ET-DPD for Polar Transmitters

In a polar transmitter, the baseband signal is decomposed into separate phase and amplitude components. The phase-modulated constant-envelope RF carrier is applied to the PA input, while the amplitude component drives the supply modulator to dynamically vary the PA drain voltage. This architecture eliminates the need for linear upconversion of amplitude-modulated signals, but introduces unique distortion mechanisms at the recombination point.

The supply-dependent gain compression in polar transmitters creates a non-ideal mapping between the desired amplitude and the actual RF output envelope. Key contributors include:

• Nonlinear shaping function mapping envelope magnitude to supply voltage
• Supply modulator saturation at high envelope peaks
• Gain collapse near the ET efficiency knee at low supply voltages
• Compression at the PA saturation point where further supply increase yields diminishing output power

Polar transmitters suffer from severe ET-induced AM/PM distortion where the PA's phase shift varies as a function of the instantaneous drain voltage. This occurs because the transistor junction capacitances (Cgs, Cgd) are voltage-dependent, causing the input and output impedance to shift with supply modulation. The resulting phase trajectory distortion must be characterized across the full supply voltage vs. input power operating plane.

A critical challenge in polar ET transmitters is the differential delay between the phase-modulated RF path and the amplitude-modulated supply path. Even sub-nanosecond misalignment causes:

• Spectral regrowth due to envelope clipping at transitions
• EVM degradation from incorrect amplitude-phase recombination
• Memory effects that cannot be corrected by memoryless DPD

ET delay alignment must be maintained across temperature and frequency.

Polar ET-DPD requires a dual-input behavioral model that accepts both the constant-envelope RF input and the dynamic supply voltage as independent variables. Common approaches include:

• Augmented Volterra series with supply-dependent kernels
• 3D Look-Up Tables (3D LUTs) indexed by instantaneous input power and supply voltage
• Decomposed models that separate static supply-dependent nonlinearity from dynamic memory effects

These models must capture the cross-term interactions between RF drive and supply modulation.

The envelope-bandwidth mismatch problem is particularly acute in polar transmitters because the amplitude path bandwidth must be 3-5x the RF signal bandwidth to accurately reproduce the envelope. When the supply modulator slew rate is insufficient:

• Tracking errors create amplitude clipping at envelope peaks
• Switching ripple artifacts intermodulate with the phase carrier
• Modulator nonlinearity introduces additional distortion terms

DPD must compensate for these modulator-induced impairments in addition to PA nonlinearity.

A transmitter topology that separates the baseband signal into a constant-envelope phase component (applied to the RF input) and an amplitude component (applied to the supply voltage via an envelope tracker). This decomposition eliminates the need for linear upconversion but introduces unique distortion mechanisms. The phase signal drives the PA into deep compression for efficiency, while the amplitude signal modulates the drain voltage. The resulting AM-AM and AM-PM distortions are distinct from Cartesian architectures because the PA operates exclusively in saturation, making the nonlinearity a strong function of the instantaneous supply voltage.

A critical distortion mechanism in polar ET transmitters where the PA's phase shift varies nonlinearly with drain voltage. As the envelope tracker modulates the supply to follow the amplitude envelope, the transistor's input and output capacitances change, causing a dynamic phase rotation. This effect is particularly severe in GaN and CMOS PAs operating in deep Class-E or Class-F saturation. The DPD must implement a 2D complex gain correction indexed by both instantaneous amplitude and supply voltage to invert this supply-dependent phase distortion.

In polar transmitters, the constant-envelope phase signal undergoes significant bandwidth expansion—often 3-5x the original signal bandwidth—due to the nonlinear arctangent operation during Cartesian-to-polar conversion. This expanded phase signal drives the PA input, requiring the DPD to linearize across a much wider bandwidth than the original modulated signal. Key challenges include:

• Aliasing in the digital predistortion path if sampling rates are insufficient
• Memory effects that span longer time scales due to the wider bandwidth
• FPGA/ASIC clock rate constraints for real-time DPD processing

Unlike linear PAs with back-off, polar transmitters intentionally operate the PA in deep saturation to maximize efficiency. The AM-AM characteristic in this region is highly nonlinear, with gain compression that varies as a function of the instantaneous drain voltage set by the envelope tracker. The DPD must model this supply-dependent gain surface using structures such as:

• 3D Look-Up Tables (3D LUTs) indexed by input power and supply voltage
• Augmented Volterra series with supply-dependent kernel coefficients
• Decomposed models that separate static supply nonlinearity from dynamic memory effects

Polar transmitters exhibit extreme sensitivity to timing mismatch between the phase path (RF input) and amplitude path (supply modulator). Even sub-nanosecond misalignment causes severe spectral regrowth and EVM degradation because the instantaneous amplitude and phase lose their coherent relationship. The DPD system must incorporate fractional delay compensation with sub-sample interpolation accuracy. Typical alignment techniques include:

• Correlation-based delay estimation using feedback receiver data
• Adaptive fractional delay filters in the digital predistortion signal path
• Joint optimization of delay and DPD coefficients during training

The supply modulator in a polar transmitter must track the wideband amplitude envelope with high fidelity. When the envelope's rate of change exceeds the modulator's slew rate, the supply voltage clips or distorts, introducing nonlinearities that the DPD cannot fully correct because they represent a hard saturation rather than a smooth nonlinearity. Mitigation strategies include:

• Crest factor reduction (CFR) co-optimized with the envelope tracker's slew-rate limits
• Shaping function de-rating to reduce peak envelope slew rates
• Predistortion of the modulator control signal to pre-compensate for known bandwidth limitations