GPS Satellite Signal Characteristics - Understanding GPS: Principles and Applications - page 137

length sequence (see Section 4.2.3). There are small fluctuations in the intervals
between the correlation intervals rather than the uniform minimum correlation
level of 1/1,023 for the maximum-length sequence using a 10-bit feedback shift reg-
ister [14]. This is because the C/A code correlation process cannot be synchronously
clocked, as was assumed for the maximum-length sequence. These small fluctua-
tions in the autocorrelation function of the C/A codes result in the deviation of the
line spectrum from the sinc 2 ( x ) envelope, as shown in Figure 4.13(b). Recall that the
power line spectrum of the maximum-length sequences matched the sinc 2 ( x ) enve-
lope exactly, except for the zero-frequency term. However, the line spectrum spac-
ing of 1,000 Hz is the same for both the C/A code and the 10-bit maximum-length
sequence code. Figure 4.13(c) illustrates that the ratio of the power in each C/A line
to the total power in the spectrum plotted in decibels can fluctuate significantly
(nearly 8 dB) with respect to the 30 dB levels that would be obtained if every line

contained the same power. Every C/A code has a few strong lines [i.e., lines above
the sinc 2 ( x ) envelope], which render them more vulnerable to a continuous wave
(CW) RF interference at this line frequency than their maximum length sequence
counterpart. For example, the correlation process between a CW line and a PRN
code ordinarily spreads the CW line, but the mixing process at some strong C/A
code line results in the RF interference line being minimally suppressed. As a result,
the CW energy “leaks” through the correlation process at this strong line frequency.
The presence of the navigation data mitigates this leakage to a certain extent. (The
effects of RF interference will be discussed further in Chapter 6.)
Keeping in mind that the GPS C/A codes have these limitations, it is often conve-
nient and approximately correct to illustrate their autocorrelation functions as fol-
lowing ideal maximum-length sequences, as shown in Figure 4.14. Note that there
are other typical simplifications in this figure. The -axis is represented in C/A code
chips instead of seconds and the peak amplitude of the correlation function has been
normalized to unity (corresponding to the PRN sequence amplitude being

−

± 1).

The autocorrelation function of the GPS P(Y) code is:

6 1871 10 12

. ×

1

() () ( )

R τ =

∫

PtPt + τ d τ (4.23)

P i i

10 12

61871 . × T

t = 0

CP

where:

P i ( t ) = P(Y) code PRN sequence as a function of time, t , for SV i
T CP = P(Y) code chipping period (97.8 ns)

= phase of the time shift in the autocorrelation function

The P(Y) code is also not a maximum-length sequence code, but because its
period is so long and its chipping rate is so fast, its autocorrelation characteristics
are essentially ideal. The P(Y) code was designed to have a one-week period made
up of 403,200 periods of its 1.5-second X1 epochs, called Z-counts. Figure 4.15
depicts a normalized autocorrelation function for P(Y) code (amplitude A

=± 1)

with the phase shift axis, , shown in units of P(Y) code chips. The autocorrelation

function for P(Y) code has similar characteristics to the C/A code, but with signifi-

τ