Aliasing Distortion

When the sampling rate Fs is less than twice the maximum frequency component (Nyquist criterion), spectral energy above Fs/2 is not lost but reflected back into the baseband spectrum.

• High-order intermodulation products (5th, 7th order) generated by the power amplifier extend far beyond the original signal bandwidth
• These products fold back into the linearization band, corrupting the feedback signal
• The DPD algorithm trains on this corrupted signal, generating incorrect predistortion coefficients

Nonlinear predistortion inherently expands the signal bandwidth by a factor of 3x to 5x the original modulated bandwidth. The observation path must accommodate this expansion.

• A 100 MHz 5G NR signal may require a 500 MHz observation bandwidth to capture 5th-order distortion products
• Insufficient ADC sampling rates directly limit the maximum correctable bandwidth
• This creates a hard trade-off between linearization performance and receiver cost

When the analog-to-digital converter in the feedback path operates below the Nyquist rate for the full nonlinear spectrum, aliasing introduces non-physical spectral components.

• Aliased products appear as in-band noise and spurious tones that do not exist at the PA output
• The DPD coefficient extraction algorithm interprets these artifacts as real distortion, leading to over-correction
• This often manifests as ACLR degradation rather than improvement after DPD is applied

Anti-aliasing filters in the observation receiver path must balance passband flatness against stopband attenuation while preserving phase linearity.

• Aggressive filtering attenuates high-order distortion products needed for accurate PA modeling
• Filter group delay variation introduces memory effect estimation errors
• Insufficient stopband rejection allows residual aliasing that biases the indirect learning architecture coefficient extraction

Multi-rate digital predistortion architectures decouple the predistorter operating rate from the baseband processing rate to combat aliasing without excessive hardware cost.

• The predistorter runs at a higher internal sampling rate (e.g., 3x to 5x the signal bandwidth) to synthesize cancellation products
• Interpolation filters up-sample the baseband signal before predistortion
• This allows out-of-band distortion cancellation while maintaining a lower-rate interface to the modem

Intentional bandpass sampling can be used in DPD observation paths, but aliasing causes spectral inversion where the frequency axis is reversed in the folded spectrum.

• The complex baseband I/Q relationship is altered, requiring correction in digital processing
• If uncorrected, the DPD model learns an inverted nonlinear characteristic
• This is particularly problematic in concurrent dual-band DPD where multiple carriers alias into overlapping baseband regions

The foundational principle stating that a continuous-time signal must be sampled at a rate greater than twice its highest frequency component to enable perfect reconstruction. In DPD systems, the feedback path must sample at a rate exceeding twice the bandwidth of the nonlinear distortion products (typically 3-5x the original signal bandwidth). Violating this criterion causes high-frequency distortion components to fold back into the band of interest as aliasing artifacts, corrupting the predistorter training data and degrading linearization performance.

A low-pass analog filter placed before the analog-to-digital converter (ADC) in the DPD observation receiver to attenuate frequency components above the Nyquist frequency. Key design considerations include:

• Passband flatness to avoid distorting the in-band feedback signal
• Transition band sharpness to maximize usable bandwidth while rejecting out-of-band energy
• Group delay variation which can introduce phase distortion if not carefully managed Insufficient filtering allows residual high-frequency distortion products to reach the ADC, causing aliasing that cannot be removed digitally.

The factor by which the DPD feedback ADC sampling rate exceeds the Nyquist minimum for the original signal bandwidth. A higher oversampling ratio:

• Captures wider intermodulation distortion products without aliasing
• Reduces the complexity and cost of the anti-aliasing filter
• Improves signal-to-noise ratio through processing gain Typical DPD systems use oversampling ratios of 3x to 5x the signal bandwidth to capture 3rd and 5th order nonlinearities. For a 100 MHz 5G NR signal, this requires ADC sampling rates of 500 MHz to 1 GHz or higher.

The physical mechanism of aliasing where frequency components above the Nyquist frequency (Fs/2) are mirrored or folded back into the sampled spectrum. The foldover frequency mapping follows: f_aliased = |f_actual - k·Fs| where k is an integer. In DPD feedback, this causes:

• 3rd-order intermodulation products at 2f2-f1 to fold into the main signal band
• 5th-order products to overlap with 3rd-order distortion regions
• Complete corruption of the inverse model training data Once folded, these components are indistinguishable from in-band distortion, making post-sampling correction impossible.

The ratio of the predistorted signal bandwidth to the original input signal bandwidth. When a DPD actuator applies nonlinear predistortion, it intentionally generates anti-phase intermodulation products that expand the signal bandwidth. For a 5th-order polynomial predistorter, the output bandwidth expands by a factor of 5x. The feedback ADC must sample at least twice this expanded bandwidth to avoid aliasing. This is the primary driver of high-speed ADC requirements in wideband DPD systems and directly impacts system cost and power consumption.

A DPD implementation strategy that decouples the predistorter operating rate from the baseband signal rate to manage aliasing. The architecture uses:

• Interpolation to upsample the baseband signal before predistortion
• Higher-rate predistorter operating at the expanded bandwidth rate
• Decimation in the feedback path to reduce data rates for coefficient estimation This approach allows the predistorter to generate and cancel wideband distortion products while keeping the coefficient estimation algorithm at a manageable rate. The trade-off is increased computational complexity and latency in the interpolation/decimation filter chains.