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
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.
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° (p/2)
11. Phase and Quandrature - General
General Expression:
y(t)=y1
(t)+y2(t)=x1
(t)coswt+x2
(t)sinwt
where
(t) is in phase (I) and y1
y1
(t) is in quandrature (Q)
2
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.
12. Codes on L1 and L2
Sp(t)=ApPp(t)DP(t)cos(2pft)+AcGP(t)DP(t)sin(2pft)
1
11where
A,A= amplitudes (power) of P(Y)-code and C/A-code
pcPP(t)= pseudorandom P(Y)-code
GP(t)= C/A-code (Gold code)
DP(t)= navigation data stream
and
Sp(t)=BpPp(t)DP(t)cos(2pft)
2
2
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)=X(t)X(t-pT)
120£p£36
1
=10.23 Mhz
T
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 2π and unit amplitude.
Common function in DSP
called the “sinc” function.
sinc(x)=sin(px)
pò
px=1
2peiwx¶w
-p
Bandwidth ºB»1
T
where
Tº 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.
t0+t
ò
ij(Dt)=1
C(t)yj
t yi
ì
í ï
1
1-
î ï
(t+Dt)dt=
Dt
T
»0
t0
if Dt = 0
if |Dt|£T
if |Dt|>T
t denotes the integration time and
where (t) and yj
yi
(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.
