Memory Effects

Caused by self-heating of the transistor junction during high-power operation. As the device dissipates power, its temperature rises with a time constant determined by the thermal capacitance of the die and package. This temperature shift alters the transistor's gain and phase characteristics, creating a low-frequency memory envelope typically in the kilohertz to megahertz range. The effect is particularly pronounced in GaN HEMTs and high-power Doherty amplifiers where instantaneous power dissipation varies dramatically with signal envelope.

Originate from bias network impedance and envelope frequency termination. Key mechanisms include:

• Baseband impedance modulation: The video bandwidth of the drain bias circuit interacts with the envelope signal, causing dynamic supply voltage variation
• Gate/base bias modulation: Non-zero impedance at the modulation frequency allows the gate voltage to shift with signal envelope
• Harmonic terminations: Improper second-harmonic termination creates mixing products that fold back into the fundamental band

Electrical memory typically operates at modulation bandwidths up to hundreds of megahertz in modern wideband systems.

Specific to compound semiconductor devices like GaN and GaAs HEMTs. Electrons become captured in deep-level traps within the semiconductor material or at the surface passivation interface. The trap occupation state depends on the recent voltage history, creating a slow-varying change in the device's threshold voltage and on-resistance. Trapping time constants range from microseconds to seconds, making them particularly problematic for signals with high peak-to-average power ratios where the amplifier transitions between deep pinch-off and saturation.

Memory effects are categorized by their time constants relative to the modulation period:

Short-term memory: Effects with time constants on the order of a few symbol periods, primarily from matching network reactances and carrier lifetime dynamics. These are well-modeled by tapped delay lines with limited depth.

Long-term memory: Effects spanning hundreds to thousands of symbols, dominated by thermal dynamics and bias circuit charging. These require specialized modeling approaches like envelope-dependent Volterra kernels or recurrent neural network architectures to capture accurately.

Memory effects dramatically increase the dimensionality of the predistortion problem. A memoryless non-linearity requires only a complex gain look-up table indexed by instantaneous amplitude. With memory, the predistorter must consider a history vector of past inputs, transforming the problem from a 1-D curve fit to a multi-dimensional surface identification. This is why memory polynomial and Volterra-based DPD models grow exponentially in coefficient count with memory depth, and why neural network architectures with built-in temporal processing—such as RVTDNNs and LSTM-based models—have become essential for wideband linearization.

Memory effects are quantified through two-tone and multi-tone intermodulation tests that reveal asymmetry in upper and lower sideband distortion products. Key characterization techniques include:

• Envelope-domain analysis: Measuring the complex gain as a function of instantaneous envelope amplitude and frequency
• Pulsed I-V measurements: Isolating thermal and trapping time constants by varying pulse width and duty cycle
• Dynamic AM-AM and AM-PM plots: Observing the spread or 'cloud' in gain curves that indicates memory, versus the clean single-line characteristic of a memoryless system

These measurements inform the required memory depth and model architecture for effective DPD.

The foundational mathematical framework for modeling non-linear dynamic systems with memory. It represents the system output as a sum of multi-dimensional convolution integrals, capturing both instantaneous non-linearity and the dependence on past inputs. While theoretically complete, its high computational complexity makes it impractical for real-time DPD without model order reduction.

A widely adopted behavioral model that extends the standard memory polynomial by including cross-terms between the signal and its lagging or leading envelope values. This structure efficiently captures complex memory effects, such as those caused by bias network impedance and thermal dynamics, while maintaining a tractable number of coefficients for real-time adaptation.

A slow-varying memory phenomenon caused by the self-heating of the transistor junction during high-power operation. As the die temperature fluctuates with the signal envelope, the transistor's gain and phase characteristics shift dynamically. These effects manifest at low modulation frequencies (kHz range) and require DPD models with long temporal memory depth to compensate.

Fast-varying memory caused by reactive components in the biasing and matching networks. Key contributors include:

• Video bandwidth (VBW) limitations of the drain bias circuit
• Baseband impedance interacting with the envelope frequency
• Trapping effects in GaN HEMT transistors These effects occur at the modulation envelope rate (MHz range) and dominate the memory behavior in wideband signals.

A neural network architecture specifically designed for DPD that processes real-valued I and Q components separately through tapped delay lines. The time-delay structure provides the network with an explicit memory mechanism, allowing it to learn the temporal dependencies of the power amplifier without requiring a pre-defined polynomial basis. This data-driven approach excels at modeling complex, coupled memory effects.

The process of dynamically updating DPD model parameters in real-time to track time-varying memory effects caused by:

• Temperature drift during sustained operation
• Device aging over the product lifecycle
• Load mismatch due to antenna impedance changes Adaptive algorithms like recursive least squares (RLS) or stochastic gradient descent are employed to maintain linearization performance without interrupting transmission.