GPS Signal - A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach - page 18

TA B L E 2 . 1 .
Output of the exclusive OR operation

TA B L E 2 . 2 .
Output of ordinary multiplication

Input Input Output Input Input Output

0 0 0 − 1 − 1 1

0 1 1 − 1 1 − 1

1 0 1 1 − 1 − 1

1 1 0 1 1 1

data generator are synchronized through the X 1 signal supplied by the P(Y) code
generator.
After code generation, the codes are combined with the navigation data through
modulo-2 adders. The exclusive OR operation is used on binary sequences repre-
sented by 0's and 1's, and its properties are shown in Table 2.1.
If the binary sequences were represented by the polar non-return-to-zero rep-
resentation, i.e., 1's and

1's, ordinary multiplication could be used instead. The
corresponding properties of the multiplication with two binary non-return-to-zero
sequences are shown in Table 2.2.
The C/A code

−

data signals are supplied to the
two modulators for the L1 frequency. Here the signals are modulated onto the
carrier signal using the binary phase shift keying (BPSK) method. Note that the
two codes are modulated in-phase and quadrature with each other on L1. That is,
there is a 90 ◦ phase shift between the two codes. We return to this issue shortly.
After the P(Y) part is attenuated 3 dB, these two L1 signals are added to form the
resulting L1 signal. The so-called standard positioning service (SPS) is based on
C/A code signals alone.
It follows that the signal transmitted from satellite k can be described as

⊕ data and the P(Y) code ⊕

2 P C C k

) cos s k D k

( t ) = ( t ) ⊕ ( t ( 2 π f L1 t )

2 P PL1 P k

) sin

D k

+ ( ) ⊕ ( ( π )

t t 2 f L1 t

2 P PL2 P k

) sin D k

+ ( t ) ⊕ ( t ( 2 π f L2 t ), (2.3)

where P C , P PL1 ,and P PL2 are the powers of signals with C/A or P code, C k is the
C/A code sequence assigned to satellite number k , P k is the P(Y) code sequence
assigned to satellite number k , D k is the navigation data sequence, and f L1 and
f L2 are the carrier frequencies of L1 and L2, respectively.
Figure 2.2 shows the three parts forming the signal on the L1 frequency. The
C/A code repeats itself every ms, and one navigation bit lasts 20 ms. Hence for
each navigation bit, the signal contains 20 complete C/A codes .
Figure 2.3 shows the Gold code C , the navigation data D , the modulo-2 added
signal C D , and the carrier. The final signal is created by binary phase-shift key-

ing (BPSK) where the carrier is instantaneously phase shifted by 180 ◦ at the time
of a chip change. When a navigation data bit transition occurs (about one third
from the right edge), the phase of the resulting signal is also phase-shifted 180 ◦ .

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