Hybrid Beamforming DPD

Hybrid beamforming DPD employs a two-tier correction strategy to address distortion sources at different stages of the transmitter:

• Digital Stage DPD: A shared predistorter in the baseband corrects nonlinearities common to all RF chains, such as the digital-to-analog converter (DAC) and shared upconverter impairments.
• Per-Branch Analog DPD: Individual predistorters compensate for power amplifier (PA) nonlinearity, IQ imbalance, and phase shifter errors unique to each antenna path. This separation prevents the digital DPD from attempting to correct analog-specific artifacts, reducing the model's complexity while maintaining linearity across the array.

As the beamforming weights change to steer the main lobe, the active impedance seen by each power amplifier fluctuates, altering its nonlinear behavior. Hybrid beamforming DPD incorporates beam-indexed lookup tables (LUTs) that store distinct predistortion coefficients for different beam configurations:

• The system detects the current beam index from the precoding matrix.
• It loads the corresponding DPD coefficient set optimized for that specific impedance state.
• For transitional beam states, interpolation between adjacent LUT entries maintains linearity without requiring exhaustive calibration for every possible angle.

To minimize hardware overhead, hybrid beamforming DPD often uses a single observation receiver that sequentially samples the output of each PA chain:

• A switch matrix or coupler network routes the attenuated PA output to a shared feedback ADC.
• The system applies time-alignment and gain normalization to compensate for path differences.
• Training occurs in a round-robin fashion, updating per-branch DPD coefficients cyclically. This approach reduces the number of feedback receivers from N to 1, critical for cost-sensitive massive MIMO deployments with 64 or more antenna elements.

In tightly packed antenna arrays, electromagnetic mutual coupling causes the output of one PA to leak into adjacent branches, creating a complex interference pattern. Hybrid beamforming DPD addresses this through:

• Coupling Matrix Estimation: The system characterizes the S-parameter network between antenna elements during a factory calibration or online training phase.
• Joint Predistortion: The DPD engine models the coupled nonlinear response, applying a MIMO Volterra series or neural network that takes adjacent branch signals as inputs.
• Decoupling Precoding: Before DPD application, a linear decoupling matrix pre-compensates for the known coupling paths, simplifying the subsequent nonlinear correction.

Hybrid beamforming DPD systems often incorporate far-field feedback to validate linearization performance in the radiated domain:

• A calibration antenna placed in the far-field captures the combined over-the-air signal.
• The system compares the received signal against the ideal beamformed reference to compute the error vector magnitude (EVM) and adjacent channel leakage ratio (ACLR).
• This OTA measurement captures array-level nonlinearities that per-branch feedback misses, such as beam-squint effects and spatial power combining artifacts. The OTA path is typically used for periodic recalibration rather than continuous real-time adaptation due to its higher latency.

Hybrid beamforming arrays with many RF chains demand computationally efficient DPD to fit within FPGA or ASIC constraints. Key reduction techniques include:

• Coefficient Sharing: Branches with similar PA characteristics (e.g., same position in a symmetric array) share a common DPD model, reducing memory and multiply-accumulate operations.
• Principal Component DPD: The system identifies the dominant spatial modes of distortion and applies DPD only in that reduced subspace, ignoring low-energy distortion modes.
• Sparse Basis Selection: Algorithms like LASSO or orthogonal matching pursuit select only the most significant Volterra kernel terms, pruning 80-90% of coefficients with minimal linearization loss.