Radio frequency systems and methods for polar phase distortion calibration

A method for operating a radio frequency system, comprising:

• providing a ρ digital electrical signal and a ϑ digital electrical signal representative of a data transmission to one or more digital to analog converters;
• converting the ρ and ϑ digital electrical signals to a ρ analog electrical signal and a ϑ analog electrical signal using the one or more digital to analog converters;
• transmitting the ρ analog electrical signal on an amplitude path, wherein the amplitude path comprises a supply modulator configured to modulate a voltage of the ρ analog electrical signal;
• transmitting the ϑ analog electrical signal on a phase path, wherein the phase path comprises:
• a mixer configured to multiply a low frequency baseband signal (fBB) by a local oscillator signal and up-convert a resultant signal from baseband frequency to radio frequency (fRF);
• and
• a limiter communicatively coupled to the at least one mixer, configured to amplify the resultant signal after it is up-converted;
• wirelessly transmitting a combination of signals on the amplitude path and the phase path at a transmission frequency;
• and
• counter-acting distortion on the phase path of the radio frequency system using distortion correction circuitry, such that distortion caused by the limiter and the mixer on the phase path is reduced, at least in part by:
• estimating coefficients of a forward kernel of the phase path by performing a regression on a mathematical representation of a transmitted phasor, wherein the forward kernel comprises a definition of the distortion on the phase path caused by the limiter and the mixer, the distortion on the phase path represented by a summation of unwanted phasors, wherein the unwanted phasors comprise intermodulated tones (eJ4iθ and eJ−4iθ) each multiplied by a respective one of the coefficients of the forward kernel;
• estimating an inverse kernel of the forward kernel;
• and
• generating and introducing a phase-path pre-distortion to the phase path using the inverse kernel.

Distortion correction circuitry, comprising:

• phase path pre-distortion circuitry configured to introduce pre-distortion to a digital signal of a polar architecture of a radio frequency system, such that distortion caused by a limiter and a mixer on a phase path of the polar architecture results in the digital signal returning to its original shape prior to inducing the pre-distortion to the digital signal, at least in part by:
• estimating coefficients of a forward kernel of the phase path by performing a regression on a mathematical representation of a transmitted phasor, wherein the forward kernel comprises a definition of the distortion on the phase path caused by the limiter and the mixer, the distortion on the phase path represented by a summation of unwanted phasors, wherein the unwanted phasors comprise intermodulated tones (eJ4iθ and eJ−4iθ) each multiplied by a respective one of the coefficients of the forward kernel;
• estimating an inverse kernel of the forward kernel;
• and
• generating and introducing a phase-path pre-distortion to the phase path using the inverse kernel;
• wherein the limiter and the mixer on the phase path comprise at least one mixer, at least one limiter, or both;
• and
• wherein the polar architecture comprises an amplitude path that comprises a supply modulator configured to modulate a voltage of an analog signal of the polar architecture.

A tangible, non-transitory, processor-readable medium, comprising processor-implemented instructions, configured to:

• receive a digital electrical signal of polar domain data via a polar architecture radio frequency system, wherein the polar architecture radio frequency system comprises an amplitude path that comprises a supply modulator configured to modulate a voltage of an amplitude path signal of the polar architecture radio frequency system;
• and
• introduce pre-distortion into the digital electrical signal, such that subsequent distortion on a phase path of the polar architecture radio frequency system, caused by a mixer and a limiter on the phase path, returns the digital electrical signal to its original form prior to the introduction of the pre-distortion, at least in part by:
• estimating coefficients of a forward kernel of the phase path by performing a regression on a mathematical representation of a transmitted phasor, wherein the forward kernel comprises a definition of the distortion on the phase path caused by the limiter and the mixer, the distortion on the phase path represented by a summation of unwanted phasors, wherein the unwanted phasors comprise intermodulated tones (eJ4iθ and eJ−4iθ) each multiplied by a respective one of the coefficients of the forward kernel;
• estimating an inverse kernel of the forward kernel;
• and
• introducing a phase-path pre-distortion to the phase path using the inverse kernel.

An electronic device, comprising:

• a radio frequency system comprising distortion correction logic configured to reduce distortions of a transmission signal caused by a mixer component and a limiter component on a phase path of a polar architecture of the radio frequency system, by:
• determining a pre-distortion that will cause nonlinearities caused by the mixer component and the limiter component to result in a subsequent transmission signal that is a similar shape to the transmission signal prior to introduction of the pre-distortion of the transmission signal, by:
• estimating coefficients of a forward kernel of the phase path by performing a regression on a mathematical representation of a transmitted phasor, wherein the forward kernel comprises a definition of the distortion on the phase path caused by the limiter and the mixer, the distortion on the phase path represented by a summation of unwanted phasors, wherein the unwanted phasors comprise intermodulated tones (eJ4iθ and eJ−4iθ) each multiplied by a respective one of the coefficients of the forward kernel;
• estimating an inverse kernel of the forward kernel;
• and
• defining the pre-distortion based upon the inverse kernel;
• introducing the pre-distortion to the transmission signal, such that the distortions of the transmission signal caused by the mixer component and the limiter component on the phase path are counter-acted;
• wherein the mixer component is configured to multiply a low frequency baseband signal (fBB) by a local oscillator signal and up-convert a resultant signal from baseband frequency to radio frequency (fRF);
• wherein the limiter component is communicatively coupled to the at least one mixer and is configured to amplify the resultant signal after it is up-converted;
• and
• wherein the radio frequency system comprises an amplitude path that comprises a supply modulator configured to modulate a voltage of an analog signal of the polar architecture.