Method of performing synchronization and frequency offset estimation based on simultaneous phase compensation of single training sequence and receiver performing the same
The present disclosure includes a method of performing synchronization and frequency offset estimation The method includes an input signal corresponding to a single received training sequence. Phase information and a phase index are generated by performing an auto-correlation function (ACF) on the input signal. A templet signal associated with a sample index of the input signal is generated based on at least one pre-stored look-up table (LUT), the phase index, a frequency bandwidth of the input signal, and the sample index. Power associated with the sample index is calculated by performing a matched filtering on the input signal based on the templet signal. A synchronization timing and a frequency offset for the input signal are simultaneously determined based on a result of the matched filtering.
1. A method of performing synchronization and frequency offset estimation, the method comprising:
receiving an input signal corresponding to a single training sequence;
generating phase information and a phase index by performing an auto-correlation function (ACF) on the input signal;
generating a templet signal associated with a sample index of the input signal based on at least one pre-stored look-up table, the phase index, a frequency bandwidth of the input signal, and the sample index;
calculating power associated with the sample index by performing a matched filtering on the input signal based on the templet signal; and
simultaneously determining a synchronization timing and a frequency offset for the input signal based on a result of the matched filtering.
2. The method of claim 1 , wherein generating the templet signal associated with the sample index includes:
obtaining a reference templet signal from a first look-up table based on the frequency bandwidth and the sample index;
obtaining a plurality of reference values from a second look-up table based on the frequency bandwidth and the sample index, the second look-up table being different from the first look-up table;
generating a first direction decision signal based on the sample index;
generating a second direction decision signal based on the sample index, the phase index, and the plurality of reference values; and
obtaining the templet signal based on the reference templet signal, the first direction decision signal, and the second direction decision signal.
3. The method of claim 2 , wherein the reference templet signal and the templet signal are each mapped on ternary lattice coordinates formed on a complex number plane.
4. The method of claim 3 , wherein the templet signal is obtained by shifting the reference templet signal on the ternary lattice coordinates based on the phase index.
5. The method of claim 3 , wherein:
the reference templet signal includes a reference real number part and a reference imaginary number part,
the templet signal includes an output real number part and an output imaginary number part, and
the reference real number part, the reference imaginary number part, the output real number part, and the output imaginary number part each have a value corresponding to one of +1, 0, and −1.
6. The method of claim 5 , wherein:
the sample index is in a range greater than or equal to zero and less than N, where N is a natural number greater than or equal to two, and
the first direction decision signal is obtained based on Equation 1:
D
(
n
)
=
{
+
j
when
0
≤
n
<
N
/
2
-
j
when
N
/
2
≤
n
<
N
[
Equation
1
]
where D(n) denotes the first direction decision signal and n denotes the sample index.
7. The method of claim 6 , wherein:
the second direction decision signal includes a real number part shift index and an imaginary number part shift index, and
the real number part shift index and the imaginary number part shift index are obtained based on Equation 2 and Equation 3:
SHIFT
R
E
(
k
,
n
)
=
{
0
when
k
<
S
RE
(
n
,
0
)
1
when
S
RE
(
n
,
0
)
≤
k
<
S
RE
(
n
,
1
)
2
others
[
Equation
2
]
SHIFT
IM
(
k
,
n
)
=
{
0
when
k
<
S
IM
(
n
,
0
)
1
when
S
IM
(
n
,
0
)
≤
k
<
S
IM
(
n
,
1
)
2
others
[
Equation
3
]
where SHIFT RE (k,n) denotes the real number part shift index, SHIFT IM (k,n) denotes the imaginary number part shift index, k denotes the phase index, and S RE (n,0), S RE (n,1), S IM (n,0), and S IM (n,1) denote the plurality of reference values.
8. The method of claim 7 , wherein the output real number part and the output imaginary number part are obtained based on Equation 4, Equation 5, and Equation 6:
T
P
,
RE
(
k
,
n
)
=
{
RE
{
T
COMP
(
n
)
·
D
(
n
)
SHIFT
RE
(
k
,
n
)
}
when
T
RE
(
n
)
=
0
RE
{
T
RE
(
n
)
·
D
(
n
)
SHIFT
RE
(
k
,
n
)
}
other
[
Equation
4
]
T
P
,
IM
(
k
,
n
)
=
{
IM
{
T
COMP
(
n
)
·
D
(
n
)
SHIFT
IM
(
k
,
n
)
}
when
T
IM
(
n
)
=
0
RE
{
T
IM
(
n
)
·
D
(
n
)
SHIFT
IM
(
k
,
n
)
}
other
[
Equation
5
]
T
COMP
(
n
)
=
T
RE
(
n
)
+
T
IM
(
n
)
·
j
[
Equation
6
]
where T P,RE (k,n) denotes the output real number part, T P,IM (k,n) denotes the output imaginary number part, T RE (n) denotes the reference real number part, T IM (n) denotes the reference imaginary number part, RE{⋅} denotes a function of obtaining a real number part, and IM{⋅} denotes a function of obtaining an imaginary number part.
9. The method of claim 1 , wherein:
the input signal includes first through N M -th sample indices, where N M is a natural number greater than or equal to two, and
generating the templet signal associated with the sample index includes:
generating first through N M -th templet signals associated with the first through N M -th sample indices.
10. The method of claim 1 , wherein:
the input signal includes first through N M -th sample indices, where N M is a natural number greater than or equal to two, and
calculating the power associated with the sample index includes:
calculating first through N M -th powers associated with the first through N M -th sample indices.
11. The method of claim 10 , wherein simultaneously determining the synchronization timing and the frequency offset for the input signal includes:
selecting one of the first through N M -th sample indices based on the first through N M -th powers;
determining a timing corresponding to the selected sample index as the synchronization timing; and
determining an offset corresponding to the selected sample index as the frequency offset.
12. The method of claim 11 , wherein a power corresponding to the selected sample index is a greatest power among the first through N M -th powers.
13. The method of claim 11 , wherein the synchronization timing is determined by performing a cross-correlation function (CCF).
14. The method of claim 11 , wherein generating the phase information and the phase index includes:
performing a quantization on the input signal;
performing the auto-correlation function (ACF) on the quantized input signal;
performing an arctangent (ATAN) function on the input signal on which the auto-correlation function (ACF) is performed;
measuring and tracking the phase information based on the input signal on which the arctangent (ATAN) function is performed; and
generating the phase index based on the phase information.
15. The method of claim 14 , wherein the phase information is measured and tracked by performing an infinite impulse response (IIR) filtering.
16. A receiver comprising:
a first calculator configured to:
receive an input signal corresponding to a single training sequence; and
generate phase information and a phase index by performing an auto-correlation function (ACF) on the input signal;
a templet generator configured to generate a templet signal associated with a sample index of the input signal based on at least one pre-stored look-up table, the phase index, a frequency bandwidth of the input signal, and the sample index; and
a second calculator configured to:
calculate power associated with the sample index by performing a matched filtering on the input signal based on the templet signal; and
simultaneously determine a synchronization timing and a frequency offset for the input signal based on a result of the matched filtering.
17. The receiver of claim 16 , wherein the templet generator includes:
a first look-up table configured to store a reference templet signal and output the reference templet signal based on the frequency bandwidth and the sample index;
a second look-up table configured to store a plurality of reference values and output the plurality of reference values based on the frequency bandwidth and the sample index, the second look-up table being different from the first look-up table;
a first decision unit configured to generate a first direction decision signal based on the sample index;
a second decision unit configured to generate a second direction decision signal based on the sample index, the phase index, and the plurality of reference values; and
a third decision unit configured to output the templet signal based on the reference templet signal, the first direction decision signal, and the second direction decision signal.
18. The receiver of claim 16 , wherein the second calculator includes:
a matched filtering unit configured to calculate first through N M -th powers associated with first through N M -th sample indices that are included in the input signal, where N M is a natural number greater than or equal to two; and
a detecting unit configured to:
select one of the first through N M -th sample indices based on the first through N M -th powers;
determine a timing corresponding to the selected sample index as the synchronization timing; and
determine an offset corresponding to the selected sample index as the frequency offset.
19. The receiver of claim 16 , wherein the first calculator includes:
a quantization unit configured to perform a quantization on the input signal;
an auto-correlation function (ACF) unit configured to perform the auto-correlation function (ACF) on the quantized input signal;
an arctangent (ATAN) unit configured to perform an arctangent (ATAN) function on the input signal on which the auto-correlation function (ACF) is performed;
a phase update unit configured to measure and track the phase information based on the input signal on which the arctangent (ATAN) function is performed; and
a phase indexing unit configured to generate the phase index based on the phase information.
20. A method of performing synchronization and frequency offset estimation, the method comprising:
receiving an input signal corresponding to a single training sequence;
generating phase information and a phase index by performing an auto-correlation function (ACF) on the input signal;
generating a templet signal associated with a sample index of the input signal based on at least one pre-stored look-up table, the phase index, a frequency bandwidth of the input signal, and the sample index;
calculating power associated with the sample index by performing a matched filtering on the input signal based on the templet signal; and
simultaneously determining a synchronization timing and a frequency offset for the input signal based on a result of the matched filtering,
wherein generating the phase information and the phase index includes:
performing a quantization on the input signal;
performing the auto-correlation function (ACF) on the quantized input signal;
performing an arctangent (ATAN) function on the input signal on which the auto-correlation function (ACF) is performed;
measuring and tracking the phase information based on the input signal on which the arctangent (ATAN) function is performed; and
generating the phase index based on the phase information,
wherein generating the templet signal associated with the sample index includes:
obtaining a reference templet signal from a first look-up table based on the frequency bandwidth and the sample index;
obtaining a plurality of reference values from a second look-up table based on the frequency bandwidth and the sample index, the second look-up table being different from the first look-up table;
generating a first direction decision signal based on the sample index;
generating a second direction decision signal based on the sample index, the phase index, and the plurality of reference values; and
obtaining the templet signal based on the reference templet signal, the first direction decision signal, and the second direction decision signal,
wherein calculating the power associated with the sample index includes:
calculating first through N M -th powers associated with first through N M -th sample indices that are included in the input signal, where N M is a natural number greater than or equal to two, and
wherein simultaneously determining the synchronization timing and the frequency offset for the input signal includes:
selecting one of the first through N M -th sample indices based on the first through N M -th powers, the selected sample index corresponding to a greatest power among the first through N M -th powers;
determining a timing corresponding to the selected sample index as the synchronization timing; and
determining an offset corresponding to the selected sample index as the frequency offset.