Satellite Signal Acquisition, Tracking, and Data Demodulation - Understanding GPS: Principles and Applications - page 225

process speeds up by (almost) a factor of three. It is not quite a factor of three
because all three search cells must be dismissed before the search process can
proceed to the next three cells. In order to generate the I and Q signals, the
receiver baseband search process has synthesized the correct Doppler (the
center frequency of the respective search process Doppler bin in the search
pattern) and the correct replica C/A code phase with the corresponding
spreading code chip rate plus code Doppler. For example, the C/A code
phase corresponding to the first of its 1,023 states is where the C/A code
setter resets the G1 and G2 registers at the beginning of the cell integrate and
dump time. The marching of time for the C/A code generator plus the code
Doppler keeps its phase aligned to this cell. If the cell is dismissed, then the
C/A code generator phase is advanced by 1/2 chip (times the number of
correlators), and the search process is continued for that Doppler bin until
the last C/A code phase state has been reached. Then the Doppler center
frequency is shifted to the next bin in the search pattern and the process is
repeated.
2. At each cell the up/down counter ( K ) is initialized to K 1. Where a

higher probability of detection and lower probability of false alarm are
desired at the expense of search speed, then B

= B =

2. If the envelope sample
exceeds the threshold, V t , then the up/down counter is incremented by one. If
the sample does not exceed the threshold, then the up/down counter is
decremented by one. As shown in Figure 5.37, one technique for obtaining
the RMS noise,

=

σ n , which is used to set the threshold, is to pass the
correlation envelopes into a recursive lowpass filter with a delay of one
search cell. A better technique is for the receiver to synthesize the RMS noise
by correlating the input signal with an unused PRN code (e.g., the G1
register output for C/A code search). The RMS output is multiplied by a
scale factor, X , to obt ain the threshold, V t . Assuming that the envelope is
forme d by

I

2

+ Q

2

, then the scale factor is determined from (5.43),

X 2ln( ), where P fa is the single trial probability of false alarm.

Typically, the envelope is determined from the Robertson approximation. In
this case, it has been determined [17] that a multiplier factor of 1.08677793
m ust be used for t he scale factor, so that: X R

=− P fa

= 1.08677793 X =

P fa .
The determination of the most suitable single trial probability of false
alarm, the overall false alarm, and the overall probability of detection is a
tuning process. The final determination must be obtained by simulation.
Assuming the Robertson envelope approximation, the scale factor range is
typically from 1.8 ( P fa =

− 2 3621724 . ln( )

25%) for low expected ( C / N 0 ) dB ( ≥ 25 dB-Hz) to 2.1

39 dB-Hz).
3. If the counter contents reach the maximum value, A , then the signal is
declared present, and the Tong search is terminated. This is typically
followed by additional vernier search processes designed to find the code
phase and Doppler combination that produces the peak detection of the
signal before the code/carrier loop closure process is begun. If the counter
reaches 0, then the signal is declared absent and the search process is

( P fa = 16%) for high expected ( C / N 0 ) dB ( ≥