Over-the-Air DPD (OTA DPD)

Unlike conventional DPD that linearizes each PA individually, OTA DPD treats the entire phased array as a single nonlinear system. The predistorter is trained on the radiated signal captured by a far-field observation receiver, inherently compensating for:

• Beamforming-dependent nonlinearity: Distortion that changes with beam angle
• Antenna crosstalk: Mutual coupling between array elements
• Active impedance mismatch: Load variation seen by each PA during beam-steering This holistic approach eliminates the need for per-element feedback paths, dramatically simplifying mmWave array calibration.

In phased arrays, the nonlinear behavior of each PA varies with the beam-steering angle due to changing active impedance. OTA DPD captures this beam-dependent distortion by:

• Training at multiple beam angles to build a beam-aware predistorter
• Using coefficient interpolation between calibrated angles for continuous coverage
• Modeling the array as a MIMO nonlinear system where spatial and temporal distortion are jointly corrected This is critical for 5G NR systems where beams are dynamically steered to track users.

Antenna crosstalk causes the output of one PA to couple into adjacent elements, creating distortion that cannot be corrected by per-element DPD. OTA DPD inherently compensates for:

• Mutual coupling: Electromagnetic interaction between closely spaced antennas
• Cross-element nonlinear mixing: Intermodulation products from coupled signals
• Array-level memory effects: Thermal and trapping effects that propagate across the array The far-field observation naturally captures these coupled effects as part of the composite nonlinear response.

Conventional per-element DPD requires dedicated feedback paths for each PA—impractical for massive MIMO arrays with 64+ elements. OTA DPD reduces complexity by:

• Using a single far-field observation receiver to capture the combined radiated signal
• Eliminating the need for on-chip couplers and per-element ADCs
• Simplifying PCB layout and reducing BOM cost
• Enabling over-the-air calibration without breaking the signal chain This architecture is essential for cost-effective mmWave base station deployment.

OTA DPD employs specialized learning architectures adapted for far-field observation:

• Indirect Learning Architecture (ILA): The predistorter is identified by placing it after the observed PA output, avoiding explicit inverse modeling
• Direct Learning Architecture (DLA): Iteratively minimizes the error between desired and radiated signals using gradient-based updates
• Model extraction: Offline training using far-field measurements across beam angles and power levels
• Online adaptation: Real-time coefficient updates to track thermal drift and aging effects The choice depends on latency requirements and computational resources available at the base station.

Implementing OTA DPD at mmWave frequencies introduces unique challenges:

• Wide modulation bandwidths (400 MHz to 2 GHz) requiring high-speed ADCs and processing
• Severe path loss demanding high-gain observation antennas and sensitive receivers
• Channel impairments: Multipath and atmospheric absorption affect far-field measurement fidelity
• Numerical stability: Ill-conditioned matrices from wideband correlated signals require regularization
• Loop delay alignment: Sub-sample timing synchronization between reference and far-field signals using fractional delay filters Solutions include direct RF sampling with RFSoC platforms and robust coefficient extraction algorithms.

A spatial filtering technique using phased antenna arrays to focus transmitted energy into directional beams. At mmWave frequencies, beamforming compensates for high path loss but introduces a critical challenge for OTA DPD: the active impedance mismatch and nonlinear behavior of each power amplifier (PA) change dynamically with the beam-steering angle. This means a single DPD lookup table calibrated for one beam direction may fail when the beam is steered elsewhere, requiring beam-indexed or continuous beam-aware linearization strategies.

Unintended signal coupling between adjacent antenna elements in a dense array. In a massive MIMO or phased-array transmitter, the output of one PA does not only radiate into free space—it also leaks into neighboring elements through mutual coupling. This creates a combined, far-field distortion that is a function of all PAs interacting, not just a single device. OTA DPD is specifically designed to linearize this composite nonlinearity, which per-element DPD cannot address because it lacks visibility into the coupled far-field waveform.

The variation in load impedance seen by each individual power amplifier in a phased array as the beam is steered. Unlike a standalone PA with a fixed 50-ohm load, an array element's load-pull changes with scan angle due to mutual coupling. This causes:

• Channel-specific AM-AM/AM-PM profiles that diverge from single-PA characterization
• Beam-dependent efficiency collapse in Doherty or envelope-tracking PAs OTA DPD must capture and correct this beam-varying nonlinearity in the far-field, where the combined effect manifests as spectral regrowth and constellation distortion.

A foundational DPD training method that identifies the predistorter by placing it after the power amplifier model in the estimation loop. In an OTA context, the ILA captures the far-field signal using a probe antenna, then uses this observed output to train a post-distorter. By the p-inverse theorem, this post-distorter is copied to the transmit side as the pre-distorter. ILA is popular for OTA DPD because it avoids the numerical instability of directly inverting the complex MIMO channel and PA nonlinearity, but it assumes the feedback path is noise-free, which is challenging in over-the-air measurements.

A DPD training method that iteratively minimizes the error between the desired linear far-field output and the actual radiated signal to extract predistorter coefficients. Unlike ILA, DLA directly optimizes the pre-distorter parameters by comparing the OTA feedback to the ideal reference. This approach is more robust to measurement noise in the feedback path but requires careful loop delay estimation and fractional delay filtering to align the reference and observed waveforms at sub-sample precision. DLA is often preferred for online OTA DPD adaptation in dynamic environments.

Slowly varying changes in power amplifier gain and phase caused by self-heating and substrate temperature fluctuations dependent on signal history. In an array, thermal effects are compounded: the heat dissipated by one PA raises the temperature of adjacent elements, creating cross-element thermal coupling. This long-term memory—spanning milliseconds to seconds—cannot be corrected by memoryless DPD. OTA DPD models must incorporate long-sequence memory kernels (e.g., LSTM or GMP with deep memory taps) to track and cancel these thermally-induced trajectory errors in the far-field constellation.