ET-DPD for Massive MIMO

Unlike single-chain transmitters, Massive MIMO ET-DPD requires independent predistortion for each antenna element. Each power amplifier in the array experiences a unique loading condition due to active impedance modulation from beamforming. A single shared DPD coefficient set is insufficient.

• Each PA chain requires its own DPD engine
• Coefficients must adapt to element-specific impedance
• Scalability demands low-complexity per-element models

In dense arrays, mutual coupling between adjacent antenna elements creates parasitic signal paths. The transmitted signal from one element couples into neighboring PAs, appearing as an additional distortion source. ET-DPD must model this inter-element interference:

• Cross-talk creates ghost nonlinearity products
• Coupling strength increases with frequency and element spacing
• A MIMO Volterra model captures both self and cross-channel distortion

In many Massive MIMO architectures, a single supply modulator drives multiple PAs to reduce cost and complexity. This creates a shared resource bottleneck:

• The modulator's slew rate must satisfy the most demanding envelope across all active elements
• ET delay alignment must be maintained for all parallel paths
• Supply voltage droop under heavy loading introduces correlated distortion across the array

Large arrays exhibit significant spatial temperature gradients across the PCB. Edge elements run cooler than center elements, creating position-dependent thermal memory effects. ET-DPD must compensate for:

• Location-dependent thermal time constants
• Drift in PA gain and phase across the array
• Interaction between dynamic supply voltage and temperature-dependent trapping in GaN PAs

Full Volterra models are computationally prohibitive for 64+ element arrays. Scalable ET-DPD employs pruned basis functions and dimensionality reduction:

• Principal Component Analysis (PCA) on coefficient space to identify dominant distortion modes
• Clustered DPD where elements with similar loading share a coefficient set
• Neural network-based models with weight sharing across elements to exploit array symmetry

In Massive MIMO arrays, the impedance seen by each power amplifier varies dynamically with the beamforming weights and steering angle. This load modulation changes the PA's nonlinear characteristics in real-time, requiring a DPD model that is aware of the active impedance presented to each element. Unlike single-antenna systems, the ET-DPD must adapt to a continuously shifting load-pull environment.

Electromagnetic coupling between densely packed antenna elements creates cross-talk interference that corrupts the intended signal at each transmitter. This mutual coupling introduces array-level nonlinearities that a per-element DPD cannot correct in isolation. Advanced ET-DPD architectures incorporate coupling matrix models to jointly linearize the entire array, canceling inter-element distortion before it radiates.

Applying independent DPD to 64 or more elements is computationally prohibitive. Scalable approaches include:

• Cluster-based linearization: Grouping PAs with similar nonlinear profiles under a shared DPD model
• Reduced-order models: Exploiting array symmetry to minimize unique coefficients
• Over-the-air feedback: Using far-field observations to update all predistorters simultaneously, eliminating per-element feedback chains

A unified behavioral framework that captures the cascaded nonlinearities of the supply modulator, power amplifier, and antenna coupling network as a single multi-input multi-output system. This joint model accepts the baseband signals for all array elements and their corresponding dynamic supply voltages, outputting predistorted waveforms that compensate for the entire transmitter array's distortion in one coordinated operation.

In dense Massive MIMO arrays, thermal gradients across the PCB cause significant variation in PA behavior between center and edge elements. ET-DPD systems must incorporate temperature-aware models that adjust predistortion coefficients based on each element's local operating temperature. This prevents under-compensation of hot center elements and over-compensation of cooler edge elements.

To meet the strict latency budgets of 5G beam switching, ET-DPD systems employ partial coefficient updates rather than full recomputation. Techniques include:

• Subspace tracking: Updating only the most significant eigenmodes of the DPD coefficient vector
• Beam-indexed LUTs: Pre-computing DPD tables for a discrete set of beam directions and interpolating between them
• Sparse adaptation: Updating only coefficients that exceed a change threshold