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 one or more inter-carrier interference terms, including:
canceling, from a received signal, an estimated common phase error to form a first compensated received signal; and
estimating a first inter-carrier interference term as an output of a function, an input of the function comprising the first compensated received signal.
2. The method of claim 1 , further comprising calculating a value of a transmitted signal, corresponding to the received signal, in a subcarrier using known phase tracking reference signal (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, 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 , further comprising estimating the common phase error using an estimated channel and phase tracking reference signal subcarriers from the received signal,
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, N PTRS being an integer greater than 1, and N c being an integer greater than 1.
5. The method of claim 4 , further comprising estimating a channel using demodulation reference signal subcarriers from the received signal,
wherein the canceling, from the received signal, the estimated common phase error, 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 [κ 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
-
1
)
]
X
[
κ
(
i
+
1
)
(
i
-
1
)
]
-
…
-
J
^
[
i
-
1
]
H
^
[
κ
1
(
2
i
-
1
)
]
X
[
κ
1
(
2
i
-
1
)
]
-
J
^
[
-
(
i
-
1
)
]
H
^
[
κ
(
2
i
-
1
)
1
]
X
[
κ
(
2
i
-
1
)
1
]
,
for
i
>
1
wherein:
κ 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[κ 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 κ ij ;
X[κ pq ] is a transmitted signal in subcarriers from among the set κ pq ;
Y[κ ii ] is the received signal in subcarriers from among the set κ ii ;
Ĵ[0] is the estimated common phase error; and
Ĵ[p], for p not equal to zero, is the estimated p-th inter-carrier interference term.
6. The method of claim 5 , wherein the estimating, based on the i-th compensated received signal, of the i-th inter-carrier interference term comprises calculating an i-th estimated inter-carrier interference term Ĵ[i] according to
[
Re
{
J
^
[
i
]
}
Im
{
J
^
[
i
]
}
]
2
×
1
=
(
T
H
T
)
-
1
T
H
[
Re
{
Y
SIC
[
κ
ii
]
}
Im
{
Y
SIC
[
κ
ii
]
}
]
2
(
N
c
(
N
PTRS
-
2
i
)
)
×
1
,
wherein:
T
=
[
A
(
N
c
(
N
PTRS
-
2
i
)
)
×
1
B
(
N
c
(
N
PTRS
-
2
i
)
)
×
1
C
(
N
c
(
N
PTRS
-
2
i
)
)
×
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
)
]
}
-
Im
{
H
^
[
κ
(
2
i
)
0
]
X
[
κ
(
2
i
)
0
]
}
;
C
=
Im
{
H
^
[
κ
0
(
2
i
)
]
X
[
κ
0
(
2
i
)
]
}
-
Im
{
H
^
[
κ
(
2
i
)
0
]
X
[
κ
(
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
]
}
.
7. The method of claim 6 , further comprising calculating a final compensated received signal Y ICI comp [l] based on a matched filter, wherein an order of the matched filter is dependent on a number of estimated inter-carrier interference terms.
8. A method, comprising:
estimating one or more inter-carrier interference terms, including:
canceling, from a received signal, an estimated common phase error to form a first compensated received signal; and
jointly estimating L inter-carrier interference terms as outputs of a function, an input of the function comprising the first compensated received signal, L being a set integer greater than 0.
9. The method of claim 8 , further comprising calculating a value of a transmitted signal in a subcarrier using known phase tracking reference signal (PTRS) pilots.
10. The method of claim 8 , 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, N PTRS being an integer greater than 1, and N c being an integer greater than 1.
11. The method of claim 10 , further comprising estimating a channel using demodulation reference signal subcarriers from the received signal,
wherein the canceling, from the received signal, the estimated common phase error to form a first compensated received signal comprises calculating the first compensated received signal Y CPEcomp [κ LL ] according to Y CPEcomp [κ LL ]=Y[κ LL ]−Ĵ[0]Ĥ[κ LL ]X[κ LL ], wherein:
κ 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[κ 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 κ LL
X[κ LL ] is the transmitted signal in subcarriers from among the set κ LL
Y[κ LL ] is the received signal in subcarriers from among the set κ LL ; and
Ĵ[0] is the estimated common phase error.
12. The method of claim 11 , 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 [κ (L−i)(L+i) ] X [κ (L−i)(L+i) ]}−Re{ Ĥ [κ (L+i)(L−i) ] X [κ (L+i)(L−i) ]};
B i =−Im{ Ĥ [κ (L−i)(L+i) ] X [κ (L−i)(L+i) ]}−Im{ Ĥ [κ (L+i)(L−i) ] X [κ (L+i)(L−i) ]};
C i =Im{ Ĥ [κ (L−i)(L+i) ] X [κ (L−i)(L+i) ]}−Im{ Ĥ [κ (L+i)(L−i) ] X [κ (L+i)(L−i) ]}; and
D i =Re{ Ĥ [κ (L−i)(L+i) ] X [κ (L−i)(L+i) ]}+Re{ Ĥ [κ (L+i)(L−i) ] X [κ (L+i)(L−i) ]}.
13. The method of claim 12 , 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 ].
14. A system, comprising:
a receiver,
the receiver comprising a processing circuit configured to estimate one or more inter-carrier interference terms, including:
canceling, from a received signal, an estimated common phase error to form a first compensated received signal; and
estimating a first inter-carrier interference term as an output of a function, an input of the function comprising the first compensated received signal.
15. The system of claim 14 , wherein the processing circuit is further configured to calculate a value of a transmitted signal, corresponding to the received signal, in a subcarrier using known phase tracking reference signal (PTRS) pilots.
16. The system of claim 14 , 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, 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.
17. The system of claim 16 , wherein the processing circuit is further configured to estimate the common phase error using an estimated channel and phase tracking reference signal subcarriers from the received signal,
wherein the estimating of the common phase error comprises calculating a phase of the estimated common phase error according to
Ĵ [0]= (( Ĥ [κ] X [κ]) H Y [κ]), wherein:
κ is a set of phase tracking reference signal subcarriers;
Ĥ[κ] 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 κ;
X[κ] is the transmitted signal in subcarriers from among the set κ;
Y[κ] is the received signal in subcarriers from among the set κ; and
H as a superscript denotes a conjugate transpose.
18. The system of claim 17 , wherein the estimating of the common phase error further comprises setting an amplitude of the estimated common phase error to be equal to 1.
19. The system of claim 14 , wherein the received signal comprises a plurality of phase tracking reference signal subcarriers comprising N c N PTRS subcarriers, arranged in N c groups, each of the N c groups comprising N PTRS adjacent subcarriers N PTRS being an integer greater than 1, and N c being an integer greater than 1.
20. The system of claim 14 , wherein the processing circuit is further configured to calculate a final compensated received signal Y ICI comp [l] based on a matched filter, wherein an order of the matched filter is dependent on a number of estimated inter-carrier interference terms.