Feedback Path Linearization

The feedback path introduces its own nonlinear impairments—mixer compression, ADC integral nonlinearity, and amplifier saturation—that corrupt the training signal. If uncompensated, the DPD adapts to cancel the receiver's distortion rather than the PA's, leading to model divergence. Feedback linearization isolates the PA's true behavior by pre-characterizing the receiver chain with a known reference signal and constructing an inverse model.

The analog-to-digital converter must capture the full peak-to-average power ratio (PAPR) of the PA output plus spectral regrowth. Insufficient effective number of bits (ENOB) causes quantization noise that masks low-level distortion products. For a 100 MHz 5G NR signal with 10 dB PAPR and 30 dB ACLR target, the ADC typically requires 12-14 bits of resolution at 491.52 Msps to preserve the distortion signature.

Gain and phase mismatches between the I and Q branches of the observation receiver's quadrature demodulator create image frequency interference. This manifests as a mirror copy of the signal spectrum that overlaps with the desired distortion products. Feedback linearization must estimate and correct these impairments using techniques like:

• Gram-Schmidt orthogonalization
• Adaptive complex coefficient equalization
• Frequency-domain pilot-based correction

A common architecture applies a digital post-distorter in the feedback path after the ADC. This block is trained offline using a calibration signal injected at the receiver input. The post-distorter's coefficients are frozen during normal DPD operation, providing a static inverse model of the receiver nonlinearity. This approach assumes the receiver characteristics remain stable over temperature and time.

The observation receiver exhibits its own memory effects from anti-alias filter group delay ripple, bias tee settling, and thermal transients. These cause the feedback signal's distortion to depend on past samples, not just the instantaneous input. A memoryless receiver linearizer fails to capture these dynamics. Volterra-based or memory polynomial models are often required to compensate for frequency-selective receiver behavior.

Accurate receiver characterization demands a training signal with known statistical properties. Common choices include:

• Multi-tone signals with precisely controlled amplitude and phase per tone
• Zadoff-Chu sequences for constant-envelope, zero-autocorrelation properties
• Chirp signals for wideband frequency response measurement The calibration signal must exercise the receiver's full dynamic range to capture compression behavior at all power levels.

The dedicated receiver chain that captures a coupled sample of the power amplifier's output, downconverts it, and digitizes it to provide the feedback signal for DPD training. Its linearity must significantly exceed that of the PA under test. Key components include a directional coupler, attenuator, downconverter, and analog-to-digital converter (ADC). Any nonlinearity in this path is indistinguishable from PA distortion, corrupting the predistorter model.

A critical impairment where the in-phase (I) and quadrature (Q) branches of the observation receiver's demodulator have unequal gain or are not exactly 90 degrees apart. This creates an image signal that overlaps with the desired spectrum, introducing errors in the amplitude and phase information used for DPD coefficient estimation. Compensation is typically performed digitally before model extraction.

Occurs when the instantaneous power of the feedback signal exceeds the full-scale range of the ADC. Clipping is a hard nonlinearity that generates severe spectral regrowth and harmonics, completely corrupting the training data. Mitigation strategies include:

• Automatic gain control (AGC) to scale the signal
• Increasing ADC bit depth and dynamic range
• Using crest factor reduction on the PA output before sampling

A technique where a digital post-distorter is applied to the captured feedback signal to compensate for known receiver nonlinearities after sampling. This is the inverse of predistortion. By characterizing the observation receiver's transfer function offline using a calibrated test signal, a correction model is created. This allows the use of lower-cost receiver components while maintaining high-fidelity feedback for PA linearization.

A distortion artifact introduced when the sampling rate of the feedback ADC is insufficient to capture the full bandwidth of the PA's nonlinear output. The DPD process expands the signal bandwidth by a factor of 3-5x. If the ADC sample rate does not satisfy the Nyquist criterion for this expanded bandwidth, out-of-band distortion products fold back into the observed spectrum, making them impossible to cancel. Anti-aliasing filters and oversampling are essential countermeasures.

The systematic process of measuring and removing the linear and nonlinear transfer function of the entire observation receiver chain. This involves:

• Injecting a known training sequence (e.g., a Zadoff-Chu sequence) at the coupler input
• Capturing the receiver's response
• Solving for the inverse model using least-squares estimation The resulting correction filter is applied to all subsequent feedback captures, ensuring the DPD algorithm trains only on PA-introduced distortion.