Communication system and phase error estimating method thereof
View Patent ↗A communication system includes a receiving circuit and a phase error estimating circuit. The receiving circuit receives an input signal x, which has an input phase θ in a polar coordinate system. According to partial differentiation performed on the natural logarithm of a function f(x, θ), the phase error estimating circuit generates an estimated phase error of the input signal x. f(x, θ) represents a probability function of receiving the input signal x at the receiving circuit.
1. A communication system for estimating a phase error, comprising:
a receiving circuit, that receives an input signal x, the input signal x having an input signal radius r and an input phase θ, wherein the input signal x is generated based on M-phase shift keying (M-PSK); and
an error estimating circuit, that generates a first harmonic coefficient h 1 (r) and a second harmonic coefficient h 2 (r) according to the input signal radius r, generates a first sine function sin(Mθ) and a second sine function sin(2Mθ) according to the input phase θ, multiplies the first harmonic coefficient h 1 (r) by the first sine function sin(Mθ) to generate a first operation result and multiplies the second harmonic coefficient h 2 (r) by the second sine function sin(2Mθ) to generate a second operation result, and generates an estimated phase error {circumflex over (θ)} according to the first operation result and the second operation result;
wherein, the estimated phase error {circumflex over (θ)} is associated with a Fourier series of
∂
∂
θ
ln
f
(
x
,
θ
)
,
and f(x, θ) represents a probability function of receiving the input signal x at the receiving circuit, and
wherein the estimated phase error {circumflex over (θ)} is used to compensate a phase of the input signal x.
2. The communication system according to claim 1 , wherein the receiving circuit further comprises:
an auto gain control (AGC) circuit, that adjusts a signal strength α 2 of the input signal, where α represents a normalization factor;
wherein, the first harmonic coefficient h 1 (r) and the second harmonic coefficient h 2 (r) are associated with the normalization factor α.
3. The communication system according to claim 2 , wherein the phase error estimating circuit generates the first harmonic coefficient h 1 (r) according to an equation:
h
1
(
r
)
=
{
0
,
r
<
d
1
α
d
2
+
d
3
α
(
r
-
d
4
α
)
,
r
≥
d
5
α
d
6
2
α
(
r
-
d
7
α
)
,
else
;
wherein, each of d 1 to d 7 represents a constant value.
4. The communication system according to claim 2 , wherein the phase error estimating circuit generates the second harmonic coefficient h 2 (r) according to an equation:
h
2
(
r
)
=
{
0
,
r
<
d
8
α
d
9
α
(
r
-
d
10
α
)
,
r
≥
d
8
α
;
wherein, each of d 8 to d 10 represents a constant value.
5. The communication system according to claim 2 , wherein the phase estimating circuit generates the estimated phase error {circumflex over (θ)} according to an equation:
{circumflex over (θ)}= h 1 ( r )sin( M θ)− h 2 ( r )sin(2 M θ).
6. A phase error estimating method applied to a communication system to estimate a phase error of an input signal x, the input signal x corresponding to an output signal that a transmitting end generates based on M-PSK, M being a value of 2 raised to a power of any positive integer, the phase error estimating method comprising:
a) receiving an input signal x, the input signal x having an input signal radius r and an input phase θ, wherein the input signal x is generated based on M-phase shift keying (M-PSK);
b) generating a first harmonic coefficient h 1 (r) and a second harmonic coefficient h 2 (r) according to the input signal radius r;
c) generating a first sine function sin(Mθ) and a second sine function sin(2Mθ according to the input phase θ;
d) multiplying the first harmonic coefficient h 1 (r) by the first sine function sin(Mθ) to generate a first operation result, and multiplying the second harmonic coefficient h 2 (r) by the second sine function sin(2Mθ) to generate a second operation result; and
e) generating an estimated phase error {circumflex over (θ)} according to the first operation result and the second operation result;
wherein, the estimated phase error {circumflex over (θ)} is associated with a Fourier series of
∂
∂
θ
ln
f
(
x
,
θ
)
,
and f(x, θ) represents a probability function of the input signal x, and
wherein the estimated phase error {circumflex over (θ)} is used to compensate a phase of the input signal x.
7. The phase error estimating method according to claim 6 , before step (b), further comprising:
adjusting a signal strength α 2 of the input signal, where α represents a normalization factor;
wherein, the normalization factor a is for generating the first harmonic coefficient h 1 (r) and the second harmonic coefficient h 2 (r).
8. The phase error estimating method according to claim 7 , wherein step (b) comprises generating the first harmonic coefficient h 1 (r) according to an equation:
h
1
(
r
)
=
{
0
,
r
<
d
1
α
d
2
+
d
3
α
(
r
-
d
4
α
)
,
r
≥
d
5
α
d
6
2
α
(
r
-
d
7
α
)
,
else
;
wherein, each of d 1 to d 7 represents a constant value.
9. The phase error estimating method according to claim 7 , wherein step (b) comprises generating the second harmonic coefficient h 2 (r) according to an equation:
h
2
(
r
)
=
{
0
,
r
<
d
8
α
d
9
α
(
r
-
d
10
α
)
,
r
≥
d
8
α
;
wherein, each of d 8 to d 10 represents a constant value.
10. The phase error estimating method according to claim 7 , wherein step (e) comprises generating the estimated phase error {circumflex over (θ)} according to an equation:
{circumflex over (θ)}= h 1 ( r )sin( M θ)− h 2 ( r )sin(2 M θ).