Global Positioning System Reference
In-Depth Information
where c i is the spreading sequence of binary digits {0,1}, p ( t ) is spreading symbol, and T c is
the period of the modulated symbol. In conventional GPS, both of C/A code signal and P(Y)
code signal use BPSK-R( n ) modulation whose spreading symbol is the energy normalized
rectangular pulse with the lasting time
(
)
T
=
1 /
n
×
1.023 MHz
:
1
,0
≤ <
tT
=
()
c
p
t
T
(3)
BPSK- R
c
0,
others
In principle, the spreading symbol of DSSS signals can be any shape. BOC modulated signal
is a variant of basic DSSS signal. The baseband BOC modulated signal can be regarded as
the result of multiplying the BPSK-R signal with a sub-carrier which is equal to the sign of a
sine or a cosine waveform:
(
)
( )
( )
s
t
=
s
t
sgn sin 2
π
f t
+
φ
(4)
BOC
BPSK- R
s
where sgn( ⋅ ) is sign function, f s is the sub-carrier frequency, and φ is the phase of sub-
carrier. Two common values of φ are 0 or π/2, for which the resultant BOC signals are
referred to as sine-phased BOC or cosine-phased BOC, respectively. In this Chapter, we
focus on sine-phased case. For information on cosine-phased BOC signal unambiguous
processing, see (Lohan et al., 2008). Using the terminology from (Betz, 2001), a sine phased
BOC modulated signal is denoted as BOC s ( m , n ), where m means the ratio of the square
wave frequency f s to 1.023 MHz, and n represents the ratio of the spreading code rate f c to
1.023 MHz. m and n are constrained to positive integer m ≥ , and the ratio M = 2 m / n is
referred to as BOC-modulation order, which is constrained to positive integer.
Under the assumption that the spreading sequence has an ideal correlation characteristic,
the power spectrum density (PSD) of BOC s (
)
ff can be expressed as (Betz, 2001)
,
s
c
(
)
sin
2
π
fT
π
f
c
2
T
tan
,
M
even
c
(
)
2
2
f
π
fT
s
()
c
Sf
=
(5)
BOC
(
)
2
s
cos
π
fT
π
f
c
2
T
tan
,
M
odd
c
(
)
2
2
f
π
fT
s
c
It can be seen that due to the effect of subcarrier, BOC modulated signals symmetrically split
the main energy component of the signal spectrum and move them away from the band
center, so that they have a higher degree of spectral separation with other BPSK-R
modulated signals on the same carrier frequency. Moreover, as noted in (Betz, 2001), BOC
modulated signals have greater root-mean-square (RMS) bandwidth compared with
traditional BPSK signals with the same spreading code frequency. The greater the RMS
bandwidth is, the better the inherent ability to mitigate white Gaussian noise and
narrowband interference during tracking will be. Consequently, with same f c , BOC
modulation provides better resistance to thermal noise and narrowband interference than
BPSK-R modulation theoretically. However, the ambiguity of the autocorrelation function of
sine-BOC modulated signal induces a risk of biased measures in code synchronization.
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