System and method for common phase error and inter-carrier interference estimation and compensation
A system and method for transmitting an orthogonal frequency-division multiplexed signal with a group distributed phase tracking reference signal subcarrier structure, and for estimating, and compensating for, both common phase error, and inter-carrier interference.
1. A method, comprising:
estimating a channel using demodulation reference signal subcarriers from a received signal;
estimating a common phase error term using the estimated channel and phase tracking reference signal subcarriers; and
estimating one or more inter-carrier interference terms, including:
canceling, from the received signal, the estimated common phase error term to form a first compensated received signal; and
estimating, based on the first compensated received signal, a first inter-carrier interference term.
2. The method of claim 1 , further comprising calculating a value of the transmitted signal in a subcarrier using known PTRS pilots.
3. The method of claim 1 , wherein the estimating of the inter-carrier interference terms further comprises:
iteratively, for a range of values of an integer i greater than 1 and less than a set integer L:
canceling, from the received signal, the estimated common phase error term, and the first through (i−1)-th inter-carrier interference terms, to form an i-th compensated received signal; and
estimating, using the i-th compensated received signal, an i-th inter-carrier interference term.
4. The method of claim 3 , wherein the estimating of the common phase error term comprises calculating a phase of the estimated common phase error term according to Ĵ[0]= ((Ĥ[ ]X[ ]) H Y[ ]), wherein:
is a set of phase tracking reference signal subcarriers;
Ĥ[ ] is a diagonal matrix the p-th diagonal element of which is equal to the estimated channel response for the p-th subcarrier from among the set ;
X[ ] is the transmitted signal in subcarriers from among the set ;
Y[ ] is the received signal in subcarriers from among the set ; and
H as a superscript denotes a conjugate transpose.
5. The method of claim 4 , wherein the estimating of the common phase error term further comprises setting an amplitude of the estimated common phase error term to be equal to 1.
6. The method of claim 5 , wherein the phase tracking reference signal subcarriers comprise N c N PTRS subcarriers, arranged in N c groups, each of the N c groups comprising N PTRS adjacent subcarriers.
7. The method of claim 6 , wherein the canceling, from the received signal, the estimated common phase error term, and the first through (i−1)-th inter-carrier interference terms, to form the i-th compensated received signal, comprises calculating the i-th compensated received signal Y SIC [ ii ] according to
Y
SIC
[
κ
ii
]
=
Y
[
κ
ii
]
-
J
^
[
0
]
H
^
[
κ
ii
]
X
[
κ
ii
]
,
for
i
=
1
Y
SIC
[
κ
ii
]
=
Y
[
κ
ii
]
-
J
^
[
0
]
H
^
[
κ
ii
]
X
[
κ
ii
]
-
J
^
[
1
]
H
^
[
κ
(
i
-
1
)
(
i
+
1
)
]
X
[
κ
(
i
-
1
)
(
i
+
1
)
]
-
J
^
[
-
1
]
H
^
[
κ
(
i
+
1
)
(
i
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i
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(
i
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-
…
-
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^
[
i
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^
[
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1
(
2
i
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]
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[
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(
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i
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)
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)
1
]
X
[
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i
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1
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,
for
i
>
1
wherein:
ij ={k 1(i+1) , . . . , k 1(N PTRS −j ), . . . , k N c (i+1 , . . . , k N c (N PTRS −j) }, wherein k pq is the q-th subcarrier of the p-th group of subcarriers of the phase tracking reference signal subcarriers;
Ĥ[ ij ] is a diagonal matrix the p-th diagonal element of which is equal to the estimated channel response for the p-th subcarrier from among the set ij ;
X[ pq ] is the transmitted signal in subcarriers from among the set pq ;
Y[ ii ] is the received signal in subcarriers from among the set ii ;
Ĵ[0] is the estimated common phase error term; and
Ĵ[p], for p not equal to zero, is the estimated p-th inter-carrier interference term.
8. The method of claim 7 , wherein the estimating, based on the i-th compensated received signal, of the i-th inter-carrier interference term comprises calculating the i-th estimated inter-carrier interference term Ĵ[i] according to
[
Re
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2
×
1
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(
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H
T
)
-
1
T
H
[
Re
{
Y
SIC
[
κ
ii
]
}
Im
{
Y
SIC
[
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ii
]
}
]
2
(
N
C
(
N
PTRS
-
2
i
)
)
×
1
,
wherein
:
T
=
[
A
(
N
C
(
N
PTRS
-
2
i
)
)
×
1
B
(
N
C
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PTRS
-
2
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)
×
1
C
(
N
C
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PTRS
-
2
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)
×
1
D
(
N
C
(
N
PTRS
-
2
i
)
)
×
1
]
2
(
N
C
(
N
PTRS
-
2
i
)
)
×
2
;
A
=
Re
{
H
^
[
κ
0
(
2
i
)
]
X
[
κ
0
(
2
i
)
]
}
-
Re
{
H
^
[
κ
(
2
i
)
0
]
X
[
κ
(
2
i
)
0
]
}
;
B
=
-
Im
{
H
^
[
κ
0
(
2
i
)
]
X
[
κ
0
(
2
i
)
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-
Im
{
H
^
[
κ
(
2
i
)
0
]
X
[
κ
(
2
i
)
0
]
}
;
C
=
Im
{
H
^
[
κ
0
(
2
i
)
]
X
[
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0
(
2
i
)
]
}
-
Im
{
H
^
[
κ
(
2
i
)
0
]
X
[
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(
2
i
)
0
]
}
;
and
D
=
Re
{
H
^
[
κ
0
(
2
i
)
]
X
[
κ
0
(
2
i
)
]
}
+
Re
{
H
^
[
κ
(
2
i
)
0
]
X
[
κ
(
2
i
)
0
]
}
.
9. The method of claim 8 , further comprising calculating a final compensated received signal Y ICI comp [l] based on a matched filter, wherein an order of the filter is dependent on a number of estimated inter-carrier interference terms.
10. A method comprising:
estimating a channel using demodulation reference signal subcarriers from a received signal;
estimating a common phase error term using the estimated channel and phase tracking reference signal subcarriers; and
estimating one or more inter-carrier interference terms, including:
canceling, from the received signal, the estimated common phase error term to form a first compensated received signal; and
jointly estimating, based on the first compensated received signal, L inter-carrier interference terms, L being a set integer greater than 0.
11. The method of claim 10 , further comprising calculating a value of the transmitted signal in a subcarrier using known PTRS pilots.
12. The method of claim 10 , wherein the estimating of the common phase error term comprises calculating a phase of the estimated common phase error term according to Ĵ[0]= ((H[ ]X[ ]) H Y[ ]), wherein:
is a set of phase tracking reference signal subcarriers;
Ĥ[ ] is a diagonal matrix the p-th diagonal element of which is equal to the estimated channel response for the p-th subcarrier from among the set ;
X[ ] is the transmitted signal in subcarriers from among the set ;
Y[ ] is the received signal in subcarriers from among the set ; and
H as a superscript denotes a conjugate transpose.
13. The method of claim 12 , wherein the estimating of the common phase error term further comprises setting an amplitude of the common phase error term to be equal to 1.
14. The method of claim 10 , wherein the phase tracking reference signal subcarriers comprise N c N PTRS subcarriers, arranged in N c groups, each of the N c groups comprising N PTRS adjacent subcarriers.
15. The method of claim 14 , wherein the canceling, from the received signal, the estimated common phase error term to form a first compensated received signal comprises calculating the first compensated received signal Y CPEcomp [ LL ] according to Y CPEcomp [ LL ]=Y[ LL ]−Ĵ[0]Ĥ[ LL ]X[ L ], wherein:
ij ={k 1(i+1) , . . . , k 1(N PTRS −j) , . . . , k N c (i+1) , . . . , k N c (N PTRS −j) }, wherein k pq is the q-th subcarrier of the p-th group of subcarriers of the phase tracking reference signal subcarriers;
Ĥ[ LL ] is a diagonal matrix the p-th diagonal element of which is equal to the estimated channel response for the p-th subcarrier from among the set LL ;
X[ LL ] is the transmitted signal in subcarriers from among the set LL ;
Y[ LL ] is the received signal in subcarriers from among the set LL ; and
Ĵ[0] is the estimated common phase error term.
16. The method of claim 15 , wherein the jointly estimating, based on the first compensated received signal, of L inter-carrier interference terms, comprises calculating the L estimated inter-carrier interference terms Ĵ according to
[
Re
{
J
^
}
Im
{
J
^
}
]
2
L
×
1
=
(
T
H
T
)
-
1
T
H
[
Re
{
Y
CPEcomp
[
κ
LL
]
}
Im
{
Y
CPEcomp
[
κ
LL
]
}
]
2
(
N
C
(
N
PTRS
-
2
L
)
)
×
1
,
wherein
:
T
=
[
A
(
N
C
(
N
PTRS
-
2
L
)
)
×
L
B
(
N
C
(
N
PTRS
-
2
L
)
)
×
L
C
(
N
C
(
N
PTRS
-
2
L
)
)
×
L
D
(
N
C
(
N
PTRS
-
2
L
)
)
×
L
]
2
(
N
C
(
N
PTRS
-
2
L
)
)
×
2
L
;
and
the respective i-th columns A i , B i , C i , and D i of A, B, C, and D are:
A i =Re{Ĥ [ (L−i)(L+i) ]X[ (L−i)(L+i) ]}−Re{Ĥ [ (L+i)(L−i) ]X[ (L+i)(L−i) ]};
B i =−Im{Ĥ [ (L−i)(L+i) ]X[ (L−i)(L+i) ]}−Im{Ĥ [ (L+i)(L−i) ]X[ (L+i)(L−i) ]};
C i =Im{Ĥ [ (L−i)(L+i) ]X[ (L−i)(L+i) ]}−Im{Ĥ [ (L+i)(L−i) ]X[ (L+i)(L−i) ]};
D i =Re{Ĥ [ (L−i)(L+i) ]X[ (L−i)(L+i) ]}+Re{Ĥ [ (L+i)(L−i) ]X[ (L+i)(L−i) ]};
17. The method of claim 16 , further comprising calculating a final compensated received signal Y ICI comp [l] according to
Y ICI comp [l]=Ĵ *[0] Y[l]+Ĵ *[1] Y[l+ 1]+ Ĵ *[−1] Y[l− 1]+ . . . + Ĵ*[L]Y[l+L]+Ĵ*[−L]Y[l−L].