Global Positioning System Reference
In-Depth Information
considered. As for the coherent technique, these
M
samples are combined as
m
=
1
R
m
2
M
S
C
=
(16)
However, (16) can be rewritten to
2
MN
n
=
0
{
r
[
n
]
c
[
n
+
τ
]
e
j
(
2
π
(
f
IF
+
f
D
M
))
nT
S
1
N
S
C
=
}
(17)
As seen in (17), the true value of the coherent integration time is no longer
T
int
but increases
to
MT
int
. Hence, it is fair to state that the coherent combination of
{
R
1
, ...,
R
M
}
is equivalent
to increase
T
int
to
MT
int
, at the cost of an increased complexity.
3.2.2 Non-coherent combination
Unlike the coherent combination, the non-coherent technique combines the squared-envelops
of the correlation values
{
}
R
1
, ...,
R
M
. The mathematical representation of the decsion variable
is then
M
m
=
1
|
R
m
|
2
.
=
S
N
(18)
By using this technique, the main correlation peak also tends to emerge from the noise floor.
However, the noise floor is averaged towards a non-zero value. This value is referred as the
squaring loss (Choi et al., 2002) and makes the non-coherent combination less effective than
the coherent one. However, the effect is not equivalent to an increasing of
T
int
.
3.2.3 Differential combination
This technique was first introduced in the communication field by (Zarrabizadeh & Sousa,
1997). As far as the satellite navigation field is concerned , (Elders-Boll & Dettmar, 2004;
Schmid & Neubauer, 2004) are among the first works using this technique and its variants.
The mathematical representation of the conventional differential combination is
m
=
2
R
m
R
m
−
1
2
M
S
D
=
(19)
As presented in (19), the complex correlator output
R
m
is multiplied by the conjugate of
the one obtained at the previous integration interval
R
m
−
1
. Then the obtained function is
accumulated and its envelope becomes the ultimate decision variable. The fact that the signal
component remains highly correlated between consecutive correlation intervals, while the
noise tends to be de-correlated, results in the improvement of the technique with respect to the
non-coherent one. In comparison with the coherent combination, this technique obtains less
de-spreading gain, but also requires less computational resources because the search-space
size is unchanged (Yu et al., 2007). Therefore, this technique can be seen as a trade-off solution
concerning the pros and cons of the coherent and the non-coherent combination techniques.
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