GPS Signal - A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach - page 20

C

D

C ⊕ D

Carrier

Final
Signal

FIGURE 2.3. The effect of BPSK modulation of the L1 carrier wave with the C/A code
and the navigation data for one satellite. The resulting L1 signal is the product of G , N ,
and the carrier signals. The plot contains the first 25 chips of the Gold code for PRN 1.

The sequence would have 512 ones and 511 zeros, and these would appear to be
distributed at random. Yet the string of chips so generated is entirely deterministic.
The sequence is pseudorandom, not random. Outside the correlation interval the
ACF of p

( t ) is − 1 / N . For the C/A code the constant term is − 1 / N =− 1 / 1023,

which is shown in Figure 2.4.
The ACF can be expressed as the sum of this constant term and an infinite series
of the triangle function r X (τ ) defined in (1.15). This infinite series is obtained

by the convolution of r X (τ ) with an infinite series of impulse functions that are

phase-shifted by mNT c :

∞

1
N +

N + 1

r P (τ ) =− r X (τ ) ∗ δ(τ + mNT c ), (2.4)

N

m =−∞

where denotes convolution. The power (line) spectrum of this periodic PRN

sequence is derived from the Fourier transform of (2.4):

∗

δ(ω) + sinc 2 m

∞

N π

NT c

1
N 2

m 2

S P (ω) = ( N + 1 ) δ ω + (2.5)

m =−∞

m

= 0

for m =± 1 , ± 2 , ± 3 ,... ; see Kaplan & Hegarty (2006), page 119.

2.3.2 Gold Sequence Generation—Overview
The generation of the Gold codes is sketched in Figure 2.5. The C/A code gener-
ator contains two shift registers known as G 1 and G 2 . These shift registers each