Integer frequency offset estimation based on the maximum likelihood principal in OFDM systems
View Patent ↗A receiver in an OFDM system may include a maximum likelihood (ML) estimator that estimates the integer part of the carrier frequency offset. The estimator may operate with or without pilot subcarriers. The estimator may calculate the integer frequency offset estimate based on the cyclic shift and phase shift of subcarriers between OFDM symbols.
1. A method comprising: receiving a plurality of symbols, each symbol including a plurality of data samples; observing a plurality of data samples in adjacent symbols; and calculating an estimate of an integer portion of a carrier frequency offset based on a cyclic shift and a phase shift of the data samples between symbols, wherein calculating the estimate comprises applying multiple phase directions to each of the observed data samples to produce multiple magnitude measurements for each of the observed data samples, wherein said calculating the estimate comprises means for solving the equation:
l
^
=
arg
max
n
{
T
(
n
)
}
,
where
T
(
n
)
=
∑
k
∈
S
2
σ
Z
2
log
(
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
+
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
)
,
where n is a symbol index, k is a subcarrier index, S 2 is a set of indices for data subcarriers, σ Z 2 is a variance, α is a cyclic prefix width ratio, and V is an observation vector.
2. The method of claim 1 , wherein each of the OFDM symbols further comprise a plurality of pilot samples corresponding to a plurality of pilot subcarriers in the OFDM symbols.
3. The method of claim 2 , wherein said calculating comprises calculating the estimate of the integer portion of a carrier frequency offset based on a cyclic shift and a phase shift of the data subcarriers and the pilot subcarriers between symbols.
4. The method of claim 3 , wherein said calculating the estimate comprises solving the equation:
l
^
=
arg
max
n
{
T
(
n
)
}
,
where
T
(
n
)
=
∑
k
∈
S
1
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
A
*
[
k
]
}
+
∑
k
∈
S
2
σ
Z
2
log
(
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
+
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
)
where n is a symbol index, k is a subcarrier index, S 1 is a set of indices for pilot subcarriers, S 2 is a set of indices for data subcarriers, σ Z 2 is a variance, α is a cyclic prefix width ratio, V is an observation vector, and A is a sequence known to the apparatus.
5. The method of claim 1 , further comprising:
transforming the received data samples into the frequency domain.
6. An apparatus comprising: an estimator including: a receiver to receive a plurality of symbols, each symbol including a plurality of data samples; a framer to observe a plurality of data samples in adjacent symbols; and a calculator to calculate an estimate of an integer portion of a carrier frequency offset based on a cyclic shift and a phase shift of the data samples between symbols, wherein the calculator is operative to calculate the estimate by applying multiple phase directions to each of the observed data samples to produce multiple magnitude measurements for each of the observed data samples, wherein the estimator is operative to calculate the estimate by solving the equation:
l
^
=
arg
max
n
{
T
(
n
)
}
,
where
T
(
n
)
=
∑
k
∈
S
2
σ
Z
2
log
(
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
+
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
)
,
where n is a symbol index, k is a subcarrier index, S 2 is a set of indices for data subcarriers, σ Z 2 is a variance, α is a cyclic prefix width ratio, and V is an observation vector.
7. The apparatus of claim 6 , wherein each of the OFDM symbols further comprise a plurality of pilot samples corresponding to a plurality of pilot subcarriers in the OFDM symbols.
8. The apparatus of claim 7 , wherein the estimator is operative to calculate the estimate of the integer portion of a carrier frequency offset based on a cyclic shift and a phase shift of the data subcarriers and the pilot subcarriers between OFDM symbols.
9. The apparatus of claim 8 , wherein the estimator is operative to calculate the estimate by solving the equation:
l
^
=
arg
max
n
{
T
(
n
)
}
,
where
T
(
n
)
=
∑
k
∈
S
1
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
A
*
[
k
]
}
+
∑
k
∈
S
2
σ
Z
2
log
(
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
+
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
)
where n is a symbol index, k is a subcarrier index, S 1 is a set of indices for pilot subcarriers, S 2 is a set of indices for data subcarriers, σ Z 2 is a variance, α is a cyclic prefix width ratio, V is an observation vector, and A is a sequence known to the receiver.
10. The apparatus of claim 6 , further comprising:
a transform module to transform the data samples into the frequency domain.
11. An apparatus comprising: estimator means including: means for receiving a plurality of symbols, each symbol including a plurality of data samples; means for observing a plurality of data samples in adjacent symbols; and means for calculating an estimate of an integer portion of a carrier frequency offset based on a cyclic shift and a phase shift of the data samples between symbols, wherein the means for calculating the estimate comprises means for applying multiple phase directions to each of the observed data samples to produce multiple magnitude measurements for each of the observed data samples, wherein the estimator means further comprises means for solving the equation:
l
^
=
arg
max
n
{
T
(
n
)
}
,
where
T
(
n
)
=
∑
k
∈
S
2
σ
Z
2
log
(
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
+
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
)
,
where n is a symbol index, k is a subcarrier index, S 2 is a set of indices for data subcarriers, σ Z 2 is a variance, α is a cyclic prefix width ratio, and V is an observation vector.
12. The apparatus of claim 11 , wherein each of the OFDM symbols further comprise a plurality of pilot samples corresponding to a plurality of pilot subcarriers in the OFDM symbols.
13. The apparatus of claim 12 , wherein the estimator means further comprises means for calculating the estimate of the integer portion of a carrier frequency offset based on a cyclic shift and a phase shift of the data subcarriers and the pilot subcarriers between OFDM symbols.
14. The apparatus of claim 13 , wherein the estimator means further comprises means for solving the equation:
l
^
=
arg
max
n
{
T
(
n
)
}
,
where
T
(
n
)
=
∑
k
∈
S
1
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
A
*
[
k
]
}
+
∑
k
∈
S
2
σ
Z
2
log
(
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
+
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
)
where n is a symbol index, k is a subcarrier index, S 1 is a set of indices for pilot subcarriers, S 2 is a set of indices for data subcarriers, σ Z 2 is a variance, α is a cyclic prefix width ratio, V is an observation vector, and A is a sequence known to the estimator means.
15. The apparatus of claim 11 , further comprising:
means for transforming the data samples into the frequency domain.
16. A computer program, encoded on a computer-readable medium, operable to cause data processing apparatus to perform operations comprising: receiving a plurality of symbols, each symbol including a plurality of data samples; observing a plurality of data samples in adjacent symbols; and calculating an estimate of an integer portion of a carrier frequency offset based on a cyclic shift and a phase shift of the data samples between symbols, wherein calculating the estimate comprises applying multiple phase directions to each of the observed data samples to produce multiple magnitude measurements for each of the observed data samples, wherein said calculating the estimate comprises solving the equation:
l
^
=
arg
max
n
{
T
(
n
)
}
,
where
T
(
n
)
=
∑
k
∈
S
2
σ
Z
2
log
(
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
+
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
)
,
where
where n is a symbol index, k is a subcarrier index, S 2 is a set of indices for data subcarriers, σ Z 2 is a variance, α is a cyclic prefix width ratio, and V is an observation vector.
17. The computer program of claim 16 , wherein each of the OFDM symbols further comprise a plurality of pilot samples corresponding to a plurality of pilot subcarriers in the OFDM symbols.
18. The computer program of claim 17 , wherein said calculating comprises calculating the estimate of the integer portion of a carrier frequency offset based on a cyclic shift and a phase shift of the data subcarriers and the pilot subcarriers between symbols.
19. The computer program of claim 18 , wherein said calculating the estimate comprises solving the equation:
l
^
=
arg
max
n
{
T
(
n
)
}
,
where
T
(
n
)
=
∑
k
∈
S
1
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
A
*
[
k
]
}
+
∑
k
∈
S
2
σ
Z
2
log
(
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
+
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
)
where n is a symbol index, k is a subcarrier index, S 1 is a set of indices for pilot subcarriers, S 2 is a set of indices for data subcarriers, σ Z 2 is a variance, α is a cyclic prefix width ratio, V is an observation vector, and A is a known sequence.
20. The computer program of claim 16 , the operations further comprising:
transforming the received data samples into the frequency domain.
21. A system comprising: one or more antennas to receive signals from a channel; and an estimator including: a receiver to receive a plurality of symbols, each symbol including a plurality of data samples; a framer to observe a plurality of data samples in adjacent symbols; and a calculator to calculate an estimate of an integer portion of a carrier frequency offset based on a cyclic shift and a phase shift of the data samples between symbols, wherein the calculator is operative to calculate the estimate by applying multiple phase directions to each of the observed data samples to produce multiple magnitude measurements for each of the observed data samples, wherein the estimator is operative to calculate the estimate by solving the equation:
l
^
=
arg
max
n
{
T
(
n
)
}
,
where
T
(
n
)
=
∑
k
∈
S
2
σ
Z
2
log
(
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
+
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
)
,
where n is a symbol index, k is a subcarrier index, S 2 is a set of indices for data subcarriers, σ Z 2 is a variance, α is a cyclic prefix width ratio, and V is an observation vector.
22. The system of claim 21 , wherein each of the OFDM symbols further comprise a plurality of pilot samples corresponding to a plurality of pilot subcarriers in the OFDM symbols.
23. The system of claim 22 , wherein the estimator is operative to calculate the estimate of the integer portion of a carrier frequency offset based on a cyclic shift and a phase shift of the data subcarriers and the pilot subcarriers between OFDM symbols.
24. The system of claim 23 , wherein the estimator is operative to calculate the estimate by solving the equation:
l
^
=
arg
max
n
{
T
(
n
)
}
,
where
T
(
n
)
=
∑
k
∈
S
1
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
A
*
[
k
]
}
+
∑
k
∈
S
2
σ
Z
2
log
(
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
+
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
)
where n is a symbol index, k is a subcarrier index, S 1 is a set of indices for pilot subcarriers, S 2 is a set of indices for data subcarriers, σ Z 2 is a variance, α is a cyclic prefix width ratio, V is an observation vector, and A is a sequence known to the estimator.
25. The system of claim 21 , further comprising:
a transform module to transform the data samples into the frequency domain.
26. A system comprising: antenna means for receiving signals from a channel; and estimator means including: means for receiving a plurality of symbols, each symbol including a plurality of data samples; means for observing a plurality of data samples in adjacent symbols; and means for calculating an estimate of an integer portion of a carrier frequency offset based on a cyclic shift and a phase shift of the data samples between symbols, wherein the means for calculating the estimate comprises means for applying multiple phase directions to each of the observed data samples to produce multiple magnitude measurements for each of the observed data samples, wherein the estimator means further comprises means for solving the equation:
l
^
=
arg
max
n
{
T
(
n
)
}
,
where
T
(
n
)
=
∑
k
∈
S
2
σ
Z
2
log
(
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
+
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
)
,
where n is a symbol index, k is a subcarrier index, S 2 is a set of indices for data subcarriers, σ Z 2 is a variance, α is a cyclic prefix width ratio, and V is an observation vector.
27. The system of claim 26 , wherein each of the OFDM symbols further comprise a plurality of pilot samples corresponding to a plurality of pilot subcarriers in the OFDM symbols.
28. The system of claim 27 , wherein the estimator means further comprises means for calculating the estimate of the integer portion of a carrier frequency offset based on a cyclic shift and a phase shift of the data subcarriers and the pilot subcarriers between OFDM symbols.
29. The system of claim 28 , wherein the estimator means further comprises means for solving the equation:
l
^
=
arg
max
n
{
T
(
n
)
}
,
where
T
(
n
)
=
∑
k
∈
S
1
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
A
*
[
k
]
}
+
∑
k
∈
S
2
σ
Z
2
log
(
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
+
cosh
(
{
V
[
k
+
n
]
ⅇ
-
j2π
n
α
}
σ
Z
2
)
)
where n is a symbol index, k is a subcarrier index, S 1 is a set of indices for pilot subcarriers, S 2 is a set of indices for data subcarriers, σ Z 2 is a variance, α is a cyclic prefix width ratio, V is an observation vector, and A is a sequence known to the estimator.
30. The system of claim 26 , further comprising:
means for transforming the data samples into the frequency domain.