Array Manifold DPD

Incorporates the array manifold vector—the phase and amplitude response of each element for a given angle of departure—directly into the DPD coefficient computation. This ensures the predistorter accounts for how nonlinear distortion combines in the far-field, not just at individual power amplifier outputs. The technique models the radiated field as a function of both the input signal and the spatial direction, enabling direction-aware linearization.

Unlike per-element DPD that linearizes each PA independently, array manifold DPD optimizes the combined far-field radiation pattern. The cost function minimizes the error between the desired and actual radiated waveforms across all angles of interest. This joint formulation inherently handles beam squint and mutual coupling effects that per-element approaches cannot correct.

Power amplifier nonlinearity in a beamforming array varies with the active impedance seen by each element, which changes as the beam is steered. Array manifold DPD builds a model that is parameterized by the steering angle, enabling the predistorter to adapt its correction as the beam direction changes. This is critical for 5G massive MIMO systems with dynamic user tracking.

In massive MIMO arrays with hundreds of elements, full array manifold DPD would be computationally prohibitive. The technique leverages principal component analysis of the spatial distortion modes to identify the dominant directions of nonlinear radiation. Only these principal spatial modes are linearized, reducing complexity from O(N²) to O(K) where K << N is the number of significant modes.

Array manifold DPD is particularly suited for hybrid beamforming architectures where a shared digital chain feeds multiple analog sub-arrays. The technique models the composite nonlinearity introduced in both the digital and analog domains, applying a single predistorter that accounts for the spatial combining performed by the analog beamformer. This avoids the need for per-branch DPD in the analog path.

In time-division duplex (TDD) systems, array manifold DPD exploits channel reciprocity to derive downlink linearization parameters from uplink measurements. The array manifold is estimated during the uplink sounding phase, and the same spatial model is used to compute the downlink predistorter. This eliminates the need for dedicated over-the-air feedback receivers in the far-field.

Compensates for active impedance mismatch that varies with beam steering angle. As the array scans, each power amplifier sees a different load impedance, altering its nonlinear characteristics. Array Manifold DPD models this angle-dependent AM-AM/AM-PM distortion and applies a predistortion function that adapts to the instantaneous beamforming vector, ensuring consistent linearity across the entire scan range.

Integrates DPD with zero-forcing or MMSE precoding in a unified optimization framework. Rather than treating linearization and beamforming as separate stages, this approach jointly computes predistorted signals that simultaneously:

• Nullify inter-user interference in the spatial domain
• Cancel in-band distortion from PA nonlinearity
• Suppress out-of-band emissions in specific spatial directions This is essential for MU-MIMO systems where distortion creates spatial interference that conventional per-antenna DPD cannot address.

Uses far-field radiated signals captured by a probe antenna or user equipment as the feedback path for DPD training. The manifold model maps the OTA observation back to individual PA outputs, enabling:

• Correction of array-level nonlinearities including mutual coupling effects
• Linearization without per-element feedback receivers, reducing hardware cost
• Compensation for beam-squint effects in wideband systems The manifold-aware training algorithm accounts for the spatial transfer function between each PA and the observation point.

Applies principal component analysis to the array manifold to identify the dominant spatial modes of nonlinear distortion. In a 64-element array, only 4-8 principal components typically capture >95% of the distortion energy. This enables:

• Dimensionality reduction from 64 per-element DPD engines to a handful of spatial-mode predistorters
• Real-time adaptation with dramatically reduced coefficient count
• Efficient FPGA implementation with minimal memory footprint The technique exploits the fact that mutual coupling and impedance variation exhibit strong spatial correlation across the array aperture.

Tailors manifold-aware linearization for hybrid analog-digital architectures where a single digital chain drives multiple analog phase shifters. The technique addresses:

• Common digital path nonlinearity shared across the sub-array
• Per-branch analog distortion from individual PA and phase shifter impairments
• Sub-array partitioning that groups elements with similar manifold characteristics The manifold model decomposes the distortion into digital-domain and analog-domain components, applying correction at the appropriate stage of the hybrid beamformer.

Incorporates instantaneous channel state information into the DPD adaptation loop. The manifold model combines:

• Array geometry (element positions, coupling matrix)
• Per-user channel estimates (path loss, angle of arrival)
• PA behavioral models (nonlinearity profiles) This enables the predistorter to prioritize linearization in spatial directions where users are actually located, rather than wasting correction effort on empty angular sectors. Particularly effective in FDD massive MIMO where uplink CSI informs downlink DPD parameter selection.