[American Institute of Aeronautics and Astronautics 22nd AIAA International Communications Satellite...

GPS CDMA NOISE ANALYSIS

Dr. Srini Raghavan, Dr. Kuang Tsai and Mr. Lamont Cooper The Aerospace Corporation

Abstract

Spectral lines of the GPS C/A codes play an important role in the amount of Code Division Multiple Access (CDMA) noise generated, which degrades the available carrier-to-noise density ratio (C/N0) to the GPS receiver. This in turn affects the code acquisition and tracking performance of the GPS signal, which are the two operations that must be performed in a GPS receiver before a complete navigation solution is calculated. Most analysis performed to date ignores the spectral line effects altogether, claiming that any significant effect is of short duration and limited geographical extent. The Aerospace Corporation felt otherwise, that the spectral line effects couldn’t be ignored, especially with GPS band sharing with other systems providing unlike-kind services. Furthermore, certain GPS applications are categorized as safety-of-life types of services, making it even more important to be rigorous in the CDMA noise calculations. A rigorous analysis is not only complex to perform but also time consuming to consider each and every scenario as it arises in the future. To overcome this difficulty, a two-step procedure is proposed in this paper for performing the interference analysis using the C/A code.

Introduction

In order to keep the code acquisition time to a reasonable value, Gold codes of length 1023 chips, at a chipping rate of 1.023 mega chips per second (MCPS) were chosen for use as coarse acquisition (C/A) codes in the Global Positioning System (GPS). Gold codes also had other desirable features such as, well-defined auto- and cross-correlation properties and a large number of codes in the code set available for use by the GPS. Selection of this code was made in the early ’70s, based on the processor technology available then. For a reasonable number of satellites using this code, the code choice was quite good in taking advantage of all the desired properties of the Gold codes without being hindered by any of its limitations. The situation has changed significantly since then in a number of ways. The user community is not just military, although the system was developed for the military use. The civilian use of GPS has grown in proportions nobody anticipated, and some of those uses include safety-of-

life applications, which implies that more stringent availability requirements will be necessary. A number of augmentation systems both ground and land based are planned and being implemented, such as WAAS (Wide Area Augmentation System) and LAAS (Local Area Augmentation System), which use C/A codes for spreading the signal. A number of GPS-like satellite navigation systems such as the European Galileo—which plans to use the same frequency band as the GPS [1] but may or may not use C/A codes—are in developmental stages. Newer blocks of the GPS are designed that also use C/A codes for the purpose of providing backward compatibility to the existing GPS receivers. So with the increase of so many C/A code transmitters, it is extremely important to accurately calculate the code division multiple access (CDMA) noise generated by these codes to make sure that there is no surprise outage of the service in a critical time of need. The problem is compounded further, although only in limited geographic regions and limited periods of time, in that the CA code signal has spectral lines spaced 1 kHz apart because of the short period of the code, which may result occasionally in much higher CDMA noise than from a long code with no spectral lines. Since it is much harder to accurately quantify the spectral line effects, past interference analyses performed by various people resorted to some kind of average performance while ignoring the worst-case spectral line effects altogether.

In an effort to accurately quantify the worst-case C/A code CDMA noise, The Aerospace Corporation has developed equations to accurately calculate the C/A code CDMA noise both in the code tracking and the acquisition modes. The analysis has shown that the CDMA noise depends on received power levels, receiver antenna gain towards the interference signals, Doppler frequency shifts of the received signal, path delays, and to a lesser degree on the particular C/A code or codes of the interfering signal. In other words, the user-satellite geometry plays a very significant role in the amount of CDMA noise experienced by the GPS receivers. A software tool called CLIMAT (CDMA Limited Interference Modeling and Analysis Tool)—which takes into account the user-GPS satellite’s geometry, received power level variations, antenna gain patterns, and the C/A code spectral line effects—has been developed by the Aerospace Corporation.

1 American Institute of Aeronautics and Astronautics

22nd AIAA International Communications Satellite Systems Conference & Exhibit 20049 - 12 May 2004, Monterey, California

AIAA 2004-3182

Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

C/A Code CDMA Noise Calculation

Since the above-mentioned effects are a function of satellite and receiver geometry, a GPS constellation-driven model of the satellite orbits and antenna specification is used to model all the effects of interference. This is particularly necessary for short-duration effects on the order of minutes, since safety-of-life uses of GPS have very stringent integrity, availability, and continuity requirements. The use of the CDMA noise model, coupled with the geometry and antenna effects, is recommended to handle interference analysis for a Global Navigation Satellite System (GNSS).

The acquisition mode is the most sensitive of all of the modes in a GPS receiver. Therefore, this study used the signal-to-noise-density (C/N0) level necessary for acquisition of the C/A code as the criterion for interference to GPS. Cross-correlation properties of the C/A code (CDMA noise) make it more susceptible to interference from increased signal levels of another C/A code. This is why the analysis of the possible use of PRN codes in the GPS C/A (Gold) code family by other systems is particularly important.

Although it has been widely known that the C/A codes used for GPS have a limited CDMA capacity [2], due in part to their short (1-millisecond) length, earlier studies [3] that focused on interference to the system used Gaussian noise models for the C/A code CDMA noise from the GPS. This simplification, in which the cross-correlation effects are random, was made despite the fact that the mutual interference of the C/A codes in a worst-case scenario is much greater than that from random noise. Therefore, when analyzing the performance of GPS in the presence of signals from other sources (depending on the GPS user and the specific requirements as discussed below), a more accurate model of CDMA noise from the GPS should be used. Although a full description of the preferred model of the C/A code as a short code is planned to be in a later report, it is sufficient to note here that the results of this model are a function of the differential ranges and Doppler frequencies of the affected satellites. In addition to the effects of the GPS signals, the way in which GPS is used plays a large role in how interference should be analyzed. Different GPS signals arrive at different elevation angles with respect to the receiver and these signals experience different antenna gain levels. The combination of these effects and the potential for interference is illustrated in Figure 1.

Using this methodology, a CDMA analysis tool termed the Aerospace-developed CDMA Limited Interference Model and Analysis Tool (CLIMAT) [2] was developed. A block diagram model is shown in Figure 2. Note that the CDMA noise density I0 in Figure 2 is not a constant unlike that typically used in other radio frequency systems (such as communications), where only average interference effects are of interest (CDMA noise density in this case is a constant, which is inversely proportional to the spreading-code chipping-rate [3] due to the relative randomness among the received code phases.).

USERANTENNA

MODEL

C/(No+Io )COMPUTATION AVAILABILITY

MODELANALYSIS

ORRESULTS

AUGMEN-TATIONS

OTHERINTERF

(MES ETC.)

Receiver C/ N0Threshold

ReceiverNoise PSD

(N0)

C

I0’

UserLocation

OTHER GNSSCONSTELLATIONS

INTERFERENCECALCULATION

I0

RECEIVEDSIGNALS FROMTHE GPSCONSTELLATION

CA,P,M,IMHPM USER

ANTENNAMODEL

C/(No+Io )COMPUTATION AVAILABILITY

MODELANALYSIS

ORRESULTS

AUGMEN-TATIONS

OTHERINTERF

(MES ETC.)

Receiver C/ N0Threshold

ReceiverNoise PSD

(N0)

C

I0’

UserLocation

OTHER GNSSCONSTELLATIONS

INTERFERENCECALCULATION

I0

RECEIVEDSIGNALS FROMTHE GPSCONSTELLATION

CA,P,M,IMHPM

ANTENNA HIGHGAIN DIRECTION

ANTENNA LOWGAIN DIRECTION

INTERFERING SIGNALS(CROSS CORRELATION)

INTENDED SIGNAL(AUTO CORRELATION)

Carrier-to-noise density ratio (C/N0) can drop tonear or below acquisition threshold of 34 dB-Hz

Figure 2. CLIMAT Block Diagram

CARRIER-TO-NOISE DENSITY CALCULATION

From Figure 2, it can be seen that the satellite availability model depends on two inputs. The first one is based on the required carrier-to-noise density ratio (C/N0), called receiver C/N0 threshold, for the receiver to satisfactorily function. In the receiver code acquisition mode, a typical number used for the threshold is 34 dB-Hz, and in the tracking mode a typical value for the threshold is 30 dB-Hz. The second

Figure 1. Combined Effects of C/A Code Self-Interference and Satellite-to-User Geometry


one is the available effective , which is equal to

. For any satellite if the available

is less than 30 dB-Hz, that particular satellite is not available for both code acquisition and tracking. On the other hand, if the available C is less than 34 dB-Hz, but greater than 30 dB-Hz, that particular satellite is not available for code acquisition. So the key question is how do we calculate the available C .

'0/C N

/

( 0 0/C N I+'0/C N

)

'0N

'0/ N

( )N

CA0,CDMA i i

i = 1

I (P CAα β= ∑

I0,Intra = Equivalent Noise Density due to interference from all other code signals from all the visible GPS Satellites. For receiving CA codes, other code signals are from P, M and IM in GPS.

( )( )N

P M IM0,Intra i i i i

i = 0

I (P P P ) (3)P M IMα β β β= + +∑ In this section the approach to the interference

calculation will be outlined. The basic approach used in the analysis is to determine the effective carrier power to one-sided noise spectral density ratio C as a

measure of the system performance. This C measure is applicable to bit error rate (BER) calculations and code acquisition, but not to code tracking for which tracking error variance is a more appropriate measure. Effective carrier-to-noise density ratio ( C ) is shown in Equation (1) and can be written as

'0/ N/ '

0N

'0/ N

Where

αi = Composite transmit/receive antenna gain, from ith satellite to the GPS user

Px = Received power; x = CA, P, M or IM code.

N+1 = Number of visible satellites from a given user location. β 's = Respective code despread factors (also know as

spectral separation coefficient) which is given by '

0 0 0,CDMA 0,Intra 0,Inter 0,External 0,Margin

C C = (1)N N+I + I I I Iν + + +

2

X BB X PN-

= H (f) S (f)S (f)df (4)β∞

∞∫

Where

C = Code signal power from the desired GPS Satellite which includes transmit/receive antenna gains and receiver implementation loss

Where SX(f) is the two-sided unit-power spectral density (psd) of the respective interfering signal from the same system (e.g., GPS) and SPN(f) is the unit psd of the signal being interfered with.

N0 = Receiver thermal noise power spectral density

2

BB PN-

= H (f) S (f)df ( 1) (2)ν∞

∞

≤∫ Where

( )N

Inter0,Inter i i Inter

i = 1

I (P (5)α β= ∑

HBB(f) is the baseband equivalent transfer function of the transmitter and the receiver bandpass filters and SPN(f) is the two-sided unit-power psd of the code being correlated at the receiver.

Where InteriP is the received power from the ith satellite in the

other interfering system (e.g., Galileo) and βInter is given by equation (5) with SInter(f) is the two-sided unit-power spectral density (psd) of the respective interfering signal from a different system (e.g., Galileo). Equations (5) and (6) can also be used to compute I0,External with appropriate changes in the parameter values and I0,Margin is any margin mandated in the system operation.

I0,CDMA = Equivalent Noise Density due to interference from similar code signals from all other visible GPS Satellites. For example, for receiving CA code,


Table 1. Despread Factor Xβ in dB/Hz

1

( )( )

X

PN

S fS f

1 MCPS NRZ

Random

10 MCPS Random

BOC(2,2) Random

BOC(5,1) Random

BOC(10,5) Random

BOC(14,2) Random

BOC(15,1) Random

1 MCPS NRZ

Random –61.8* –70.2 –73.4 –82.4 –88.1 –91.2 –91.6

10 MCPS NRZ

Random –70.2 –71.9 –71.1 –77.0 –80.9 –83.5 –84.2

BOC(10,5) Random –88.1 –80.9 –80.1 –87.9 –73.2 –82.6 –88.7

* For C/A codes this value is much higher, as explained in the next section. BOC – Binary Offset Carrier modulation used in modernized GPS military signal. Also, some versions of this are proposed for future GPS and Galileo civilian use.

Spectral separation coefficients (SSC) or despread factors calculated using equation (4) for some sample signals are given in Table 1. . For example, the despread factor for interference from P-code (which is standard) to a C/A code signal is –70.2 dB/Hz and from a C/A code assumed strictly random the despread factor is –61.8 dB-Hz. The interference noise density (I0) is simply obtained by adding the received interference power to the corresponding despread factor. This method works well for all the code combinations in Table 1 except for C/A codes for which the I0’s are much higher than can be obtained from Table 1 because of the spectral line effects of the C/A code. Equations (3) and (4) can also be used to calculate the remaining interference psd in Equation (1) by choosing the appropriate psd for . ( )XS f

CODE ACQUISITION MODEL

As mentioned earlier, code acquisition is the most sensitive aspect of the system operation when it comes to susceptibility to CDMA noise. This section summarizes the CDMA noise calculation as applied to the C/A code acquisition process, and provides sample numerical examples illustrating its susceptibility to CDMA noise. A generic noncoherent code acquisition circuit is shown in Figure 3; the corresponding baseband model used for analysis is shown in Figure 4. It is assumed that the search for the correct code phase is performed serially with a step size of ½ code chip. The analysis culminates in closed-form expressions for CDMA noise power spectral density at the output of the

squarer, which are then used for calculating the I0,Intra term of the effective (C ) in Equation (1). '

0/ N

( )2

+

++

X

X

Local Oscillator/Reference CodeGenerator

C(t+Td)Cos(δ.) 2πfct

Received GPS Signal + Noise +Interference

( )2I & DFilter

I & DFilter

I&D Filter/ThresholdDetector

I2

Q2

C(t+Td)Sin(.)2πfct

( )2

+

++

XX

XX

Local Oscillator/Reference CodeGenerator

C(t+Td)Cos(δ.) 2πfct

Received GPS Signal + Noise +Interference

( )2I & DFilter

I & DFilter

I&D Filter/ThresholdDetector

I2

Q2

C(t+Td)Sin(.)2πfct

Figure 3. Noncoherent Code Acquisition Circuit

LPFH1(f)

LPFH2(f)

•2r(t)

a(t)*

m(t) y(t) x(t) z(t)

ThresholdDevice

Code-phase/FrequencySelect (Ta, fa)

exp[+j2πfct]*

RF/IF(BIF)

Figure 4. Baseband Code Acquisition Model

The two (baseband) input waveforms to the correlator in Figure 4 can be expressed as


]}2[exp{)()()()()(

0 aaar tfjTtcAtatntstr

ϕπ +⋅⋅−⋅=+=

where a(t) denotes the locally generated reference code waveform, s(t) denotes the received GPS signal (including M interference sources):

0( ) ( ) exp{ [2 ( ) ]}

M

i i i i i i ii

s t A c t T j f t t Tπ θ ϕ=

= ⋅ − ⋅ ⋅ + − +∑

and n(t) denotes the zero-mean white Gaussian thermal noise process with autocorrelation function

).(2)(sinc2)( 0IFIF0 τδττ ⋅≈⋅= NBBNRn The following assumptions are made in the analysis:

(A1) The propagation delays {Ti} and Doppler shifts {fi} remain unchanged while dwelling in any particular acquisition code-phase Ta. (A2) The pre-squarer low-pass filter h1(t) is real and rejects all frequency components beyond one half the C/A code repetition rate fR=1/TR. (A3) The BPSK-modulated navigation data bits are equally probable ±1, and the navigation data processes {θi(t)} are slow-varying with respect to the pre-squarer low-pass filter h1(t). (A4) The random carrier phases {ϕi} are independent of the navigation data processes {θi(t)}, and are independent and uniformly distributed as uniform over (−π, +π).

The first set of examples consists of three worst-case scenarios described in Tables 3, 4, and 5, respectively. These scenarios were taken at three different time instants over a stretch of about 14 minutes during which the carrier-to-noise-density ratio C/N0 was degraded significantly as observed from the output of the CLIMAT. The descriptions of each scenario include the total number of satellites visible to the receiver, as well as the corresponding received power levels (including user antenna gain) in dBw, Doppler frequency shift in hertz, and path delay in units of C/A code chip. Assuming a thermal noise density level of N0=−201.5 dBw/Hz and a zero frequency offset between the desired and reference code waveforms, the resulting increments in post-squarer CDMA noise density level as a function of the acquisition code-phase used in the reference waveform are given in Figures 5, 6, and 7, respectively. A common feature of these figures is that the average CDMA noise increment is markedly lower than numerous “instantaneous” noise increments irregularly scattered across the entire reference code-phase space. Also, as evidenced in Figures 8 and 9, the same feature prevails when the frequency offset between the desired code waveform and the reference code waveform is non-zero.

(A5) The additive zero-mean white Gaussian thermal noise process n(t) is independent of both the navigation data processes {θi(t)} and the random carrier phases {ϕi}.

Table 2 summarizes the equations needed for calculating of the power spectral density (PSD) of the filtered squarer output z(t). As can be seen from these equations, the PSD expression has three components: an interference-on-interference (I×I) component, a noise-on-noise component (N×N), and an interference-on-noise (I×N) component due to the interaction between the interfering code signals and the thermal noise. Furthermore, since the contributions from these components vary, depending on the underlying Doppler conditions, none of these components can be safely

ignored in evaluating the CDMA noise. Since the bandwidth of the post-squarer low-pass filter H2(f) is small—typically on the order of the navigation data bandwidth—the peak of the PSD Sz(f) can be taken as the “noise density level” at the input of the threshold device in Figure 4. Therefore, the increase in this noise density level (from the case of noise-alone to the case of noise-plus-interference) provides a proportional measure of the post-squarer CDMA noise. Taking the square root of the post-squarer CDMA noise density value approximates the CDMA noise density level at the correlator output (i.e., input of the squarer). This is a good approximation when the signal-to-noise ratio is very low, which is the case when the reference code offset is more than a chip.

Numerical Examples Two sets of numerical examples are presented in this section to illustrate the susceptibility of the code acquisition process to CDMA noise. In both sets of examples, the increase in post-squarer CDMA noise density level is calculated using the equations summarized in Table 2. All discrete PSD components at f=0 are suppressed because they convey only DC power.


The second set of examples consists of a collection of scenarios over a stretch of 2000 seconds involving three GPS satellites in view, one scenario per second. The

received power of the desired code waveform is set at a constant level that is 34 dB above a thermal noise density of N0=−200.5 dBw/Hz. The received power

Table 2. Summary of Equations to Calculate C/A Code CDMA Noise PSD 2

2 )()()( fHfSfS xz ⋅=

)()()()( NN,NI,II, fSfSfSfS xxxx ××× ++=

( ) ( )( )∑ ∑−

= +=× −++−−⋅⋅+⋅=

1

0 1,,,,,,

2,4

12II, ]~~[]~~[)()(

M

i

M

inanainianaininix fffSfffSBfBfS δ

( )∑=

× ++−⋅⋅+⋅=M

iaibaibix ffSffSDfDfS

0,,

2212

NI, )~()~()()( δ

)(4)(4)( 420

2420NN, fANfGANfS rrx Λ⋅+⋅⋅=× δ

)()()()( )3(

,)2(

,)1(

,, fSfSfSfS nininini ++=

( ) ( ) ( ) ( ) [ ]

=⋅−≠−⋅⋅+⋅−

→∗⋅= ⋅⋅

0,10,)2(sinc1sinc1

)(sinc)(31

2122

12

fffTfT

fHfTTfSb

R

Rb

R

b

R

TT

RTfTT

RTT

bbbπ

( ) ( ) [ ]

=⋅≠−⋅⋅

→∗=Λ ⋅⋅

0,0,)2(sinc1

)()()(1

32

2112

12

1 fffT

fHfHfR

RR

T

RTfT π

( ) 2

,1

2

,1222

,

2

0

2

,1222

)~()~(2

)~(

annaiinirni

M

iaiiir

fHfHAAAB

fHAAB

⋅⋅⋅⋅⋅=

⋅⋅⋅= ∑

=

γγ

γ

2

,124

02

0

2

,124

02

)~(4

)~(4

aiiiri

M

iaiiir

fHAAND

fHAGAND

γ

γ

⋅⋅=

⋅⋅⋅= ∑=

( )RTdvvHduuh 12

12

1 )()( →==G ∫∫

( ) ( )( ) (( ))( ) ( )( )(max)

,22(max)

,1)3(

,

(min),

(max),

22(min),

(max),

1)2(,

(min),

22(min),

1)1(,

~sinc~)(

~~sinc~~)(

~sinc~)(

nibnibTni

ninininiTni

niniTni

TTfTTfS

TTfTTfS

TfTfS

b

b

b

−⋅⋅−=

−⋅⋅−=

⋅⋅=

10 ,0

( ) ( ) exp[ 2 ]R

R

T

i i i a i a RT c t T c t T j m f t dtγ π= − − ⋅ + ⋅∫

( )( )( )

Duration)Bit Data Navigation (

~,~max~

~,~min~),0[mod~

(max),

(min),

=

=

=

∈=

b

nini

nini

bbii

TTTT

TTT

TTTT

( )

( )( )( ))Rate Repetition CodeC/A /1(

1intint~

),[~~

2/21

,

,

22,,,

,

==

+⋅=

−=

+−∈⋅−=

RR

ff

ai

aiai

ffRaiaiai

Tf

m

ffffmff

R

ai

RR


from interfering satellites was set at 10 dB higher than the power level of the desired signal. A Doppler shift and a path delay are associated with each scenario, and these Doppler/delay values are used to arrive at a figure similar to those in Figures 5, 6, and 7, from which a scenario-specific average and maximum increments in post-squarer CDMA noise are obtained. Figure 10 collects the average/maximum CDMA noise increments of all 2000 scenarios and displays them as a function of the scenario time line. Consistent with what was observed in the first set of examples, the average CDMA noise increments are markedly lower than the maximum CDMA noise increments. Finally, as evidenced in Figure 11, the same observation holds even when the discrete PSD components are included in the computation.

Table 4. Description of Scenario 5


Doppler 7 2139.57:=Delay 7 74.09 1023⋅:=P 7 157.57−:=

Doppler 6 3382.34−:=Delay 6 82.10 1023⋅:=P 6 163.76−:=

Doppler 5 2915.6−:=Delay 5 80.21 1023⋅:=P 5 162.69−:=

Doppler 4 880.66−:=Delay 4 73.79 1023⋅:=P 4 157.27−:=

Doppler 3 2122.13:=Delay 3 70.54 1023⋅:=P 3 154.90−:=

Doppler 2 3114.91−:=Delay 2 74.90 1023⋅:=P 2 158.36−:=

Doppler 1 1176.3−:=Delay 1 65.59 1023⋅:=P 1 154.32−:=

Doppler 0 2142.25:=Delay 0 81.24 1023⋅:=P 0 163.31−:=

i 0 M..:=M 7:=

Scenario #4 of "1+7"

k 0:=

Incr

ease

d N

oise

Lev

el (d

B)

Doppler 7 1869.01:=Delay 7 73.48 1023⋅:=P 7 156.97−:=

Doppler 6 3477.41−:=Delay 6 83.14 1023⋅:=P 6 164.22−:=

Doppler 5 3103.15−:=Delay 5 81.13 1023⋅:=P 5 163.25−:=

Doppler 4 1202.71−:=Delay 4 74.11 1023⋅:=P 4 157.58−:=

Doppler 3 1870.60:=Delay 3 69.93 1023⋅:=P 3 154.67−:=

Doppler 2 3255.69−:=Delay 2 75.83 1023⋅:=P 2 159.26−:=

Doppler 1 1439.28−:=Delay 1 68.98 1023⋅:=P 1 154.39−:=

Doppler 0 1875.13:=Delay 0 80.62 1023⋅:=P 0 162.96−:=

i 0 M..:=M 7:=


Average = 1.3 dBScenario #5 of Case ‘1+7’ facq = f0

1, 2046..

0 256 512 768 1024 1280 1536 1792 20480

1

2

3

4

5

6

7

8

9

10

11

12

Code Phase Offset (Tc/2)

k 0 1, 2046..:=

0 256 512 768 1024 1280 1536 1792 20480

1

2

3

4

5

6

7

8

9

10

11

12


Incr

ease

d N

oise

Lev

el (d

B)


Figure 6. C/N0 Degradation at the Detector Input- Scenario 5

Figure 5. C/N0 Degradation at the Detector Input- Scenario 4



Scenario #4 of Case ‘1+7’ facq = f0+1000 Hz

k 0 1, 2046..:=

0 256 512 768 1024 1280 1536 1792 20480

1

2

3

4

5

6

7

8

9

10

11

12


Incr

ease

d N

oise

Lev

el (d

B)

Doppler6 1581.60:=Delay6 72.96 1023⋅:=P6 156.1−:=

Doppler6 0:=Delay6 0 1023⋅:=P6 300.00−:=

Doppler5 3267.80−:=Delay5 82.10 1023⋅:=P5 163.76−:=

Doppler4 1513.13−:=Delay4 74.52 1023⋅:=P4 157.99−:=

Doppler3 1608.44:=Delay3 69.40 1023⋅:=P3 154.48−:=

Doppler2 3381.86−:=Delay2 76.89 1023⋅:=P2 160.16−:=

Doppler1 1694.27−:=Delay1 69.46 1023⋅:=P1 154.52−:=

Doppler0 1590.90:=Delay0 80.70 1023⋅:=P0 162.66−:=

i 0 M..:=M 6:=


Figure 9. C/N0 Degradation at the Detector Input—Scenario 4 with 1000 Hz Offset

0.0

0.5

1.0

1.5

2.0

2.5

3.0

506000 506400 506800 507200 507600 508000

Time of Week (sec)

Incr

ease

d N

oise

Den

sity

Lev

el (d

B) MAX

AVG


k 0 1, 2046..:=

0 256 512 768 1024 1280 1536 1792 20480

1

2

3

4

5

6

7

8

9

10

11

12


Incr

ease

d N

oise

Lev

el (d

B)

Figure 10. C/N0 Degradation at the Detector Input—Scenario 34+10 dB, without DC

MAX

AVG

0.0

0.5

1.0

1.5

2.0

2.5

3.0

506000 506400 506800 507200 507600 508000

Time of Week (sec)

Incr

ease

d N

oise

Den

sity

Lev

el (d

B)

Figure 7. C/N0 Degradation at the Detector Input—Scenario 6

Scenario #4 of Case ‘1+7’ facq = f0+100 Hz

k 0 1, 2046..:=

0 256 512 768 1024 1280 1536 1792 20480

1

2

3

4

5

6

7

8

9

10

11

12


Incr

ease

d N

oise

Lev

el (d

B)

Figure 11. C/N0 Degradation at the Detector Input—Scenario 34+10 dB, with DC

Figure 8. C/N0 Degradation at the Detector Input—Scenario 4 with 100 Hz Offset


SystemView Simulation

A simulation of the block diagram of the baseband noncoherent acquisition circuit shown earlier in Figure 3 is described in this section. The received signal, corrupted by thermal noise and other interference sources, is despread by the reference code with an estimated code phase and carrier Doppler to form the in-phase and quadrature components, which in turn are low-pass filtered (Integrate & Dump Filter), squared and added to form I2 + Q2 signal. This signal is further filtered, if necessary, using another I & D filter and the output is compared against a threshold in the detector to decide whether the estimated code phase is within the tracking range of the code tracking loop. In this paper, instead of measuring the detection and false-alarm rates of the detector, effective carrier-to-noise density ratio (C/N0

’) is measured at the input of the detector from which C/N0 at the correlator output (input of squarer) is deduced. By comparing the C/N0 for noise-only case with noise-plus-interference case, a C/N0 degradation number is obtained.

Figure 12. SystemView Simulation Block Diagram

A block diagram of a simulation of the above acquisition circuit using SystemView software (copyright of Elanix Corporation) is shown in Figure 12. Tokens 4, 12, 14, 15, 1, and 384 are used to generate C/A code signal and Gaussian noise samples. Tokens 7, 11, 193, and 383 are amplifiers to set the gains for the desired C/N0 ratio. Token 427 is a DCMA noise generator for which details are shown in Figure 13. For each visible satellite, received power levels including user antenna gain in the direction of that particular satellite, Doppler frequency shifts and path delays as obtained from CLIMAT as explained before are input to the simulation. Code acquisition circuit is shown in Figure 14. Figure 13. SystemView Simulation—C/A Code CDMA

Noise Generators

Figure 14. SystemView Simulation Block Diagram—Code Acquisition Circuit


Simulation Results Conclusions

As an example, the desired signal and the interfering signals were generated according to the scenario 6 parameters as described in Table 6. Also, noise samples corresponding to a noise spectral density of –201.5 dBW/Hz were added to the signal. After correlation with the reference code at some trial code phase offset, followed by I & D filtering and squaring, samples were collected at the squarer output. The probability density function (PDF) was calculated from these samples using histograms and plotted in Figure 15. An additional noise source was added at the input to replace the CDMA noise from the interfering satellites, and the noise density was set at a level to increase the overall noise level by +1.25 dB and +2.5 dB over the quiescent noise level. The PDFs were calculated as described before and were plotted for comparison in Figure 15. As can be seen from this figure, the PDFs corresponding to the C/A code CDMA noise (marked Sn+N+I(CA) in Figure 15) and a thermal noise increase of 1.25 dB (marked Sn+N(+1.25dB)) match very closely, indicating that an equivalent noise increase due to the C/A code CDMA noise in scenario 6 corresponds to 1.25 dB. This number is more in line with the analytical results presented earlier using the closed-form solution (see Figure 7).

A two-step procedure is proposed to analyze the impact of C/A code CDMA noise on the GPS C/A code operation. Step 1 is to use the commonly used methodology of calculating C , ignoring the C/A code spectral line effect. Step 2 is necessary only when the is different from C/No by more than 0.25 dB or the C/No is very close to 34 dB-Hz. In Step 2, a more comprehensive analysis model such as used in CLIMAT should be utilized.

'0/ N

'0/C N

Aerospace has developed a comprehensive interference analysis tool called CDMA Limited Interference Model and Analysis Tool (CLIMAT) to analyze the worst-case impact of the C/A code CDMA noise on the code acquisition and tracking performance of the GPS C/A codes. This tool combines geometric considerations of the user and the satellite orbits with the analytical modeling of the interference phenomenon. Analytical model validation has been done using a commercially available communication systems simulation software tool called SystemView (copyright by Elanix Inc.), and there is a good agreement between the analytical and the simulation results.

Numerical results obtained using the CLIMAT have shown that under certain scenarios, the carrier-to-noise density (C/N0) degradation due to worst-case CDMA noise could exceed 1.5 dB, whereas traditional methods used in the past indicate a degradation of less than 0.5 dB. This 1 dB or more of the degradation difference may not be very detrimental to the GPS operation in most of the applications but could be important enough in safety-of-life type applications. Also, when GPS frequency band sharing with dissimilar services is considered over 1 dB of C/N0 degradation may make all the difference between satisfying and not satisfying the mission requirement.

SystemView

20.e-3

20.e-3

120.e-3

120.e-3

220.e-3

220.e-3

320.e-3

320.e-3

420.e-3

420.e-3

120.e-3

100.e-3

80.e-3

60.e-3

40.e-3

20.e-3

0

Bin

Cou

nt

Amplitude

PDF of samples at the 50 Hz Filter Output

Sn+N Sn+N+I(CA)

Sn+N(+1.25dB)

Sn+N(+2.5dB)

Although it is desirable to use CLIMAT in all sharing studies, because of the complexity of the model involved, it is suggested that a tiered approach be taken in the interference analysis. In the first step, C/N0 degradation can be calculated using the more traditional but simple method (for example, convolving GPS and interfering signal power spectral densities to determine the peak interference contribution). If the degradation is less than 0.5 dB and the resulting C/N0 is above 36 dB-Hz, there is no need to run CLIMAT to determine the degradation with any further precision. If, however, the degradation is more than 0.5 dB or the resulting C/N0 is less than 36 dB-Hz, a more comprehensive study should be done.

Figure 15. PDF of Samples at Threshold Device Input—SystemView Simulation



CLIMAT was developed primarily to study C/A code-related issues, but it can very easily be modified to analyze other codes such as being proposed for L2C, L5, or any other codes.

References

[1] S. Lazar, S. Raghavan, and D. Turner, “GPS Spectrum: Sharing or Encroachment,” GPS World 11, no. 9 (September 2000): 46–56.

[2] S. Raghavan et al., “The CDMA Limit of C/A

Codes in GPS Applications-Analysis and Laboratory Test Results,” in Proceedings of the ION GPS-99, 12th International Technical Meeting of the Satellite Division of the Institute of Navigation, Nashville, TN, September 15, 1999.

[3] Bradford W. Parkinson and James J. Spilker Jr.,

eds., Global Positioning System: Theory and Applications, Volume I (Volume 163 in Progress in Astronautics and Aeronautics) (Washington, DC: AIAA, 1996), page 63, Volume 1.

[4] R. L. Peterson, R. E. Ziemer, and D. E. Borth,

Introduction to Spread Spectrum Communications (Englewood Cliffs, NJ: Prentice Hall, 1995).

[5] Kuang Tsai, “Cross-Code Interference for GPS

C/A Code Acquisition,” Aerospace IOC, February 26, 2002.

[6] A. J. Van Dierendonck, “Scenario 34+10 dB”

description, personal communication.

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