# US 7,412,469 B2 · Power amplifier pre-distorter training

> Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt

- Number: US 7,412,469 B2
- Document ID: US7412469B2
- Status: Granted
- Kind: B2
- Application number: 10/595,677
- Filed: 2003-11-25
- Published: 2007-06-14
- Granted: 2008-08-12
- Earliest claimed: 2003-11-25
- Assignees: Telefonaktiebolaget L M Ericsson (publ)
- Inventors: Spendim Dalipi
- Web page: https://patentgrep.com/patent/US7412469B2

## CPC

- H03F 1/3258: {based on polynomial terms}
- H03F 1/3247: {using feedback acting on predistortion circuits (H03F1/3264 takes precedence)}
- H03F 2201/3224: Predistortion being done for compensating memory effects
- H03F 2201/3233: Adaptive predistortion using lookup table, e.g. memory, RAM, ROM, LUT, to generate the predistortion
- H03F: AMPLIFIERS

## Abstract

A power amplifier pre-distorter is formed by a FIR filter structure which includes an individual look-up table for each filter tap, where each look-up table represents a sample polynomial in a variable representing signal amplitude, and means for selecting, from each filter tap look-up table, a filter coefficient that depends on the amplitude of corresponding complex signal value to be multiplied by the filter tap. A training method for such a pre-distorter sets (S1) the entries of table T0 and T1 to predetermined values. Then it measures and stores (S2) a batch of input signals x and feedback signals y. New estimates of T0 and T1 are determined (S3) using an iteration of a least mean square based iterative procedure. Then it is tested (S4) whether the tables have converged. If the tables have converged, the current estimates are provided as the final tables. Otherwise another iteration (S2-S4) of the least mean square procedure is performed.

## Claims

### Claim 1

A training method for a power amplifier pre-distorter formed by a Finite Impulse Response (FIR) filter structure comprising an individual look-up table for each filter tap, each look-up table representing a discretized polynomial in a variable representing input signal amplitude, and means for selecting, from each filter tap look-up table, a filter coefficient that depends on the amplitude of a corresponding complex signal value to be multiplied by the filter tap, said training method comprising the steps of:
storing measured unamplified input signal samples and corresponding power amplifier output signal feedback samples;
determining look-up table filter coefficients for each filter tap by separate independent iterative procedures using said stored samples, wherein said iterative procedures are least mean square based, said step of determining comprising:
calculating a refined filter coefficient estimate Tqi (b) corresponding to a filter tap with a delay q and a signal amplitude bin b from a previous filter coefficient estimate Tqi−1(b) in accordance with the equation:
T
q
⁢
⁢
i
⁡
(
b
)
=
T
q
⁢
⁢
i
-
1
⁡
(
b
)
+
μ
q
·
1
N
b
·
∑

x
k
-
q

∈
M
b
⁢
x
k
-
y
k

x
k
-
q

2
·
x
k
-
q
*
where:
μq is a predetermined constant associated with filter tap q;
Nb is the number of stored input signal samples that have an amplitude that falls within a predetermined window Mb around the center amplitude of bin b;
xk−q is a stored input signal sample that has a delay q;
yk is a power amplifier output signal feedback sample corresponding to power amplifier input signal sample xk; and,
* denotes complex conjugation.

### Claim 2

A training method for a power amplifier pre-distorter formed by a Finite Impulse Response (FIR) filter structure comprising an individual look-up table for each filter tap, each look-up table representing a discretized polynomial in a variable representing input signal amplitude, and means for selecting, from each filter tap look-up table, a filter coefficient that depends on the amplitude of a corresponding complex signal value to be multiplied by the filter tap, said training method comprising the steps of:
storing measured unamplified input signal samples and corresponding power amplifier output signal feedback samples;
determining look-up table filter coefficients for each filter tap by separate independent iterative procedures using said stored samples, wherein said iterative procedures are least mean square based, said step of determining comprising:
calculating a refined filter coefficient estimate Tqi (b) corresponding to a filter tap with a delay q and a signal amplitude bin b from a previous filter coefficient estimate Tqi−1 (b) in accordance with the equation:
{
T
q
⁢
⁢
i
⁡
(
b
)
=
T
q
⁢
⁢
i
-
1
⁡
(
b
)
+
μ
q
·
u
⁡
(
b
)
⁢
1
N
b
·
∑

x
k
-
q

∈
M
b
⁢
(
x
k
-
y
k
)
·
x
k
-
q
*
u
⁡
(
b
)
=
1

x
b

_
2
where:
μq is a constant associated with filter tap q;
Nb is the number of stored input signal samples that have an amplitude that falls within a predetermined window Mb around the center amplitude | xb| of bin b;
xk−q is a stored input signal sample that has a delay q;
yk is a power amplifier output signal feedback sample corresponding to input signal sample xk; and,
* denotes complex conjugation.

### Claim 3

A training method for a power amplifier pre-distorter formed by a Finite Impulse Response (FIR) filter structure comprising an individual look-up table for each filter tap, each look-up table representing a discretized polynomial in a variable representing input signal amplitude, and means for selecting, from each filter tap look-up table, a filter coefficient that depends on the amplitude of a corresponding complex signal value to be multiplied by the filter tap, said training method comprising the steps of:
storing measured unamplified input signal samples and corresponding power amplifier output signal feedback samples;
determining look-up table filter coefficients for each filter tap by separate independent iterative procedures using said stored samples, wherein said iterative procedures are least mean square based, said step of determining comprising:
calculating a refined filter coefficient estimate Tqi (b) corresponding to a filter tap with a delay q and a signal amplitude bin b from a previous filter coefficient estimate Tqi−1 (b) in accordance with the equation:
T
q
⁢
⁢
i
⁡
(
b
)
=
T
q
⁢
⁢
i
-
1
⁡
(
b
)
+
μ
q
·
(
x
k
-
y
k
)
·
x
k
-
q
*

x
k
-
q

2
⁢
:
⁢
⁢

x
k
-
q

∈
M
b
where:
μq is a constant associated with filter tap q;
xk−q is a stored input signal sample that has that has a delay q and an amplitude that falls within a predetermined window Mb around the center amplitude of bin b;
yk is a power amplifier output signal feedback sample corresponding to input signal sample xk; and,
* denotes complex conjugation.

### Claim 4

A training method for a power amplifier pre-distorter formed by a Finite Impulse Response (FIR) filter structure comprising an individual look-up table for each filter tap, each look-up table representing a discretized polynomial in a variable representing input signal amplitude, and means for selecting, from each filter tap look-up table, a filter coefficient that depends on the amplitude of a corresponding complex signal value to be multiplied by the filter tap said training method comprising the steps of:
storing measured unamplified input signal samples and corresponding power amplifier output signal feedback samples;
determining look-up table filter coefficients for each filter tap by separate independent iterative procedures using said stored samples, wherein said iterative procedures are least mean square based, said step of determining comprising:
calculating a refined filter coefficient estimate Tqi (b) corresponding to a filter tap with a delay q and a signal amplitude bin b from a previous filter coefficient estimate Tqi−1 (b) in accordance with the equation:
{
T
q
⁢
⁢
i
⁡
(
b
)
=
T
q
⁢
⁢
i
-
1
⁡
(
b
)
+
μ
q
·
u
⁡
(
b
)
·
(
x
k
-
y
k
)
·
x
k
-
q
*
⁢
:
⁢
⁢

x
k
-
q

∈
M
b
u
⁡
(
b
)
=
1

x
b

_
2
where:
μq is a constant associated with filter tap q;
xk−q is a stored input signal sample that has a delay q and an amplitude that falls within a predetermined window Mb around the center amplitude | xb| of bin b; xk is a power amplifier input signal sample that yk−q is a power amplifier output signal feedback sample corresponding to input signal sample xk; and,
* denotes complex conjugation.

### Claim 5

A power amplifier pre-distorter formed by a Finite Impulse Response (FIR) filter structure comprising an individual look-up table for each filter tap, each look-up table representing a discretized polynomial in a variable representing input signal amplitude, and means for selecting, from each filter tap look-up table, a filter coefficient that depends on the amplitude of a corresponding complex signal value to be multiplied by the filter tap, wherein the pre-distorter comprises:
means for storing measured unamplified input signal samples and corresponding power amplifier output signal feedback samples;
means for determining look-up table filter coefficients for each filter tap by separate independent iterative procedures using said stored samples, wherein said iterative procedures are least mean square based, said means for determining comprising:
means for calculating a refined filter coefficient estimate Tqi (b) corresponding to a filter tap with a delay q and a signal amplitude bin b from a previous filter coefficient estimate Tqi−1 (b) in accordance with the equation:
T
q
⁢
⁢
i
⁡
(
b
)
=
T
q
⁢
⁢
i
-
1
⁡
(
b
)
+
μ
q
·
1
N
b
·
∑

x
k
-
q

∈
M
b
⁢
x
k
-
y
k

x
k
-
q

2
·
x
k
-
q
*
where:
μq is a predetermined constant associated with filter tap q;
Nb is the number of stored input signal samples that have an amplitude that falls within a predetermined window Mb around the center amplitude of bin b;
xk−q is a stored input signal sample that has a delay q;
yk is a power amplifier output signal feedback sample corresponding to input signal sample xk; and,
* denotes complex conjugation.

### Claim 6

A power amplifier pre-distorter formed by a Finite Impulse Response (FIR) filter structure comprising an individual look-up table for each filter tap, each look-up table representing a discretized polynomial in a variable representing input signal amplitude, and means for selecting, from each filter tap look-up table, a filter coefficient that depends on the amplitude of a corresponding complex signal value to be multiplied by the filter tap, wherein the pre-distorter comprises:
means for storing measured unamplified input signal samples and corresponding power amplifier output signal feedback samples;
means for determining look-up table filter coefficients for each filter tap by separate independent iterative procedures using said stored samples, wherein said iterative procedures are least mean square based, said means for determining comprising:
means for calculating a refined filter coefficient estimate Tqi (b) corresponding to a filter tap with a delay q and a signal amplitude bin b from a previous filter coefficient estimate Tqi−1 (b) in accordance with the equation:
{
T
q
⁢
⁢
i
⁡
(
b
)
=
T
q
⁢
⁢
i
-
1
⁡
(
b
)
+
μ
q
·
u
⁡
(
b
)
⁢
1
N
b
·
∑

x
k
-
q

∈
M
b
⁢
(
x
k
-
y
k
)
·
x
k
-
q
*
u
⁡
(
b
)
=
1

x
b

_
2
where:
μq is a constant associated with filter tap q,
Nb is the number of stored input signal samples that have an amplitude that falls within a predetermined window Mb around the center amplitude | xb| of bin b;
xk−q is a stored input signal sample that has a delay q;
yk is a power amplifier output signal feedback sample corresponding to input signal sample xk; and,
* denotes complex conjugation.

### Claim 7

A power amplifier pre-distorter formed by a Finite Impulse Response (FIR) filter structure comprising an individual look-up table for each filter tap, each look-up table representing a discretized polynomial in a variable representing input signal amplitude, and means for selecting, from each filter tap look-up table, a filter coefficient that depends on the amplitude of a corresponding complex signal value to be multiplied by the filter tap, wherein the pre-distorter comprises:
means for storing measured unamplified input signal samples and corresponding power amplifier output signal feedback samples;
means for determining look-up table filter coefficients for each filter tap by separate independent iterative procedures using said stored samples, wherein said iterative procedures are least mean square based, said means for determining comprising:
means for calculating a refined filter coefficient estimate Tqi (b) corresponding to a filter tap with a delay q and a signal amplitude bin b from a previous filter coefficient estimate Tqi−1 (b) in accordance with the equation:
T
q
⁢
⁢
i
⁡
(
b
)
=
T
q
⁢
⁢
i
-
1
⁡
(
b
)
+
μ
q
·
(
x
k
-
y
k
)
·
x
k
-
q
*

x
k
-
q

2
⁢
:
⁢
⁢

x
k
-
q

∈
M
b
where:
μq is a constant associated with filter tap q;
xk−q is a stored input signal sample that has that has a delay q and an amplitude that falls within a predetermined window Mb around the center amplitude of bin b;
yk is a power amplifier output signal feedback sample corresponding to input signal sample xk; and,
* denotes complex conjugation.

### Claim 8

A power amplifier pre-distorter formed by a Finite Impulse Response (FIR) filter structure comprising an individual look-up table for each filter tap, each look-up table representing a discretized polynomial in a variable representing input signal amplitude, and means for selecting, from each filter tap look-up table, a filter coefficient that depends on the amplitude of a corresponding complex signal value to be multiplied by the filter tap, wherein the pre-distorter comprises:
means for storing measured unamplified input signal samples and corresponding power amplifier output signal feedback samples;
means for determining look-up table filter coefficients for each filter tap by separate independent iterative procedures using said stored samples, wherein said iterative procedures are least mean square based, said means for determining comprising:
means for calculating a refined filter coefficient estimate Tqi (b) corresponding to a filter tap with a delay q and a signal amplitude bin b from a previous filter coefficient estimate Tqi−1 (b) in accordance with the equation:
{
T
q
⁢
⁢
i
⁡
(
b
)
=
T
q
⁢
⁢
i
-
1
⁡
(
b
)
+
μ
q
·
u
⁡
(
b
)
·
(
x
k
-
y
k
)
·
x
k
-
q
*
⁢
:
⁢
⁢

x
k
-
q

∈
M
b
u
⁡
(
b
)
=
1

x
b

_
2
where:
μq is a constant associated with filter tap q;
xk−q is a stored input signal sample that has that has a delay q and an amplitude that falls within a predetermined window Mb around the center amplitude | xb| of bin b;
xk is a power amplifier input signal sample that yk−q is a power amplifier output signal feedback sample corresponding to input signal sample xk; and,
* denotes complex conjugation.