Crest Factor Reduction for ET (CFR-ET Co-Optimization)

The primary goal of CFR-ET co-optimization is to hard-limit the signal's peak-to-average power ratio to a value the supply modulator can track. Without CFR, extreme signal peaks demand instantaneous voltages that exceed the modulator's slew rate and output swing capabilities, causing hard clipping. The co-optimization process defines a target PAPR ceiling—typically 6-8 dB for modern handsets—that balances efficiency gains against acceptable Error Vector Magnitude (EVM) degradation from the CFR clipping itself.

The CFR algorithm is tuned to ensure the residual signal's maximum envelope rate of change does not exceed the supply modulator's voltage slew rate (V/µs). When the envelope bandwidth surpasses the modulator's tracking bandwidth—a condition called envelope-bandwidth mismatch—the supply voltage lags the RF envelope, causing severe distortion. Co-optimization involves iterative simulation where the CFR clipping profile is shaped to smooth sharp envelope transitions, effectively acting as a bandwidth-limiting filter for the envelope path.

Co-optimization requires a system-level distortion budget where total allowable EVM is partitioned between CFR and the ET system. CFR introduces in-band distortion through peak clipping and filtering, while the ET PA introduces supply-dependent nonlinearity. The joint optimization trades off these two error sources:

• Aggressive CFR: Reduces PAPR and prevents modulator overload but increases in-band EVM from clipping noise.
• Conservative CFR: Preserves signal fidelity but risks modulator saturation and catastrophic out-of-band emissions. The optimal operating point minimizes total EVM while achieving the target efficiency.

The shaping function—which maps instantaneous signal magnitude to supply voltage—is designed concurrently with the CFR profile. A conventional shaping function assumes a specific PAPR distribution; if CFR alters that distribution, the shaping table must be re-optimized. Co-design ensures the shaping function's iso-gain contours align with the clipped signal's amplitude statistics, preventing operation in regions of severe supply-dependent gain compression. This joint optimization often uses a 3D look-up table indexed by both instantaneous power and the CFR-processed envelope.

CFR techniques inherently generate out-of-band spectral regrowth that threatens ACLR compliance. The co-optimization framework must ensure that the CFR algorithm's peak-cancellation filtering does not push the transmitter over spectral mask limits. Advanced approaches use peak windowing with carefully designed window functions that concentrate distortion energy close to the carrier, where the ET system's DPD can still partially correct it. The joint design validates that the cascaded CFR + ET-DPD chain meets the 3GPP ACLR requirement of -45 dBc for adjacent channels.

CFR-ET co-optimization cannot be performed purely in simulation due to complex interactions between the switching ripple artifact of the supply modulator and the PA's nonlinear input capacitance. The process requires hardware-in-the-loop iteration where:

• The CFR profile is applied to a vector signal generator.
• The ET PA output is captured by a high-dynamic-range digitizer.
• Residual distortion is analyzed to update both the CFR clipping threshold and the ET-aware DPD coefficients. This closed-loop methodology converges on a joint configuration that maximizes system power-added efficiency (PAE) while maintaining spectral compliance.

The fundamental metric that Crest Factor Reduction seeks to minimize. PAPR is the ratio of the peak signal power to the average signal power, expressed in dB. High PAPR signals, common in OFDM-based 5G NR waveforms, force the supply modulator to track extreme voltage excursions, reducing efficiency and risking clipping. CFR directly manipulates the baseband waveform to lower this ratio before the signal reaches the envelope tracking system.

A critical bottleneck that CFR-ET co-optimization directly addresses. This mismatch occurs when the bandwidth of the signal's instantaneous envelope exceeds the supply modulator's tracking bandwidth. CFR reduces the envelope bandwidth by clipping and filtering signal peaks, effectively slowing down the required voltage transitions. This prevents the modulator from being overdriven and generating severe nonlinear distortion.

A widely used CFR algorithm that applies a smooth time-domain window function (e.g., Gaussian, Kaiser, or raised-cosine) around detected signal peaks above a threshold. Unlike hard clipping, peak windowing provides superior control over spectral regrowth by concentrating the added distortion within the allocated channel bandwidth. The window length is a key co-optimization parameter, trading off PAPR reduction against Error Vector Magnitude (EVM) degradation.

A CFR technique that subtracts a pre-designed, spectrally shaped cancellation pulse from the original signal at each detected peak location. The cancellation pulse is typically designed to match the transmit pulse-shaping filter, ensuring that the added distortion falls strictly in-band. In an ET context, the pulse amplitude and rate must be constrained to avoid creating new envelope peaks that exceed the supply modulator's slew rate capability.

The maximum rate of voltage change (dV/dt) that the envelope tracking power supply can physically deliver, typically measured in V/µs. CFR-ET co-optimization uses this hardware limit as a hard constraint. The CFR algorithm is tuned to ensure that the post-reduction signal envelope never demands a voltage transition faster than this rate. Exceeding the slew rate causes the modulator output to lag, creating a timing misalignment and severe AM/AM distortion.

The deterministic mapping from instantaneous baseband signal magnitude to target PA supply voltage. In a co-optimized system, the shaping function is designed jointly with the CFR parameters. A more aggressive CFR allows for a more aggressive iso-gain contour mapping, pushing the PA deeper into compression for higher efficiency without violating linearity constraints. The shaping function effectively translates the CFR's PAPR reduction into tangible efficiency gains.