GPS Signal - A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach - page 23

G 1 Generator

G 1

1 23456789 0

1.023MHz
Clock

Reset

Phase Selector

G 2 i Gold Code

C/A code
XG i (t)

S 1 S 2

G 2

1 23456789 0

1023
Decode

1kHz

G 2 Generator 50Hz

÷ 20

FIGURE 2.5. C/A code generator. The code generator contains two shift registers, G 1 and
G 2 . The output from G 2 depends on the phase selector. The different configurations of the
phase selector makes the different C/A codes.

content of the last cell is “read out” as output. The special properties of such shift
registers depend on how information is “read in” to cell 1.
For a tapped linear feedback shift register, the input to cell 1 is determined by
the state of the other cells. For example, the binary sum from cells 3 and 10 in a
10-cell register could be the input. If cells 3 and 10 have different states (one is 1
and the other 0), a 1 will be read into cell 1 on the next clock pulse. If cells 3 and
10 have the same state, 0 will be read into cell 1. If we start with 1 in every cell, 12
clock pulses later the contents will be 0010001110. The next clock pulse will take
the 1 in cell 3 and the 0 in cell 10 and place their sum (1) in cell 1. Meanwhile, all
other bits have shifted cell to the right, and the 0 in cell 10 becomes the next bit in
the output. A shorthand way of denoting this particular design is by the modulo-2
polynomial f x 3 x 10 . Such a polynomial representation is particularly

( x ) = 1 + +

h 2 x 2 h 3 x 3

useful because if 1 / f ( x ) = h 0 + h 1 x + + +··· , then the coefficients

h 0 , h 1 , h 2 , form the binary output sequence.

The C/A code is generated by two 10-bit LFSRs of maximal length 2 10

...

− 1.

x 3 x 10 One is the 1 + + register already described and is referred to as G 1 .The

x 10 . Cells 2, 3, 6, 8, 9, and 10
are tapped and binary-added to get the new input to cell 1. In this case, the output
comes not from cell 10 but from a second set of taps. Various pairs of these second
taps are binary-added. The different pairs yield the same sequence with different
delays or shifts (as given by the “shift and add” or “cycle and add” property: a

x 2 x 3 x 6 x 8 x 9

other has f ( x ) = 1 + + + + + +