Apparatus and method of deciding received symbol in M-PSK system
View Patent ↗An apparatus for and method of deciding symbols in a M-ary phase shift keying (MPSK) system are provided. The apparatus includes: a linear transform unit performing linear transform, to which a phase error is applied, of a received pair of symbols; and a symbol decision unit deciding a transmitted symbol corresponding to the received pair of symbols according to the sign value of the transformed symbol pair. According to the apparatus and method, degradation of a symbol error rate caused by a phase error when an MPSK signal is demodulated can be improved and a phase error can be estimated through a simple method.
1. A symbol decision apparatus of a M-ary phase shift keying (M-PSK) system, the apparatus comprising:
a linear transform unit performing linear transform, to which a phase error is applied, of a received pair of symbols, wherein the linear transform unit transforms the pair of received symbols (Xn,Yn) according to the following equation:
[
U
i
V
i
]
=
[
-
sin
(
π
(
2
i
-
3
)
M
+
Ψ
)
cos
(
π
(
2
i
-
3
)
M
+
Ψ
)
-
sin
(
π
(
2
i
-
1
)
M
+
Ψ
)
cos
(
π
(
2
i
-
1
)
M
+
Ψ
)
]
[
X
n
Y
n
]
where i is a transmitted symbol index having a value among 1, . . . , M, M is the level of modulation of the PSK system, and ψ is the estimated phase error; and
a symbol decision unit deciding a transmitted symbol corresponding to the received pair of symbols according to the sign value of the transformed symbol pair, wherein the symbol decision unit decides an i-th transmitted symbol if the transformed symbols (Ui,Vi) of the pair are a positive number and a negative number, respectively.
2. The apparatus of claim 1 , further comprising a phase error estimation unit estimating the phase error by using the mean value of a pair of received symbols estimated as a predetermined transmitted symbol in at least one pair of the received symbols, and providing the estimated phase error to the linear transform unit.
3. The apparatus of claim 2 , wherein the phase error estimation unit comprises:
a transmitted symbol estimation unit estimating a pair of received symbols corresponding to a transmitted symbol having only a quadrature component in the at least one pair of received symbols; and
a phase error decision unit deciding an angle between the mean value of in-phase symbols and the mean value of quadrature symbols of the estimated symbol pair, as the phase error.
4. The apparatus of claim 3 , wherein the transmitted symbol estimation unit transforms the pair of received symbols (Xn,Yn) according to the following equation:
[
Y
1
Y
2
]
=
[
-
sin
(
π
2
-
π
M
)
cos
(
π
2
-
π
M
)
-
sin
(
π
2
+
π
M
)
cos
(
π
2
+
π
M
)
]
[
X
n
Y
n
]
where M is the level of modulation of the PSK system, and if the transformed symbols (Y 1 ,Y 2 ) of the pair are a positive number and a negative number, respectively, the transmitted symbol estimation unit estimates the pair of the received symbols (Xn,Yn) as a pair of received symbols corresponding to a transmitted symbol having only the quadrature component, and
the phase error decision unit estimates the phase error ψ according to the following equation:
Ψ
=
π
2
(
1
-
sgn
X
_
N
)
-
sgn
X
_
N
tan
-
1
(
Y
_
N
X
_
N
)
where sgn(x) is a function that is −1 if x is a negative number and is 1 if x is equal to or greater than 0, and X N and Y N are the mean values, respectively, of the estimated N pairs of symbols (Xn,Yn).
5. A symbol decision method of an M-PSK system, the method comprising:
performing linear transform, to which a phase error is applied, of a received pair of symbols, wherein in the performing of the linear transform the pair of received symbols (Xn,Yn) is transformed according to the following equation:
[
U
i
V
i
]
=
[
-
sin
(
π
(
2
i
-
3
)
M
+
Ψ
)
cos
(
π
(
2
i
-
3
)
M
+
Ψ
)
-
sin
(
π
(
2
i
-
1
)
M
+
Ψ
)
cos
(
π
(
2
i
-
1
)
M
+
Ψ
)
]
[
X
n
Y
n
]
where i is a transmitted symbol index having a value among 1, . . . , M, M is the level of modulation of the PSK system, and ψ is the estimated phase error; and
deciding a transmitted symbol corresponding to the received pair of symbols according to the sign value of the transformed symbol pair wherein in the deciding of the transmitted symbol an i-th transmitted symbol is decided if the transformed symbols (Ui,Vi) of the pair are a positive number and a negative number, respectively.
6. The method of claim 5 , further comprising estimating the phase error by using the mean value of a pair of received symbols estimated as a predetermined transmitted symbol in at least one pair of the received symbols.
7. The method of claim 6 , wherein the estimating of the phase error comprises:
estimating a pair of received symbols corresponding to a transmitted symbol having only a quadrature component in the at least one pair of received symbols; and
deciding an angle between the mean value of in-phase symbols and the mean value of quadrature symbols of the estimated symbol pair, as the phase error.
8. The method of claim 3 , wherein in the estimating of the pair of the received symbols the pair of received symbols (Xn,Yn) are transformed according to the following equation:
[
Y
1
Y
2
]
=
[
-
sin
(
π
2
-
π
M
)
cos
(
π
2
-
π
M
)
-
sin
(
π
2
+
π
M
)
cos
(
π
2
+
π
M
)
]
[
X
n
Y
n
]
where M is the level of modulation of the PSK system, and if the transformed symbols (Y 1 ,Y 2 ) of the pair are a positive number and a negative number, respectively, the pair of the received symbols (Xn,Yn) is estimated as a pair of received symbols corresponding to a transmitted symbol having only the quadrature component, and
in the deciding of the angle, the phase error ψ is estimated according to the following equation:
Ψ
=
π
2
(
1
-
sgn
X
_
N
)
+
sgn
X
_
N
tan
-
1
(
Y
_
N
X
_
N
)
where sgn(x) is a function that is −1 if x is a negative number and is 1 if x is equal to or greater than 0, and X N and Y N are the mean values, respectively, of the estimated N pairs of symbols (Xn,Yn).