Indirect Learning Architecture (ILA)

The defining characteristic of ILA is the placement of the predistorter training block after the power amplifier (PA) in the estimation loop. Instead of solving for the PA's inverse directly, the architecture assumes the predistorter can be identified as the post-inverse of the PA. The identical predistorter model is copied to the forward path for linearization. This structure converts a complex nonlinear inverse modeling problem into a simpler post-distortion identification task.

ILA fundamentally avoids the mathematical complexity of directly computing the inverse nonlinear transfer function of the power amplifier. Direct inverse computation is often ill-conditioned and computationally expensive. By training a post-distorter that sees the PA's output as its input and the desired linear signal as its target, ILA sidesteps explicit inversion. This makes it highly practical for real-world PAs with strong nonlinearities and memory effects.

Once the post-distorter coefficients converge in the estimation loop, an exact structural copy of the trained model is placed in the forward transmission path. This 'copy-exactly' methodology assumes that the predistorter and post-distorter are functionally identical. The fidelity of this assumption is critical; any mismatch between the estimation and forward paths degrades linearization performance, making precise hardware calibration essential.

A key behavioral characteristic of ILA is its sensitivity to feedback path noise. The post-distorter is trained on the PA's actual output, which contains measurement noise from couplers and ADCs. This noise becomes part of the target signal for coefficient extraction, biasing the solution. In contrast to Direct Learning Architecture (DLA), ILA does not inherently filter this noise, requiring high-SNR feedback receivers for optimal performance.

ILA supports both offline batch training and online adaptive updates. In batch mode, a captured data record is used for least-squares coefficient extraction. For tracking time-varying PA behavior, adaptive ILA implementations use iterative algorithms like Recursive Least Squares (RLS) or Least Mean Squares (LMS) to update coefficients sample-by-sample. This flexibility makes ILA suitable for both laboratory characterization and field-deployed real-time systems.

The coefficient extraction in ILA often involves solving a least-squares problem with a potentially ill-conditioned data matrix, especially for wideband signals with high PAPR. Regularization techniques such as ridge regression or Tikhonov regularization are frequently employed to improve numerical stability. Without proper conditioning, the extracted predistorter coefficients can amplify out-of-band noise, degrading ACLR rather than improving it.

An extended Volterra-based model frequently used as the predistorter structure within an ILA estimation loop. GMP incorporates cross-terms between delayed signal samples and their envelope powers.

• Captures complex memory effects including lagging and leading envelope dependencies
• Model complexity scales with polynomial order, memory depth, and cross-term depth
• Often paired with ILA for wideband GaN PA linearization
• Coefficient extraction via least squares in the ILA post-inverse path

A critical preprocessing step for ILA that accurately measures and aligns the time delay between the transmitted reference signal and the observed feedback signal. Misalignment corrupts the post-inverse identification.

• Integer delay: cross-correlation peak detection
• Fractional delay: Farrow structure interpolation filters
• ILA is sensitive to delay mismatch because it directly compares time-aligned samples
• Typical accuracy requirement: < 0.01 sample periods

The robustness of the ILA coefficient extraction process against ill-conditioned data matrices. When the PA exhibits strong nonlinearity, the regression matrix in the post-inverse path can become nearly singular.

• Ridge regression (Tikhonov regularization) adds a penalty term λ||α||²
• Singular value decomposition (SVD) truncates small singular values
• ILA is more susceptible to instability than DLA because it inverts the PA characteristic directly
• Regularization parameter λ must balance bias vs. variance

A technique to derive ILA-extracted DPD coefficients for uncalibrated operating conditions by interpolating between known coefficient sets. Reduces the calibration overhead for multi-state PA operation.

• Linear interpolation between adjacent power/temperature/frequency points
• Polynomial fitting of coefficient trajectories across operating states
• Enables fast adaptation without re-running the full ILA extraction
• Critical for Doherty PAs with load-dependent nonlinear characteristics

A linearization method that captures and corrects the combined nonlinear distortion of an entire antenna array in the far-field. ILA can be adapted for OTA by placing the predistorter model after the array's aggregate behavioral model.

• Addresses beamforming-dependent nonlinearity and antenna crosstalk
• Single feedback receiver captures far-field combined response
• ILA post-inverse identifies a single predistorter for the entire array
• Contrasts with per-element DPD which requires individual PA feedback paths