Cross-Band Memory Effect

The primary physical cause is dynamic self-heating of the transistor junction. When a high-power signal in Band A causes the die temperature to rise, the gain and phase characteristics of the amplifier shift. This thermal time constant (microseconds to milliseconds) means the distortion in Band B is modulated by the past envelope history of Band A, not just its instantaneous value. This is distinct from electrical memory effects caused by bias network impedance.

Standard 1D memory polynomials fail to capture cross-band memory because they only index terms based on a single band's history. The 2D Memory Polynomial (2D-MMP) solves this by including cross-terms like:

• x1(n-m) * |x2(n-m-k)|^p These terms explicitly model how the lagging envelope of Band 2 influences the distortion of Band 1. Without these cross-memory terms, the predistorter cannot cancel intermodulation products that have a historical dependency.

In 3GPP Carrier Aggregation scenarios, two component carriers spaced tens of megahertz apart are amplified simultaneously. The cross-band memory effect causes the error vector magnitude (EVM) in one carrier to be modulated by the traffic pattern of the other. This leads to dynamic ACLR degradation that cannot be corrected by static look-up tables. Real-time adaptive DPD with cross-band memory taps is mandatory for maintaining spectral mask compliance.

While cross-modulation is an instantaneous nonlinear effect where the envelope of one signal transfers directly to another, the cross-band memory effect introduces a time lag. The distortion at time t in Band B is a function of the envelope of Band A at time t-τ. This requires the predistorter to have a multi-dimensional tapped delay line structure, significantly increasing the number of coefficients compared to memoryless 2D-DPD.

Extracting coefficients for a model with cross-band memory is computationally intensive. The Joint Coefficient Estimation process must solve a large least-squares problem where the regressor matrix includes both intra-band and inter-band memory terms. The matrix condition number worsens with the number of cross-terms, requiring robust algorithms like regularized least squares (RLS) or principal component analysis (PCA) to avoid overfitting and numerical instability.

Implementing cross-band memory compensation in FPGA-based DPD requires a significant increase in multiply-accumulate operations. A 2D-MMP model with memory depth M and nonlinearity order K has O(M²K) terms, compared to O(MK) for a 1D model. This demands high-bandwidth memory access and parallel processing pipelines. Multi-rate DPD architectures are often employed to run the cross-band correction at a lower sample rate to manage power consumption.

The foundational behavioral model for capturing the cross-band memory effect. It extends the standard memory polynomial by introducing cross-terms that depend on the envelope magnitudes of both concurrent bands. This allows the model to predict how the past envelope history of one carrier influences the current nonlinear distortion of another. The model structure is essential for synthesizing effective multi-band predistorters.

A dedicated predistortion function block designed specifically to cancel intermodulation products generated by the cross-band memory effect. Unlike a standard in-band DPD, this block synthesizes a correction signal intended for an adjacent transmit band. Its implementation is critical for reducing spectral regrowth that falls outside the main carrier's allocated channel.

The rigorous mathematical foundation for understanding cross-band interactions. Derived from the passband Volterra series, this model analytically describes baseband nonlinear behavior, including cross-band memory. While computationally complex, it provides the theoretical basis for simpler models like the 2D-MMP and validates the existence of envelope-dependent coupling between frequency bands.

An advanced model structure that captures complex nonlinear interactions, including the cross-band memory effect, with high fidelity. The MB-GMP incorporates not only cross-band envelope terms but also sample-crossing terms between bands. This provides a more complete description of the PA's behavior under concurrent multi-band excitation, balancing accuracy with computational feasibility.

A parameter identification technique where all coefficients of a multi-band predistorter, including those for cross-band memory terms, are estimated simultaneously in a single optimization step. This approach is superior to sequential estimation because it correctly accounts for the statistical correlation between the distortion generated in different bands, leading to a more robust and globally optimized linearization solution.

A closed-loop adaptation method for identifying a multi-band DPD model that includes cross-band memory effects. In this architecture, a post-distorter is trained on the PA's output and then copied to the forward path. The MB-ILA framework is specifically structured to handle the identification of cross-band model coefficients, making it a practical standard for adaptive multi-band linearization systems.