Acquisition of Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 262

quantities - detection signal power and detection noise power - are defined as
follows: First, the highest output is considered as the desired signal. Second, the
remaining outputs, excluding 9 outputs around the signal, are considered to be
noise. Since the signal output may spread into its neighborhood bins, 4 outputs

around the highest output (9 total outputs) are arbitrarily chosen and are excluded
in the detection noise power calculation. Third, the detection signal power P ds
and detection noise power P dn are defined as

±

b) 2 P ds ≡ (S −

b) 2

(n −

N

P dn ≡ (10.24)

N

where b is the dc bias obtained from the noise components, S is the amplitude of
the highest output, n is the individual noise component, and N is the total noise
components. Since there are 2500 time domain outputs from the acquisition,
N = 2491 because 9 components are excluded from the detection noise power

calculation. From experimental results it appears that when
P ds
P dn

1 / 2

≥ 7 . 5 r

P ds
P dn

dB ≡ 10 log P ds

≥ 17 . 5 dB (10.25)

P dn

a good combination of probability of detection and false alarm rate can be
achieved. The quantity in this equation can be considered as the postdetection
signal-to-noise ratio ( S / N ), which is different from the S / N used in Section 10.2.
In the postdetection S / N , the bias is subtracted from both the signal and the noise.
Comparing with the threshold derived from the previous section, this method
provides the following advantages:

1. It usually takes less noncoherent integrations to detect a true signal.
2. It yields a high signal detection probability. Some signals that can
not be detected with the previous threshold can be detected with this
new threshold.
3. It generates less false detections.

In this detection criterion, the output distribution is not considered.
It should be noted that in calculating S / N conventionally, the signal and the
noise power contains the dc components. The quantity (P ds /P dn ) dB is different
from the conventional S / N ,where

S 2
n 2 /N

S
N =

P s
P n =

( 10 . 26 )