Method and apparatus for phase noise mitigation
An approach is provided to mitigate phase noise by correcting common phase error and inter-carrier-interference in a received signal. The approach involves determining a received signal includes phase noise comprising at least a common phase error component and an inter-carrier-interference component. The approach also involves causing the common phase error to be corrected based on one or more pilot carriers. The approach further involves causing an estimate of a main signal component to be subtracted from the one or more pilot carriers. The approach additionally involves determining a sequence of estimated coefficients of a multiplicative phase noise sequence. The approach also involves causing the inter-carrier-inference to be corrected by processing the multiplicative phase noise sequence using the sequence of estimated coefficients. The approach further involves causing an equalized data signal to be output based on the corrected common phase error and the corrected inter-carrier-interference.
1. A method comprising:
determining a received signal includes phase noise comprising at least a common phase error component and an inter-carrier-interference component;
causing, at least in part, the common phase error to be corrected based, at least in part, on one or more pilot carriers;
causing, at least in part, an estimate of a main signal component to be subtracted from the one or more pilot carriers;
determining a sequence of estimated coefficients of a multiplicative phase noise sequence, wherein the determination of the sequence of estimated coefficients comprises processing an estimated value of a first coefficient of the sequence of estimated coefficients to produce a result based on the first coefficient and subtracting the result when estimating a next coefficient of the sequence of estimated coefficients to hone in on an estimated value of the next coefficient;
causing, at least in part, the inter-carrier-inference to be corrected by processing the multiplicative phase noise sequence using the sequence of estimated coefficients; and
causing, at least in part, an equalized data signal to be output based, at least in part, on the corrected common phase error and the corrected inter-carrier-interference.
2. A method of claim 1 , further comprising:
causing, at least in part, a unitary normalization of one or more respective units of each coefficient of the sequence of estimated coefficients to have a same unitary magnitude in a time domain.
3. A method of claim 2 , wherein the unitary normalization comprises:
causing, at least in part, the sequence of estimated coefficients to be subjected to an Inverse Fast Fourier Transform to generate an output sequence and enforce the unitary magnitude on the output sequence;
causing, at least in part, the output sequence to be subjected to a Fast Fourier Transform to generate a new sequence of estimated coefficients having the same unitary magnitude in the time domain; and
causing, at least in part, the new sequence of estimated coefficients to be used in the inter-carrier-interference correction.
4. A method of claim 1 , wherein the determination of the estimated sequence of coefficients comprises:
determining a negative conjugate symmetry of a first part of the sequence of estimated coefficients to generate a second part of the sequence of estimated coefficients; and
causing, at least in part, the sequence of estimated coefficients to include the first part and the second part of the sequence of estimated coefficients.
5. A method of claim 4 , wherein the first part of the sequence of estimated coefficients includes at least four estimated coefficients.
6. A method of claim 1 , wherein the sequence of estimated coefficients includes at least two estimated coefficients, the number of estimated coefficients being based, at least in part, on a determined system resource availability.
7. A method of claim 1 , wherein the determination of the sequence of estimated coefficients is based, at least in part, on an equation
P
^
(
m
)
=
∑
k
∈
S
Y
~
(
k
)
E
*
(
k
-
m
)
∑
k
∈
S
E
(
k
-
m
)
2
.
8. A method of claim 1 , further comprising:
causing, at least in part, a unitary normalization of one or more respective units of each coefficient of the sequence of estimated coefficients to have a same unitary magnitude in a time domain,
wherein the unitary normalization is based, at least in part, on an equation
P
^
(
k
)
=
P
^
(
k
)
-
P
^
*
(
-
k
)
2
.
9. A method of claim 1 , wherein the determination of the sequence of estimated coefficients is based, at least in part, on an equation
P
^
(
m
)
=
∑
k
∈
S
[
Y
~
(
k
)
E
*
(
k
-
m
)
-
Y
~
*
(
k
)
E
(
k
+
m
)
]
∑
k
∈
S
[
E
(
k
-
m
)
2
+
E
(
k
+
m
)
2
]
.
10. An apparatus comprising:
at least one processor; and
at least one memory including computer program code for one or more programs,
the at least one memory and the computer program code configured to, with the at least one processor, cause the apparatus to perform at least the following,
determine a received signal includes phase noise comprising at least a common phase error component and an inter-carrier-interference component;
cause, at least in part, the common phase error to be corrected based, at least in part, on one or more pilot carriers;
cause, at least in part, an estimate of a main signal component to be subtracted from the one or more pilot carriers;
determine a sequence of estimated coefficients of a multiplicative phase noise sequence, wherein the determination of the sequence of estimated coefficients comprises processing an estimated value of a first coefficient of the sequence of estimated coefficients to produce a result based on the first coefficient and subtracting the result when estimating a next coefficient of the sequence of estimated coefficients to hone in on an estimated value of the next coefficient;
cause, at least in part, the inter-carrier-inference to be corrected by processing the multiplicative phase noise sequence using the sequence of estimated coefficients; and
cause, at least in part, an equalized data signal to be output based, at least in part, on the corrected common phase error and the corrected inter-carrier-interference.
11. An apparatus of claim 10 , wherein the apparatus is further caused to:
cause, at least in part, a unitary normalization of one or more respective units of each coefficient of the sequence of estimated coefficients to have a same unitary magnitude.
12. An apparatus of claim 11 , wherein the unitary normalization comprises:
causing, at least in part, the sequence of estimated coefficients to be subjected to an Inverse Fast Fourier Transform to generate an output sequence;
causing, at least in part, the output sequence to be subjected to a Fast Fourier Transform to generate a new sequence of estimated coefficients having the same unitary magnitude; and
causing, at least in part, the new sequence of estimated coefficients to be used in the inter-carrier-interference correction.
13. An apparatus of claim 10 , wherein the determination of the estimated sequence of coefficients comprises:
determining a negative conjugate symmetry of a first part of the sequence of estimated coefficients to generate a second part of the sequence of estimated coefficients; and
causing, at least in part, the sequence of estimated coefficients to include the first part and the second part of the sequence of estimated coefficients.
14. An apparatus of claim 13 , wherein the first part of the sequence of estimated coefficients includes at least four estimated coefficients.
15. An apparatus of claim 10 , wherein the sequence of estimated coefficients includes at least two estimated coefficients, the number of estimated coefficients being based, at least in part, on a determined system resource availability.
16. An apparatus of claim 10 , wherein the determination of the sequence of estimated coefficients is based, at least in part, on an equation
P
^
(
m
)
=
∑
k
∈
S
Y
~
(
k
)
E
*
(
k
-
m
)
∑
k
∈
S
E
(
k
-
m
)
2
.
17. An apparatus of claim 10 , wherein the apparatus is further caused to:
cause, at least in part, a unitary normalization of one or more respective units of each coefficient of the sequence of estimated coefficients to have a same unitary magnitude in a time domain, the unitary normalization being based, at least in part, on an equation
P
^
(
k
)
=
P
^
(
k
)
-
P
^
*
(
-
k
)
2
.
18. An apparatus of claim 10 , wherein the determination of the sequence of estimated coefficients is based, at least in part, on an equation
P
^
(
m
)
=
∑
k
∈
S
[
Y
~
(
k
)
E
*
(
k
-
m
)
-
Y
~
*
(
k
)
E
(
k
+
m
)
]
∑
k
∈
S
[
E
(
k
-
m
)
2
+
E
(
k
+
m
)
2
]
.
19. A non-transitory computer-readable storage medium carrying one or more sequences of one or more instructions which, when executed by one or more processors, cause an apparatus to:
determine a received signal includes phase noise comprising at least a common phase error component and an inter-carrier-interference component;
cause, at least in part, the common phase error to be corrected based, at least in part, on one or more pilot carriers;
cause, at least in part, an estimate of a main signal component to be subtracted from the one or more pilot carriers;
determine a sequence of estimated coefficients of a multiplicative phase noise sequence, wherein the determination of the sequence of estimated coefficients comprises processing an estimated value of a first coefficient of the sequence of estimated coefficients to produce a result based on the first coefficient and subtracting the result when estimating a next coefficient of the sequence of estimated coefficients to hone in on an estimated value of the next coefficient;
cause, at least in part, the inter-carrier-inference to be corrected by processing the multiplicative phase noise sequence using the sequence of estimated coefficients; and
cause, at least in part, an equalized data signal to be output based, at least in part, on the corrected common phase error and the corrected inter-carrier-interference.
20. A non-transitory computer-readable storage medium of claim 19 , wherein the apparatus is further caused to:
cause, at least in part, a unitary normalization of one or more respective units of each coefficient of the sequence of estimated coefficients to have a same unitary magnitude.
21. A non-transitory computer-readable storage medium of claim 20 , wherein the unitary normalization comprises:
causing, at least in part, the sequence of estimated coefficients to be subjected to an Inverse Fast Fourier Transform to generate an output sequence;
causing, at least in part, the output sequence to be subjected to a Fast Fourier Transform to generate a new sequence of estimated coefficients having the same unitary magnitude; and
causing, at least in part, the new sequence of estimated coefficients to be used in the inter-carrier-interference correction.
22. A non-transitory computer-readable storage medium of claim 19 , wherein the determination of the estimated sequence of coefficients comprises:
determining a negative conjugate symmetry of a first part of the sequence of estimated coefficients to generate a second part of the sequence of estimated coefficients; and
causing, at least in part, the sequence of estimated coefficients to include the first part and the second part of the sequence of estimated coefficients.
23. A non-transitory computer-readable storage medium of claim 22 , wherein the first part of the sequence of estimated coefficients includes at least four estimated coefficients.
24. A non-transitory computer-readable storage medium of claim 19 , wherein the sequence of estimated coefficients includes at least two estimated coefficients, the number of estimated coefficients being based, at least in part, on a determined system resource availability.
25. A non-transitory computer-readable storage medium of claim 19 , wherein the determination of the sequence of estimated coefficients is based, at least in part, on an equation
P
^
(
m
)
=
∑
k
∈
S
Y
~
(
k
)
E
*
(
k
-
m
)
∑
k
∈
S
E
(
k
-
m
)
2
.
26. A non-transitory computer-readable storage medium of claim 19 , wherein the apparatus is further caused to:
cause, at least in part, a unitary normalization of one or more respective units of each coefficient of the sequence of estimated coefficients to have a same unitary magnitude in a time domain, the unitary normalization being based, at least in part, on an equation
P
^
(
k
)
=
P
^
(
k
)
-
P
^
*
(
-
k
)
2
.
27. A non-transitory computer-readable storage medium of claim 19 , wherein the determination of the sequence of estimated coefficients is based, at least in part, on an equation
P
^
(
m
)
=
∑
k
∈
S
[
Y
~
(
k
)
E
*
(
k
-
m
)
-
Y
~
*
(
k
)
E
(
k
+
m
)
]
∑
k
∈
S
[
E
(
k
-
m
)
2
+
E
(
k
+
m
)
2
]
.