Satellite Signal Acquisition, Tracking, and Data Demodulation - Understanding GPS: Principles and Applications - page 177

Figure 5.16 illustrates how the early, prompt, and late envelopes change as the
phases of the replica code signals are advanced with respect to the incoming SV sig-
nal. For ease of visualization, only 1 chip of the continuous PRN signal is shown,
and the incoming SV signal is shown without noise. Figure 5.17 illustrates the nor-
malized early minus late envelope discriminator error output signals corresponding
to the four replica code offsets in Figure 5.16. The closed code loop operation
becomes apparent as a result of studying these replica code phase changes, the enve-
lopes that they produce, and the resulting error output generated by the early minus
late envelope code discriminator. If the replica code is aligned, then the early and
late envelopes are equal in amplitude and no error is generated by the discriminator.
If the replica code is misaligned, then the early and late envelopes are unequal by an
amount that is proportional to the amount of code phase error between the replica
and the incoming signal (within the limits of the correlation interval). The code
discriminator senses the amount of error in the replica code and the direction (early
or late) from the difference in the amplitudes of the early and late envelopes. This
error is filtered and then applied to the code loop NCO, where the output frequency
is increased or decreased as necessary to correct the replica code generator phase
with respect to the incoming SV signal code phase.
The discriminator examples given thus far have assumed that each channel of
the GPS receiver contains three complex code correlators to provide early, prompt,
and late correlated outputs. In early generations of GPS receiver designs, analog
correlators were used instead of digital correlators. There was strong emphasis on
reducing the number of expensive and power-hungry analog correlators, so there
were numerous code tracking loop design innovations that minimized the number
of correlators. The tau-dither technique time shares the early and late replica code
with one complex ( I and Q ) correlator. This suffers a 3-dB loss of tracking threshold
in the code loop because only half the energy is available from the early and late sig-
nals. This loss of threshold is unimportant in an unaided GPS receiver design
because there is usually more than a 3-dB difference between the conventional code

Incoming signal

Replica signals
Early

Prompt

Late

Normalized correlator output

L P

1
1/2
0

1
1/2
0

1
1/2
0

1
1/2
0

P L E

P

L

E

P

E L

E

1 3/4 1/4 0 +1 +1/4 1

− 1/4

0 +1/4 +3/4

− 1 − 1/2 0 − − − − 1 − 1/2 0 1/2 1 −

(a)
Figure 5.16 Code correlation phases: (a) replica code 1/2-chip early, (b) replica code 1/4-chip
early, (c) replica code aligned, and (d) replica code 1/4-chip late.

(b) (c) (d)