# US 8,571,160 B2 · Frequency estimation

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- Number: US 8,571,160 B2
- Document ID: US8571160B2
- Status: Granted
- Kind: B2
- Application number: 12/222,107
- Filed: 2008-08-01
- Published: 2009-09-17
- Granted: 2013-10-29
- Earliest claimed: 2008-03-17
- Assignees: Nokia Corporation
- Applicants: Teemu Taneli Sipila
- Inventors: Teemu Taneli Sipila
- Web page: https://patentgrep.com/patent/US8571160B2

## CPC

- H04L 27/2657: {Carrier synchronisation}
- H04L 25/021: {Estimation of channel covariance}
- H04L 25/0212: {of impulse response}
- H04L 25/0228: {with direct estimation from sounding signals}
- H04L 27/2678: {using cyclostationarities, e.g. cyclic prefix or postfix}
- H04L 27/2607: {Cyclic extensions}
- H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M)

## Abstract

For estimating a difference between a frequency of a base station and a locally generated frequency of a mobile equipment in a mobile communications network, wherein at least a signal in a plurality of signals transmitted from the base station and received by the mobile equipment comprises a plurality of symbols each of which includes a cyclic prefix, a correlation between a symbol and its cyclic prefix is used for estimating the frequency difference.

## Claims

### Claim 1

A method, comprising:
determining a correlation between a symbol received from a transmitter and a cyclic prefix of the symbol and outputting a result indicative thereof, wherein the correlation is determined based at least in part on the correlation between a late frequency difference estimate and an early frequency difference estimate; and
estimating a frequency difference between a frequency of the transmitter and a locally generated frequency of a receiver according to the result of the correlation between the late frequency difference estimate and the early frequency difference estimate.

### Claim 2 (depends on 1)

The method according to claim 1, which method is used in an orthogonal frequency division multiplexing (OFDM) system, wherein the difference between the frequency of the transmitter and the locally generated frequency of the receiver is a carrier frequency offset (CFO).

### Claim 3 (depends on 1)

The method according to claim 1, wherein a correlation between a symbol and the cyclic prefix is carried out at the time of occurrence of the cyclic prefix.

### Claim 4 (depends on 1)

The method according to claim 1, wherein a signal defines a frame and one of its symbols is provided as a preamble occurring at the beginning of the frame and including a cyclic prefix, and wherein a correlation between a preamble and the cyclic prefix is used for estimating the frequency difference.

### Claim 5 (depends on 1)

The method according to claim 1, wherein the late frequency difference estimate is generated by using the equation
y
L
=
y
L
⁡
[
n
^
]
=
y
⁡
[
n
^
]
=
∑
η
=
0
N
FFT
-
1
⁢
p
←
*
⁡
[
η
]
⁢
r
⁡
[
n
^
-
η
]
,
where
p
←
*
⁡
[
η
]
is a complex conjugate of a preamble in reversed order and r[{circumflex over (n)}−η] is a received signal, and {circumflex over (n)} is a correct timing instant where the cyclic prefix occurs.

### Claim 6 (depends on 1)

The method according to claim 1, wherein the cyclic prefix is provided as a replica of last samples of an actual symbol.

### Claim 7 (depends on 6)

The method according to claim 6, wherein the early frequency difference estimate is generated by using the equation:
y
E
=
y
E
⁡
[
n
^
]
=
∑
η
=
0
N
FFT
-
1
⁢
p
←
E
*
⁡
[
η
]
⁢
r
⁡
[
n
^
-
N
g
-
η
]
where
p
←
E
*
⁡
[
η
]
is a complex conjugate of a preamble in reversed order, Ng is a number of the last samples of the actual symbol, r[{circumflex over (n)}−Ng−η] is a received signal and {circumflex over (n)} is a correct timing instant where the cyclic prefix occurs.

### Claim 8 (depends on 1)

The method according to claim 1, wherein said receiver is included in a mobile equipment and/or said transmitter is included in a base station.

### Claim 9

An apparatus, comprising:
correlation determining means for determining a correlation between a symbol received from a transmitter and a cyclic prefix of the symbol and for outputting a result indicative thereof, wherein the correlation is determined based at least in part on the correlation between a late frequency difference estimate and an early frequency difference estimate; and
estimating means for estimating a frequency difference between a frequency of the transmitter and a locally generated frequency of a receiver according to the result of the correlation between the late frequency difference estimate and the early frequency difference estimate.

### Claim 10 (depends on 9)

The apparatus according to claim 9, wherein the correlation determining means determines a correlation between a symbol and the cyclic prefix at the time of occurrence of the cyclic prefix.

### Claim 11 (depends on 9)

The apparatus according to claim 9, wherein a signal defines a frame and one of its symbols is provided as a preamble occurring at the beginning of the frame and including a cyclic prefix, wherein the correlation determining means determines a correlation between a preamble and a cyclic prefix of the preamble.

### Claim 12 (depends on 9)

The apparatus according to claim 9, wherein the correlation determining means determines a correlation between a symbol and a cyclic prefix of the symbol which is a replica of last samples of an actual symbol.

### Claim 13

An apparatus, comprising:
a processor; and
a memory including computer program code, the memory and the computer program code configured to, with the processor, cause the apparatus at least to determine a correlation between a symbol received from a transmitter and a cyclic prefix of the symbol and output a result indicative thereof, wherein the correlation is determined based at least in part on the correlation between a late frequency difference estimate and an early frequency difference estimate, and
estimate a frequency difference between a frequency of the transmitter and a locally generated frequency of a receiver according to the result of the correlation between the late frequency difference estimate and the early frequency difference estimate.

### Claim 14 (depends on 13)

The apparatus according to claim 13, wherein the memory and the computer program code are further configured to, with the processor, cause the apparatus at least to be used in an orthogonal frequency division multiplexing (OFDM) system, wherein the difference between the frequency of the transmitter and the locally generated frequency of the receiver is a carrier frequency offset (CFO).

### Claim 15 (depends on 13)

The apparatus according to claim 13, wherein the memory and the computer program code are further configured to, with the processor, cause the apparatus at least to determine a correlation between a symbol and a cyclic prefix of the symbol at the time of occurrence of the cyclic prefix.

### Claim 16 (depends on 13)

The apparatus according to claim 13, wherein a signal defines a frame and one of its symbols is provided as a preamble occurring at the beginning of the frame and including a cyclic prefix, wherein the memory and the computer program code are further configured to, with the processor, cause the apparatus at least to determine a correlation between a preamble and a cyclic prefix of the preamble.

### Claim 17 (depends on 13)

The apparatus according to claim 13, wherein the memory and the computer program code are further configured to, with the processor, cause the apparatus at least to determine the late frequency difference estimate
y
L
=
y
L
⁡
[
n
^
]
=
y
⁡
[
n
^
]
=
∑
η
=
0
N
FFT
-
1
⁢
p
←
*
⁡
[
η
]
⁢
r
⁡
[
n
^
-
η
]
,
where
p
←
*
⁡
[
η
]
is a complex conjugate of a preamble in reversed order and r[{circumflex over (n)}−η] is a received signal, and {circumflex over (n)} is a correct timing instant where the cyclic prefix occurs.

### Claim 18 (depends on 13)

The apparatus according to claim 13, wherein the memory and the computer program code are further configured to, with the processor, cause the apparatus at least to determine a correlation between a symbol and a cyclic prefix of the symbol which is a replica of last samples of an actual symbol.

### Claim 19 (depends on 18)

The apparatus according to claim 18, wherein the memory and the computer program code are further configured to, with the processor, cause the apparatus at least to generate the early frequency difference estimate
y
E
=
y
E
⁡
[
n
^
]
=
∑
η
=
0
N
FFT
-
1
⁢
p
←
E
*
⁡
[
η
]
⁢
r
⁡
[
n
^
-
N
g
-
η
]
where
p
←
E
*
⁡
[
η
]
is a complex conjugate of a preamble in reversed order, Ng is a number of the last samples of the actual symbol, r[{circumflex over (n)}−Ng−η] is a received signal and {circumflex over (n)}is a correct timing instant where the cyclic prefix occurs.

### Claim 20

An apparatus, comprising:
a processor; and
a memory including computer program code, the memory and the computer program code configured to, with the processor, cause the apparatus at least to generate a correlation between a symbol received from a transmitter and a cyclic prefix of the symbol and output a result indicative thereof, wherein the correlation is determined based at least in part on the correlation between a late frequency difference estimate and an early frequency difference estimate, and
estimate a frequency difference between a frequency of the transmitter and a locally generated frequency of a receiver according to the result of the correlation between the late frequency difference estimate and the early frequency difference estimate.

### Claim 21 (depends on 20)

The apparatus according to claim 20, wherein said receiver is included in a mobile equipment and/or said transmitter is included in a base station.

### Claim 22

A mobile equipment, comprising:
a correlation determiner configured to determine a correlation between a symbol received from a transmitter and a cyclic prefix of the symbol and output a result indicative thereof, wherein the correlation is determined based at least in part on the correlation between a late frequency difference estimate and an early frequency difference estimate; and
an estimator configured to estimate a frequency difference between a frequency of the transmitter and a locally generated frequency of the mobile equipment according to the result of the correlation between the late frequency difference estimate and the early frequency difference estimate.

### Claim 23 (depends on 22)

The mobile equipment according to claim 22, wherein the correlation determiner is configured to be used in an orthogonal frequency division multiplexing (OFDM) system, wherein the difference between the frequency of the transmitter and the locally generated frequency of the mobile equipment is a carrier frequency offset (CFO).

### Claim 24 (depends on 22)

The mobile equipment according to claim 22, wherein the correlation determiner is configured to determine a correlation between a symbol and a cyclic prefix of the symbol at the time of occurrence of the cyclic prefix.

### Claim 25 (depends on 22)

The mobile equipment according to claim 22, wherein a signal defines a frame and one of its symbols is provided as a preamble occurring at the beginning of the frame and including a cyclic prefix, wherein the correlation determiner is configured to determine a correlation between a preamble and a cyclic prefix of the preamble.

### Claim 26 (depends on 22)

The mobile equipment according to claim 22, wherein the correlation determiner is configured to determine the late frequency difference estimate
y
L
=
y
L
⁡
[
n
^
]
=
y
⁡
[
n
^
]
=
∑
η
=
0
N
FFT
-
1
⁢
p
←
*
⁡
[
η
]
⁢
r
⁡
[
n
^
-
η
]
,
where
p
←
*
⁡
[
η
]
is a complex conjugate of a preamble in reversed order and r[{circumflex over (n)}−η] is a received signal, and {circumflex over (n)} is a correct timing instant where the cyclic prefix occurs.

### Claim 27 (depends on 22)

The mobile equipment according to claim 22, wherein the correlation determiner configured to determine a correlation between a symbol and a cyclic prefix of the symbol which is a replica of last samples of an actual symbol.

### Claim 28 (depends on 27)

The mobile equipment according to claim 27, wherein the correlation determiner configured to generate the early frequency difference estimate
y
E
=
y
E
⁡
[
n
^
]
=
∑
η
=
0
N
FFT
-
1
⁢
p
←
E
*
⁡
[
η
]
⁢
r
⁡
[
n
^
-
N
g
-
η
]
where
p
←
E
*
⁡
[
η
]
is a complex conjugate of a preamble in reversed order, Ng is a number of the last samples of the actual symbol, r[{circumflex over (n)}−Ng−η] is a received signal and {circumflex over (n)} is a correct timing instant where the cyclic prefix occurs.

### Claim 29

A mobile equipment, comprising:
correlation determining means for determining a correlation between a symbol received from a transmitter and a cyclic prefix of the symbol and for outputting a result indicative thereof, wherein the correlation is determined based at least in part on the correlation between a late frequency difference estimate and an early frequency difference estimate; and
estimating means for estimating a frequency difference between a frequency of the transmitter and a locally generated frequency of a mobile equipment according to the result of the correlation between the late frequency difference estimate and the early frequency difference estimate.

### Claim 30

A computer program embodied on a computer readable medium, the computer program being configured to control a processor to perform:
determining a correlation between a symbol received from a transmitter and a cyclic prefix of the symbol and outputting a result indicative thereof, wherein the correlation is determined based at least in part on the correlation between a late frequency difference estimate and an early frequency difference estimate; and
estimating a frequency difference between a frequency of the transmitter and a locally generated frequency of a receiver according to the result of the correlation between the late frequency difference estimate and the early frequency difference estimate.

### Claim 31 (depends on 30)

The computer program according to claim 30, which the processor is in an orthogonal frequency division multiplexing (OFDM) system, wherein the difference between the frequency of the transmitter and the locally generated frequency of the receiver is a carrier frequency offset (CFO).

### Claim 32 (depends on 30)

The computer program according to claim 30, wherein a correlation between a symbol and the cyclic prefix is carried out at the time of occurrence of the cyclic prefix.

### Claim 33 (depends on 30)

The computer program according to claim 30, wherein a signal defines a frame and one of its symbols is provided as a preamble occurring at the beginning of the frame and including a cyclic prefix, and wherein a correlation between a preamble and the cyclic prefix is used for estimating the frequency difference.

### Claim 34 (depends on 30)

The computer program according to claim 30, wherein the late frequency difference estimate is generated by using the equation
y
L
=
y
L
⁡
[
n
^
]
=
y
⁡
[
n
^
]
=
∑
η
=
0
N
FFT
-
1
⁢
p
←
*
⁡
[
η
]
⁢
r
⁡
[
n
^
-
η
]
,
where
p
←
*
⁡
[
η
]
is a complex conjugate of a preamble in reversed order and r[{circumflex over (n)}−η] is a received signal, and {circumflex over (n)} is a correct timing instant where the cyclic prefix occurs.

### Claim 35 (depends on 30)

The computer program according to claim 30, wherein the cyclic prefix is provided as a replica of last samples of an actual symbol.

### Claim 36 (depends on 35)

The computer program according to claim 35, wherein the early frequency difference estimate is generated by using the equation:
y
E
=
y
E
⁡
[
n
^
]
=
∑
η
=
0
N
FFT
-
1
⁢
p
←
E
*
⁡
[
η
]
⁢
r
⁡
[
n
^
-
N
g
-
η
]
where
p
←
E
*
⁡
[
η
]
is a complex conjugate of a preamble in reversed order, Ng is a number of the last samples of the actual symbol, r[{circumflex over (n)}−Ng−η] is a received signal and {circumflex over (n)} is a correct timing instant where the cyclic prefix occurs.

### Claim 37 (depends on 13)

The apparatus according to claim 13, wherein said receiver is included in a mobile equipment and/or said transmitter is included in a base station.

### Claim 38 (depends on 1)

The method according to claim 1, wherein the late frequency difference estimate is based on a late channel estimate and the early frequency difference estimate is based on an early channel estimate.