Method and apparatus for providing a Cartesian training waveform
One provides ( 401, 402 ) both an in-phase signal component ( 501 ) and a quadrature signal component ( 601 ) wherein the latter has a non-zero portion. These two signal components are then combined ( 403 ) to provide a Cartesian training waveform that can be used when training a linear amplifier that uses Cartesian feedback linearization. By one approach, the non-zero portion of the quadrature signal component can be coincident with a zero-crossing portion of the in-phase signal. In many application settings this non-zero portion of the quadrature signal component can be less (and sometimes considerably less) than a peak amplitude of the in-phase signal component. One may also shape the in-phase signal component to have a smoothed envelope. This may include, for example, using a smoothed sine wave such as a raised-sine function.
1. A method of providing a Cartesian training waveform for use when training a linear amplifier that uses Cartesian feedback linearization, comprising:
providing an in-phase signal component having a zero-crossing portion;
providing a quadrature signal component having a non-zero portion;
combining the in-phase signal component and the quadrature signal component such that the zero-crossing portion of the in-phase signal component is coincident in time with the non-zero portion of the quadrature signal component to provide a Cartesian training waveform exhibiting a gradual change in phase.
2. The method of claim 1 wherein the non-zero portion of the quadrature signal component has an amplitude that is less than a peak amplitude of the in-phase signal component.
3. The method of claim 2 wherein the non-zero portion of the quadrature signal component amplitude is minimized.
4. The method of claim 1 wherein the quadrature signal component also has at least one zero amplitude portion, wherein the at least one zero amplitude portion coincides temporally with a maximum amplitude of the in-phase signal.
5. The method of claim 1 wherein the in-phase component comprises, at least in substantial part, a sine wave.
6. The method of claim 5 wherein the sine wave comprises a smoothed sine wave.
7. The method of claim 6 wherein the smoothed sine wave comprises a raised-sine function.
8. An apparatus comprising:
a linear amplifier that uses Cartesian feedback linearization and that comprises, in part, a Cartesian training waveform input;
a training waveform source having an output operably coupled to the Cartesian training waveform input and being configured and arranged to:
provide an in-phase signal component having a zero-crossing portion;
provide a quadrature signal component having a non-zero portion;
combine the in-phase signal component and the quadrature signal component such that the zero-crossing portion of the in-phase signal component is coincident in time with the non-zero portion of the quadrature signal component to provide a Cartesian training waveform to the output exhibiting a gradual change in phase.
9. The apparatus of claim 8 wherein the non-zero portion of the quadrature signal component has an amplitude that is less than a peak amplitude of the in-phase signal component.
10. The apparatus of claim 8 wherein the non-zero portion of the quadrature signal component amplitude is minimized.
11. The apparatus of claim 8 wherein the in-phase signal component lacks any abrupt power changes over time.
12. The apparatus of 8 wherein the in-phase component comprises, at least in substantial part, a sine wave.
13. The apparatus of claim 12 wherein the sine wave comprises a smoothed sine wave.
14. The apparatus of claim 13 wherein the smoothed sine wave comprises a raised-sine function.
15. The apparatus of claim 8 wherein the training waveform source comprises:
means for providing an in-phase signal component;
means for providing a quadrature signal component having a non-zero portion;
means for combining the in-phase signal component and the quadrature signal component to provide the Cartesian training waveform.