Global Positioning System Reference
In-Depth Information
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50 bps navigation data stream, the modulo-2 addition inverts 20,460 adjacent digits
of the C/A-code. A binary 1 becomes 0 and vice versa. A binary 0 leaves the next
20,460 C/A-codes unchanged. Let the receiver reproduce the original code sequence
that is shifted in time to match the transmitted code. We can then modulo-2 add the
receiver-generated code with the received, phase-modulated carrier. The sum is the
demodulated 50 bps telemetry data stream.
The modulo-2 addition method must be generalized one additional step because
the L1 carrier is modulated by three data streams: the navigation data, the C/A-codes,
and P(Y)-codes. Thus, the task of superimposing both code streams and the navi-
gation data stream arises. Two sequential superimpositions are not unique, because
the C/A-code and the P(Y)-code have identical bit transition epochs (although their
length is different). The solution is called quadrature phase shift keying (QPSK). The
carrier is split into two parts, the inphase component (I) and the quadrature component
(Q). The latter is shifted by 90°. Each component is then binary phase-modulated, the
inphase component is modulated by the P(Y)-code, and the quadrature component is
modulated by the C/A-code. Therefore, the C/A-code signal carrier lags the P(Y)-
code carrier by 90°. For the L1 and L2 carriers we have
[78
Lin
—
8.3
——
Sho
PgE
S
1
(t)
A
P
P
p
(t)D
p
(t)
cos
(
2
A
C
G
p
(t)D
p
(t)
sin
(
2
=
π
f
1
t)
+
π
f
1
t)
(3.80)
S
p
B
P
P
p
(t)D
p
(t)
cos
(
2
2
(t)
=
π
f
2
t)
(3.81)
In these equations the symbols denote
[78
p
Superscript identifying the PRN number of the satellite
A
P
,A
C
,B
P
Amplitudes (power) of P(Y)-codes and C/A-code
P
p
(t)
Pseudorandom P(Y)-code
G
p
(t)
C/A-code (Gold code)
D
p
(t)
Telemetry or navigation data stream
The products
P
p
(t)D
p
(t)
and
G
p
(t)D
p
(t)
imply modulo-2 addition. The P(Y)-code
by itself is a modulo-2 sum of two pseudorandom data streams
X
1
(t)
and
X
2
(t
−
pT )
as follows:
P
p
(t)
=
X
1
(t)X
2
(t
−
pT )
(3.82)
0
≤
p
≤
36
(3.83)
1
T
=
10.23 MHz
(3.84)
Expression (3.82) defines the code according to the PRN number
p
. Using (3.83), one
can define thirty-seven mutually exclusive P(Y)-code sequences. At the beginning of
