One of the most promising features of the modernized global navigation satellite systems signals is the presence of pilot channels that, being data-transition free, allow for increasing the coherent integration time of the receivers. Generally speaking, the increased integration time allows to better average the thermal noise component, thus improving the postcorrelation SNR of the receiver in the acquisition phase. On the other hand, for a standalone receiver which is not aided or assisted, the acquisition architecture requires that only the pilot channel is processed, at least during the first steps of the procedure. The aim of this paper is to present a detailed investigation on the impact of the code cross-correlation properties in the reception of Galileo E1 Open Service and GPS L1C civil signals. Analytical and simulation results demonstrate that the S-curve of the code synchronization loop can be affected by a bias around the lock point. This effect depends on the code cross-correlation properties and on the receiver setup. Furthermore, in these cases, the sensitivity of the receiver to other error sources might increase, and the paper shows how in presence of an interfering signal the pseudorange bias can be magnified and lead to relevant performance degradation.
In the context of Global Navigation Satellite Systems (GNSS) receivers, the interest on the new modulations that will be used for the modernized GPS L1C and Galileo E1 Open Service (OS) civil signals grew rapidly in past years. The definition of new signals structure results from an agreement between the European Commission and Unites States of America. A common Multiplexed Binary Offset Carrier Modulation (MBOC) signal baseline has been adopted, with the aim of assuring the compatibility and interoperability between GPS and Galileo systems [
One of the main features of the modernized civil and open access signals is the presence of the pilot channels. Pilot channel has been introduced to allow the receivers to perform coherent integration over a long time, without facing the issue of unpredictable data transitions. As a consequence, the receiver is able to acquire satellite signals at lower SNR than the nominal value. In order to deal with such a need in current GPS receiver, assistance data have been defined and standardized [
In this paper, the distortion of the discrimination function (S-curve) due to codes cross-correlation properties is assessed, considering the features of the modulation schemes adopted in Galileo E1 OS and GPS L1C civil signals and also investigating different receiver configurations (reception of data/pilot channels, variable correlators spacing).
This article is based on the preliminary results presented in [
After this introduction, the paper is organized as follows: Section
The MBOC signal baseline assures more power to the high-frequency spectral components if compared to the baseline BOC(1,1) and BPSK(1) modulations. This feature leads to a sharpener code correlation peak allowing to achieve improved tracking performance [
Both Galileo E1 OS and GPS L1C signals include two channels: the pilot signal, without any data message, that is spread by a ranging (pseudo-random noise—PRN) code; and the data channel, spread by a ranging code and modulated by a data message. At the receiver side, it is possible to consider only one of the two channels in order to exploit peculiar characteristics, as for example, if long integration times have to be used. The Galileo and the GPS signals differ on the modulation formats (CBOC versus TMBOC), on the data/pilot power allocations and on the code properties. Concerning the signals in space, it must be remarked that both the signals will be received with the same total power, that is −157 dBW [
In addition, codes belonging to different families (memory codes for Galileo E1 OS signals, Weil codes for GPS L1C) will be used by the two systems in tiered code structures featuring different lengths, as summarized in Table
Galileo E1 OS and GPS L1C code lengths.
Transmitted Channel | Code Length [chips] | Tiered Code Duration [ms] | ||
---|---|---|---|---|
Primary | Secondary | |||
Galileo E1 OS Spreading Codes |
|
4092 | — | 4 |
|
4092 | 25 | 100 | |
GPS L1C Spreading Codes |
|
10230 | — | 10 |
|
10230 | 1800 | 18000 |
The differences in terms of code properties, modulation formats (and consequent different spectral occupation), and relative power levels are then expected to lead to different system performance. As an example considering the levels of interference robustness, it has been noticed that receiving only a single channel in case of continuous wave interference [
The main features of the E1 Open Service signal can be summarized as follows: 50% power split between data ( optimized memory codes; use of a tiered code structure including 4 ms primary and 100 ms secondary codes on the pilot channel.
Both pilot and data channel components take advantage of the CBOC(6,1,1/11) modulation: each PRN code chip is shaped by a weighted combination of BOC(1,1) and BOC(6,1) spreading symbols.
The chip shapes (normalized with unitary power) of the two Galileo E1 OS channels are reported in Figure
Chip shape of Galileo E1 OS data channel (in blue) and pilot channel (in green), CBOC modulation (BOC(1,1)
The theoretical autocorrelation functions computed on single chip of data (
Theoretical CBOC circular correlation functions computed on single chip. Chip shape: BOC(1,1) ± BOC(6,1).
In order to obtain unitary autocorrelation peaks, Figure
Assuming now to demodulate the received signal (data and pilot channels) by using only the pilot component (local signal replica), the resulting correlation function
The corresponding discrimination function is depicted in Figure
Discrimination function (coherent Early-Late, spacing Δ = 1 chip) and its zoom, obtained using a single chip of the Galileo E1 OS signal and varying
It is then possible to conclude that the intrinsic CBOC correlation and discrimination functions always appear symmetrical, regardless to the data/pilot relative power levels. Possible biases around the lock point will be due to other effects (codes cross-correlation impact), as it will be demonstrated in the following sections.
The L1C signal, similarly to the Galileo E1 OS, consists of a data ( 75% of power in the pilot component for enhanced signal tracking; advanced Weil-based spreading codes; use of a long overlay code (18 s) on the pilot channel.
The L1C MBOC implementation modulates the entire data component and 29 of every 33 code chips of the pilot channel with BOC(1,1), while 4 of every 33 pilot channel chips with a BOC(6,1) waveform. The code chip shapes for the BOC(1,1) data channel and the TMBOC(6,1,4/33) pilot channel are shown in Figure
Code chip shape of GPS L1C data channel (in blue) and pilot channel (in green), due to the BOC(1,1) and TMBOC(6,1,4/33) modulations. PRN codes are neglected.
The optimized L1C signal has been designed to assure interoperability with Galileo E1 OS signal. The unequal power split improves the pilot tracking threshold by 1.87 dB compared with a 50% power split used in Galileo. It has been shown that a TMBOC pilot usage extends most of the advantages exploited by BOC(1,1) by more than 1 dB over BOC(1,1). The L1C modulation has been introduced to enhance the signal robustness in critical environments [
The TMBOC implementation assures a MBOC-like spectrum, but implies a slightly different correlation function with respect to the Galileo E1 CBOC case. Notice that, using this kind of waveform, it is not possible to repeat the previous analysis concerning the theoretical S-curve for a single code chip: the TMBOC is in fact defined over a sequence of 33 chips. In order to obtain meaningful correlation and discrimination functions, it is necessary to use a whole code period.
Two are the signal elements that affect the discrimination function shape: the modulation and the code. While the former has already been investigated in the previous section, the impact of the code is the focus of the current one.
Both the Galileo E1 OS and the GPS L1C signals are taken into account, with specific analyses on how different code families can affect the shape of the discrimination function. In detail the memory codes (introduced for Galileo E1 OS) and the Weil codes (specific for GPS L1C) will be discussed.
Memory codes are foreseen for the Galileo E1 OS signal [
It must be noted that, in spite of what happens for the Gold codes used by the GPS L1 current signal [
In addition, as explained in [
Proceeding with our analysis, the discrimination function of the Galileo E1 OS CBOC signal (obtained correlating only the pilot channel) might present an asymmetry and a change in the slope around the zero lag. An example is given in Figure
Discrimination function (coherent Early-Late, Δ = 1 chip) and its zoom, obtained for a Galileo E1 OS signal using memory codes (4 ms primary codes, PRN 1). Received signal: both data and pilot channels, local signal: pilot channel only. The S-curve does not result symmetrical around the zero lag (bias = 6.61 m).
The codes foreseen for the GPS L1C TMBOC signal are Weil codes [
Also in this case, in spite of what happens for the Gold codes, the auto- and cross-correlation functions of the PRNs (
The effect of the Weil codes on the S-curve is again the introduction of an asymmetry caused by the cross-correlation contribution. In this case, due to the code length (10 ms, instead of 4 ms memory codes), the impact on the discrimination function results attenuated. This can be derived by observing Figure
Data (blue line) and pilot (green line) auto-correlation functions, data/pilot cross-correlation function (red line), obtained for a GPS L1C signal using Weil codes (10 ms, PRN 1 data and pilot channels).
The cross-correlation term is not symmetrical, but the impact is this case is reduced. This is due to the fact that Weil codes are longer (10 ms) and consequently present better correlation properties. In fact, the longer the codes, the smaller the cross-correlation functions they have. This fact causes in a lighter effect on the S-curve asymmetry. The price to pay is that longer integration times are needed to align the local code with the incoming signal.
Simulating the GPS L1C signal with the PRN 1 Weil codes for data and pilot channels, the discrimination function in Figure
Discrimination function (coherent Early-Late, Δ = 1 chip) obtained for a GPS L1C signal using Weil codes (10 ms, PRN 1). Received signal: both data and pilot channels, local signal: pilot channel only. The S-curve does not result symmetrical around the zero lag (bias = 0.09 m).
As previously outlined, in addition to the code and modulation features, the actual impact of cross-correlations on the discrimination function also depends on the receiver setup. Several parameters and architectural choices, including the correlator type and spacing, can lead to discrimination functions with different shapes and slopes in the lock point, affecting the receiver performance. A complete analysis of the shape and the slope of this discrimination function with MBOC signals has then been performed varying the correlator spacing and considering the well-known coherent early-late discriminator.
Simulation results obtained using a Galileo E1 OS-like signal are presented in Figure
Theoretical coherent Early-Late discrimination function (a) and its zoom (b) varying the correlator spacing (Δ) and considering only the pilot channel of Galileo E1 OS (CBOC modulated chip without code cross-correlation effect,
Observing the slope around the lock point in Figure
A detailed analysis on the changes of the S-curve slope has been performed varying the spacing with a tiny step in the range (0, 1] chip. The results are shown in Figure
Theoretical S-curve slope varying the correlator spacing, considering both data and pilot channels of a Galileo E1 OS-like signal (CBOC modulated chip without code effect,
It is easy to observe from Figure
Previous analyses have been repeated also using a GPS L1C-like signal. The shape of the S-curve for the pilot channel (TMBOC modulation) using arbitrary spacings is depicted in Figure
Theoretical coherent early-late discrimination function (a) and its zoom (b) varying the correlator spacing (Δ), considering only the pilot channel of a GPS L1C-like signal (TMBOC modulation,
A detailed analysis of the S-curve slope varying the spacing has been performed considering both data and pilot channels of GPS L1C, as reported in Figure
Theoretical S-curve slope varying the correlator spacing, considering the data and pilot channels of a GPS L1C-like signal (BOC and TMBOC modulations,
On the other hand, the S-curve slope obtained using the pilot channel (TMBOC modulation) shows a similar behavior than the results with the Galileo pilot. In addition, as in the CBOC case, a variation on the early-late spacing does not lead to an inversion on the S-curve slope. These two cases are also compared in Figure
Comparison between theoretical slopes of the discrimination function varying the correlator spacing (Δ) and considering only the pilot channels of a GPS L1C-like signal (TMBOC modulation,
The slopes in Figures
The distortion induced by the cross-correlation of the channel not locally processed is not just threatening for the bias induced, but also the sensitivity to other error sources might increase. In this section, we show how the presence of an interfering source induces larger errors than expected. In order to compare the results, the interference error envelope (IEE) defined in [
IEE result for Galileo E1 OS and GPS L1C signals in presence of CW interference and are then presented in Figures
Interference Error Envelope comparison assuming different correlator spacings (Δ = 1 ÷
Interference Error Envelope comparison assuming different correlator spacings (Δ = 1 ÷
Observing the results in Figure
This effect can be explained taking into account previous remarks about code features and receiver setup. As previously shown in Figure
Similar results have been obtained simulating a GPS L1C-like pilot channel in presence of a CW interference (see Figure
In this case, the asymmetry on the envelope can be noticed only for the spacing
In conclusion, it must be remarked that both using Galileo E1 OS and GPS L1C signals the code cross-correlation distortion on the S-curve can be magnified by an inappropriate choice of the correlator spacings and it can lead to noticeable worsening in receiver performance in presence of an interfering signal. Such an effect can be noticed only in case of receiving a single channel (i.e., the pilot channel), whereas it is not present if the received signal is correlated with a coherent local replica including both data and pilot channels.
A comparative analysis of GPS L1C and Galileo E1 OS signals has been performed, pointing out how, when only the pilot channel is locally received in order to perform acquisition with long integration times, the residual cross-correlation due to the unprocessed channel cannot be neglected. Analytical and simulation results have been presented in order to demonstrate that in such a case the discrimination function can be affected by a bias around the lock point. The distortion can be noticed only in case of receiving a single channel (i.e., the pilot channel), whereas it is not present if the received signal is correlated with a coherent local replica including both data and pilot channels. It has also been shown how the distortion of the S-curve increases the sensitivity to other error sources, as for example to the presence of interfering signals. Moreover, the paper demonstrated that, in this case, inappropriate choices of the correlator spacing can lead to a discrimination function with reduced slope, thus enhancing the vulnerability of the receiver.