GPS signals contain information to identify each satellite, the satellite's location, timing details, and navigation data. Signals are modulated using phase-shift keying onto two carrier frequencies, L1 and L2. The C/A code and encrypted P-code are modulated onto L1, while only the P-code is modulated onto L2. Digital signal processing techniques like filtering, frequency translation, correlation and cross-correlation are used in GPS receivers to acquire and track satellite signals. Anti-spoofing of the P-code led to techniques like squaring, code-aided squaring, cross-correlation and Z-tracking to still allow civilian use of the encrypted signal.

1. GPS Signal Structure
• Sources:
– GPS Satellite Surveying, Leick
– Kristine Larson Lecture Notes
http://www.colorado.edu/engineering/ASEN/asen
4519/asen4519.html

2. GPS Signal Requirements
• Method (code) to identify each satellite
• The location of the satellite or some
information on how to determine it
• Information regarding the amount of time
elapsed since the signal left the satellite
• Details on the satellite clock status

3. Important Issues to Consider
• Methods to encode information
• Signal power
• Frequency allocation
• Security
• Number and type of codes necessary to
satisfy system requirements

4. Overview of Satellite Transmissions
• All transmissions derive from a
fundamental frequency of 10.23 Mhz
– L1 = 154 • 10.23 = 1575.42 Mhz
– L2 = 120 • 10.23 = 1227.60 Mhz
• All codes initialized once per GPS week at
midnight from Saturday to Sunday
– Chipping rate for C/A is 1.023 Mhz
– Chipping rate for P(Y) is 10.23 Mhz

5. Schematic of GPS codes and carrier phase

6. GPS Signal Characteristics

7. Digital Modulation Methods
• Amplitude Modulation (AM) also known as
amplitude-shift keying. This method requires
changing the amplitude of the carrier phase
between 0 and 1 to encode the digital signal.
• Frequency Modulation (FM) also known as
frequency-shift keying. Must alter the frequency
of the carrier to correspond to 0 or 1.
• Phase Modulation (PM) also known as phase-
shift keying. At each phase shift, the bit is flipped
from 0 to 1 or vice versa. This is the method used
in GPS.

8. Modulation Schematics

9. Modulo-2 recovery of GPS code
Modulo-2 arithmetic: 0 + 0 = 0; 0 + 1 = 1; 1 + 0 = 1; 1 + 1 = 0
Bit shifts aligned
MUST MOD-2 ADD RECEIVER-GENERATED CODE TO RECOVER

10. Superposition of codes - details
• Superposition of two codes is not unique because
the bit transition occurs at the same epoch;
remember that both codes and phases are multiples
of the fundamental frequency
• Need to impose an additional constraint to arrive
at a solution - quadri-phase-shift keying (QPSK),
which puts the two codes 90° (π/2)

11. Phase and Quandrature - General
General Expression:
y(t) = y1(t) + y2(t) = x1(t)cosωt + x2 (t)sinωt
where
y1(t) is in phase (I) and y1(t) is in quandrature (Q)
All spectral components of y1(t) are 90° out of phase
with those of y2(t). This allows this the two signals to
be separated in the receiver.
2

12. Codes on L1 and L2
S1
p
(t) = ApP p
(t)DP
(t)cos(2πf1t) + AcGP
(t)DP
(t)sin(2πf1t)
where
Ap, Ac = amplitudes (power) of P(Y) - code and C / A- code
PP
(t) = pseudorandom P(Y) - code
G
P
(t) = C / A- code (Gold code)
DP
(t) = navigation data stream
and
S2
p
(t) = BpP p
(t)DP
(t)cos(2πf2t)

13. Codes on L1 and L2 (con’t.)
Pp
(t)DP
(t) and GP
(t)DP
(t) imply modulo- 2 addition
and the P(Y) - code is also a modulo - 2 sum of two
pseudorandom data streams:
Pp
(t) = X1
(t)X2
(t − pT)
0 ≤ p ≤ 36
1
T
=10.23 Mhz

14. GPS signal strength - frequency domain
Note that C/A code is below noise
level; signal is multiplied in the
Receiver by the internally calculated
code to allow tracking.
C/A-code chip is 1.023 Mhz
P-code chip is 10.23 Mhz
Power = P(t) = y2
(t)
The calculated power spectrum
derives from the Fourier
transform of a square wave
of width 2 and unit amplitude.π
Common function in DSP
called the “sinc” function.
sinc(x) =
sin(πx)
πx
=
1
2π
e
iωx
∂ω
−π
π
∫
Bandwidth ≡ B ≈
1
T
where
T ≡ is chip duration

15. Digital Signal Processing Techniques
• Filtering: Allows one to remove some
portion of the frequency spectrum that may
contain unwanted signal.
– Low Pass Filter: lets all frequencies below a
cutoff frequency through.
– High Pass Filter: lets all frequencies above a
cutoff frequency through.
– Band Pass Filter: lets all frequencies within a
specified window pass through. The window
is called the passband

16. DSP Techniques, con’t.
• Frequency Translation and Multiplication:
technique to shift frequency spectrum of some
signal to another portion of the frequency domain.
– Up-conversion: translate signal to higher frequencies.
– Down-conversion: translate signal to lower frequencies.
Commonly done in GPS receivers. Multiply signal by
sine function in a “mixer.” Special case is signal
squaring and may be used to recover the pure carrier
phase from a bi-phase modulated ranging signal.

17. DSP Techniques, con’t.
• Spread Spectrum: broadly defined as a mechanism
by which the bandwidth of the transmitted code is
much greater than the baseband information signal
(e.g. the navigation message in GPS)
– FDMA: Frequency Division Multiple Access. Requires
different carriers. Used by GLONASS.
– TDMA: Time Division Multiple Access. Several channels
share transmission link. Used by many cellular telephone
providers and LORAN-C.
– CDMA: Code Division Multiple Access. Requires
pseudorandom codes by transmitted and also generated for
correlation within the receiver. Used by GPS.

18. DSP Techniques, con’t.
• Cross-correlation: Used by GPS receivers
to determine what signal is coming from a
specific satellite. Can be generalized to
extracting information from any
multiplexed digital signal.
Cij (Δt) =
1
τ
yi (t)y j (t + Δt)dt =
1
1−
Δt
T
≈ 0
⎧
⎨
⎪
⎩
⎪t0
t 0 +τ
∫
if Δt = 0
if | Δt | ≤ T
if | Δt | > T
where τ denotes the integration time and
yi (t) and yj (t) are continuous functions ( e.g. PRN codes)

19. PRN Cross-correlation
Correlation of receiver generated PRN code (A) with incoming data
stream consisting of multiple (e.g. four, A, B, C, and D) codes

20. Schematic of C/A-code acquisition
Since C/A-code is 1023 chips long and repeats every 1/1000 s, it is inherently
ambiguous by 1 msec or ~300 km. Must modulo-2 add the transmitted and
received codes after correlation to increase SNR and narrow bandwidth.

21. Methods to Cope with Anti-spoofing
• Anti-spoofing: Implemented in 1994 to make P-
code unavailable to non-military users. Encrypted
P-code is referred to as Y-code.
– Squaring: Yields half-wavelength carrier and
greatly reduces SNR. Old technology.
– Code-aided squaring: Uses mathematical
similarity of the Y-code to P-code. L1 carrier is
down-converted and multiplied with a local
replica of the P-code, then squared. Results in
less reduction of SNR than simple squaring.

22. Anti-spoofing Methods, con’t.
• Cross-correlation: Takes advantage of the fact that both
L1 and L2 are modulated with the same P(Y)-code, despite
lack of knowledge of the actual P-code. Yields the
difference in pseudoranges, P1(Y) - P2(Y), and the phase
difference of L1 and L2. Again less SNR loss compared
with squaring. Can be difficult to track at low elevation
angles. Technique employed in Trimble 4000SSi/SSE.
• Z-tracking: Takes advantage of the fact that Y-code is the
modulo-2 sum of the P-code with a lower encryption rate.
Yields L1 and L2 Y-code pseudoranges and the full carrier
phases of L1 & L2. This method yields the best SNR.
Multipath performance is better than other methods.
Technique employed in Ashtech Z-12 and micro-Z.

23. AS Technologies Summary Table
Trimble 4000SSi
Ashtech Z-12 & µZ
From Ashjaee & Lorenz, 1992