Performance Comparison of L1 & L2C Signals in Weak Signal Environments

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Performance Comparison of L1 & L2C Signals in Weak Signal Environments Powered By Docstoc
					Performance Analysis of Doppler Aided Tracking
      Loops in Modernized GPS Receivers
                                                       Sana Ullah Qaisar
                                      School of Surveying and Spatial Information Systems,
                                           University of New South Wales, Australia

BIOGRAPHY                                                           having the pilot channel and relatively slower dynamics, is
                                                                    used as aiding source in the considered arrangement. The
Sana Ullah Qaisar received his Masters degree in                    L2C PLL, operated with a wide loop bandwidth, absorbs
Telecommunication Engineering from the University of                the dynamic stress and provides Doppler estimates to the
New South Wales (UNSW), Australia in 2003. He has                   L1 PLL (affected by wide-band interference) operating at
gained experience in the telecommunications industry and            narrow-band. The tracking error associated with such
served as faculty member at National University of                  collaboration between two tracking loops is analyzed. It is
Computer & Emerging Sciences, Pakistan. He is currently             shown that a 7 dB-Hz RFI margin (equivalent to that
pursuing his PhD at School of Surveying & Spatial                   achieved with a moderate quality inertial sensor), can be
Information Systems, UNSW. His research interests                   achieved through the local Doppler-assistance.
include synchronization algorithms for baseband
processing and FPGA-based receiver design for                       INTRODUCTION
modernized GNSS signals.
                                                                    In a modernized GPS receiver, multiple civil signals can
ABSTRACT                                                            be simultaneously tracked. Conventionally, each of the
                                                                    civil signals will be tracked in an independent channel.
The GPS modernization program deploys new generations               However, collaboration across multiple channels can be
of satellites designated Block IIR-M, Block IIF and Block           established to improve the tracking performance of
III-A, equipped to transmit multiple civil signals. The co-         individual channels as well as to enhance the overall
existence of multiple civilian signals in a GPS receiver has        robustness of the receiver. The aim of this paper is to
been a focus in recent research activities. In the literature       develop and evaluate such collaboration for „carrier
to date, correlator outputs of individual channels are              tracking‟, while each channel is tracking a different carrier
combined in ways either to increase the power available             frequency.
for processing or to reduce the error in tracking
measurements. These combinations are typically made at              For channels operating on the same carrier frequency (e.g.
the discriminator level, after the discriminator or after the       data and pilot channels in L2C and L5 GPS signals), the
loop filter. The combinations have been considered both             output of individual channels has been combined in the
for channels operating on the same carrier frequency (e.g.          following ways. Spilker & Van Dierendonck (1999)
data and pilot channels of L5) as well as channels across           proposed to combine (non-coherently) the coherent
different carrier frequencies. In a modernized GPS                  integration output of L5 data and pilot channels at the
receiver, tracking multiple civil signals, the relationship         code discriminator. Muthuraman et al. (2006) proposed
between Doppler frequencies (proportional to the                    differential combinations of L2C data and pilot channels
corresponding carrier frequencies) of all signals is known          at the discriminator level. Both of the above combination
and therefore Doppler estimates of one PLL can be                   schemes aim to increase the signal energy available for
utilized by another PLL tracking a different frequency.             tracking. In another approach, the measurements of
While such benefits are conventionally achieved through             independent data and pilot channels are combined to
ultra-tight GPS/INS coupling, this paper presents                   reduce the tracking error. For example, Hegarty (1999)
performance analysis of a Doppler-aided tracking loop               proposed to run independent discriminators on data and
architecture, where the Doppler assistance is obtained              pilot channels and then combine their outputs using
from another loop in the same receiver. L1 C/A and L2C              weights that are inversely proportional to their output
are the two civil signals selected for the analysis, because        variances, in the context of the L5 signal. Also, Tran et al.
this pair of signals will be available long before any other        (2002) applied the above optimal weights technique for
combination. The analysis, however, is relevant to any              tracking the L2C signal. For any tracking combination
pair of signals from a single satellite. The L2C carrier,           across different carrier frequencies, the ionospheric and
Doppler effects must be addressed carefully. Gernot et al.                                           20-ms

(2008) proposed a combined L1/L2C tracking scheme                    L2 CM code
                                                                    (511.5 Kcps)                                             L2 CM     DATA
where the relationship between phase variations (due to
ionosphere) in the two signals is utilized for combining
the tracking measurements. Ries et al. (2002) discuss the         The L2C code
                                                                  (1.023 Mcps)
possibility of L1/L5 joint tracking by aiding the L1                                                                          L2 CL
tracking with L5 carrier NCO, assuming the ionospheric
                                                                     L2 CL code
drift to be less than 50 Hz.                                        (511.5 Kcps)

This paper presents a Doppler-aided carrier tracking
architecture for the modernized GPS receivers. The GPS
civil signals transmitted by Block IIR-M satellites, i.e. L1    Fig. 1. The L2C code structure
and L2C, are selected for evaluating the performance of
the proposed architecture. The slower (relative to L1 GPS
signal) dynamics and the pilot channel (where coherent                              1.     CM             0
discriminators with an extended linearity region can be
used), make the L2C PLL a natural choice for operating at
wider loop bandwidth to look after the carrier Doppler,                                    CM            CM
while the L1 loop bandwidth can be set as tight as 0.5 Hz
to mitigate the wide-band noise. The Doppler estimates
from the L2C PLL, after appropriate scaling, are fed to the     Fig. 2. Choices of local replica code for tracking the L2C data channel
                                                                (only two chips are shown)
L1 tracking loop. The aim of this paper is to evaluate the
error introduced by this local-aiding and analyze what RFI
                                                                return-to-zero (RZ) CM code. In the second option, each
margin can be achieved through such locally Doppler-
                                                                CM chip is extended to the duration of two chips to make
aided carrier tracking loops. The results of this research
                                                                it a non-return-to-zero (NRZ) CM code. The E-L DLL
reveal that for an L1 PLL, without Doppler aiding, 22 dB-
                                                                discriminator (0.5 chip correlator spacing) response,
Hz is the minimum C/No that can be tracked within the
                                                                multipath envelope and cross-correlation performance of
acceptable error threshold, while it can go down to 15 dB-
                                                                the two options are compared in Fig. 3 through Fig. 5
Hz in the Doppler-aided mode thus offering a 7 dB-Hz
                                                                respectively, suggesting RZ CM code as the obvious
RFI margin. The C/No refers to effective carrier to noise
                                                                choice for tracking as it is better in all three of these
ratio throughout this paper.
                                                                criteria. Moreover, the correlation noise with NRZ CM
                                                                code will be twice as much as with the RZ CM code
The paper is organized as follows. The next section
                                                                (Qaisar et al. 2008). For all experiments conducted in this
describes the structure of the L2C signal and the choices
                                                                research, RZ CM code is therefore used for tracking the
of local replica code for tracking the L2C signal. The PLL
                                                                L2C data channel. The same arguments apply to the pilot
performance of the L1 and L2C signals is then discussed.
                                                                channel where RZ CL code is used for tracking.
Aided tracking architectures are then evaluated and
finally, some concluding remarks are given.
                                                                TRACKING LOOP PERFORMANCE
                                                                In a phase locked loop implementation, illustrated in Fig.
                                                                6, the IF carrier is matched with the NCO generated
The L2C signal is composed of two codes, namely L2 CM
                                                                replica carrier and the difference in phases of the two
and L2 CL. The L2 CM code is 20 milliseconds long and           carriers is determined by the discriminator, while the loop
has 10230 chips while the L2 CL code is 1.5 seconds long        filter is responsible for removing noise in the phase
and has 767250 chips. The CM code is modulo-2 added to          measurements as well as for looking after the signal
data (i.e. it modulates the data) and the resultant sequence    dynamics. The performance of a PLL is measured as
of chips (data channel) is time-multiplexed with the CL         variance of the total phase jitter, contributed by the
code (pilot channel) on a chip-by-chip basis. The               thermal noise, clock errors, platform vibration and
individual CM and CL codes are clocked at 511.5 KHz             dynamic stress. The total phase jitter for a two-quadrant
while the composite L2C code has a frequency of 1.023           arctangent discriminator is given as (Kaplan 1996, Van
MHz. This time-multiplexed L2C sequence, modulates the          Dierendonck 1997):
L2 (1227.6 M Hz) carrier (IS-GPS-200D, 2006). Fig. 1
illustrates the code structure with corresponding chipping
rates.                                                                                                                               (1)

With the new L2C code structure, two basic options can          where
be used for tracking the data channel (M. Tran 2002,
Fontana et al. 2001). As shown in Fig. 2, the two options                  is the 1-sigma thermal noise in degrees
differ in the choice of alternate chips. In the first option,           is the 1-sigma vibration-induced oscillator jitter in
the local code alternates between CM chips and zeros, the            degrees
                                            1                                                                                  IF Carrier                      I&D
                                                                                                     NRZ CM
                                                                                                     RZ CM                                                               Discri-
        DLL discriminator output

                                                                                                                                                  NCO          Filter
                                                                                                                       Fig. 6. Generic PLL implementation


                                                  -2 -1.5 -1 -0.5               0    0.5      1    1.5     2
                                                                       Code offset (chips)
                                                                                                                       where      is the single-sided loop filter bandwidth,         is
Fig. 3. E-L DLL discriminator (0.5 chip correlator spacing) response for                                               the coherent observation interval,         is the single-sided
different replica codes in L2C data channel                                                                            noise power spectral density and is the signal power. It
                                                                                                                       is clear from (1) that minimizing         leads to more noise
                                                                                                                       filtering and thus the resulting phase jitter is reduced.
                                                                                                     NRZ CM
                                                                                                                       There is a limit, however, to which the        can be reduced
                                          600                                                        RZ CM             without affecting the total phase jitter, as discussed later in
                                                                                                                       the paper.
 Tracking error (chips)

                                          200                                                                          The equation for vibration (when the oscillator is installed
                                            0                                                                          in an environment where it is subjected to mechanical
                                                                                                                       vibrations) induced oscillator jitter is (Kaplan 1996):



                                       0               0.5         1.0        1.5          2.0       2.5
                                                                    Multipath delay (chips)

Fig. 4. Multipath envelopes of L2C signal for different replica codes.
The correlator spacing is set to 0.5 chips.
                                                                                                                               is the input frequency in Hz
                                                                                                                               is the oscillator vibration sensitivity
                                                                                                                                is random vibration modulation frequency in Hz
                                                                                                                                    = power curve of random vibration in g2/Hz
                 Cumulative probability

                                                                                                                       For a third order loop (considered in this paper), the Allan
                                          0.6                                                                          phase jitter is (Kaplan 1996):

                                                                                                    NRZ CM                                                                         (4)
                                                                                                    RZ CM
                                                                                                                       where          is the Allan deviation and is the short term
                                                                                                                       stability gate time for Allan variance measurement.
                                                 -70             -60          -50            -40           -30
                                                             Relative cross-correlation power (dB)                     The dynamic stress refers to the phase jitter introduced
                                                                                                                       due to abrupt platform motion such as a step, acceleration
Fig. 5. Cross-correlation performance of the L2C signal with different                                                 or a jerk in the input phase or frequency. For a third order
replica codes. The RZ CM code has a 3dB relative improvement                                                           PLL, the phase error due to dynamic stress is given by
                                                                                                                       (Kaplan 1996):
                                             is the Allan variance-induced oscillator jitter in
                                             is the dynamic stress error in the PLL tracking                                                                                       (5)
                                                                                                                       where               is the maximum value of jerk
The variance of thermal noise jitter                                                                     is given by
                                                                                                                       experienced by the GPS receiver.
(Kaplan 1996, Dierendonck 1997):
                                              18Hz, 20ms, 10g/s   10Hz, 20ms, 1g/s     2Hz, 20ms, 0.01g/s
                                         20                                                                                                        50
                                                                                                                                                                                       Data channel
      Total RMS phase jitter (degrees)

                                                                                                                                                   40                                  Dataless channel

                                                                                                                      RMS phase jitter (degrees)
                                                                                                                                                                                       Optimal combination



                                         15               20          25              30             35                                            0
                                                                  C/No (dBHz)                                                                      15         20             25               30             35
                                                                                                                                                                         C/No (dBHz)

Fig. 7. Total phase jitter for a 3rd order carrier tracking loop for the given                                    Fig. 8. Performance (phase jitter) of different PLL implementations
loop bandwidth, coherent integration time and dynamic stress. Oscillator
specifications are given in Table-I

                                                                 TABLE-I                                            L2C carrier from
                                                          Oscillator specifications                                   data channel

                                                  Allan               Vibration                                                                                Discri-
                                                                                              Vibration                                                 I&D                 α
                                                deviation             sensitivity                                                                              minator
                                                                                             .005 g /Hz                                                                                      Loop
  1                                              1×10-11                1×10-9                  (200-                                                                             D          Filter

                                                                                              2000)Hz                                                          Discri-
                                                                                                                                                        I&D    minator
The 15 threshold is compliant to model a PLL as a linear
feedback system (Dierendonck 1997, Egziabher et al.
2003). For phase errors above 150, the navigation signals                                                           L2C carrier from
might still be tracked and decoded, at the expense of                                                                pilot channel
performance degradation. Fig.7 illustrates the total phase
jitter as a function of C/No for a third order PLL (tracking                                                      Fig. 9. The optimal linear-combination implementation of data and pilot
L1 carrier frequency: 1575.42 MHz), including all of the                                                          channels in L2C PLL
above mentioned effects. A coherent integration of 20
milliseconds is used (throughout this paper) while the                                                            where is the combined output,            and     are the
oscillator specifications are given in Table-I (Kaplan                                                            individual outputs of data and pilot discriminators
1996):                                                                                                            respectively while and are the weighting coefficients.
                                                                                                                  The optimal choice for values of these coefficients that
The L2C Signal Tracking                                                                                           minimizes the variance, with the constraint         are:

One of the key objectives of the L2C signal was to offer a                                                                                                                                                    (8)
better solution for weak signal tracking (Fontana et al.,
2001). The pilot channel incorporated in the L2C signal
allows for a coherent discriminator, where the thermal
phase jitter is expressed as:

                                                                                                            (6)   and hence the total phase variance becomes:

Furthermore, the co-existence of data and pilot channels in
the L2C signal has been exploited to reduce the phase                                                                                                                                                         (10)
jitter. Tran and Hegarty (2002) proposed to run
independent discriminators on the data and pilot channel                                                          The performance of data, dataless and combined
and then combine their outputs using weights that are                                                             implementations is illustrated in Fig. 8. The optimal
inversely proportional to their output variances. The error                                                       combination offers the best performance followed by the
variance of a carrier tracking loop operating on both data                                                        dataless and data channels respectively. The combined
and pilot channel is given as:                                                                                    option, however, cannot be implemented because at low
                                                                                                                  C/No levels and large dynamics the phase error on data
                                                                                                          (7)     channel will grow outside its linearity region ( ) and
                                                                                                                      18Hz, 20ms, 10g/s        10Hz, 20ms, 1g/s       2Hz, 20ms, 0.01g/s
                           1400                                                                                  20


                                                                              Total RMS phase jitter (degrees)
                           1200                                                                                                                                            L2C
 Carrier Doppler (Hertz)


                                                            L2C                                                  10

                           400                                                                                   5
                                  5   10         15    20         25                                             15               20                25            30                35
                                                                                                                                               C/No (dB Hz)
                                      time (minutes)

Fig. 10. The carrier Doppler in L1 and L2C signals, computed from         Fig. 11. Comparison of the total phase jitter in 3rd order PLL of L1 and
almanac data (PRN-17), showing that the L2C has a slower rate of          L2C signals
change of Doppler than L1.
                                                                                                                        C/No=15dBHz             C/No=25dBHz           C/No=35dBHz
consequently the data discriminator will not be able to                                                          30

                                                                              RMS phase jitter (degrees)
correctly assess the phase error. To avoid the use of any                                                        20
irrelevant information from the data discriminator, Julian
et al. (2004) proposed a method that checks the                                                                  10
consistency between the data and pilot discriminator                                                                            L2C
outputs as:


                                                                                                                  0.1                      1                          10
                                                                   (11)                                                             Single-sided PLL bandwidth (Hz)

otherwise                                                                 Fig. 12. Loop bandwidth vs. total phase jitter for L1 and L2C carrier
                                                                          tracking loops

                                                                          However, it should be noted that the phase jitter of the two
where the value of is chosen to be tight such as          in              signals shown here are with reference to their
Julian et al. (2004). Fig. 9 illustrates this implementation              corresponding loops. This is not to say that L2
for the L2C signal, followed in this paper, where D                       measurements are more accurate than L1 but to show that
denotes the decision block described in (11) and (12).                    L2C PLL is more robust than L1 PLL. It can be observed
                                                                          from Fig. 11 that the difference in the phase jitter of the
Performance Comparison of L1 & L2C Tracking                               two signals diverges as the C/No level drops, suggesting
                                                                          L2C is a better candidate for the aiding signal. Similarly,
The carrier Doppler in L1 and L2C signals is proportional                 Fig.12 indicates that an L2C PLL would be a better choice
to their carrier frequencies and hence the „rate of change                for operating at wider bandwidth. Fig. 12 also informs that
of Doppler‟ in the two carriers is different. Fig. 10 shows               for a given carrier to noise ratio, there is a bandwidth for
the carrier Doppler of L1 and L2C signals, computed from                  which the phase jitter is a minimum and as the loop noise
a recent almanac data, for the PRN-17 Block IIR-M                         bandwidth is decreased below or increased above this
satellite, indicating that the rate of change of Doppler in               minimum value, the total phase jitter increases because the
the L2C signal is slower than that in L1.                                 contribution to total phase jitter by the various error
                                                                          sources is changed (Egziabher et al. 2003). It is also
Also, it can be observed from equations (3) through (5)                   shown by Egziabher et al. (2003) that the 1-sigma
that all stochastic components of total PLL jitter are                    standard deviation in the Doppler estimates,             , is
directly proportional to the carrier frequency; hence the
                                                                          smaller for L2 than for L1 and their relationship is given
individual jitter contributions and the total phase jitter in
the L2C signal would be smaller than that of the L1
signal. Fig 11 and Fig. 12 compare the total PLL jitter in
the two signals for the specifications given in Table-I, as a
function of C/No and PLL bandwidth respectively.
                                               L2 Carrier                           I&D                                                                         L2 Carrier                           I&D

                                                                                                    Discri-                                                                                                          Discri-
                                                                                                    minator                                                                                                          minator

                                                                                    Loop                                                                                                             Loop
                                                              NCO                   Filter
                                                                                                                                                                               NCO                   Filter

                                                                       L1/L2                                                                                                            L1/L2

                                                              NCO                                                                                                              NCO                Filter


                                               L1 Carrier                           I&D                                                                         L1 Carrier                           I&D

Fig. 13. L2C PLL feeding the L1 tracking                                                                         Fig. 15. L2C PLL aiding the L1 PLL

                                            4000                                                                                                             4000
Prompt correlator output (absolute value)

                                                                                               L2C pilot         Prompt correlator output (absolute value)                                                      L2C pilot
                                            3000                                               L2C data                                                      3000                                               L2C data
                                                                                               L1                                                                                                               L1
                                            2000                                                                                                             2000

                                            1000                                                                                                             1000

                                               0                                                                                                                0

                                            -1000                                                                                                            -1000

                                            -2000                                                                                                            -2000

                                            -3000                                                                                                            -3000

                                            -4000                                                                                                            -4000
                                                 0     1000   2000        3000               4000         5000                                                    0     1000   2000        3000               4000         5000
                                                              time (milliseconds)                                                                                              time (milliseconds)

Fig. 14. Tracking output from L1 and L2C in-phase prompt correlators                                             Fig. 16. Tracking output from L1 and L2C in-phase prompt correlators
for a real Block IIR-M signal (PRN-17), collected by the Namuru GPS                                              for a real Block IIR-M signal (PRN-17), collected by the Namuru GPS
receiver, following the architecture shown in Fig. 13                                                            receiver, following the architecture shown in Fig. 15

where     and      are the L-band carrier frequencies. All of                                                    Directly Fed Carrier Tracking Loops
the above comparisons assess L2C as a promising choice
for aiding signal. In this research, L2C PLL should                                                              The conventional aiding approach, such as proposed by
therefore be set into aiding mode while the L1 as the aided                                                      Ries et al. (2005) suggests one PLL to track both of the
mode.                                                                                                            signals for reducing the receiver complexity. Fig. 13
                                                                                                                 illustrates this architecture for tracking both L1 and L2C
AIDED PLL ARCHITECTURE                                                                                           carriers from the L2C PLL. However, in such a direct
                                                                                                                 feeding, phases of the two local carriers will be identical
The concept of Doppler aiding is not new. With Doppler                                                           while they should be independently synchronized with
aiding, platform dynamic stress of the aided tracking loop                                                       those of the corresponding incoming carriers. As a result,
is removed and its loop bandwidth is reduced to mitigate                                                         the L1 local carrier will have a periodic phase offset with
the wide-band interference (Akos et al. 2004). However,                                                          its incoming signal leading to a periodic residual
Doppler aiding across different carrier tracking loops                                                           frequency error. This effect can be observed in Fig. 15
hosted on the same receiver platform has not been                                                                which shows the in-phase prompt correlator outputs of the
evaluated. For the considered collaboration between L1                                                           real L1 and L2C signals simultaneously tracked from the
and L2C carrier tracking loops, one of the two PLL should                                                        “Namuru” GPS Receiver (Qaisar and Dempster 2007).
be set in aiding mode while other one goes to the aided                                                          The effect observed here is due to the fact that the total
mode.                                                                                                            electron count encountered on the signal path through
There are two basic options for coupling the carrier                                                             ionosphere is not changed over the time (Gernot et al.
tracking loops, discussed as follows.                                                                            2008) otherwise a random behavior of L1 in-phase prompt
                                                                                       where         represents the noise variance of the optimal
         L1 carrier                              I&D            minator                linear combination of data and pilot channels, shown in
                                                                                       Fig. 8.
                                                                                       Similarly, L1 PLL jitter can be given as:

      L2C carrier from                Doppler estimates                                The tracking errors from L2C PLL, fed to the L1 PLL can
        data channel                   from L2C PLL                                    be expressed as:

                      I&D   minator     α
                                             D         Filter
                                                                                       where             is the error in L1 PLL, coming from the
                            Discri-                                                    L2C PLL. All of the error components from L2C PLL
                      I&D   minator
                                                                                       except          are correlated, as shown in equations (3)
                                                                                       through (5). The error in aided L1 tracking loop can
                                                                                       therefore be classified into correlated and un-correlated
      L2C carrier from                                                                 error as:
       pilot channel

          Fig. 17. L2C PLL data/pilot combination, aiding the L1 PLL                                                                           (17)

     correlator output will be observed.
     Aided Carrier Tracking Loops
                                                                                       respectively. The total error in the aided L1 PLL can now
     In order to resolve this ionosphere problem, L2C can be                           be given as:
     used to aid L1 carrier with an architecture shown in Fig.
     15. In this configuration, each of the two loops is fully
     operational and the Doppler estimates from the L2C PLL
     and fed to the L1 PLL as aiding. The tracking results
     shown in Fig. 16 verify that ionospheric phase shift                                                                                      (19)
     problem is resolved with this architecture and that the
     phase of L1 signal is tracked.

     L2C-Aided L1 Carrier Tracking Loops
                                                                                       where      and     are the correlation coefficients, defined
     In order to take full advantage of the L2C tracking                               as:
     capabilities, the architecture shown in Fig. 17 is
     implemented. The purpose of this tracking loop
     collaboration is to remove the dynamic stress load                                                                                        (20)
     (dominant source of error at smaller loop bandwidths)
     from a narrow-band PLL, thus allowing it to keep the
     tracking lock in weak signal conditions in the event of                                                                                   (21)
     abrupt platform maneuvers. However, the tracking error
     introduced by this architecture must be evaluated for                             Note that the dynamic stress of the L1 PLL has been
     acceptable performance level.                                                     removed in (19).
i.       The Tracking Error Analysis                                                   The Performance Evaluation
     The L2C PLL jitter can be expressed as:                                           To evaluate the tracking performance of Doppler-aided
                                                                                       architecture, in this paper, the L2C PLL is set to operate at
                                                                                       nominal loop bandwidth of 10 Hz while a range of 0.1 to
                                                                                (14)   40 Hz is tested for the optimal bandwidth of the aided L1
                                                                                       PLL under a dynamic stress of 0.25 g/s. Three levels of L1
                                                                                       C/No (15 dB-Hz, 25 dB-Hz and 35 dB-Hz) were trialed
while the L2C C/No level is set to 45 dB-Hz to ensure a
higher quality of Doppler estimates as the concern here is                                       40
to examine the scenarios where L1 is affected by the                                             30
interference but L2C is not. The performance of L1 PLL is                                        20

                                                                    RMS phase jitter (degrees)
assessed as a function of loop bandwidth and C/No,                                               15
respectively.                                                                                    10

Loop Bandwidth

Fig. 18 shows the L1 PLL performance as a function of                                                     C/No=15dBHz
loop bandwidth in the presence of dynamic stress, without                                                 C/No=25dBHz
Doppler aiding. The minimum loop bandwidth, as already
discussed in the paper, is dependent on the carrier-to-noise                                     0.1                     1                          10
                                                                                                                  Single-sided PLL bandwidth (Hz)
ratio. However, it can be observed that for C/No levels
below 25 dB-Hz, the tracking error grows above the 15
                                                                Fig. 18. Loop bandwidth vs. total phase jitter in the non-aided L1PLL
degrees threshold. In other words, C/No levels below 25         with dynamic stress included
dB-Hz cannot be tracked in this arrangement.

If the dynamic stress is excluded (i.e. if perfect Doppler                                             C/No=15dBHz           C/No=25dBHz            C/No=35dBHz
estimates or static receiver conditions are assumed), the                                        40
PLL performance should be improved as shown in Fig.                                              30
19. This Figure also indicates the quality of Doppler                                            20

                                                                    RMS phase jitter (degrees)
estimates from the L2C PLL. As compared to the perfect                                           15
Doppler estimate (dynamic stress excluded) case, the L2C                                         10
PLL estimates are good enough for weak C/No levels
(which is of more interest here) than for higher values of
C/No. This is because at higher C/No levels, the noise
from L2C PLL has more impact on the low noise in the
aided L1 PLL and hence the effective tracking error in the                                                Dynamic stress excluded
aided L1 PLL is significantly increased. Similarly at low                                                 Dynamic stress removed through aiding
C/No levels, the increase in effective tracking error is                                         0.1                     1                          10
                                                                                                                  Single-sided PLL bandwidth (Hz)
relatively small. Also, the minimum C/No level that can
be tracked in the aided L1 PLL is 15 dB-Hz, at a loop
                                                                Fig. 19. Loop bandwidth vs. total phase jitter in the L1 PLL with
bandwidth of approximately 0.5 Hz. This means that the          dynamic stress excluded and removed through Doppler assistance from
locally-aided loop is able to continue tracking at as small a   L2C PLL
loop bandwidth as 0.5 Hz.

Effective Carrier to Noise Ratio                                                                 40
The gain achieved in Doppler-aided PLL (reported above)                                          20
                                                                    RMS phase jitter (degrees)

appears more convincing when the results are arranged in                                         15
the form of Fig. 20 through Fig. 22 (i.e. as a function of                                       10
C/No). Fig. 20 illustrates the L1 PLL performance in the
stand-alone mode, i.e. without any Doppler aid but
including its dynamic stress. At 10 Hz loop bandwidth,                                                  BL=1Hz

approximately 25 dB-Hz signal is tracked with acceptable                                                BL=2Hz
level of performance (the figures match with those shown
in Fig. 18).
                                                                                                 10         20               30            40            50
When the dynamic stress on the L1 PLL is excluded, the                                                                       C/N0 (dBHz)

PLL performance should be enhanced as shown in Fig. 21.
However, the performance of L1 PLL aided by L2C PLL             Fig. 20. Carrier-to-noise ratio vs. total phase jitter in the non-aided L1
and including the dynamic stress, shown in Fig. 22, is of       PLL with dynamic stress included
more interest here. In this case, it can be observed that the
15o threshold is exceeded when the C/No has dropped             Again a higher quality of Doppler estimates can be
below 15 dB-Hz, thus gaining a 7 dB-Hz RFI margin.              observed for lower C/No levels for reasons explained
Also, comparing Fig. 20 and Fig. 21 gives an indication of      above. It is suggested that the L2C PLL discussed here
the quality of Doppler estimates (difference in the perfect     can be used for aiding both L1 and L2C code tracking
Doppler estimates shown in Fig. 21 and the Doppler              loops as well for improved code tracking performance and
estimates provided by the L2C PLL) from the L2C PLL.            enhanced receiver robustness.
                                                                             guidance and technical discussions carried out in this
                                 40                                          work.
                                 20                                          REFERENCES
    RMS phase jitter (degrees)

                                 10                                          Spilker, J. J. and A. J. Van Dierendonck (1999), Proposed
                                                                             New Civil GPS Signal at 1176.45 MHz, ION GPS 1999
                                                                             Nashville, TN, pp 1717-1725.
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                                                C/N0 (dBHz)                  Muthuraman, K., S.K. Shanmugam and G. Lachapelle
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PLL with dynamic stress excluded
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                                      BL=5Hz                                 Gernot, C, Kyle O‟Keefe and Gerard Lachapelle,
                                      BL=10Hz                                Combined L1 / L2C Tracking Scheme for Weak Signal
                                 1                                           Environments, Proceedings of ION GNSS 2008, Session
                                 10       20    30            40   50
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 Fig. 22. Carrier-to-noise ratio vs. total phase jitter in the L1 PLL with   Ries, L., Macabiau, C. O. Nouvel, Q. Jeandel, W. Vigneau
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CONCLUSIONS                                                                  NAVSTAR Global Positioning System Interface
In a modernized GPS receiver, tracking multiple civil                        Specification IS-GPS-200 revision D, 7 March 2006.
signals, collaboration across multiple carrier tracking
loops can be established to combat un-usual tracking                         Fontana, R., W. Cheung, P. Novak, T. Stansell (2001),
conditions such as both interference and dynamics. A                         The New L2 Civil Signal, Proceedings of US. Institute of
tracking architecture for such collaboration between L1                      Navigation (Salt Lake City, UT, Sept. 11-14), pp. 617-
and L2C carrier tracking loops is evaluated. The robust                      631.
L2C PLL is set to operate at wider-band to provide
Doppler estimates to the narrow-band L1 PLL under the                        Qaisar, S. and A. G. Dempster, Evaluating            the
wide-band interference and dynamic stress conditions.                        acquisition potential of GPS L1 and L2C codes        for
From the results reported in this paper it appears that a 7                  weak signal environments, IEEE Transactions           on
dB-Hz margin against RFI can be achieved through the                         Aerospace and Electronic Systems, 2009, submitted    for
Doppler-aided tracking loop architecture. Future work will                   review.
investigate the inclusion of additional signals in the
collaboration and alteration of the loop bandwidth in real                   Qaisar S., N. C. Shivaramaiah and A. G. Dempster,
time.                                                                        Exploiting the spectrum envelope for GPS L2C signal
                                                                             acquisition, proc. of European Navigation Conference,
ACKNOWLEDGEMENTS                                                             April 2008. Toulouse, France, 2008.

This research work is supported by the Australian                            Van Dierendonck, A.J. (1997), GPS Receivers in Global
Research Council Discovery Project DP0556848. The                            Positioning System: Theory and Applications, Volume I,
author would like to thank Associate Professor Andrew G.                     AIAA.
Dempster, University of New South Wales, for his
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Applications, Artech House.

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Description: Performance Comparison of L1 & L2C Signals in Weak Signal Environments