Power amplifier pre-distorter training
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 (S 1 ) the entries of table T 0 and T 1 to predetermined values. Then it measures and stores (S 2 ) a batch of input signals x and feedback signals y. New estimates of T 0 and T 1 are determined (S 3 ) using an iteration of a least mean square based iterative procedure. Then it is tested (S 4 ) whether the tables have converged. If the tables have converged, the current estimates are provided as the final tables. Otherwise another iteration (S 2 -S 4 ) of the least mean square procedure is performed.
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 T qi (b) corresponding to a filter tap with a delay q and a signal amplitude bin b from a previous filter coefficient estimate T qi−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:
μ q is a predetermined constant associated with filter tap q;
N b is the number of stored input signal samples that have an amplitude that falls within a predetermined window M b around the center amplitude of bin b;
x k−q is a stored input signal sample that has a delay q;
y k is a power amplifier output signal feedback sample corresponding to power amplifier input signal sample x k ; and,
* denotes complex conjugation.
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 T qi (b) corresponding to a filter tap with a delay q and a signal amplitude bin b from a previous filter coefficient estimate T qi−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:
μ q is a constant associated with filter tap q;
N b is the number of stored input signal samples that have an amplitude that falls within a predetermined window M b around the center amplitude | x b | of bin b;
x k−q is a stored input signal sample that has a delay q;
y k is a power amplifier output signal feedback sample corresponding to input signal sample x k ; and,
* denotes complex conjugation.
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 T qi (b) corresponding to a filter tap with a delay q and a signal amplitude bin b from a previous filter coefficient estimate T qi−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:
μ q is a constant associated with filter tap q;
x k−q is a stored input signal sample that has that has a delay q and an amplitude that falls within a predetermined window M b around the center amplitude of bin b;
y k is a power amplifier output signal feedback sample corresponding to input signal sample x k ; and,
* denotes complex conjugation.
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 T qi (b) corresponding to a filter tap with a delay q and a signal amplitude bin b from a previous filter coefficient estimate T qi−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:
μ q is a constant associated with filter tap q;
x k−q is a stored input signal sample that has a delay q and an amplitude that falls within a predetermined window M b around the center amplitude | x b | of bin b; x k is a power amplifier input signal sample that y k−q is a power amplifier output signal feedback sample corresponding to input signal sample x k ; and,
* denotes complex conjugation.
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 T qi (b) corresponding to a filter tap with a delay q and a signal amplitude bin b from a previous filter coefficient estimate T qi−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:
μ q is a predetermined constant associated with filter tap q;
N b is the number of stored input signal samples that have an amplitude that falls within a predetermined window M b around the center amplitude of bin b;
x k−q is a stored input signal sample that has a delay q;
y k is a power amplifier output signal feedback sample corresponding to input signal sample x k ; and,
* denotes complex conjugation.
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 T qi (b) corresponding to a filter tap with a delay q and a signal amplitude bin b from a previous filter coefficient estimate T qi−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:
μ q is a constant associated with filter tap q,
N b is the number of stored input signal samples that have an amplitude that falls within a predetermined window M b around the center amplitude | x b | of bin b;
x k−q is a stored input signal sample that has a delay q;
y k is a power amplifier output signal feedback sample corresponding to input signal sample x k ; and,
* denotes complex conjugation.
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 T qi (b) corresponding to a filter tap with a delay q and a signal amplitude bin b from a previous filter coefficient estimate T qi−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:
μ q is a constant associated with filter tap q;
x k−q is a stored input signal sample that has that has a delay q and an amplitude that falls within a predetermined window M b around the center amplitude of bin b;
y k is a power amplifier output signal feedback sample corresponding to input signal sample x k ; and,
* denotes complex conjugation.
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 T qi (b) corresponding to a filter tap with a delay q and a signal amplitude bin b from a previous filter coefficient estimate T qi−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:
μ q is a constant associated with filter tap q;
x k−q is a stored input signal sample that has that has a delay q and an amplitude that falls within a predetermined window M b around the center amplitude | x b | of bin b;
x k is a power amplifier input signal sample that y k−q is a power amplifier output signal feedback sample corresponding to input signal sample x k ; and,
* denotes complex conjugation.