Satellite Signal Acquisition, Tracking, and Data Demodulation - Understanding GPS: Principles and Applications - page 230

Received signal

Frequency

Conversion
to baseband Correlation
Reference signal

Upper
sideband
selection
filter

|.| 2

Acquisition
test
statistic

∑

Frequency

Conversion
to baseband

Lower
sideband
selection
filter

|.| 2 Correlation

Figure 5.41 Sideband acquisition processing of the M code signal.

Acquisition in jamming requires long integration times. Coherent integration
times are limited by data bit boundaries, oscillator stability, and dynamics. They
also lead to narrow Doppler bins. Consequently, a large number of noncoherent
integrations is employed in jamming. Detection performance is readily predicted
using standard theory. The output signal-to-noise plus interference ratio (SNIR)
after correlation is given by

T
L

C
NJ

025 .

ρ o = (5.52)

+

0 0

where T is the coherent integration time used in the correlations, L is the implemen-
tation loss expressed as a number greater than or equal to unity, the factor of 0.25
accounts for splitting the received signal power into four distinct segments (upper
and lower sidebands, even and odd spreading symbols) in each coherent integration
time, and J 0 is the effective power spectral density of the received jamming signal (see
Section 6.2).
The detection probability is found using the generalized Marcum Q function.
Using the notation P N ( X , Y ) [22] as the probability that the random variable with
2 N degrees of freedom and SNIR of X exceeds threshold value of Y allows the detec-
tion probability to be expressed

( )

PP = ρ , V (5.53)

d 4 N ot

n

where N n is the number of coherent integrations times used, and V t is the detection
threshold calculated to provide the needed false alarm probability for the given
number of noncoherent integrations. The factor of four in the subscript in (5.53)
accounts for the fact that the number of complex quantities being noncoherently
combined is four times the number of coherent integration times used, reflecting the
combination of upper and lower sidebands, and even and odd spreading symbols.