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Code and Carrier Phase Tracking Performance of a Future Galileo RTK Receiver Thomas Pany, Markus Irsigler, Bernd Eissfeller Institute of Geodesy and Navigation, University FAF Munich, Germany Jón Winkel IfEN GmbH, Munich, Germany

INTRODUCTION The Institute of Geodesy and Navigation of the University of the Federal Armed Forces (FAF) Munich takes part in a project to develop a future real-time kinematic (RTK) receiver capable of tracking navigation signals broadcasted from the modernized GPS and Galileo. One important point in this project is the assessment of the pseudorange code and phase accuracy of the new navigation signals. It determines the achievable positioning accuracy, a very high code accuracy can potentially improve the success-rate of resolving the integer ambiguities of the phase measurements [6], and it is of importance for the stability of the signal tracking process. Tracking of GPS signals has been extensively discussed in the literature but the results are often not directly applicable for the new signals. Especially binary offset carrier (BOC) signals, which might be part of Galileo as well as of the modernized GPS, need to be investigated in more detail. We implement in Matlab/Simulink and C a simulation of parts of a global navigation satellite system (GNSS) receiver, consisting of the radio frequency (RF) frontend and of the tracking channel. The frontend simulation yields bandlimited signals at the intermediate frequency (IF) and includes the bandpass filter in the satellite and receiver. The simulation of the tracking channel tries to be close to a software correlation (SWC) receiver. We implement standard tracking techniques which have been developed for GPS signals and assess their performance in the new signal environment. No new techniques, (e.g. new multipath mitigation techniques) are discussed here. The simulation gives us the possibility to directly assess the accuracy of the new signals. However, to gain more insight and a deeper understanding we also use and develop analytical formulas and methods. We investigate the pseudorange code and phase measurement accuracy due to thermal noise and due to multipath, both being the two most important accuracy limiting factors. We will also show that for highest precision applications the formula for the ionospheric carrier phase advance should be adopted for BOC signals and we discuss the possibility to track single side-lobes of the BOC signal spectrum.

FUTURE NAVIGATION SIGNALS A future RTK receiver will face a signal scenario outlined in [10], [4] and [9]. The signals differ in many parameters like carrier frequency, modulation scheme and data rate such that at a first glance for each signal a detailed analysis should be performed. However, signal tracking and the multipath performance depend to a large extent only on the modulation scheme. Other parameters are of less importance, resp. their influence can be easily included. Thus we subdivide all signals according to their modulation scheme into binary phase shift keying (BPSK) and BOC signals. The first type of signals is described by the code rate (or chipping rate) fc and is denoted as BPSK( fc ). BOC signals are characterized additionally by the subcarrier frequency fs and are denoted as BOC( fs, fc ). Both constants are multiples of 1.023 MHz.

Tab. 1 Considered Galileo and GPS signals Signal L1 E2-L1-E1, OS E5a E2-L1-E1, PRS

Frequency [10.23 MHz] 154 154 115 154

Min. Rec. Power [dBW] Typical C/N0 [dBHz] -160 45 -155 50 -155 50 -155 50

Modulation BPSK(1) BOC(2,2) BPSK(10) BOC(14,2)

Code Chip Length [m] 293.05 146.53 29.31 146.53

Data Rate [bit/s] 50 200 50 1000, DF

From the GPS and Galileo signals we select four to demonstrate the methods developed in the following sections. The signals are listed in Tab. 1. Each of the signal is representative for all those future navigation signals having the same modulation scheme (with respect to the code and phase measurement accuracy and multipath performance). The well known L1 C/A code signal uses a BPSK(1) modulation scheme which will also be used by the future L2 civil signal. A BPSK(10) modulation scheme is used by the currently emitted P code on L1 and L2, by the future L5 signal and by the Galileo E5a and E5b signal. A BOC(2,2) signal might be modulated on the Galileo E1-L1-E2 carrier and could be part of the open service (OS), a BOC(14,2) might be modulated on the same carrier and could be part of the public regulated service (PRS). It should be emphasized that the first three signals of Tab. 1 are representative for all freely accessible signals of the modernized GPS and Galileo. Thus they are of special importance for a future civil RTK system. Although the BOC(14,2) will be most likely part of the PRS we include it in our analysis too, because it shows the most complex autocorrelation function (ACF) and the most significant difference to the well known BPSK signals. For all signals we choose a minimum received power and a data rate listed in Tab. 1. Also data-free (DF) channels are considered. For Galileo signals it should be noted that these values are only preliminary. The relation of the typical signal-to-noise ratio C/N0 to the minimum received power can be determined by looking at a L1 C/A-code receiver, which shows typical C/N0 values of 45 dBHz. Thus the difference between C/N0 and the minimum received power is -205 dBWs if a minimum received power of –160 dBW is assumed for the current L1 C/A code signal.

GPS/GALILEO RECEIVER SIMULATION To gain insight into the process of tracking the new navigation signals and to assess their performance we implement a Matlab/Simulink simulation of a GNSS receiver. The simulation consists of two parts which run at a different sample rate. The simulation of the receiver frontend runs at a high sample rate of 12.6 GHz sufficient to simulate all effects at the RF level. The simulation of the tracking channel runs at a sample rate being about 10-40 MHz and mimics a SWC receiver. The division of the tracking process into 2 parts is based on writing the emitted satellite signal s(t) as

s (t ) =

∞

∑c

k

p(tf c − k ) .

(1)

k =−∞

The time is denoted as t, the pseudo random noise (PRN) code sequence is ck and p(φ) is the single chip function. For example if a BOC signal is considered p(φ) takes the form

p(φ ) = 2rect(φ )sign(sin(2πφ f s / f c )) cos(2πφ f RF / f c ) .

(2)

The carrier frequency is fRF , the code rate is fc and the subcarrier frequency fs. The function ‘rect’ represents a rectangular pulse of unit amplitude and duration. Bandpass filtering of the signal within the satellite to keep the power spectral density within the allocated frequency band is not included in (1). However, it will be included in the receiver frontend (cf. Fig. 1).

The signal s(t) is a convolution of the code sequence ck with the waveform of a single chip p(φ). Therefore it is sufficient to consider the effect of ionospheric delays, filtering and even down conversion on p(φ) only. This simplifies the calculations since p(φ) is different from 0 only if 040 dBHz. The carrier phase could not be tracked for C/N0 values below 32 dBHz and cycle slips occur. Fig. 7 shows the same graph (upper blue line and red circles plus error bars) for the E2-L1-E1 BOC(14,2) signal and three different PLL discriminators. Again (10) resp. (13) is a reasonable well approximation. Note however, that here the simulation time is only 10 s, causing larger error bars compared to Fig. 6.

Fig. 6 E5a pseudorange phase measurement accuracy plotted as a function of signal-to-noise ratio. The blue line refers to (10), the red circles plus error bars to the MC simulation.

Fig. 7 E2-L1-E1, PRS pseudorange phase measurement accuracy plotted as a function of signal-to-noise ratio. The blue lines refer to (10) and (13), the red circles plus error bars to a MC simulation of an arctan discriminator (11), the green circle plus error bars to a MC simulation of an arctan2 discriminator and the black circles plus error bars to a MC simulation of a coherent PLL (12). Tracking of Data-Free Channels The modernized GPS and Galileo will broadcast navigation signals, where only the code is modulated on the carrier frequency but no data. The main benefit of such data-free channels is that there is no need for the phase discriminator to eliminate the unknown data bit. If Ip denotes the punctual I-channel value and Qp the punctual Q-channel value the output of an arctan phase discriminator Sph is given by

S ph = atan Q p I p

(11)

and the division removes the unknown data bit [3]. As a negative consequence another tracking point occurs at 0.5 cycles, besides the point at 0 cycles. This ambiguity can be reduced by replacing the ‘arctan’ function in (11) with an ‘arctan2’ function which gives the arc tangent of Qp/Ip, taking into account which quadrant the point (Qp, Ip) is in. Thus the discriminator output can be twice as large as in the case of (11) without causing cycle slips or a loss-of-lock. Equivalently one can say, that the tracking error threshold of the PLL is increased by 6 dB [4]. The performance at low C/N0 values can be further improved if a coherent phase discriminator described by

(n f RB (0) )

S ph = Q p

(12)

is used [12]. In that way the so-called squaring loss is avoided and the variance of the phase measurements is approximately given by (cf. [12]) 2 σ Ph =

c2 4π

2

2 f RF

BPLL C / N0

(13)

.

Fig. 7 and Fig. 8 show the improved tracking quality of the arctan2 discriminator and of the coherent discriminator. We track the identical IF signal with three independent tracking channels. The first channel is equipped with an arctan phase discriminator (11) and an early-power minus late-power code discriminator, the second one with an arctan2 phase discriminator and an early-power minus late-power code discriminator and the third one uses a coherent phase discriminator (12) and a coherent early minus late code discriminator. In Fig. 8 two cycle slips (at 3 s and 4.2 s) occur in the first (arctan) tracking channel which do not show up in the other two tracking channels. In Fig. 7 the pseudorange phase measurement accuracy as a function of signal-to-noise ratio is shown. The accuracy is determined from a MC simulation running 10 times, each time for 1 s. Only points without cycle slips are shown. One sees that the arctan2 and the coherent PLL can track the signal at a lower signal power. Furthermore (10) and (13) are a reasonable good description of the measurement accuracy, but longer simulation runs are necessary to get a better accuracy especially at low C/N0 values.

Fig. 8 E2-L1-E1, PRS estimated phase pseudorange plotted as a function of time for a signal-to-noise ratio of 27 dBHz. The blue line refers to an arctan phase discriminator (11), the green to an arctan2 discriminator and the red line to a coherent phase discriminator (12).

Ionospheric Influence On BOC Signals The influence of a homogeneous ionosphere on GPS navigation signals has been well examined [11]. In a mm accurate approximation, neglecting scintillation effects and terms of the order f -n, n>2, the ionosphere increases the measured code pseudorange and decreases the phase pseudorange by the following values 40.3TEC 40.3TEC BPSK BPSK . (14) I CODE = =− and I CODE 2 2 f RF f RF The constant TEC is the total electron content along the signal propagation path. Both formulas refer to the carrier frequency fRF. Since BOC signals, especially the BOC(14,2), have the maximum power spectral density at the left and right edge of the allocated frequency band, one might ask if (14) is still valid. Furthermore one could ask if the code correlation function (4) is deformed by the ionosphere, such that code tracking is not possible for high TEC values. Both problems have been investigated in [13] and it is shown that the code correlation function does not change its shape significantly even for high TEC values. As a result code tracking is not affected by the ionospheric influence. Furthermore, the standard formula (14) for the ionospheric code delay gives the delay with mm accuracy. The conclusions are different for the ionospheric phase advance since the phase measurement error due to thermal noise is usually of the order of 1 mm. Therefore it is suggested to replace the standard ionospheric advance formula (14) by BOC I PHASE =−

 40.3TEC  1 1 +   2 f RF  f RF − f s f RF + f s 

(15)

to account for the separation of the two main peaks of the BOC signal spectrum. The process of carrier phase tracking itself (cycle slips, signal-to-noise ratio) is not negatively influenced by the ionospheric advance.

SIDE-LOBE TRACKING In addition to conventional code tracking (ACF tracking) of BOC signals described above, tracking of just one peak of the BOC spectrum (i.e. side-lobe tracking) has been suggested in various places in the literature, especially in the context of signal acquisition. This method will be described in the following, but no simulation, as in the case of ACF tracking, has been performed. This will be performed within the near future. For BOC signals like the BOC(14,2) with extreme spectrum splitting, side-lobe tracking might be a useful means to monitor the ACF tracking for false locks in the code correlation function RB. The procedure described in [1] and [8] involves filtering the side-bands and then acquiring them. However, it can be shown that this side-band filtering is not necessary. Not having to implement a special side-band filter has many advantages: 1) lower implementation complexity and 2) no additional distortions are introduced, which is especially important when switching between sideband and ACF mode. Side-band tracking can be realized by correlating the BOC signal with a reference signal, which is only modulated by the code (i.e. without the square-wave). This can of course not happen on the carrier frequency fRF, i.e. on L1 in the case of the BOC(14,2) as the code and the code with the square-wave are perpendicular. The reference signal must have a different frequency. An IF fIF different from zero must be chosen and the PLL of Fig. 2 must be initialized with a nonvanishing frequency offset even in the case of no Doppler shift. Intuitively one would assume the correct frequency offset somewhere near the maximum of the spectral side-lobes, although it is not obvious exactly for what reference frequency a correlation will happen. Therefore the frequency offset must be introduced as an unknown in the analysis, which makes the whole derivation very lengthy. Suffice it to say that this analysis can be done and the result is that a correlation does, in fact, occur at the offset frequencies, i.e. at fIF ± nfs, n being an integer. Note that these frequencies do not correspond to the maximum of the spectral side-lobes. The maximum of the spectral side-lobes at IF level are located at approximately

1  f max ≈ f IF ±  n / 2 + 2 π 

 n2π 2 − 6  f s . 

(16)

0.7

0.6

Normalized correlation function

0.5

0.4

0.3

0.2

0.1

0

-0.1

-0.2 -1

-0.5

0

0.5

1

Delay in [chips]

Fig. 9 Correlation function between the code alone and a BOC modulated code. The blue and red curve correspond to the real part of a BOC(2,2) and a BOC(14,2). The magenta and the green curve are the corresponding imaginary parts. In Fig. 9 the theoretical correlation functions at the carrier offset are shown for BOC(2,2) and BOC(14,2) signals. Note that the imaginary part is not zero for this kind of cross-correlation. Further note that the amplitude of the correlation function in Fig. 9 is larger than 0.5, meaning that more than half the available power in the signal is received. There are points in the correlation functions where the derivative is zero. This could potentially become a problem when constructing the S-function. Therefore care must be taken when choosing the correlator spacing, as a bad choice might result in a S-function with zero slope at the tracking point (see also Fig. 5). Another concern is that even with a proper choice of d, the tracking loop might get stuck on one if those plateaus. This, however, is not a stable state and noise and other fluctuations would rapidly ‘kick’ the tracking loop off the zero slope.

MULTIPATH PERFORMANCE The presence of multipath signals generally results in ranging errors (code multipath) and carrier phase errors (carrier multipath). The actual ranging or carrier phase errors error depend on various signal and receiver parameters: ♦ Signal type (e.g. rectangular chip shape, raised cosine, binary offset carrier) ♦ Signal bandwidth ♦ Code rate ♦ Relative power levels of multipath signals (signal attenuation α due to reflection) ♦ Actual number of multipath signals ♦ Geometric path delay of multipath signal ♦ Correlator spacing d (early minus late) ♦ Type of discriminator (e.g. early minus late, early-power minus late power, dot product) ♦ Carrier frequency fRF (carrier multipath)

Within the framework of this paper, the main focus will be drawn to the code multipath performance of the signals described above. The influence of multipath will be illustrated by means of multipath error envelopes. In these diagrams, the resulting ranging errors are plotted as a function of the geometric path delay (i.e. the geometric path length difference between the direct and the delayed signal component). The computation of multipath error envelopes is based on the assumptions, that the direct signal component is always available (no shadowing effects), that only one multipath signal is present and that the multipath signal undergoes an attenuation of 3 dB (α=0.5) [17].

In addition to the multipath environment, the multipath performance strongly depends on the characteristics of the incoming signal, namely signal type, signal bandwidth and code rate fc. Signal type and bandwidth determine the shape of the signal’s correlation function RB. The correlation functions for the signals discussed above are illustrated in Fig. 3. and can be used to set up the corresponding code discriminators, i.e. the S-functions (7). Although different types of discriminators can be implemented, the following analyses base on the assumption that an early minus late discriminator is used. This type of discriminator is obtained by subtracting a late copy of the correlation function from a corresponding early copy. The correlator spacing between early and late code is set to d=0.05 for all signals, thus allowing an intuitive comparison of each signal’s multipath performance. The code discriminators which are used to determine the code multipath performance are illustrated in Fig. 4. Pseudorange determination is generally performed by tracking the zero-crossing of the code discriminator. The presence of multipath signals results in a shift of the tracking point along the x-axis. The resulting offset ∆R can be deemed to be the ranging error caused by the multipath signal. This effect is illustrated in Fig. 10 for the BOC(2,2) signal. There, a multipath signal with a relative path delay (PD) of 0.25 chips (dotted blue line) superimposes with the direct signal component (solid blue line). As a result, the resulting discriminator (dashed red line) which is used to track the incoming signal is obviously distorted. Additionally, a significant shift ∆R of the zero-crossing (tracking point) along the x-axis can be observed. The resulting multipath error ∆R in chips can be converted to m by simply multiplying with the code chip length c/fc. The multipath error envelopes for each type of signal can be computed by constantly increasing the geometric path delay of the multipath signal (beginning with a relative path delay of 0 m) and determining the corresponding zerocrossing offset ∆R. The error envelopes have been computed twice, firstly for a multipath carrier phase shift of 0° with respect to the direct signal component and secondly for a shift of 180°. These computations were carried out for the four signals listed in Tab. 1. The results are summarized in Fig. 10. While maximum multipath errors occur for the BPSK(1) signal, the BOC(14,2) shows the most promising multipath performance with ranging errors less than 2 m. The BPSK(10) and the BOC(2,2) signal exhibit similar maximum ranging errors. As already mentioned, multipath performance is also characterized by the sensitivity in terms of relative path delay. With respect to this criterion, the BPSK(10) signal shows the best performance being sensitive only for multipath signals with a relative path delay of less than 30 m. The BPSK(1) signal, however, is sensitive for multipath signals with a relative path delay of up to approximately 300 m.

Fig. 10 Deformation of an early-minus-late discriminator by the influence of multipath (left2) and multipath error envelopes for the BPSK(1), BPSK(10), BOC(2,2) and BOC(14,2) signal. The correlator spacing between early code and late code is d=0.05 for all signals.

2

The correlator spacing has been set to d=0.25 for visualisation purposes

The illustration of the multipath error envelopes in Fig. 10 is based on a very narrow correlator spacing. Since the multipath error envelope for each signal was computed by using identical values for the correlator spacing (d=0.05), the multipath performances can be easily compared. On the other hand, the use of narrow correlator spacing together with short code chip lengths (as it is the case for the BPSK(10) signal) might not be feasible because these two parameters define the tracking threshold of the DLL. This threshold is directly proportional to the correlator spacing d and the code chip length c/fc. Thus, further examination is required to determine optimum correlator spacing for each signal.

CONCLUSIONS A set of techniques (MC simulation, analytical formulas and algorithms) has been developed to assess the performance of BOC and BPSK navigation signals. The techniques have been applied to assess the performance of a future GNSS receiver tracking a selection of signals. The pseudorange code measurement accuracy due to thermal noise has been analyzed by an analytical formula and by a MC simulation. Both methods are in an excellent agreement. The accuracy has been calculated as a function of the discriminator spacing and the optimal spacing with respect to thermal noise can be extracted. Note that other design parameters (e.g. DLL tracking stability) might give other values and in the receiver design process a compromise must be found. The pseudorange phase measurement accuracy due to thermal noise is evaluated for a BPSK(10) and for a BOC(14,2) signal via a MC simulation. The results are in a reasonable agreement with the well known formula for a Costas phase discriminator (10) resp. for a coherent phase discriminator (13). Both do not depend on the modulation scheme. The performance gain of an arctan2 phase discriminator and of a coherent phase discriminator to track data-free channels at low signal-to-noise ratio values was demonstrated. For BOC signals an adopted formula for the ionospheric advance is given and the possibility to track only one side-lobe of the BOC signal spectrum (i.e. side-lobe tracking) has been outlined. The code multipath performance has been derived by algorithms analyzing the code correlation function (4) which was generated via the simulation of the GNSS receiver frontend. This provides an easy way to generate the bandlimited correlation functions. The multipath envelopes for the 4 different signals have been compared under the assumption of an identical discriminator spacing. We conclude that tracking of BOC signals is possible with techniques developed originally for BPSK signals. The performance of the BOC signals (especially code multipath and code accuracy) is quite different as compared to the well known GPS signals. Consequently the new signals must be evaluated in more detail as well as the possibility to implement new tracking techniques. In addition to that also other parameters (e.g. acquisition, navigation data demodulation, interference, tracking stability, carrier multipath, …) must be considered to assess the overall performance of a future RTK system.

ACKNOWLEDGMENTS The investigations and developments of a future GNSS RTK receiver are supported within the scope of the research project FKZ: 50NA0003 in contract with DLR.

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