Acquisition of Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 263

Comparing with Equation (10.24), the dc bias b is included in the signal and the
noise power. The conventional S / N ratio has also been tried for signal detection.
The result is inferior to this method. As a result this newly defined post detection
threshold is used for signal detection.
In later sections, when a simulated signal is used, the conventional S / N will be
used because the noise is well behaved. In the study using real signals, the post-
detection S / N will be used because the noise floor distribution is not predicable.

10.16 FINE FREQUENCY CALCULATION ( 18 )

For processing a strong signal, a frequency accuracy of 50 Hz is adequate

to find the navigation data phase transition. For weak signals this frequency
accuracy is inadequate because a higher correlation peak is needed. The closer
the measured frequency is to the true frequency, the higher is the correlation
peak. The correlation is used to determine the phase transition. It is desirable to
have a frequency resolution of around a few Hz (e.g., 2 Hz). In order to achieve
this resolution, long data must be used. The navigation data, however, limits the
usage of long data for coherent processing. The following approach is used to
achieve high-frequency resolution.
The approach to measure fine frequency is through squaring of the processed
input signal in units of 1 ms. The acquisition can find the initial phase of the
C/A code, which can be used to strip off the C/A code. After the C/A code is
removed from the input signal, the phase transition caused by the navigation data
still exists. It is well known that if a bi-phase coded signal is squared, the phase
transition can be eliminated and the output is a cw signal with a frequency equal
to twice the input frequency. This method, however, decreases the signal-to-noise
ratio because the noise is also squared.
An estimation of this approach with squaring will be briefly discussed ( 18 ) .If
the signal amplitude is A and the noise is n , the received signal x is

±

x = A + n ( 10 . 27 )

The corresponding S / N in dB is

S
N

dB = 20 log A

( 10 . 28 )

σ n

where σ n is the standard deviation of the noise. Let us define a signal y as the
square of the x , the result is

x 2 A 2 n 2 y = = + 2 An + ( 10 . 29 )