GPS Satellite Signal Characteristics - Understanding GPS: Principles and Applications - page 135

Since the satellite L1 antenna array has a minimum gain of 13.4 dB for C/A code at
the worst-case off-axis angle of 14.3º, the minimum L1 antenna transmitter power
for C/A code is log 10 −1 [(26.8 - 13.4)/10] 21.9W. Note that a minimum of 32.9W of

L1 power and 6.6W of L2 power (for a total of 39.5W) must be delivered to the sat-
ellite antenna arrays to maintain the specification. The efficiency of the high-power
amplifier (HPA) subassembly determines how much actual power must be provided
in the satellite.

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4.3.3 Autocorrelation Functions and Power Spectral Densities
The autocorrelation characteristics of the GPS PRN codes are fundamental to the
signal demodulation process. The power spectral densities of the GPS PRN codes
determine the channel bandwidths required to transmit and receive the spread spec-
trum signals
As would be expected, the GPS PRN codes have periodic correlation triangles
and a line spectrum that closely resemble the characteristics of maximum-length
shift register PN sequences, but with several subtle differences. This is because the
GPS PRN codes are not shift register sequences of maximum length. For example,
for the C/A code 10-bit shift register, there are only 30 usable maximum-length
sequences, and among these available maximum-length sequences, the cross-
correlation properties between different codes are not as good as that desired for
GPS. Another problem is that the autocorrelation function of maximum-length
sequences has sidelobes when the integration time is one (or a few) code periods.
(This can be a problem to a lesser extent with the C/A codes as well.) In a GPS
receiver, the integration and dump time associated with the correlation of its replica
C/A code with the incoming SV C/A code (similar to autocorrelation) is typically 1
to 5 ms (i.e., 1 to 5 C/A code periods). Except for a highly specialized mode of oper-
ation called data wipeoff, the integration and dump time never exceeds the 50-Hz
data period of 20 ms. During search modes, these short integration and dump peri-
ods for the maximum-length sequences increase the probability of high sidelobes
leading to the receiver locking onto a wrong correlation peak (a sidelobe). For these
reasons, the Gold codes described earlier were selected for the C/A codes.
Using the exclusive-or of two maximum length shift registers, G1 and G2 (with
a programmable delay), there are 2 n - 1 possible delays. Therefore, there are 1,023
possible Gold codes for the GPS C/A code generator architecture (plus two addi-
tional maximum-length sequences if the G1 and G2 sequences were used independ-
ently). However, there are only 45 Gold code combinations for the architecture of
the C/A code generator defined in [10], using two taps on the G2 register to form the
delay. The 32 Gold codes with the best properties were selected for the GPS space
segment. (There were only four more unique two-tap combinations selected for the
pseudolites since two of these codes are redundant.) Extensions of the GPS C/A code
for such applications as the WAAS, wherein augmentation C/A code signals are
transmitted from geostationary satellites, required a careful analysis of their proper-
ties and their effect on the space segment codes before their implementation. (Refer
to Chapter 8 for details on the WAAS C/A code generation.)
Neglecting the navigation data, the autocorrelation function of the GPS C/A
code signal is: