Off-symbol correlation technique
A method of correlating a signal to a synchronization pattern is disclosed. The signal has a waveform with frequency and phase angle components that may be varied, at each repeated signal pulse, to communicate a change in a bit pattern of the signal. A synchronization pattern is generated using knowledge of phase rotation direction due to two consecutive bits in a synchronization key. The signal is compared with the synchronization pattern. It is determined whether the comparison of the signal and the synchronization pattern indicate a correlation between the signal and the synchronization pattern.
1. A method of correlating a signal to a synchronization pattern, the signal having a waveform with frequency and phase angle components that may be varied, at each repeated signal pulse, to communicate a change in a bit pattern of the signal, the method comprising:
generating a synchronization pattern using a synchronization key;
comparing the signal to the synchronization pattern according to a correlator function C(n) defined as
C
(
n
)
=
∑
k
=
0
N
-
2
s
(
n
+
k
)
h
″
(
k
)
where
s(n) is the signal,
N is a number of signal pulses in the synchronization pattern to be used in said correlator function,
h″(k) is the synchronization pattern having a value of t(k)+jt(k+1) when k is even and t(k+1)+jt(k) when k is odd, and
t(k) is a function expressing a value of the bit pattern of the signal having a value of one of +1 and −1; and
determining whether the comparison of the signal and the synchronization pattern indicate a correlation between the signal and the synchronization pattern.
2. The method of claim 1 , wherein said determining includes phase quantizing the signal to determine said correlation.
3. The method of claim 1 , wherein the phase quantizing is octant quantizing.
4. The method of claim 1 , wherein the waveform is a Continuous Phase Modulation (CPM) waveform.
5. The method of claim 4 , wherein the waveform is a Gaussian Minimum Shift Key (GMSK) waveform.
6. The method of claim 4 , wherein the waveform is a Minimum Shift Key (MSK) waveform.
7. A method of correlating a signal to a synchronization pattern, the signal having a waveform with frequency and phase angle components that may be varied, at each repeated signal pulse, to communicate a chance in a bit pattern of the signal, the method comprising:
generating a synchronization pattern using a synchronization key;
comparing the signal to the synchronization pattern according to a correlator function C(n) defined as
C
(
n
)
=
∑
k
=
0
N
/
2
-
1
s
(
n
+
2
k
)
·
(
t
(
k
)
-
jt
(
k
+
1
)
)
+
j
∑
k
=
0
N
/
2
-
2
s
(
n
+
2
k
+
1
)
·
(
t
(
2
k
+
2
)
-
jt
(
2
k
+
1
)
)
where
s(n) is the signal,
N is a number of signal pulses in the synchronization pattern to be used in said correlator function, and
t(k) is a function expressing a value of the bit pattern of the signal having a value of one of +1 and −1: and
determining whether the comparison of the signal and the synchronization pattern indicate a correlation between the signal and the synchronization pattern.
8. A correlator that correlates a signal to a synchronization pattern, the signal having a waveform with frequency and phase angle components that may be varied, at each repeated signal pulse, to communicate a change in a bit pattern of the signal, the correlator comprising:
means for generating a synchronization pattern using a synchronization key;
means for comparing the signal with the synchronization pattern according to a correlator function C(n) defined as
C
(
n
)
=
∑
k
=
0
N
/
2
-
1
s
(
n
+
2
k
)
·
(
t
(
k
)
-
jt
(
k
+
1
)
)
+
j
∑
k
=
0
N
/
2
-
2
s
(
n
+
2
k
+
1
)
·
(
t
(
2
k
+
2
)
-
jt
(
2
k
+
1
)
)
where
s(n) is the signal,
N is a number of signal pulses in the synchronization pattern to be used in said correlator function, and
t(k) is a function expressing a value of the bit pattern of the signal having a value of one of +1 and −1; and
means for determining whether the comparison of the signal and the synchronization pattern indicate a correlation between the signal and the synchronization pattern.
9. The correlator of claim 8 , wherein the waveform is a Continuous Phase Modulation (CPM) waveform.
10. The correlator of claim 8 , wherein the waveform is a Minimum Shift Key (MSK) waveform.
11. The correlator of claim 8 , further comprising means for phase quantizing the signal to determine said correlation.