Global Positioning System Reference
In-Depth Information
results in a lower
C
/
N
0
threshold, but with less effect than reducing
B
n
. Reducing the
correlator spacing,
D
, also reduces the DLL jitter at the expense of increased code
tracking sensitivity to dynamics. Narrowing
D
should be accompanied by increas-
ing the front-end bandwidth
B
fe
to avoid “flattening” of the DLL correlation peak in
the region where the narrow correlators are being operated. In fact, (5.23) shows
that there is no benefit to reducing
D
to less than the spreading code rate divided by
the front-end bandwidth.
As
D
becomes vanishingly small, the trigonometric functions in (5.22) can be
replaced by their first-order Taylor Series expansions about zero, and this equation
becomes
B
1
1
n
σ
≅
1
+
(chips)
(5.24)
tDLL
T
B
2
B
fe
∫
2
fe
c
()(
2
)
( )
(
)
( )
∫
2
π
CN
f S
2
f df
T CN
S
f df
0
s
0
s
−
B
2
−
B
2
fe
fe
B
/
2
fe
−
∫
The term
fS fdf
S
2
()
is called the root-mean-squared (RMS) bandwidth of
B
/
2
fe
the signal, and it is a measure of the “sharpness” of the correlation peak. Clearly,
signals with larger RMS bandwidths offer the potential for more accurate code
tracking. In fact, the frequency-squared term in the RMS bandwidth indicates that
even very small amounts of high frequency content in the signal can enable more
accurate code tracking. Intuitively, these high frequency components produce
sharper edges and more distinct zero crossings in the waveform, enabling more accu-
rate code tracking.
The use of carrier-aided code (practically a universal design practice) effectively
removes the code dynamics, so the use of narrow correlators is an excellent design
tradeoff for C/A code receivers. For C/A code receivers where the correlation inter-
val in units of time is an order of magnitude greater than for P(Y) code, reducing the
correlator spacing reduces the effects of thermal noise and multipath (see Section
6.3) on C/A, but this also requires increasing the front-end bandwidth, which
increases the vulnerability to in-band RF interference.
Note that the thermal noise is independent of tracking loop order in (5.23) Also
note that the thermal noise is the same for either C/A code or P(Y) code when
expressed in units of chips. However, all other things being equal, the thermal noise
is ten times larger for the C/A code than the P(Y) code because the chip wavelength
of the C/A code is ten times longer than for P(Y) code. For example, from (5.23), this
is readily observed if the measurement is converted to meters. To convert to meters,
multiply (5.23) by
c
·
T
c
(e.g., by 293.05 m/chip for C/A code or by 29.305 m/chip
for P(Y) code).
Figure 5.28(a) uses (5.23) to compare C/A code and P(Y) code accuracy in units
of meters. (Figure 5.28 also includes results for the M code that will be explained in
Section 5.6.4.) A one-chip correlator
E-L
spacing (e.g.,
D
=
1) and normalized
receiver bandwidth
b
2 (i.e., the front-end receiver bandwidth is equal to
twice the chip rate) is used for each BPSK-R result. Figure 5.28(b) uses (5.23) to
B
fe
/R
c
=
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