Direct Learning Architecture DPD

DLA operates as a closed-loop adaptive controller that directly minimizes the error between the ideal linear output and the actual PA output. Unlike indirect architectures that swap input-output roles, DLA places the predistorter in the forward path and uses the true PA output as feedback.

• Minimizes EVM (Error Vector Magnitude) iteratively
• Converges to the optimal predistorter coefficients without model inversion
• Handles non-invertible PA characteristics that indirect methods cannot correct

A critical sub-component where a post-distorter model is trained using the PA output as input and the desired linear signal as the target. This identified inverse model is then copied to the pre-distorter in the forward transmission path.

• Enables offline training without disrupting live transmission
• Supports periodic coefficient updates during guard intervals
• Decouples identification from linearization for numerical stability

DLA employs iterative algorithms such as Newton-Raphson or stochastic gradient descent to refine predistorter coefficients. Each iteration reduces the residual nonlinear distortion by recalculating the error gradient.

• Typical convergence within 10-50 iterations for memory polynomial models
• Learning rate scheduling prevents oscillation near the optimum
• Compatible with regularization techniques to prevent overfitting to measurement noise

DLA supports online coefficient tracking to compensate for time-varying PA behavior caused by temperature drift, aging, and supply voltage fluctuations. The architecture continuously monitors residual distortion and triggers re-training when performance degrades.

• Integrates with thermal sensors for proactive coefficient adjustment
• Maintains ACLR compliance during long-duration transmissions
• Implements forgetting factors to prioritize recent measurement data

In MIMO systems, DLA extends to estimate a multi-input multi-output predistorter that jointly compensates for per-branch PA nonlinearity and antenna crosstalk. The error vector now spans all array elements simultaneously.

• Models the S-parameter coupling matrix between adjacent elements
• Requires multi-channel observation receivers for parallel feedback
• Computational complexity scales with O(N²) for N-element arrays

Direct learning requires careful conditioning of the autocorrelation matrix used in least-squares coefficient estimation. Ill-conditioned matrices from highly correlated basis functions can cause divergence.

• Tikhonov regularization adds a diagonal loading term to stabilize inversion
• Orthogonal basis functions (e.g., orthogonal memory polynomials) improve conditioning
• Condition number monitoring triggers fallback to previous coefficients if instability detected

A complexity-reduction strategy that pairs naturally with DLA in massive MIMO arrays. Rather than running separate DLA loops for each of 64+ antenna branches, a common set of basis function coefficients is applied across clusters of PAs exhibiting similar nonlinear behavior. DLA's iterative error minimization can be performed on a representative subset of branches, with coefficients shared to the remaining elements. This dramatically reduces the computational overhead of real-time DLA adaptation while maintaining acceptable linearization performance.

The adaptive mechanisms that enable DLA to track time-varying PA nonlinearity caused by temperature drift, aging, and changing operating conditions. Key approaches include:

• Recursive Least Squares (RLS): Updates coefficients with exponential forgetting factor for tracking
• Stochastic Gradient Descent: Low-complexity sample-by-sample updates
• Block-based adaptation: Periodic batch updates using captured data buffers DLA's closed-loop structure makes it inherently suitable for online adaptation, as the error signal directly drives coefficient convergence.

A critical extension of DLA for phased array systems. In massive MIMO, the active impedance seen by each PA changes dynamically with beamforming weights, causing the nonlinear behavior to vary. Beamforming-aware DLA incorporates knowledge of the current beamforming vector into the predistorter model, enabling the DLA training loop to adapt coefficients as the beam steers. Without this awareness, a DLA-trained predistorter optimized for one beam direction may fail when the array scans to a different angle.

A feedback architecture variant that captures the far-field radiated signal rather than individual PA outputs for DLA training. The combined array output is measured by a probe antenna and used as the error reference in the DLA loop. Benefits include:

• Single feedback receiver for entire array
• Inherently accounts for antenna mutual coupling and array effects
• Eliminates need for per-branch couplers Challenges include reduced signal-to-noise ratio and the need to de-embed individual PA contributions from the combined field.