Global Positioning System Reference
In-Depth Information
Carrier
f
(
t
)
Code
C
(
t
)
Data
D
(
t
)
0
1
2
20
21
Time [ms]
FIGURE 2.2. L1 signal structure:
f
(
t
)
is the carrier wave and
C
(
t
)
is the discrete C/A code
sequence. As seen, this signal repeats itself every ms.
D
(
t
)
is the discrete navigation data
bit stream. One navigation bit lasts 20 ms. The three parts of the L1 signal are multiplied to
form the resulting signal. This figure is not to scale but is only used for illustrative purpose.
The GPS C/A spectrum is illustrated in Figure 3.4.
In summary: For GPS the code length is 1023 chips, 1.023 MHz chipping rate
(1 ms period time), 50 Hz data rate (20 code periods per data bit),
∼
90% of signal
power within
∼
2 MHz bandwidth.
2.3
C/A Code
In this section, the spreading sequences used in GPS are described. We restrict
ourselves to the C/A code sequences, as we deal only with L1 signals in this topic.
The spreading sequences used as C/A codes in GPS belong to a unique family of
sequences. They are often referred to as
Gold codes
, as Robert Gold described
them in 1967; see Gold (1967). They are also referred to as pseudo-random noise
sequences, or simply PRN sequences, because of their characteristics.
2.3.1 Gold Sequence
The pseudorandom noise (PRN) codes transmitted by the GPS satellites are deter-
ministic sequences with noiselike properties. Each C/A code is generated using
a tapped linear feedback shift register (LFSR); cf. Strang & Borre (1997), Sec-
tion 14.1. It generates a maximal-length sequence of length
N
2
n
1elements.
A Gold code is the sum of two maximum-length sequences. The GPS C/A
code uses
n
=
−
=
10. The sequence
p
(
t
)
repeats every ms so the chip length is
1ms
s, which corresponds to a metric length of 300 m
when propagating through vacuum or air. For further details on the generation of
the Gold codes, we refer to Section 2.3.3. The ACF for this C/A code is
/
1023
=
977
.
5ns
≈
1
µ
NT
c
1
NT
c
r
p
(τ )
=
p
(
t
)
p
(
t
+
τ)
dt
.
0
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