are available in both L1 and L5 bands. A receiver does not need to acquire independently the signals in both bands coming from a same satellite, since their carrier Doppler and code delay are closely related. Therefore, the question of which one to acquire first rises naturally. Although the common thought would tell the L1 band signals which are narrowband, an accurate comparison has never been done, and the decision is not as easy as it seems. Indeed, L5 band signals have several advantages such as stronger power, lower carrier Doppler, or a pilot channel, unlike the Global Positioning System (GPS) L1 C/A signal. The goal of this paper is therefore to compare the acquisition of L1 and L5 bands signals (GPS L1 C/A and L5, Galileo E1 and E5a/b) to determine which one is more complex and by which factor, in terms of processing time and memory, considering hardware receivers and the parallel code search. The results show that overall the L5 band signals are more complex to acquire, but it depends strongly on the conditions. The E5 signal is always more complex to acquire than E1, while the L5 signal can have a complexity close to the L1 C/A in some cases. Moreover, precise assistance providing accurate Doppler could significantly reduce the L5 complexity below the L1 complexity.
Keywords: acquisition, complexity, Galileo, GPS, GNSS, hardware receiver
1. Introduction
The first stage of a Global Navigation Satellite System (GNSS) receiver is the acquisition, whose aim is to detect the signal and roughly estimate the code delay and the carrier frequency [1]. This is a computationally demanding operation since there are numerous possibilities to test, and today’s receivers are targeting higher and higher sensitivities and the ability to process more and more signals. Nowadays, Fast Fourier Transforms (FFT) are omnipresent in acquisition architectures to accelerate the acquisition, and the amount of memory needed is a major factor in a design [2].
There are now several signals available per constellation, and it is not necessary to acquire the different signals coming from one satellite independently. Indeed, considering two signals coming from the same satellite (for example Global Positioning System (GPS) L1 C/A and L5 signals): They are synchronized (the primary codes start at the same time, and the data and secondary code transitions are synchronized) [3]. The path traveled is the same, therefore the code delay is about the same (there is a slight difference due to the ionosphere that affects them differently [4]. However, knowing one gives precious information on the second); the relative speed being the same, the Doppler are proportional with a known factor (even with the offset due to the local oscillator). Therefore, the main question is: “Which signal should be acquired first?”, to then help the acquisition of the other(s) signal(s). This paper aims to answer this question, and quantify it with application examples.
The answer to this question is not so simple, because each signal has its own advantages and drawbacks. For example, L5 band signals, such as the GPS L5 and Galileo E5 signals, have a high chipping rate (10 times higher than L1 frequency signals). This high chipping rate implies a high sampling frequency, which implies itself a significant amount of samples to store and process, and a lower ratio between the clock frequency of the acquisition process and the sampling frequency leading to a longer processing time [5]. Therefore, L1 band signals, such as the GPS L1 C/A and Galileo E1 signals, are much more interesting on this side, since there is potentially a factor five or ten in the number of samples to process and in the processing speed, thanks to the ratio of the processing and sampling frequencies. Moreover, the L5 and E5 signals have longer primary codes than the L1 C/A and E1 signals, which a priori implies the testing of more code delays, larger FFTs for the correlations, and a bigger amount of memory to store correlation results.
However, the L5 band signals also have advantages: (1) They have a higher power (1.5 dB for the pilot channel of the L5 signal compared to the L1 C/A signal, and 2 dB for the E5a/b signals compared to the E1 signal for the pilot channels), which means that similar detection performance can be obtained with lower integration times; (2) They have a pilot channel, whereas the GPS L1 C/A signal does not have one, therefore this lasts one must limit its coherent integration time, which can lead to a longer total integration time; (3) They have a lower carrier Doppler and Doppler rate (115/154 ≈ 75%), which can reduce the search space and some constraints for the acquisition architecture; and (4) They have a secondary code, which on one side complicates the acquisition, but on another side makes the data synchronization much easier, simplifying the transition to the tracking.
The goal of this paper is therefore to compare in detail the acquisition of the L1 and L5 bands signals, in terms of processing time and memory requirements. More specifically, the GPS L1 C/A and L5 signals, and the Galileo E1 and E5 signals will be considered since these are the only signals in these two bands defined in an official interface specification and broadcasted currently. Two cases will be considered, one where there is no assistance at all (equivalent to a cold start), and one there is enough assistance to determine the secondary code delay, such that the receiver does not need to search it (kind of warm start). Indeed, it is relatively easy to have an estimate of the current secondary code chip. One chip of the L5 or E5 secondary codes lasts 1 ms, which is equivalent to 300 km. Therefore, if the receiver has an estimate of the current time better than 1 ms and an estimate of its position and of the satellites position better than 300 km (achievable with almanac), it is possible to estimate the current secondary code chip, and thus there is no need to search it via a correlation. If an estimate is available but not so accurate, the number of possibilities can still be reduced, e.g., to three or four, instead of 20 or 100.
The remainder of the paper is organized as follows. Section 2 describes briefly the GNSS signals considered, summarizes their characteristics, and introduces the acquisition search method chosen (parallel code search) and the elements of interest. Section 3 provides mathematical expressions of the processing time and the memory requirements for all the possible implementations: Data channel verses pilot channel, assistance verses no assistance, coherent integration only verses use of non-coherent integration, parallel verses semi-parallel verses serial implementation. Then, Section 4 describes the methodology used for the comparison, details all the parameters selected, and compares the acquisition of the GPS L1 C/A and L5 signals, and the acquisition of the Galileo E1 and E5 signals by evaluating the expressions given in Section 3. Finally, Section 5 summarizes the outcomes.
5. Conclusions
This paper performed a very detailed comparison of the complexity of the acquisition of L1 and L5 bands signals, to determine which signal should be acquired first to then help the other, to verify the common thought that L5 band signals acquisition is more complex, and especially to quantify this ratio.
Such detailed comparison is needed because many parameters influence positively or negatively each band and each signal, such as the chipping rate, the sampling frequency, the carrier frequency, the length of the primary and secondary codes, the signal power, or the availability of a pilot channel; it is therefore difficult to make accurate estimation.
In a first part, general expressions of the processing time and memory requirements have been presented and are summarized in Table 2. Such expressions are applicable for any GNSS signal, and depend on several parameters. Some parameters depend on the signal considered, such as the number of samples in one code period (which depends on the code length and sampling frequency), or the length of the secondary code; and some parameters do not depend on the signal considered but depend on the context and design, such as the number of non-coherent integrations or the number of bits used for the quantization.
In a second part, the comparisons have been performed by evaluating the aforementioned expressions. An accurate estimation of the processing time and memory requirements has thus been done, providing all the details of the methodology, and considering many details (such as the search space that influences the probability of false alarm at the cell level and the signal-to-noise ratio required). In order to have a general view and not just one example, the following has been considered: Five sensitivities (from −140 dBm to −160 dBm with a step of 5 dBm); both unassisted and assisted case; and both coherent only integration (when applicable) and the use of non-coherent integration. Studies have been included to evaluate the impact of each element (Table 7 and Table 18).
For GPS, the L1 C/A and L5 signals have been compared. Table 10 and Figure 12 provide the ratio between the complexity of each of them considering the processing time of one frequency bin and the memory requirements, and Table 12 provides the final ratio of complexity which takes also into account the average number of frequency bins browsed until the signal detection. The developments have been validated by Matlab simulations (Table 13). The acquisition of the L5 signal is most of the time more complex. Without assistance, if the sensitivity or the coherent integration time is moderate, acquiring the L5 signal is much more complex (ratios higher than 50 most often, i.e., it may require 50 times more memory, or have a processing time that is 50 times longer, or e.g., 10 times more memory, with a 5 times longer processing time). For very high sensitivity with long coherent integration time, the complexity ratio for one frequency bin is smaller, but still to the detriment of the L5 signal, except at −160 dBm. With assistance, the complexity ratios are smaller for any sensitivity, but only those for unlimited coherent integration time are of interests, since the ratios for one frequency bin become between 0.1 and 4.6. i.e., the GPS L5 signal acquisition may be significantly less complex than the GPS L1 C/A signal one in some high sensitivity cases if only one or few frequency bins that have to be tested (which would require very accurate Doppler assistance). When considering more frequency bins, the L5 signal is more complex to acquire, except few cases.
For Galileo, the E1 signal has been compared with itself first, considering two different sampling frequencies, 4.096 MHz and 6.144 MHz, the first one being close to the minimum and the second one offering the same code loss as a BPSK signals sampled at about twice the chipping rate. Table 19 provides the ratios of complexity, and shows using a sampling frequency of 6.144 triples the complexity most of the time. It is therefore recommended to use the minimum sampling frequency of 4.096 MHz and use techniques to remove the side peaks of the main correlation peak.
Then, the E1 and E5 signals have been compared. Table 20 and Figure 14 provide the ratios of complexity for one frequency bin, and shows that the acquisition of the E5 signal is always more complex. Without assistance, acquiring the E5 signal is much more complex (ratios higher between 25 and 45). With assistance, the complexity ratios are smaller for any sensitivity, the lowest ratios being for unlimited coherent integration times; but the minimum ratio is still around 6 (without considering the input memory, else the ratios increase with the sensitivity), which makes the Galileo E5 signal acquisition significantly more complex than the Galileo E1 one even in the best case. Considering more frequency bins reduces these ratios (Table 22), however the E5 signal is still more complex to acquire.
In conclusion, the GPS and Galileo L5 band signals are overall more complex to acquire than the GPS and Galileo L1 band signals, although in some particular cases the difference may be negligible or limited. In particular, the L5 signal could show better performance in presence of very accurate assistance to avoid a significant increase of the number of frequency bins when using very long coherent integration times.
The methodology and the expressions and developments provided in this paper can be easily used to compare the complexity of current or future GNSS signals in specific cases for a wide variety of hardware implementations.
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