Acquisition of Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 226

TABLE 10.1 Input Power and S/Nwith Different
Bandwidths

Input Power
(dBm)

Input S / N
(dB/2 MHz)

S / N
(dB/kHz)

C/N 0
(dB/Hz)

− 130 − 19 dB 14 dB 44 dB

− 140 − 29 dB 4 dB 34 dB

− − −

150 39 dB 6dB 24dB

The nominal input signal strength is at − 130 dBm (sometimes referred as
− 160 dBw.) If the gain of the receiving antenna is assumed to be unity, the
signal strength is − 130 dBm. The input bandwidth of a C/A code receiver is
approximately 2 MHz (2.046 MHz knoll to knoll,) and the corresponding noise
floor is at about − 111 dBm ( − 114 + 3). Referenced to this 2 MHz input band-
width, the input S/N

=− − +

19 dB ( 130 111). The noise floor for 1 kHz is at

− 144 dBm; thus the corresponding S/N = 14 dB ( − 130 + 144). The noise floor

for 1 Hz is at − 174 dBm; thus C/N 0 = − +

44 dB ( 130 174). Table 10.1 shows

these relations.
Under normal conditions the S / N at the input of the receiver is about

19 dB,
which is too weak to be detected. In order to detect the signal, processing must be
provided to increase the S / N . The two general processing methods are referred
to as coherent and noncoherent integrations. Before the discussion of these two
methods, the limit of receiver sensitivity, the desired probability of detection,
and the probability of false alarm will be presented because they are related to
the S / N .

−

10.3 LIMITATION OF RECEIVER SENSITIVITY ( 4-10 )

The sensitivity of a GPS receiver depends on two processing procedures: the
acquisition and the tracking. In acquisition, long data can be used to improve
the sensitivity. The tracking program, however, cannot use long data to improve
sensitivity because of the finite length of the navigation data. The receiver must
determine the navigation data every 20 ms. A maximum of 40 ms of data can
be used to determine a navigation phase transition: 20 ms before the navigation
data transition and 20 ms after.
The probability of error P e for a BPSK (bi-phase shift keyed) signal, where
the navigation data belong, is ( 4 )

2 erfc E b

1

P e = ( 10 . 1 )

N 0

where the erfc is the complementary error function, E b is the energy in a bit,
and N 0 is the noise power density, which can be considered as noise power
per Hertz. The error function and complementary function will be discussed in