Carrier and Code Tracking - A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach - page 100

80

d = 1
d = 0.5
d = 0.1
d = 0.1 (C/A)

60

40

20

0

−20

−40

−60

−80

0 100 200 300 400 500

Multipath delay δ [m]

FIGURE 7.18. Multipath error envelope for noncoherent early/late detector for BOC(1,1).
Negative ranging error corresponds to destructive interference.

over time as the two signal components interfere. As a measure of the magnitude
of the fluctuations we define the relative amplitude as

A 2
A 1 .
In practice, the amplitude of the direct component is larger than the reflected
component and thus

α =

is somewhat less than one.
Equation (7.29) is graphed as the upper half of Figure 7.17 for

α

α = 0 . 5andfor

three values of the correlator spacing d 0. The upper part of the

figure corresponds to constructive interference while the lower part corresponds
to destructive interference; see Equation (7.30). All actual multipath errors lie
within the combined envelope!

= 0 . 1 , 0 . 5, and 1 .

In Figure 7.17 the initial slope is a function of multipath amplitude and delay δ

only. It is independent of correlator and PRN chipping rate f c . We recall the C/A-
code pseudorange multipath error can approach 147 m, theoretically. However,
errors of 10 m or less are far more common. Large errors can be encountered in
urban environments.
Our investigation assumes infinite GPS signal bandwidth. Bandwidths of 10-
20 MHz yield results that are similar to those for the infinite bandwidth case.
For short-delay multipath (small

δ ), the finite bandwidth effects are much less

significant.

In conclusion: Multipath propagation deforms the ideal correlation peak because
the received signal is a sum of signal components. The multipath components
arrive later at the receiver and contribute additional correlation peaks. Thus, the
early-late correlator samples may not be centered on the true arrival time of the
direct path.