Wideband digital predistortion

1. A system comprising:

a digital pre-distortion circuit configured to:

receive a complex baseband signal; and

generate a pre-distorted signal, the generating of the pre-distorted signal comprising:

applying to the complex baseband signal a first correction for an N th order distortion of a power amplifier at an I th harmonic frequency zone centered at about an I th harmonic of a carrier frequency; and

applying to the complex baseband signal a second correction for the N th order distortion at a J th harmonic frequency zone centered at about a J th harmonic of the carrier frequency different than the I th harmonic of the carrier frequency.

2. The system of claim 1 , wherein the digital pre-distortion circuit is further configured to:

determine a value for a first complex basis function for the N th order distortion at the I th harmonic frequency zone based at least in part on the complex baseband signal;

determine a value for a second complex basis function for the N th order distortion at the I th harmonic frequency zone based at least in part on the complex baseband signal;

apply a first filter to generate a first filter response based at least in part on the value for the first complex basis function; and

apply a second filter to generate a second filter response based at least in part on the value for the second complex basis function.

3. The system of claim 2 , wherein the digital pre-distortion circuit is further configured to before determining the value for the first complex basis function, translate the first complex basis function by the carrier frequency.

4. The system of claim 2 , wherein the digital pre-distortion circuit is further configured to:

receive a complex feedback signal based at least in part on an output of the power amplifier;

compare the complex feedback signal to the pre-distorted signal; and

determine a coefficient for the first filter based at least in part on the compare of the complex feedback signal to the pre-distorted signal.

5. The system of claim 2 , wherein the digital pre-distortion circuit is further configured to:

generate a feedback matrix based at least in part on a complex feedback signal;

generate a first an harmonic frequency zone basis vector based at least in part on the value for the first complex basis function;

generate a second harmonic frequency zone basis vector based at least in part on the value for the second complex basis function;

generate a basis matrix comprising the first frequency zone basis vector and the second frequency zone basis vector;

determine a coefficient for the first filter based at least in part on the basis matrix to the feedback matrix.

6. The system of claim 2 , wherein the value for the first complex basis function is based at least in part on a first value of the complex baseband signal at a first time, wherein the digital pre-distortion circuit is further configured to:

apply a first tap of the first filter to the first value of the complex baseband signal at the first time; and

apply a second tap of the first filter to a second value of the complex baseband signal at a second time that is before the first time.

7. The system of claim 1 , wherein the digital pre-distortion circuit is further configured to:

determine a first magnitude of the complex baseband signal at a first time;

generate an I th harmonic frequency zone output based at least in part on a first LUT value from a first tap LUT; and

generate a Jth harmonic frequency zone output based at least in part on a second LUT value from the first tap LUT.

8. The system of claim 1 , wherein the digital pre-distortion circuit is further configured to:

generate an I th harmonic frequency zone exponent for the I th harmonic frequency zone based at least in part on the N th order distortion of the power amplifier;

generate a I th harmonic frequency zone multiplier based at least in part on the harmonic frequency zone exponent;

select a LUT value from a first tap LUT of the I th harmonic frequency zone based at least in part on a first magnitude of the complex baseband signal at a first time;

generate a first tap LUT product for the I th harmonic frequency zone based at least in part on the LUT value and the I th harmonic frequency zone multiplier; and

generate an I th harmonic t frequency zone output based at least in part on the first tap LUT product for the I th harmonic frequency zone and an I th harmonic frequency zone carrier component;

determine a value for a first complex basis function for the N th order distortion of the power amplifier at a J th harmonic frequency zone, wherein the first complex basis function is based at least in part on the complex baseband signal; and

apply a first filter to generate a first response based at least in part on the value for the first complex basis function.

9. The system of claim 1 , wherein the digital pre-distortion circuit is further configured to up-sample the complex baseband signal to generate an up-sampled complex baseband signal, wherein the applying of the first correction and the applying of the second correction is based at least in part on the up-sampled baseband signal.

10. The system of claim 1 , wherein the digital pre-distortion circuit is further configured to:

up-sample the complex baseband signal to an up-sampled frequency generate an up-sampled complex baseband signal, wherein the pre-distorted signal is at the up-sampled frequency;

determine a real component of the pre-distorted signal; and

apply a Hilbert transform to the real component of the pre-distorted signal.

11. The system of claim 1 , wherein the generating of the pre-distorted signal further comprises:

up-sampling the complex baseband signal to generate an up-sampled complex baseband signal, wherein the applying the first correction and the applying the second correction are based at least in part on the up-sampled complex baseband signal; and

applying to the complex baseband signal a third correction for a 1 st order term of the power amplifier at a K th harmonic frequency zone centered at the carrier frequency based at least in part on the complex baseband signal.

12. The system of claim 1 , wherein the J th harmonic frequency zone is the highest frequency zone corrected by the digital pre-distortion circuit, and wherein N is greater than J.

13. The system of claim 7 , wherein the digital pre-distortion circuit is further configured to:

receive a complex feedback signal based at least in part on an output of the power amplifier;

compare the complex feedback signal to the pre-distorted signal; and

populate the first tap LUT based at least in part on the comparing.

14. The system of claim 7 , wherein the digital-pre-distortion circuit is further configured to:

generated an I th harmonic frequency zone exponent based at least in part on an the N th order distortion of the power amplifier;

generated an I th harmonic frequency zone multiplier for the first time based at least in part on the I th harmonic frequency zone exponent;

select the first LUT value from a first tap LUT of the I th harmonic frequency zone based at least in part on the first magnitude of the complex baseband signal; and

generate a first tap LUT product for the I th harmonic frequency zone based at least in part on the first LUT value and the I th harmonic frequency zone multiplier for the first time, wherein the I th harmonic frequency zone output is based at least in part on the first tap LUT product for the I th harmonic frequency zone and an I th harmonic frequency zone carrier component.

15. The system of claim 14 , wherein the generate of the I th harmonic frequency zone multiplier for the first time comprises raising a first value of the complex baseband signal at the first time to the I th harmonic frequency zone exponent.

16. The system of claim 14 , wherein the generate of the first tap LUT product for the I th harmonic frequency zone comprises multiplying the first LUT value and the harmonic frequency zone multiplier.

17. The system of claim 14 , wherein the digital pre-distortion circuit is further configured to, for the I th harmonic frequency zone:

determine a second magnitude of the complex baseband signal at a second time before the first time;

generate an I th harmonic frequency zone multiplier for the second time based at least in part on the I th harmonic frequency zone exponent and a second value of the complex baseband signal at the second time;

select a third look up table (LUT) value from a second tap LUT of the I th harmonic frequency zone based at least in part on the second magnitude of the complex baseband signal; and

generate a second tap LUT product for the I th harmonic frequency zone based at least in part on the third LUT value and the I th harmonic frequency zone multiplier for the second time, wherein the I th harmonic frequency zone output is also based at least on part on the second tap LUT product.

18. A method comprising:

receiving a complex baseband signal; and

generating a pre-distorted signal, wherein the generating comprises:

applying to the complex baseband signal a first correction for an N th order distortion of a power amplifier at an I th harmonic frequency zone centered at about an I th harmonic of a carrier frequency; and

applying to the complex baseband signal a second correction for the N th order distortion at a J th harmonic frequency zone centered at about a J th harmonic of the carrier frequency different than the I th harmonic of the carrier frequency.

19. The method of claim 18 , further comprising:

determining a value for a first complex basis function for the N th order distortion at the I th harmonic frequency zone based at least in part on the complex baseband signal;

determining a value for a second complex basis function for the N th order distortion at the I th harmonic frequency zone based at least in part on the complex baseband signal;

applying a first filter to generate a first filter response based at least in part on the value for the first complex basis function; and

applying a second filter to generate a second filter response based at least in part on the value for the second complex basis function.

20. The method of claim 18 , further comprising:

determining a first magnitude of the complex baseband signal at a first time;

for the I th harmonic frequency zone:

generating an I th harmonic frequency zone exponent based at least in part on an the N th order distortion of the power amplifier;

generating an I th harmonic frequency zone multiplier for the first time based at least in part on the I th harmonic frequency zone exponent;

selecting a first look up table (LUT) value from a first tap LUT of the I th harmonic frequency zone based at least in part on the first magnitude of the complex baseband signal;

generating a first tap LUT product for the I th harmonic frequency zone based at least in part on the first LUT value and the I th harmonic frequency zone multiplier for the first time; and

generating an I th harmonic frequency zone output based at least in part on the first tap LUT product for the I th harmonic frequency zone and an I th harmonic frequency zone carrier component;

for the J th harmonic frequency zone:

generating a J th harmonic frequency zone exponent based at least in part on the N th order distortion of the power amplifier generating a J th harmonic frequency zone multiplier based at least in part on the Jth harmonic frequency zone exponent;

selecting a second LUT value from a first tap LUT of the J th harmonic frequency zone based at least in part on the first magnitude of the complex baseband signal;

generating a first tap LUT product for the J th harmonic frequency zone based at least in part on the second LUT value and the J th harmonic frequency zone multiplier; and

generating a J th harmonic frequency zone output based at least in part on the first tap LUT product for the J th harmonic frequency zone and a J th harmonic frequency zone carrier component.

21. The method of claim 18 , further comprising:

generating an harmonic frequency zone exponent for the I th harmonic frequency zone based at least in part on the N th order distortion of the power amplifier;

generating a I th harmonic frequency zone multiplier based at least in part on the I th harmonic frequency zone exponent;

selecting a LUT value from a first tap LUT of the I th harmonic frequency zone based at least in part on a first magnitude of the complex baseband signal at a first time;

generating a first tap LUT product for the I th harmonic frequency zone based at least in part on the LUT value and the harmonic frequency zone multiplier; and

generating an I th harmonic t frequency zone output based at least in part on the first tap LUT product for the I th harmonic frequency zone and an I th harmonic frequency zone carrier component;

determining a value for a first complex basis function for the N th order distortion of the power amplifier at a J th harmonic frequency zone, wherein the first complex basis function is based at least in part on the complex baseband signal; and

applying a first filter to generate a first response based at least in part on the value for the first complex basis function.

22. A digital predistortion system comprising:

means for receiving a complex baseband signal; and

means for generating a pre-distorted signal, the generating of the pre-distorted signal comprising:

applying to the complex baseband signal a first correction for an N th order distortion of a power amplifier at an I th harmonic frequency zone centered at about an I th harmonic of a carrier frequency; and

applying to the complex baseband signal a second correction for the N th order distortion at a J th harmonic frequency zone centered at about a J th harmonic of the carrier frequency different than the I th harmonic of the carrier frequency.