GPS Receiver-Related Subjects - Fundamentals of Global Positioning System Receivers: A Software Approach - page 326

20

18 S / N 1 = − 19 dB

No strong signal

16

14

12

10

S / N 1 = − 16 dB

8

S / N 1 = −13 dB

6

4

2
− 40

− 39 − 38 − 37 − 36 − 35 − 34 − 33 − 32 − 31 − 30

( S / N ) 2 in dB per 2 MHz
bandwidth

FIGURE 12.17 Processed weak signal (S/N) p versus input weak signal (S/N) 2 as a
function of strong input signals.

where A 1 is the amplitude, C 1 is the C/A code with the correct initial phase, f
is the carrier frequency, and θ is the carrier phase. This signal can be subtracted
from the input signal in the time domain. If all these values are measured cor-
rectly, the strong signal can be removed almost thoroughly from the input. If all
the quantities are not measured accurately, the strong signal can only be partially
removed.
The other approach to remove the strong signal is referred to as the sub-
space projection. Although this idea applies to multiple-dimensional problems,
a two-dimensional problem will be used to illustrate the basic idea. In the two-
dimensional case, a signal y received by the receiver consists of two signals:
a strong one S 1 and a weak one S 2 . The strong signal S 1 can be obtained by
acquisition on signal y . The strong signal can be either obtained correctly or
with errors. Figure 12.18 shows the strong signal S 1 , weak signals S 2 ,andthe
projection of y on the strong signal S 1 p .Since S 1 and S 2 are near orthogonal, they
can be considered nearly perpendicular to each other. Figure 12.18a shows that
the signal S 1 is measured correctly and S 1 =

S 1 p . The vector sum represents the
received signal y , and there is no noise. The weak signal S 2 can be found through

S 2 = y − S 1 ( 12 . 10 )

Figure 12.18b shows that the amplitude of the strong signal is measured
wrongly from the received signal y . If the direct subtraction is used, the result