Memory Depth

The physical construction of the transistor dictates the duration and nature of memory effects.

• Gallium Nitride (GaN): Exhibits significant charge-trapping effects requiring deeper memory (often 5-7 taps) to model long-term transient behaviors.
• Laterally-Diffused Metal-Oxide Semiconductor (LDMOS): Dominated by shorter-term thermal memory; typically requires moderate depth (3-5 taps).
• Gallium Arsenide (GaAs): Generally has weaker memory effects, often adequately modeled with shallow depth (2-3 taps).

Memory depth must span the physical duration of the amplifier's impulse response, not just a fixed number of samples.

• Wideband signals (e.g., 100 MHz for 5G NR) have short symbol periods. A depth of 4 taps covers only 40 ns, which may miss long-term thermal effects lasting microseconds.
• Narrowband signals (e.g., 5 MHz LTE) have longer symbol periods. The same 4-tap depth covers 800 ns, capturing a much longer physical memory span.
• Rule of thumb: The temporal span (Memory Depth / Sample Rate) must exceed the slowest thermal time constant of the amplifier.

Each additional memory tap multiplies the number of basis functions and coefficients in the model.

• For a Generalized Memory Polynomial (GMP) with nonlinear order K and memory depth M, the coefficient count scales with M × K.
• Doubling memory depth from 3 to 6 can quadruple the number of cross-terms in a full GMP model.
• FPGA resource impact: Each complex multiply-accumulate (CMAC) operation consumes DSP slices. Deeper memory directly increases logic utilization and power consumption, potentially violating timing closure.

Excessive memory depth introduces highly correlated basis functions, degrading the condition number of the data matrix.

• Ill-conditioned matrices lead to coefficient estimation instability, where small measurement noise causes large coefficient variance.
• This manifests as overfitting: the model memorizes training data noise rather than learning the true amplifier physics.
• Mitigation requires regularization (e.g., Ridge regression) or basis function orthogonalization, adding further computational overhead.

Power amplifiers exhibit both short-term and long-term thermal memory effects that dictate minimum required depth.

• Short-term (die-level): Microsecond-scale heating at the transistor junction. Captured by shallow memory (2-4 taps at typical sample rates).
• Long-term (package-level): Millisecond-scale thermal diffusion through the substrate and heat sink. Requires very deep memory or a separate envelope memory polynomial structure.
• Ignoring long-term thermal memory causes drift in linearization performance during sustained transmission bursts.

The chosen memory depth must be validated against measured data, not assumed.

• Sweep depth systematically: Train models with M = 1, 2, 3, ... taps and measure Normalized Mean Squared Error (NMSE) on a held-out test set.
• Diminishing returns point: The depth at which adding another tap improves NMSE by less than 0.5 dB is the practical optimum.
• Cross-validation prevents selecting a depth that overfits the specific training signal statistics.

The foundational behavioral model that introduces memory depth as a core parameter. It uses a polynomial with tapped delay lines to capture both nonlinear distortion and memory effects.

• Structure: A sum of polynomials applied to delayed input samples
• Key parameter: M (memory depth) defines the number of past samples
• Complexity scales as O(K × M) where K is nonlinear order
• Serves as the baseline against which more complex models are compared

An enhanced model that extends the memory polynomial by including cross-terms between the signal and its lagging or leading envelope samples.

• Introduces lagging cross-terms: |x(n-l)|² · x(n-m)
• Introduces leading cross-terms: |x(n+l)|² · x(n-m)
• Captures complex memory effects missed by standard MP
• Memory depth applies to both signal and envelope dimensions

A complexity reduction technique that removes insignificant kernels from a full Volterra series based on a significance metric. Memory depth directly determines the number of kernels that must be evaluated and pruned.

• Full Volterra kernels grow exponentially with memory depth
• Pruning retains only the most critical distortion terms
• Common metrics: kernel magnitude, correlation with output error
• Essential for making high-memory-depth models practical

An adaptive filtering algorithm that recursively updates predistorter coefficients as memory depth changes. The forgetting factor λ controls how quickly old data is discounted.

• Convergence speed is affected by memory depth dimensionality
• Larger memory depth → larger covariance matrix → slower updates
• RLS complexity: O(N²) where N = number of coefficients
• Often paired with orthogonalization to improve conditioning

The systematic process of decreasing the number of coefficients in a behavioral model while preserving linearization performance. Memory depth is a primary target for reduction.

• Techniques include Orthogonal Matching Pursuit (OMP) and PCA
• Goal: minimize memory depth without degrading ACPR improvement
• Critical for FPGA implementations with limited DSP slices
• Trade-off: reduced memory depth vs. residual nonlinearity

A model variant that incorporates memory effects of the signal's envelope magnitude rather than just the complex baseband samples. This captures long-term thermal and bias-related memory.

• Envelope memory depth is typically longer than signal memory depth
• Captures slow-varying effects: thermal time constants, bias modulation
• Structure: combines standard MP terms with envelope-dependent terms
• Particularly important for GaN and Doherty amplifiers