Testing GPS L5 Acquisition and Tracking Algorithms Using a ...

Testing GPS L5 Acquisition and Tracking Algorithms Using a Hardware Simulator C. Mongrédien, G. Lachapelle and M.E. Cannon Position, Location and Navigation (PLAN) Research Group Department of Geomatics Engineering Schulich School of Engineering University of Calgary

BIOGRAPHY Cécile Mongrédien is a PhD candidate in the Department of Geomatics Engineering at the University of Calgary, Canada, where she is a member of the Position, Location and Navigation research group. In 2004, she graduated from ENAC (French University for Civil Aviation), Toulouse, France, as an electrical engineer majoring in digital communications. Her research includes GPS modernization as well as GNSS receiver design. Dr. Gérard Lachapelle holds a CRC/iCORE Chair in Wireless Location in the Department of Geomatics Engineering. He has been involved with GPS developments and applications since 1980 and has authored/co-authored numerous related publications and software. More information is available on the following website: http://plan.geomatics.ucalgary.ca. Dr. Elizabeth Cannon is Dean of the Schulich School of Engineering at the University of Calgary. She has been involved with GPS research since 1984 and has published numerous papers on static and kinematic positioning. She is a Past President of the ION and the recipient of the 2001 Kepler Award. ABSTRACT The ever increasing demand for navigation and location services has fostered the need for higher performance Global Navigation Satellite Systems (GNSSs). The GPS L5 signal, part of the US effort to modernize GPS, was designed to respond to the above demand in terms of measurement accuracy, tracking robustness and tracking sensitivity. These improvements were achieved through the design of a more efficient signal structure. However, in order to fully exploit these improvements, new architectures have to be designed for the acquisition, tracking and data demodulation processes.

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This paper focuses on acquisition and tracking. First, a cascaded acquisition algorithm is proposed. The first step, referred to as coarse acquisition, is used to estimate the Doppler frequency and PRN code delay of all the visible satellites. The second step, referred to as fine acquisition, is then used to estimate the NH code delay and refine the Doppler frequency estimate. In order to do so, an intermediate tracking step, meant to remove the residual Doppler frequency prior to NH code alignment, is introduced. An innovative data/pilot combined tracking algorithm is then introduced. This algorithm coherently recombines the data and pilot correlators’ output prior to the implementation of a common discriminator and loop filter. This implementation enables optimal noise mitigation (as the noise samples are independent and combined prior to any non-linear operation) and alleviates the problem of half-cycle slips occurrence on the data channel. INTRODUCTION The US government plans to augment the only fully operational civil GPS signal (GPS C/A) by implementing two new civil signals on the GPS satellites to be launched in the coming years. The GPS L2C signal will be implemented on the Block IIR-M satellites. The two first IIR-M satellites were successfully launched in September 2005 and September 2006 (although the latter has not been brought online). The GPS L5 signal will be implemented on the Block IIF satellites. The first IIF satellite launch is currently scheduled for March 2008. The GPS L5 signal, designed to support safety-of-life applications such as aviation navigation, is the focus of this paper. It was designed to provide improved inherent multipath and narrow-band interference mitigation capacities, as well as improved tracking and data demodulation sensitivity.

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As described in the following section, GPS L5 has a data (I5) and a pilot (Q5) channel that are perfectly synchronized and orthogonal. The pilot component is implemented to enable more robust carrier tracking and facilitate re-acquisition in degraded environments. To provide more reliable data demodulation, Forward Error Correction (FEC) is applied to the navigation message on the I5 channel. NH codes are modulated on top of the PRN on each channel. Introduced to improve narrowband interference mitigation capacities, they also improve cross-correlation amongst spreading codes and facilitate data bit synchronization. To be fully beneficial, such a new signal structure calls for new receiver structure in terms of acquisition, tracking and data demodulation. Especially, different strategies can be envisioned for GPS L5 Pseudo-Random Noise (PRN) and NH code acquisition. Furthermore, various data/pilot combining strategies can be investigated both at the acquisition and tracking stages. Finally, the use of an FEC on a new navigation message format necessitates a completely new data decoding algorithm. The latter aspect, however, is beyond the scope of this paper which focuses on implementing and testing GPS L5 acquisition and tracking algorithms. The major innovations brought by GPS L5, with respect to GPS C/A signal structure, are, in light of acquisition, the additional NH code modulation and the use of a pilot channel. Accordingly, focus will be given on finding optimal ways to acquire the NH code and to recombine the data and pilot channel power. In terms of tracking, the presence of the NH modulation is not a major concern anymore; the focus then becomes to optimize the use of the pilot and data channel in terms of noise mitigation and resistance to cycle slips. The performance of the proposed acquisition and tracking schemes are then evaluated using a GPS L5 hardware simulator. GPS L5 SIGNAL STRUCTURE The GPS L5 signal is fully described in the GPS L5 Interface Control Document (IS-GPS-705 2005) and only its main characteristics are summarized herein. The L5 signal is transmitted at 1176.45 MHz with a minimum specified received power of -154.9 dBW, equally shared between the two quadrature components. The structure of the signal is given by:  d (t )c XI (t )NH 10 (t ) cos(2πf L 5 t + φ )  s(t ) = 2 P    + c XQ (t )NH 20 (t )sin (2πf L5 t + φ ) 

(1)

Where • P is the total power of the received GPS L5 signal, • d is the binary Non-Return to Zero (NRZ) materialization of the navigation message encoded with a convolutional FEC,

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• c XI and c XQ are the binary NRZ materialization of data and pilot PRN code respectively, • NH 10 and NH 20 are the binary NRZ materialization of the data and pilot NH code respectively • f L 5 is the L5 carrier frequency, and • φ is the time-varying carrier phase delay (in radians). As illustrated in Equation 1, each of the two quadrature components, referred to as I5 and Q5, is bi-phase modulated with a different PRN of length 10230 chip. The PRN codes are generated at a 10.23 MChip/s rate, resulting in a 1 ms period. For the I5 component, the PRN code is further modulated by the navigation message and a 10-bit NH sequence (NH10 = 0000110101). For the Q5 component, the PRN code is further modulated by a 20-bit NH sequence (NH20 = 00000100110101001110). Each bit of the NH sequences is 1 ms, resulting in a 10 and 20 ms NH10 and NH20 sequence respectively. Note that, due to the FEC encoding, the data channel will be transmitting the encoded navigation message at a 100 Hz rate in order to maintain an effective navigation message rate of 50 Hz. The data and pilot channel being perfectly synchronized, it is then possible to transmit the NH10 and NH20 sequences in perfect alignment with the 10 ms data symbols and the 20 ms data bits respectively. The L5 PRN codes are generated from two different maximum length sequence generator, XA and XBi, of 13 stages each. XA generates a truncated sequence of 8190 chips and XBi a sequence of 8191 chips. Both sequences are modulo-2 added to generate a 10230 chip length L5 sequence. Note that, due to their desired length, the L5 PRN codes are not Gold Codes. As such, their crosscorrelation properties are not optimal. However, owing to their increased length, and to a careful selection of initial stages, they provide a minimum isolation 2.5 dB better than current GPS C/A code, as illustrated in Table 1. Table 1: GPS L5 Code Isolation Properties Minimum Side Peaks Minimum Cross-Correlation Protection [dB] Peaks Protection [dB] R(I,I) R(Q,Q) C(I) C(Q) C(I,Q) Without NH codes -29.2 -29.0 -26.4 -26.4 -62.1 With NH codes -29.7 -29.4 -27.7 -27.5 -62.1 R(I,I) = auto-correlation of all I5 codes, R(Q,Q)= auto-correlation of all Q5 codes, C(I)= cross-correlation vs. all I5 and Q5 codes, C(Q)= cross-correlation vs. all I5 and Q5 codes, C(I,Q) = cross-correlation of (I,Q) pair.

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The pilot channel allows significant phase tracking sensitivity gain. The absence of data enables the use of a pure PLL (i.e. the carrier tracking no longer needs to be insensitive to 180 degree phase shifts) and of longer coherent integration time. The NH codes help to further spread the power across the spectrum by narrowing the code spectral line separation from 1 kHz to 100 Hz and 50 Hz in the data and pilot channel respectively, enhancing the GPS L5 signal mitigation capacities against narrow-band interferences. Additionally, they improve the spreading code cross-correlation properties, and make the data bit synchronization more robust. It is important to underline that, even though the NH code improves the minimum isolation over 1 ms coherent integration, i.e. in the [-5115; +5114] chips range, it creates several secondary peaks when the correlation is taken over the full I5 or Q5 spreading sequences (that is the NH-modulated PRN sequences). As underlined in Ries et al. (2002) and Macabiau et al. (2003), these peaks create a risk for biased acquisition, as they are only 14 dB lower than the main peak. This 14 dB separation is obtained assuming no frequency error. However, due to their short length, the NH code correlation properties are greatly affected by residual Doppler. As demonstrated later in this paper, in presence of frequency errors as small as 30 Hz, this side peak protection is dramatically reduced. HARDWARE SIMULATOR AND TEST SET-UP To fully realize the potential of GPS L5, new acquisition and tracking algorithms will be introduced herein. However, in the absence of any operational GPS satellite that transmits on the L5 frequency, it is necessary to use a signal simulator to test and verify these algorithms. The relevance of this testing is, obviously, conditioned by the faithfulness with which the simulator can replicate a typical GNSS environment. To this end, the use of a hardware simulator provides the best opportunity so far. Its ability to individually simulate any component of the GNSS error source budget provides the levels of flexibility, controllability, and reproducibility necessary to validate receiver algorithms. The Spirent GSS 7700 hardware simulator is used herein to simulate the GPS L5 RF signals. However, the GPS L5 software developed in the frame of this research takes IF samples as its input. To this end, a NovAtel Euro-L5 card is used as an RF frontend to output the digital I and Q samples at 28 MHz. These IF samples are then buffered using an Altera UP-2 FPGA development board and stored using a National Instrument Data Acquisition (NI-DAQ) card in a PC. This set-up is shown in Figure 1. A rubidium clock is used to provide the time reference.

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Figure 1: Test Set-Up It is important to remember that, in terms of error generation, the main concern for acquisition and tracking is a change in the signal characteristics during coherent integration time. This implies that, at this stage, satellite clock and ephemeris errors or atmospheric errors will have a negligible impact. On the other hand, thermal noise and multipath can significantly impair the receiver’s ability to acquire and track a given PRN. Even though simulation of specular multipath is possible with the hardware simulator, this was not done herein. Conversely, the emphasis was on assessing the impact of noise. To this end, the same simulation was run several times using various power levels. It is possible to access, through the hardware simulator, the GPS L5 signal powers received by the user’s antenna. However, to provide greater insight, their carrier-to-noise ratio (C/No) is approximated using the Euro-L5 card (which is also a four-channel L5 receiver) tracking output. GPS L5 ACQUISITION GPS L5 acquisition is considered here as the rough estimation of the incoming signals’ local carrier and local code. It is possible to define the local codes as the PRN codes only, or as the NH-modulated PRN codes. The latter definition is taken herein, as the NH code alignment is required to proceed to a useful tracking state (that is, one that includes navigation message decoding). Several NH code acquisition strategies have been investigated in the past (Tran & Hegarty 2002, Macabiau et al 2003, Yang et al 2004). They can be classified in two broad categories, the combined and cascaded schemes. The combined schemes try to acquire the PRN and NH code delays in a single step. This can be done on the pilot channel since, in the absence of data bit transitions, the Q5 spreading sequence is fully periodic. However, as will be illustrated in a later section, this approach suffers from very stringent frequency requirements that either increase the computational load tremendously, or significantly degrade the NH codes correlation properties (increasing the risk of false acquisition). This approach was previously discussed in Tran & Hegarty (2002) and Hegarty et al (2003). However, the authors fail to address this frequency issue. The cascaded schemes, on the other hand, implement acquisition in two steps. The first step aims at roughly estimating the Doppler frequency and PRN code delay of the visible satellites while the second step provides the NH code delay and a refined Doppler frequency estimate. This latter approach, investigated in

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Macabiau et al (2003) and Yang et al (2004), is followed herein. Note, however, that the acquisition scheme investigated here is intended to mimic a ‘cold start’ acquisition; if the receiver were in re-acquisition mode or possessed some a priori time and/or frequency information, the combined scheme would certainly be worth pursuing. GPS L5 COARSE ACQUISITION The GPS L5 coarse acquisition is very similar to the traditional GPS C/A acquisition. Indeed, both processes can be seen as a two-dimensional search in time (code delay) and frequency over a given uncertainty region. The signal detection is then based on a hypothesis testing that can be summarized as hypothesis H1, the signal is present and hypothesis H0, it is not. The two type of error associated with this statistical test, namely the false alarm and miss, can be traded against each other but never jointly minimized. The acquisition strategy studied here is the Single Dwell Time Search (SDTS) described in Holmes (1990). The full uncertainty region is searched to locate the maximum correlation peak. If this peak exceeds a certain threshold, the system can proceed to the next phase; if not, the satellite is declared absent. The threshold is typically computed based on the desired probability of false alarm, and on the observed noise level under hypothesis H0. It is important to recall that hypothesis H1 and H0 refer to each individual bin, and not to the full search space. As a consequence, if the list of visible satellites is unknown, there is a high statistical risk that the noise will be, in some bins, higher than the calculated threshold. In such cases, additional steps, such as those described in Kaplan (2006) for the Tong Detector or the M of N Detector have to be implemented. This is not shown herein, as the results for the SDTS provide sufficient insight about GPS L5 detection performance. Now that the classical acquisition theory has been reviewed, some words about the specifics of the GPS L5 acquisition are in order. First, some particular implementation aspects will be discussed, and then, the statistical detection performance will be addressed. Coarse Acquisition Implementation It is important to note that, during the coarse acquisition step, the coherent integration time is constrained to exactly 1 ms by both the PRN code period and the potential NH bit transitions. However, because the PRN code alignment is yet to be performed, destructive summations during this coherent integration are still possible. To circumvent this problem, a zero-padding strategy has been described by Yang et al (2004) and is implemented herein. By correlating 2 ms of incoming signal with 1 ms of locally generated samples appended

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by 1 ms of zero, it is possible to ensure that a full one-ms correlation peak will be found in the first millisecond of the resulting correlation. It is possible to find a correlation peak in the second millisecond of the correlation but this peak will be non-existent or highly degraded in the presence of NH bit transition(s). The SDTS was originally described in the time domain; however, it is possible, in software receivers, to implement it in the frequency domain (Yang, 2000). This is done here to speed up the correlation process, as, in the frequency domain, all possible code offsets can be searched in one operation. To further improve the efficiency of this algorithm two additional steps are taken: (1) the FFTs of all the local PRN codes are computed and stored offline, and (2) the Doppler removal is implemented simultaneously for all the satellites by applying a circular shift on the FFT of the incoming signal. It is important to underline that, by performing the Doppler removal in the frequency domain, the potential effects of code Doppler variation are supposed negligible. These effects are rarely considered in GPS C/A acquisition; but, because GPS L5 has a faster chipping rate and a lower carrier frequency the code Doppler to carrier Doppler ratio drops from 1540 for GPS C/A to 115 for GPS L5. It is then of major importance to assess the impact of such effects on the correlation. In the case at hand, the coherent integration is limited to 1 ms and the maximum Doppler error due to satellite motion is less than 4 kHz. Under such conditions, it can be shown that the maximum possible error is 0.03 chips; entailing negligible resolution and/or power loss in terms of PRN code phase acquisition. In fact, it has been shown in Bastide (2004) that, provided the coherent integration time remains limited to 1 ms, the code Doppler effects can be neglected up to 200 ms total pre-detection time. Statistical Detection Performance Considering a static receiver, and assuming no receiver clock drift effect, the uncertainty region is set to [-4; +4] kHz and [0; 10229] chip in the frequency and time domain respectively. As suggested in Bastide (2004), to account for the fact that the GPS L5 uncertainty region is approximately ten times bigger than that of GPS C/A, the probability of false alarm is set to 10e-4 instead of 10e-3, as is typically used for GPS C/A. The benefits of recombining the power of the data and pilot channels were demonstrated in Bastide et al (2002) and are summarized herein. The non-coherent combining algorithm is illustrated in Figure 2. Note that, in addition to non-coherently summing the data and pilot correlators’ output every millisecond, M non-coherent summations can be used to further improve the post-detection Signalto-Noise Ratio (SNR).

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Figure 2: GPS L5 Coarse Acquisition Structure The correlator outputs after 1 ms coherent integration can be written as (Holmes 1990): sin (πε f ,k TP ) P ~ cos(ε φ ,k ) + nIP ,Data ,k Dk R (ε τ ,k ) πε f ,k TP 4 sin (πε f ,k TP ) P ~ QPData (k ) = Dk R (ε τ ,k ) sin (ε φ ,k ) + nQP ,Data ,k (2) πε f ,k TP 4 sin (πε f ,k TP ) P~ IPPilot (k ) = R (ε τ ,k ) cos(ε φ ,k ) + nIP ,Pilot ,k πε f ,k TP 4 sin (πε f ,k TP ) P~ QPPilot (k ) = R (ε τ ,k ) sin (ε φ ,k ) + nQP ,Pilot ,k πε f ,k TP 4 IPData (k ) =

showed that the worst case would happen if crosscorrelation occurred on both the data and pilot code simultaneously, resulting in a 19 dB-Hz cross-correlation peak. Although seldom encountered in real life, this worst case cross-correlation is accounted for herein, and results in a shift of the test statistic distribution under H0. Finally, note that the theoretical detection performance results displayed in Figure 3 account for the effects of front-end filtering, but not for those of code delay and Doppler uncertainty. The latter, however, would merely result in a left-shift of the curves that can easily be assessed based on code and frequency resolution. Zero-padding effects included, the Doppler removal offers a 500 Hz frequency resolution; while the 28 MHz complex sampling rate provides a 0.35 chips code resolution. This leads to a maximum frequency and code error of 250 Hz and 0.18 chips respectively; or, in terms of power degradation to a 0.9 dB and 1.8 dB loss respectively.

Where: • Dk is the sign of the k-th navigation data bit, ~

• R is the correlation of the local spreading code with the filtered incoming one, • ε τ ,k is the k-th code group delay error, • ε f , k is the k-th frequency (Doppler) error, • ε φ , k is the k-th phase error, • n IP , Data ,k , nQP , Data, k , n IP , Pilot ,k and nQP , Pilot , k are independent Gaussian noise with equal power, +∞ N No ~ 2 Pn = G ( f ) H ( f ) df = R (0) o , ∫ 4TP −∞ 4TP • G ( f ) is the normalized GPS L5 Power Spectrum Density (PSD), and • H ( f ) is the Fourier transform of the front end filter. The correlators’ output noises being Gaussian, the test statistic will follow central and non-central chi-square distribution under hypothesis H0 and H1 respectively. This result will hold true for both the single and noncoherently combined scenarios; as well as for different numbers of non-coherent summations. Note that, intrasystem cross-correlation peak being the main cause of false alarm during the acquisition, the test statistic is made more robust by assuming the presence of a crosscorrelation peak due to a strong interfering satellite in the incorrect bins (that is, under H0). Hegarty et al (2003)

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Figure 3: Probability of Detection versus total C/No using a 1 ms coherent integration time. In accordance with Bastide et al (2002), the acquisition threshold, using a 1 ms coherent integration time, 15 noncoherent integrations, and a non-coherent combining scheme, is found to be approximately 34 dB-Hz. Note, however, that in order to maximize the available power, a potentially superior strategy, referred to as coherent combining, was introduced in Yang et al (2004). This algorithm relies on the perfect orthogonality of the data and pilot channels. By definition the pilot channel is a quarter of a cycle late with respect to the data channel; however, in the presence of the navigation data bits, this results in the pilot channel being either a quarter of a cycle ahead or behind the data channel. This implies that after Doppler removal our data and pilot correlation outputs are either aligned or in phase opposition. It is then possible to recombine them prior to squaring, according to these two hypotheses, and select the one with the highest amplitude. This strategy reduces the squaring losses; however, because the recombining of the data and

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pilot channel has to be done in every bin of the search space, the noise floor level is raised. To illustrate this increase and compare the performance of these two combining methods, the post-detection deflection coefficient is computed for both strategies for various C/No. The deflection coefficient is defined in Kay (1993) and is used to exactly characterize detection performance of mean-shifted Gaussian problem, or approximate them in other cases. It can be expressed as: d2 =

[E (T / H1 ) − E (T / H 0 )]2 var(T / H 0 )

(3)

Empirical deflection coefficients are shown in Figure 4 and illustrate a noticeable improvement for the coherent over non-coherent combining. Note that the deflection coefficients shown herein were calculated and then averaged over 10 s of incoming samples, using 1 ms coherent integration and no additional non-coherent summation. The latter strategy is thus recommended here.

Combined with a 100 K sky temperature, the resulting noise density is approximately -200 dBW-Hz, i.e. 5 dB more than that of GPS C/A (ibid.). This means that, all things being added, the generic C/No (available for acquisition) will be approximately 44.1 and 46.5 dB-Hz on L5 and L1 respectively. In other words, the generic power, as seen by the receiver after front-end filtering and down conversion, is expected to be higher on L1 than L5. However, it is important to remember that GPS L5 PRN codes offer improved correlation properties that will reduce the risk of false acquisition. Furthermore, even though the interference environment is expected to be heavier on L5 than L1 (both frequency bands are protected aeronautical frequency band), the use of NH synchronization sequence will help reduce the impact of narrow-band interferences on GPS L5, ensuring that GPS L5 meets the aviation requirements on acquisition threshold and time to first fix (Bastide 2004). False Frequency Lock So far, the cross-correlation issue was discussed in the time domain (that is, based on the correlation properties of the PRN codes). This analysis, however, overlooked the potential occurrence of cross-correlation in the frequency domain. Along the frequency axis, the ratio between two neighbouring peaks can be determined using the power roll-off function. This function derives from the sinc term in Equation 2 and is illustrated in Figure 5. It can be seen that this ratio, assuming no noise and no code delay uncertainty, will vary between 0 dB and 4 dB depending on the location of the true Doppler frequency with respect to that of the different search bins.

Figure 4: Acquisition Sensitivity for Single and Combined Channel Scenario As illustrated in Figure 3 and Figure 4 the detection performance is directly related to the C/No of the searched signal. While the C/No seen by the receiver will vary based on testing environment and implementation losses, a generic comparison between GPS L5 and C/A signals is proposed here. The minimum specified power to be measured above 5o elevation at the output of a 3 dBi linearly polarized antenna (located near ground) is -154.9 and -158.5 dBW for GPS L5 and C/A respectively (ISGPS-200 2006, IS-GPS-705 2005). Furthermore the full GPS L5 power is equally split between the data and pilot channel, implying a minimum transmitted power of -157.9 dBW on each individual L5 channel. While it is possible to recombine the power of both channels, both coherent and non-coherent implementations entail losses that limit the recombining gain to approximately 2 dB. Additionally, GPS L5 will suffer increased front-end filtering losses due to its wider PSD (Hegarty et al 1999).

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Figure 5: Correlator Output along the frequency axis, at the correct PRN code delay In presence of noise, this separation does not provide satisfying detection performance. This problem is particularly sensitive in the case of L5 because of the NH modulation. Indeed, until the NH code is acquired, it is impossible to increase the frequency resolution by increasing the coherent integration time as could be done

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with GPS C/A. This phenomenon will be revisited in greater details in light of the fine acquisition. FINE ACQUISITION Assuming a successful (and unbiased) coarse acquisition, the PRN code phase offset is known within [-0.2; +0.2] chip and the PRN Doppler frequency within [-250; +250] Hz. The next required step is then to acquire the NH code phase offset. In order to do so, the complex onems coherent integration peaks need to be correlated with the local NH codes. This is somewhat similar to a coherent integration over the full NH codes’ period and thus necessitates a reduction of the frequency uncertainty. More explicitly, it can be seen, upon examination of Equation 2, that the effects a frequency error on the complex correlation peaks will be: (1) a power degradation due to the sinc term, and (2) a phase rotation due to the sin and cos terms. As shown in Macabiau et al (2003), and illustrated in Figure 6, this significantly degrades the NH code correlation for frequency error as small as 30 Hz.

Doppler) that may be encountered using the direct NH alignment strategy (especially if several non-coherent summations are needed for the PRN correlation peak extraction). In light of the above, the first strategy is adopted herein. More specifically, a one-ms FLL-based tracking is implemented prior to the NH code acquisition. It would be possible to recombine the data and pilot channel so as to increase the overall SNR. However, due to the presence of unknown data bit transitions on the data channel, and to the discrepancies in the NH codes period, it was decided here to perform this fine acquisition step, based on the pilot channel only. The resulting power loss is expected to be relatively small. Indeed, using one 20 ms coherent integration, instead of non-coherently summing four 10 ms coherent integrations should result in an approximate 1 or 2 dB loss. Furthermore, this implementation enables direct and simultaneous acquisition of the NH20, NH10 and data bit boundary; whereas a combined scheme would not give the NH20 bit boundary, requiring an additional step if coherent integration longer than 10 ms are envisioned. Finally, it benefits from the fact that, when compared to that of the NH10, the NH20 correlation properties exhibit superior characteristics due to the presence of 14 null correlation points surrounding the main peak. PRN-ONLY TRACKING To validate the use of an intermediate tracking step, it is of major importance to ensure that: (1) the pull-in range of the FLL and DLL encompass the frequency and code delay uncertainty at the output of the coarse acquisition, and that (2) the lock threshold of both loops are above the calculated acquisition threshold. Once this is accomplished, issues regarding its optimization and duration will be addressed.

Figure 6: NH20 Correlation Properties in Presence of Frequency errors To reduce the frequency uncertainty, two methods have been previously introduced. The first one, introduced by Macabiau et al (2003), implements a PRN-Only tracking step prior to NH code phase acquisition. This step is introduced to ensure minimal frequency error and thus preserve the NH correlation properties. The second method, suggested in Macabiau et al (2003), and further investigated in Yang et al (2004), implements the NH code alignment directly after the coarse acquisition. The Doppler removal is performed at the correlation stage by generating the local NH code at various frequencies within a [-250; +250] Hz range, using 25 Hz steps. However, as the latter implementation only addresses the phase rotation effect, it produces poorer results. Furthermore, the former implementation helps alleviate the PRN correlation peak migration issue (due to code

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Pull-in Range and Sensitivity Analysis The FLL pull-in range is mainly determined by the discriminator and coherent integration time used. While the coherent integration time is constrained to 1 ms, several FLL discriminators are available. Two of them are compared herein, namely the decision oriented crossproduct (Kaplan 2006), and the arctangent discriminators. It is important to note that some common discriminators, such as the cross or the extended arctangent (Kaplan 2006), are missing. This stems from the necessity to design discriminators that are insensitive to NH bit transition. The aforementioned discriminators can be written, in units of cycle per second, as (Kaplan, 2006): sign(dot ).cross (4) DCP = 2πTP a tan (cross / dot ) (5) D A tan = 2πTP Where, assuming no external disturbance,

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cross = IPk −1QPk − IPk QPk −1 Dk Dk −1 sin (2πε f ,k TP ) dot = IPk −1 IPk + IPk −1QPk Dk Dk −1 cos(2πε f ,k TP )

The output of these discriminators is shown in Figure 7. It can be seen that both discriminators have a pull-in range of [-250; +250] Hz, which matches the Doppler uncertainty after the coarse acquisition. However, they both exhibit sharp edges that might cause some problems when the frequency error reaches the limits of the pull-in region, as will be discussed later. The DLL pull-in range is determined by the Early-Late spacing used. As specified earlier the code phase offset is known within a range of [-0.2; +0.2] chips, constraining the Early-Late spacing to values greater than 0.4 chips. While this can appear unusually wide in view of spacing used for GPS C/A Narrow Correlators, one must recall that, in order to be efficient, this technology relies on wide front-end filtering to include the side lobes of the GPS C/A PSD. However, the main lobe of the GPS L5 PSD occupies 20 MHz out of the 24 allocated for GPS at this frequency. As such, Narrow Correlator technology is not applicable to GPS L5 and the Early-Late spacing is set to one chip.

Figure 7: FLL Discriminator Outputs using a 1 ms coherent Integration Time It is a well-known fact that the tracking sensitivity of a receiver is determined by that of the carrier tracking loop. The FLL tracking sensitivity analysis, in turn, can be done using the rule-of-thumb given by Kaplan (2006): 1 (6) 3σ FLL + θ e ≤ 4TP Where θ e is the dynamic stress error, and σ FLL the frequency error standard deviation.

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In the case of a static receiver, the FLL frequency error budget is dominated by noise. In light of the above, and using the theoretical frequency tracking error variance given in Kaplan (2006), Equation 6 can be rewritten as: 3 2πTP

8BL C No

    1 + 1  ≤ 1 C  4TP   TP  No  

Or, equivalently, 9B  C 1 2π 2 ≥ 2L 1 + + No TP 9 B L TP π 

   

(7)

(8)

Where BL is the FLL loop bandwidth. Assuming a 1 ms coherent integration time and a 10 Hz loop filter bandwidth, the FLL loss of lock threshold is 25 dB-Hz, which is well below the acquisition threshold determined earlier. It is important to notice, however, that this threshold is given with respect to each particular tracking channel (one for each satellite) available powerMiriam Lewis Page 8 04/10/2006. In cases where a Binary Phase Shift Keying (BPSK) modulation is used (as for GPS C/A), the signal power is located in a unique channel, and this threshold directly applicable to the signal power. However, in cases where a Quadrature Phase Shift Keying (QPSK) modulation is used (as for GPS L5), the signal power is equally split between two channels, and this threshold only applicable to the available tracking power. If, for instance, a single channel tracking is implemented, the available tracking power is only half of that of the full signal power and the loss of lock threshold becomes, with respect to the full signal power, 28 dB-Hz. It is important to note that, although still well below the acquisition threshold, this tracking sensitivity could be improved if tracking schemes making a better use of the GPS L5 signal power were implemented. This will be described hereafter. Data/Pilot Combined Tracking In order to improve the performance of the PRN-only tracking algorithm, it is possible to implement a data/pilot combined tracking. Such algorithms have been investigated in the past (Hegarty, 1999; Julien, 2005), and several implementations were proposed. They were discussed, however, in light of full tracking (that is, after NH code acquisition). In the context of PRN-only tracking, the situation is much simpler as both channels still exhibit the exact same tracking characteristics. The unique objective is then to improve noise mitigation; which is accomplished using a simple weighted combination of the data and pilot discriminator, on both the code and carrier tracking loop. Note that this combining issue will be addressed in greater detail in full tracking mode.

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Lock Detector and False Frequency Lock It is important, in PRN-only tracking mode, to ensure that the signal is effectively being tracked, prior to any NH code alignment attempt. To this end, Van Dierendonck (1997) introduced a code and carrier lock detector. However, neither is practical here. The C/No estimator relies on noise estimation in different bandwidths, which is only feasible when short and long coherent integration can be implemented; and the carrier lock detector is not applicable to an FLL where the phase can take any value. In light of the above, the following FLL detector was derived and implemented: cross 2 − dot 2 (9) C2 f = cross 2 + dot 2 Assuming, no external disturbance, this equals: C2 f ≈ cos(4πε f ,k TP )

such sign change does degrade the NH20 correlation properties, but only by 2 dB.

(10)

Ideally, an FLL detector locked around 0.95, would guarantee a frequency error less than 25 Hz. However, as illustrated in Figure 8, this detector remains very noisy, even after smoothing. Despite this behaviour, it has been considered that this detector, if not a good frequency error estimator, could still be used as a reliable frequency lock indicator. This detector, unfortunately, cannot detect the 500 Hz offset false lock described hereafter.

Figure 9: NH20 Correlation Power in Presence of Periodic Sign Changes As illustrated in Figure 10, for a strong signal, this degradation is not sufficient to prevent NH code delay acquisition and transition into full pilot-only tracking However, as the NH10 correlation function no longer exhibits a dominant correlation peak, further data decoding operations are impossible. Thus, one way to detect these false locks is to monitor the data C/No and/or carrier lock on the data channel when transiting into full tracking mode. Note that these detectors can be implemented on the data channel regardless of the tracking strategy used (i.e. even in pilot-only tracking mode).

Figure 8: Smoothed FLL Lock Detector versus time for several C/No Looking at Figure 7, it is straightforward to notice that with an input frequency error close to 250 Hz, the FLL discriminator could easily undergo a frequency slip that would result in a 500 Hz tracking error. It can be inferred, looking at Equation 2, that the effects of such false frequency lock will be: (1) a power degradation of about 4 dB due to the sinc term, and (2) a sign change every two milliseconds. As illustrated in Figure 9, the occurrence of

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Figure 10: Pilot (Top) and Data (Bottom) Correlator Output in Presence of Periodic Sign Changes GPS L5 TRACKING Once the NH codes have been acquired, a more accurate and reliable tracking can be envisioned. To this end, the

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use of longer coherent integration time and/or pure PLL tracking is of major interest. Their use is, however, mostly restricted to the pilot channel, as unknown data bit transitions (that is, 180o phase shifts) still occur on the data channel. The problem then becomes to find optimal ways to implement and combine the data and pilot tracking for both code and carrier loops. Data/Pilot Combining As mentioned earlier, it is possible to improve the overall tracking performance of the receiver by implementing a data/pilot combined tracking. This was done, at the PRNonly tracking stage, using a simple weighted sum of the discriminators’ output. However, contrary to the PRNonly tracking mode where both channels required very similar implementations, very different implementation can be envisioned for each channel once the NH alignment has been performed. This, in turn, makes the combining of the two channels more tedious. Indeed, as one endeavours to jointly benefit from the reliability of pure pilot tracking, and the improved noise resistance of combined tracking, critical decisions need to be made. Julien (2005) introduced several discriminator combinations to do so. These combinations, however, provided a diminishing return with decreasing C/No (i.e. when they were the most needed). Because of such restrictions, Ries et al (2002) and Bastide (2004) recommended a pure pilot tracking. This approach, however, reduced the available power by 3 dB. In light of the above, a better combining strategy is desired. As mentioned in Yang et al (2004), in tracking mode the data and pilot channels can be combined at three different stages to drive a single Numerically Controlled Oscillator (NCO): at the discriminator output, at the loop filter output or at the correlator output. The latter approach provides the best noise mitigation performance, as the noises are added prior to any non-linear operations. This approach is similar to the one described in the frame of acquisition. For clarity, the concept is illustrated in Figure 11. After Doppler removal and spreading code wipe-off, the data and pilot correlators’ output are either in phase opposition (Figure 11a) or aligned (Figure 11b). It is then possible to recombine them according to either scenario and select the one with the highest amplitude (highlighted in red in Figure 11). It is then possible to recombine the remaining in-phase and quadrature Early, Prompt and Late correlators accordingly to form the so-called composite correlators.

Figure 11: Data/Pilot Coherent Combining It is important to note that, at this stage, the phase of the pilot correlation is no longer affected by unknown sign change. This implies that, granted it is used as the reference in the discrimination test, it is possible to estimate the sign of the data bit and to remove its effect on the data correlators. The resulting composite correlators recombine the full signal power and are data bit transition-free. The risk of selecting the wrong data/pilot coherent combination supposes very weak correlator outputs that would make any tracking perilous, and, as such, is considered a negligible threat. Also note that, even though this combining strategy requires an additional testing step (to discriminate amongst the two possible coherent summations), this implementation can help reduce the complexity of the tracking as only one discriminator and one loop filter will be needed for each loop. This combining strategy is implemented herein on both carrier and code tracking loop, but only upon convergence of a pure-pilot tracking. A coherent discrimination (i.e. based on the in-phase correlators’ output only) is thus implemented herein. Note that a non-coherent test (i.e. using both the in-phase and quadrature components) would be needed if this strategy were to be applied in FLL and/or PRN only tracking mode. Further details about each individual tracking loop are provided in the next subsections. Carrier Tracking The Pilot-only carrier tracking is initialized here as an FLL, which, after convergence, transits into a PLL. The coherent integration time is set to 10 ms. The use of longer integration, even thought technically possible is avoided at this stage to widen the FLL pull-in range and limit the risk of loss of lock. Once the pilot-only tracking is locked, coherent combining is implemented. Further tuning of the loop filter bandwidth and coherent integration time is then desired. However, since the PLL overall performance is a trade-off between its noise mitigation capacities and its resistance to dynamics and oscillator induced errors, such tuning requires extensive knowledge of the PLL error sources, and has not been performed yet. The atan2 FLL and PLL discriminators were used in both pilot only and combined mode. They can be written as (Kaplan, 2006): a tan 2(cross, dot ) (11) DFLL , A tan 2 = 2πTP a tan 2(QP, IP ) (12) DPLL , A tan 2 = 2π While Julien (2005) underlined the potential drawbacks entailed by the self normalization (especially in light of

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low C/No), these discriminators were selected for their wide linear tracking region and low tracking sensitivity.

very precise carrier aiding should help reduce the impact of dynamics on code tracking, and limit the occurrence of such problem.

Code Tracking As mentioned earlier, it is not possible to implement a Narrow-Correlator on the GPS L5 code tracking loop. As discussed in Betz and Kolodzieski (2000), for a given front-end filter bandwidth, a point of diminishing return will be reached when decreasing the Early-Late spacing. Indeed, as can be seen in Figure 12, front-end filtering tends to round-off the correlation function, deteriorating the separation between the Early and Late value around the peak. To avoid this problem a one-chip Early-Late spacing is implemented herein.

Figure 13: Normalized Dot-Product Discriminator Output using a 1 chip Early-Late Spacing

Figure 12: Impact of Front-End Filtering on the GPS L5 PRN codes correlation function To optimize the code tracking performance, several discriminators and normalization were investigated herein. Following the spirit of the discussion in Julien (2005), it was decided to implement a dot-product discriminator with an Early-plus-Late normalization, as given by: (2 − δ ) . (I E − I L )I P + (QE − QL )QP (13) VDLL ,DP 2 = (I E + I L )I P + (QE + QL )QP 2 Where δ is the Early-Late spacing, in chips. Even though the use of an Early-plus-Late type of discrimination necessitates the use of an additional correlator, this choice was motivated by: (1) the reduction of the squaring losses for both the discriminator and normalization, and (2) the cancellation of the quadratic term in ε τ . As shown in Figure 13, the linear tracking covers the [-0.5; +0.5] chip range. Outside this region, this discriminator offers a less favourable behaviour as it tends to always underestimate the code tracking error. This can make tracking perilous as it implies that the receiver will be unable to correct a growing error. However, the use of a wide Early-Late spacing and of a

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Tracking Results It is important to recall here that the scenario used in the hardware simulator assumed a static receiver located in Calgary. This scenario was run several times over periods of two minutes with various signal power level (ranging from 41 to 50 dB-Hz using 3 dB increments). After correction of the occasional false frequency lock, each of the nine visible satellites could be tracked successfully (i.e. at the simulated frequency) and preliminary navigation message decoding could be achieved (i.e. successful PRN identifications and consistent Z-counts were obtained after FEC decoding and subframe synchronization). The results presented herein, however, focus on the benefits of the data/pilot coherently combined tracking scheme. To this end, results are shown for PRN 15 only, with a simulated C/No of approximately 44 dB-Hz. These results are representative of what is observed throughout the full (visible) constellation and simulated signal powers. The noise mitigation performance of the coherent combining schemes is illustrated in terms of tracking accuracy and C/No in Figure 14 and Figure 15 respectively. It can be observed that the 3 dB gained through coherent combining translates in a less noisy code and carrier tracking. In terms of reliability and sensitivity, it can be seen in Figure 16 that, as for the Pilot channel, the coherently combined correlation is not affected by unknown sign change. In summary, the use of the composite correlators’ output can ensure: (1) an improved tracking accuracy thanks to a higher C/No and the potential use of longer coherent integrations, (2) an increased tracking reliability since the threat of half-cycle slips is completely removed, and that

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of full cycle slips significantly reduced, and (3) an enhanced tracking sensitivity through the use of a pure PLL discriminator.

Figure 16: 10 ms correlator Outputs for the Data, Pilot and Coherently Combined Channels CONCLUSION Several acquisition and tracking algorithms were implemented and tested using a GPS L5 hardware simulator.

Figure 14: Doppler and Code Doppler Estimate in Pilot-Only and Coherently Combined Tracking Mode

The GPS L5 acquisition is greatly affected by the NH codes modulated on top of the PRN, on both the data and pilot channels. Firstly, they restrict the duration of the coherent integration to 1 ms. This, in turn, limits the achievable coherent correlation gain and frequency resolution during PRN code acquisition. Secondly, their correlation properties degrade rapidly in presence of residual Doppler error. To alleviate this problem, an intermediate tracking step is introduced to reduce the frequency uncertainty prior to NH code alignment. Additionally, GPS L5 acquisition also suffers form a degraded C/No (when compared to GPS C/A). This, however, is compensated by an increased PRN code cross-correlation protection and improved narrow-band interference mitigation capacities. A new data/pilot coherently combined algorithm was introduced that enables the use of longer coherent integration time and pure PLL tracking using composite Early, Late and Prompt correlators that recombine the full signal power and are data bit transition-free. This, in turn, is expected to allow a 5 dB gain in tracking sensitivity over GPS C/A (front-end filtering effect included). ACKNOLEDGMENTS The authors would like to thank the Informatics Circle Of Research Excellence and the GEOIDE Networks of Centres of Excellence for their financial support.

Figure 15: C/No Estimate for the Data, Pilot and Coherently Combined Channels

REFERENCES Bastide, F. (2004), Analysis of the Feasibility and Interest of Galileo E5a/E5b and GPS L5 Signals for Use with Civil Aviation, Ph.D. Thesis, Institut National Polytechnique de Toulouse, No 2137. Bastide, F., O. Julien, C. Macabiau, B. Roturier (2002), Analysis of L5/E5 Acquisition, Tracking and Data Demodulation Thresholds, Proceedings of the US Institute of Navigation GNSS (Portland, OR, USA, Sept. 24-27). Betz, J. and R. Kolodziejski (2000), Extended Theory of Early-Late Code Tracking for a Bandlimited GPS Receiver, Navigation: Journal of The Institute of Navigation, Vol.47, No.3, Fall 2000.

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Hegarty, C. (1999), Evaluation of the Proposed Signal Structure for the New Civil GPS Signal at 1176.4 MHz, WN99W0000034, The Mitre Corporation. Hegarty, C., T. Kim, S. Ericson, P. Reddan, T. Morrissey, A.J. Van Dierendonck (1999), Methodology for Determining Compatibility of GPS L5 with Existing Systems and Preliminary Results, Proceedings of the US Institute of Navigation AM (Cambridge, MA, USA, June 28-30) Hegarty, C., M. Tran, and A.J. Van Dierendonck (2003), Acquisition Algorithms for the GPS L5 Signal, Proceedings of the US Institute of Navigation GNSS (Portland, OR, USA, Sept. 9-12) IS-GPS-200 (2006), Interface Specification – Navstar GPS Space Segment / Navigation User Interfaces, ARINC Incorporated, March 2006 IS-GPS-705 (2005), Interface Specification – Navstar GPS Space Segment / Navigation L5 User Interfaces, ARINC Incorporated, September 2005 Julien, O. (2005), Design of Galileo L1F Tracking Loops, Ph.D. Thesis, Department of Geomatics Engineering, University of Calgary, UGCE Report 20227. Kay, S.M. (1993), Fundamentals of Statistical Signal Processing: Detection Theory, Prentice Hall Signal Processing Series.

Ries, L., C. Macabiau, O.Nouvel, Q. Jeandel, W. Vigneau, V. Calmettes and J-L. Issler (2002), A Software Receiver for GPS-IIF L5 Signal, Proceedings of the US Institute of Navigation GNSS (Portland, OR, USA, Sept. 24-27). Tran, M. (2004), Performance Evaluation of the New GPS L5 and L2 Civil (L2C) Signals, Navigation: Journal of the Institute of Navigation, Vol.51, No.3, Fall 2004. Tran, M. and C. Hegarty (2002), Receiver Algorithms for the New Civil GPS Signals, Proceedings of the US Institute of Navigation NTM (San Diego, CA, USA, Jan 28-30) Van Dierendonck, A.J. (1997) GPS Receivers in Global Positioning System: Theory and Applications Volume I, Progress in Astronautics and Aeronautics Volume 164, AIAA. Yang, C. (2000), GPS Code Correlation with FFT under Pseudo-Quadrature Sampling, Proceedings of the US Institute of Navigation NTM (Anaheim, CA, USA, Jan. 26-28) Yang, C., C. Hegarty, and M. Tran (2004), Acquisition of the GPS L5 Signal Using Coherent Combining of I5 and Q5, Proceedings of the US Institute of Navigation GNSS (Long Beach, CA, USA, Sept. 21-24).

Kaplan, E.D. (2006), Understanding GPS Principles and Applications (second edition), Artech House Mobile Communications Series. Macabiau, C., L. Ries, F. Bastide, J-L. Issler (2003), GPS L5 Receiver Implementation Issues, Proceedings of the US Institute of Navigation GNSS (Portland, OR, USA, Sept. 9-12).

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