Multi-User DPD

Unlike single-user DPD that only minimizes distortion on a per-antenna basis, Multi-User DPD formulates a unified optimization problem. The predistorter simultaneously accounts for PA nonlinearity and the precoding matrix to ensure that the radiated signal at each user's receiver is linear. This joint approach prevents the independent linearization of each PA from inadvertently creating interference that degrades the multi-user signal-to-interference-plus-noise ratio (SINR).

A core function is the suppression of nonlinear crosstalk between user streams. Key mechanisms include:

• Nonlinear Precoding: The DPD engine integrates with precoding to shape the distortion so it falls into the null space of unintended users' channels.
• Spatial Filtering: Exploits the array's degrees of freedom to direct distortion away from active users.
• Iterative Refinement: Alternating optimization loops between linearization and interference minimization until convergence.

Multi-User DPD is fundamentally CSI-aware. The predistorter's coefficients are not static; they adapt based on the instantaneous channel matrix. A change in user location or the scattering environment requires a recalculation of the joint linearization-precoding solution. This tight coupling makes the architecture sensitive to channel aging and requires frequent updates in high-mobility scenarios.

The computational load scales aggressively with the number of users and antennas. The joint optimization involves inverting large matrices that grow with the product of user count, antenna elements, and DPD nonlinear order. Practical implementations often employ:

• Dimensionality reduction via principal component analysis of the distortion.
• Sub-array partitioning to break the problem into smaller, parallel tasks.
• Sparse basis function selection to prune negligible cross-terms.

A prominent implementation is Zero-Forcing (ZF) DPD, which applies a strict constraint to nullify inter-user interference completely while correcting PA nonlinearity. The ZF solution forces the cascade of the predistorter, PA array, and wireless channel to appear as an identity matrix at the user terminals. This guarantees interference-free reception but may require higher transmit power to overcome the null-steering constraint.

Advanced Multi-User DPD operates at the symbol level rather than the waveform level. By exploiting knowledge of the intended constellation points for each user, the predistorter can intentionally introduce controlled distortion that constructively interferes at the receiver. This technique, known as Symbol-Level Precoding, improves the received EVM and reduces the peak-to-average power ratio compared to block-level linearization.

A joint linearization and precoding framework that applies a zero-forcing constraint to nullify inter-user interference while simultaneously correcting PA nonlinearity. Unlike conventional two-stage approaches that separate precoding from DPD, ZF-DPD computes a single combined transformation matrix. This ensures that the nonlinear distortion from each PA chain does not corrupt the spatial nulls intended for other users. The technique is particularly effective in line-of-sight dominant channels where inter-user interference is the primary impairment, but may suffer from noise enhancement in low-SNR regimes.

A DPD method that utilizes instantaneous channel state information to adapt linearization parameters based on the propagation environment and user location. By incorporating CSI into the predistortion optimization, the system can prioritize linearity in spatial directions where users are actively receiving, while relaxing constraints in null spaces. This enables spatially selective linearization that allocates correction effort where it matters most. The approach requires real-time CSI feedback from user equipment, making it most practical in TDD systems where reciprocity can be exploited.

A nonlinear precoding technique that optimizes the transmitted waveform on a per-symbol basis to exploit constructive interference and improve received signal quality. Rather than treating all distortion as harmful, SL-DPD intelligently steers nonlinear products into spatial directions where they constructively combine with the intended signal at the receiver. Key characteristics include:

• Operates at the symbol rate rather than the sample rate
• Exploits constructive interference regions in the constellation
• Requires knowledge of both CSI and intended symbols for all users
• Achieves superior energy efficiency by reducing back-off requirements

An array linearization technique specifically optimized to suppress spectral regrowth and minimize adjacent channel leakage power in specific spatial directions. In MU-MIMO systems, regulatory compliance requires controlling ACLR not just in the boresight direction but across the entire sector. OOB-DPD formulates the predistortion optimization with spatial weighting that penalizes out-of-band emissions in directions where sensitive receivers may operate. This is critical for spectrum sharing scenarios and dense deployments where inter-operator interference must be carefully managed.

A deep learning approach for array linearization that models the antenna array as a graph structure to capture the spatial dependencies of mutual coupling and crosstalk. Each antenna element becomes a node, with edges representing coupling paths between elements. The GNN learns to propagate distortion information across the array topology, enabling accurate prediction of how nonlinearity from one PA chain affects adjacent elements. This approach scales efficiently to massive MIMO arrays because the learned message-passing functions are shared across nodes, avoiding the parameter explosion of fully-connected neural architectures.

A dimensionality reduction technique for massive MIMO linearization that identifies and compensates for the dominant spatial modes of nonlinear distortion. By performing principal component analysis on the array's distortion covariance matrix, the system can focus correction effort on the few spatial eigenmodes that carry the majority of distortion energy. Benefits include:

• Order-of-magnitude reduction in DPD coefficient count
• Preserves linearization performance in dominant spatial directions
• Naturally adapts to changing beamforming weights
• Enables real-time adaptation with limited feedback bandwidth