Dynamic Deviation Reduction (DDR)

DDR models isolate the static AM-AM/AM-PM response from dynamic memory effects. The static kernel captures the amplifier's instantaneous nonlinear transfer function, while dynamic deviation terms model only the low-order perturbations around this static response. This separation exploits the observation that memory effects are typically small deviations from the dominant static nonlinearity, enabling a parsimonious model structure that avoids the exponential complexity of full Volterra series.

The standard DDR formulation truncates dynamic deviations to first-order terms, dramatically reducing complexity:

• 1st-order DDR: Includes only terms with a single delayed sample deviation
• 2nd-order DDR: Adds cross-products of two delayed deviations
• Parameter count scales linearly with memory depth rather than exponentially

For most modern power amplifiers, first-order DDR captures over 95% of memory effects with fewer than 50 coefficients, compared to hundreds or thousands in full Volterra models.

The DDR model expresses the output as:

y(n) = f_static[x(n)] + Σ f_dynamic[x(n), x(n-k) - x(n)]

Where:

• f_static is a memoryless polynomial of the current input
• f_dynamic captures interactions between the current sample and deviations of past samples from the current value
• The deviation term x(n-k) - x(n) is small for narrowband signals, justifying low-order truncation

This formulation inherently decorrelates static and dynamic contributions, improving numerical conditioning during coefficient extraction.

DDR models exhibit superior matrix conditioning compared to memory polynomial or full Volterra formulations:

• The separation of static and dynamic bases reduces column cross-correlation in the regression matrix
• Condition numbers typically 10-100x lower than equivalent-complexity memory polynomials
• Enables reliable coefficient extraction via ordinary least squares without heavy regularization
• Critical for real-time adaptive DPD where matrix inversion must be numerically stable under varying signal statistics and limited precision arithmetic.

DDR models are particularly effective for wideband and mmWave applications:

• At mmWave frequencies, short-term memory effects from bias network resonances dominate
• First-order DDR naturally captures these effects without over-parameterization
• For multi-band scenarios, cross-band modulation products can be incorporated as additional dynamic deviation terms
• DDR-based DPD has been demonstrated on GaN Doherty PAs with 200 MHz instantaneous bandwidth at 28 GHz, achieving ACLR improvements exceeding 15 dB with fewer than 40 coefficients.

DDR vs. Generalized Memory Polynomial (GMP):

• DDR: Separates static nonlinearity from dynamic deviations; parameters scale as O(K×M) for K nonlinearity order and M memory depth
• GMP: Includes all cross-terms between delayed samples and envelope powers; parameters scale as O(K×M²)
• For equivalent modeling accuracy (NMSE < -40 dB), DDR typically requires 30-50% fewer coefficients
• DDR's structured basis functions align with the physical origin of memory effects, improving extrapolation to unseen signal conditions compared to the purely mathematical GMP expansion.