Global Positioning System Reference
In-Depth Information
2.2 Ambiguous problem
The difference of the spreading chip waveforms between BPSK-R signals and BOC signals
leads their difference in ACF shapes, and thus makes the distinction of acquisition and
tracking performance. The ACF of BPSK-R modulated signals is a triangle, but BOC signals
have sawtooth-like, piecewise linear ACF. The normalized BOC(
m
,
n
) ACF without filter can
be expressed as (Yao, 2009)
⎧
⎡
⎤
⎛
22
k
2
−
k
⎞
()
k
+
1
(
)
−
1
−
+
2
k
−
1
−
2
M
−
2
k
+
1
τ
,
τ
≤
T
⎪
⎢
⎥
⎜
⎟
()
c
R
τ
=
⎨
M
(6)
⎝
⎠
⎣
⎦
BOC
⎩
0,
others
where
kM
τ
⎢ ⎥
, and ⎡
⎢ ⎥
means the smallest integer not less than
x
. In Figure 1, the
normalized ACF envelopes of BPSK-R(1) signal and BOC(2,1) signal are drawn.
=⋅
⎡
⎤
Fig. 1. BPSK-R(1) and BOC(2,1) Normalized ACF Envelopes
From Figure 1 we can see that these two signals have the same spreading chip rate 1.023
MHz, but their ACFs have entirely different shapes. Compared with the triangular ACF of
BPSK-R(1) signal, that of BOC(2,1) signal has a sharper main peak, which means better
tracking accuracy in thermal noise. However, the ACF of BOC signal has multiple side
peaks within
τ=± chips. At the acquisition and tracking stages, these side peaks could be
mistaken for the main peak.
1
When the traditional acquisition and tracking algorithms are employed to process
BOC(2
n
,
n
) signal, the shapes of statistic and the discriminator curve are shown in Figure
2(a) and Figure 2(b), respectively.
The traditional acquisition and tracking of DSSS signal have been very well discussed
(Ziemer & Peterson, 1985). From Figure 2(a) we can see that since there are significant
amount of signal energy located at side peaks of BOC ACF, under the influence of noise it is
quite likely that one of side peak magnitudes exceeds the main peak, and false acquisition
will happen. For
M
-order BOC signal, the energy ratio between the
i
-th largest side peak
and the main peak is
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