Multi-Band Generalized Memory Polynomial (MB-GMP)

The defining feature of the MB-GMP model is the inclusion of cross-band envelope coupling terms. These terms make the nonlinear distortion in one frequency band a function of the instantaneous envelope magnitude of the other concurrently transmitted bands.

• Mechanism: Introduces basis functions of the form x₁(n-m) * |x₂(n-m)|^k to model how the signal in Band 2 modulates the gain of Band 1.
• Purpose: Captures cross-modulation effects, which are a primary source of distortion in concurrent multi-band transmitters.
• Result: This enables the model to predict and correct intermodulation products that standard single-band GMP models cannot see.

The MB-GMP model constructs a multi-dimensional basis by combining memory polynomials from individual bands with cross-products of delayed samples and envelope powers.

• Core Equation: The output for band i is a summation over multiple kernels: standard memory polynomial terms, envelope memory terms, and cross-band terms.
• Indexing: Uses a multi-index structure (k, m, l) where k is the nonlinearity order, m is the memory depth, and l indexes the cross-band signal.
• Flexibility: The model can be pruned to include only statistically significant cross-terms, balancing modeling accuracy against computational complexity.

Unlike simpler 2D-DPD models, the MB-GMP incorporates sample-crossing signal terms that use both the current and lagging samples of the cross-band signal.

• Function: These terms, such as x₁(n) * conj(x₂(n-m)), capture the interaction between the instantaneous signal of one band and the delayed complex conjugate of another.
• Significance: This is critical for modeling cross-band memory effects, where the past envelope history of an interfering signal affects the present distortion of the desired signal.
• Application: Essential for linearizing Doherty amplifiers and other architectures with strong long-term memory in multi-band operation.

The MB-GMP model allows for independent control of nonlinearity orders for in-band, cross-band envelope, and sample-crossing terms, preventing model bloat.

• Parameter Tuning: Separate maximum orders (K_a, K_b, K_c) are defined for aligned envelope, lagging envelope, and signal-crossing terms, respectively.
• Efficiency: This granularity allows an engineer to assign a high nonlinearity order to dominant in-band distortion while using a lower order for weaker cross-band interactions.
• Outcome: Produces a parsimonious model that achieves high accuracy with fewer coefficients than a full Volterra series, making it suitable for real-time FPGA implementation.

All coefficients for the multi-band model, including cross-terms, are estimated simultaneously using a joint coefficient extraction process based on the Least Squares (LS) algorithm.

• Methodology: The basis functions for all bands are concatenated into a single, large regression matrix. The coefficient vector is then solved for in one step using the Moore-Penrose pseudo-inverse.
• Advantage: This joint estimation is superior to sequential extraction as it accounts for the statistical correlation between the distortion generated in different bands.
• Implementation: Typically performed offline using captured time-domain waveforms in an Indirect Learning Architecture (ILA) setup.

To meet the stringent latency and resource constraints of FPGA-based DPD, the MB-GMP model is often subjected to aggressive hardware-optimized pruning.

• Techniques: Includes near-neighbor pruning (removing terms with similar memory/order indices) and magnitude-based pruning (discarding coefficients below a threshold).
• Goal: Reduce the number of active basis functions and multipliers without significantly degrading Adjacent Channel Leakage Ratio (ACLR) correction.
• Result: A sparse polynomial structure that maintains the essential cross-band cancellation physics while fitting into a real-time Look-Up Table (LUT) or direct computation engine.

The overarching linearization architecture designed for power amplifiers transmitting two or more widely spaced carrier signals simultaneously. Unlike single-band DPD, this approach must account for cross-band distortion products generated by the nonlinear mixing of carriers within the amplifier. The MB-GMP model serves as the mathematical engine within this architecture, providing the basis functions needed to synthesize correction signals that cancel both in-band and out-of-band interference.

Nonlinear interference products generated by the interaction of multiple carrier signals within a power amplifier. These fall into three critical categories:

• Inter-band IMD: Products falling in the frequency gap between transmit bands.
• Cross-modulation: Envelope transfer from one carrier onto another.
• In-band distortion: Spectral regrowth within each carrier's own channel. The MB-GMP model explicitly captures these effects through cross-band envelope terms and sample-crossing terms that correlate the instantaneous states of all concurrent signals.

A foundational behavioral model that extends the standard memory polynomial to two dimensions by including cross-terms dependent on the envelope magnitudes of both concurrent bands. While effective for dual-band scenarios, the 2D-MMP has limitations:

• Captures cross-band memory effects but may miss higher-order interactions.
• Computational complexity scales quadratically with memory depth.
• The MB-GMP generalizes this concept to N bands with more flexible basis function selection, offering superior accuracy-to-complexity trade-offs for tri-band and higher-order configurations.

The signal processing procedure for estimating the parameters of a multi-band DPD model from observed PA input and output waveforms. Key techniques include:

• Joint coefficient estimation: Simultaneously solving for all coefficients, including cross-band terms, in a single least-squares optimization.
• Multi-Band Indirect Learning Architecture (MB-ILA): A closed-loop method where a post-distorter is identified from the attenuated PA output and then copied to the forward path predistorter.
• Sequential extraction: Iteratively estimating per-band and cross-band coefficients to reduce computational burden.

The primary regulatory compliance metric for multi-band transmitters. MB-ACLR measures the ratio of power leaked into adjacent channels to the power in the main channels across all active carriers. The MB-GMP model is specifically optimized to minimize this metric by:

• Canceling spectral regrowth in each band's adjacent channels.
• Suppressing inter-band IMD that falls into neighboring licensed spectrum.
• Meeting stringent 3GPP and FCC emission masks for carrier aggregation scenarios.

A signal conditioning technique that jointly reduces the peak-to-average power ratio (PAPR) of a composite multi-band signal before amplification. MB-CFR is a critical preprocessing step that works in tandem with MB-GMP-based DPD:

• Prevents amplifier saturation that would drive the PA into deeply nonlinear regions beyond the DPD's correction capability.
• Reduces the dynamic range requirements for the predistorter.
• Enables higher average power efficiency while maintaining linearity.