Coupling Matrix DPD

Unlike behavioral models that treat crosstalk as a black box, this method directly incorporates the S-parameter matrix of the antenna array into the predistortion engine.

• The coupling matrix quantifies the mutual coupling and reflection coefficients between every element pair.
• By inverting this matrix, the DPD can pre-compensate for the linear coupling before the signal reaches the PA.
• This separates the problem into a linear decoupling stage and a nonlinear PA linearization stage.

The core innovation is the two-stage architecture that isolates distortion sources.

• Stage 1 (Linear Decoupling): Applies the inverse of the antenna coupling matrix to the digital baseband signals, ensuring that the signal intended for element i does not leak into element j.
• Stage 2 (Per-Element DPD): Once the array is effectively decoupled, each PA sees a consistent, predictable load, allowing standard single-antenna DPD models to operate with high fidelity.
• This prevents the DPD from wasting modeling capacity on linear crosstalk, focusing it entirely on nonlinear compensation.

Beam steering changes the active impedance seen by each power amplifier, which alters its nonlinear behavior. Coupling Matrix DPD addresses this at the source.

• The coupling matrix is a function of the array geometry and is independent of the beamforming weights.
• By nullifying the coupling paths, the DPD effectively presents a constant, nominal impedance to each PA output stage.
• This drastically reduces the variation in PA distortion characteristics as the beam scans, simplifying the adaptation rate required for the nonlinear DPD coefficients.

The explicit matrix inversion introduces a known, fixed computational cost that scales with the number of antennas.

• Matrix Dimension: An N-element array requires an N x N complex matrix multiplication per sample.
• Hardware Efficiency: For moderate array sizes, this is highly efficient on FPGA-based DPD implementations using parallel multiply-accumulate structures.
• Scalability Limit: For massive MIMO arrays with hundreds of elements, the O(N²) complexity can become a bottleneck, motivating hybrid approaches like Sub-Array DPD where coupling is only modeled within clusters.

Coupling Matrix DPD pairs naturally with Over-the-Air DPD observation strategies to linearize the true radiated field.

• A probe antenna in the far-field captures the combined signal, which includes both PA nonlinearity and array coupling effects.
• The coupling matrix model allows the system to mathematically back-propagate the error through the coupling network to isolate the distortion contribution of each individual PA.
• This enables far-field linearization without requiring a dedicated feedback receiver per antenna branch, reducing system cost.

Real-world arrays suffer from manufacturing tolerances, aging, and thermal drift that alter the coupling matrix. The architecture must account for this.

• Offline Calibration: The initial S-parameter matrix is measured in an anechoic chamber or computed via full-wave electromagnetic simulation.
• Online Adaptation: Advanced implementations couple this with Blind DPD Adaptation techniques to track slow changes in the coupling coefficients during live operation.
• This hybrid approach ensures the decoupling stage remains accurate over the lifecycle of the base station without requiring intrusive recalibration.

The fundamental electromagnetic phenomenon that Coupling Matrix DPD aims to invert. When antenna elements are placed in close proximity, energy radiated by one element induces currents in its neighbors. This alters each element's input impedance and distorts the radiation pattern. The effect is quantified by the S-parameter matrix, where off-diagonal terms (e.g., S₂₁) represent the coupling coefficient between elements. Without explicit modeling, this coupling creates a spatially dependent nonlinearity that single-element DPD cannot correct.

The dynamic variation in load impedance seen by each power amplifier as the beam is steered. When the array phase shifts change to direct the beam, the mutual coupling environment changes, causing each PA to see a different reflection coefficient (Γ). This load modulation shifts the PA's operating point, altering its AM-AM and AM-PM characteristics. Coupling Matrix DPD must account for this by modeling the S-parameter network between PAs and antennas, enabling the predistorter to adapt as the beam scans across angles.

A signal processing technique that operates in the digital baseband to subtract the predicted interference caused by adjacent transmitters. Unlike Coupling Matrix DPD—which models the physical coupling network—cross-coupling cancellation treats the crosstalk as an additive interference term:

• Linear crosstalk: Corrected via simple subtraction of filtered copies of adjacent branch signals
• Nonlinear crosstalk: Requires modeling the cascade of PA nonlinearity followed by coupling paths
• Implementation: Often uses a parallel Hammerstein structure to capture frequency-dependent coupling effects

A broader class of linearization techniques that recognize the beam-dependence of array nonlinearity. While Coupling Matrix DPD focuses on the S-parameter network, beamforming-aware DPD generalizes the approach by incorporating the beamforming weight vector as an input to the predistorter model. Key distinctions:

• Single-beam DPD: Linearizes one direction at a time
• Multi-beam DPD: Jointly optimizes across multiple simultaneous beams
• Over-the-Air feedback: Uses far-field measurements to capture the combined effect of coupling and beamforming

An adaptive linearization strategy specifically designed for Doherty and envelope tracking PAs operating in arrays. As the beam scans, the load-pull effect shifts the PA's efficiency and linearity contours. Load modulation DPD uses:

• Real-time impedance sensing: Directional couplers at each PA output
• Dynamic coefficient lookup: Pre-characterized DPD tables indexed by estimated reflection coefficient
• Adaptive basis functions: Volterra kernels that expand/contract based on instantaneous load conditions This complements Coupling Matrix DPD by addressing the PA-level effects of the coupling-induced impedance variation.

A linearization technique that captures the far-field radiated signal using a probe antenna, rather than sampling individual PA outputs. This inherently captures the combined effect of mutual coupling, beamforming, and PA nonlinearity as observed in the intended direction. When combined with Coupling Matrix DPD:

• The S-parameter model provides the initial inverse estimate
• OTA feedback provides closed-loop correction for model inaccuracies
• Enables direction-specific linearization where ACLR is minimized in the target spatial sector rather than uniformly