Indirect Learning Architecture (ILA)

ILA avoids the complexity of directly calculating a PA's inverse model. Instead, it places a copy of the predistorter in a post-distortion feedback path. The error signal is calculated between the PA's input (attenuated) and the output of this post-distorter. By minimizing this error, the post-distorter learns the PA's inverse function. Once converged, these identical coefficients are copied directly to the pre-distorter in the forward transmission path.

The ILA training loop follows a specific sequence:

• The original input signal passes through the predistorter and then the PA.
• The PA output is attenuated and fed to a post-distorter (a copy of the predistorter).
• The error is the difference between the predistorter input (reference) and the post-distorter output.
• An adaptive algorithm (e.g., LMS, RLS) updates the post-distorter coefficients to minimize this error.

ILA's mathematical validity rests on a critical assumption: the PA model and its inverse are commutable. The architecture assumes that the cascade of the predistorter followed by the PA is equivalent to the PA followed by the post-distorter. This holds perfectly for static non-linearities but can introduce residual error in PAs with strong memory effects, where the order of operations matters.

A defining feature of ILA is the direct coefficient copy. After training converges, the learned parameters from the post-distorter are transferred identically to the forward predistorter. No further transformation or inversion is needed. This makes ILA computationally efficient for real-time adaptation, as the training block and linearization block are structurally identical, simplifying hardware implementation on FPGAs and ASICs.

ILA and DLA represent two fundamental DPD identification strategies:

• ILA: Trains a post-distorter on the PA output and copies coefficients. Fast, non-iterative, but assumes commutability.
• DLA: Directly minimizes the error between the desired linear output and the actual PA output. More accurate for strong memory effects but requires iterative optimization and a pre-existing PA model. ILA is preferred for initial acquisition and fast tracking, while DLA is used for fine-tuning.

Real-world ILA implementations must address several challenges:

• Feedback Path Calibration: The observation receiver must be precisely linear to avoid corrupting the training signal.
• Time Alignment: The reference and feedback signals must be aligned to within a fraction of a sample period.
• Noise Sensitivity: ILA can amplify measurement noise in the inverse model, requiring robust regularization.
• Peak Power Handling: The post-distorter must handle the PA's saturated output without numerical overflow.

The primary alternative to ILA. In DLA, the predistorter coefficients are updated by directly minimizing the error between the desired linear output and the actual PA output. This requires a forward model of the PA to compute gradients, making it a closed-loop, iterative approach. Unlike ILA, DLA does not assume the PA model is invertible, but it typically converges more slowly and requires more complex optimization algorithms.

The process of dynamically updating DPD model parameters in real-time to track changes in PA behavior. In ILA, adaptation occurs by periodically re-estimating the postdistorter coefficients and copying them to the predistorter. Key triggers include:

• Temperature drift in the amplifier
• Load mismatch from antenna impedance changes
• Aging effects in the transistor
• Carrier frequency reconfiguration

The mathematical process of identifying a function that, when cascaded with the PA, produces a linear overall response. ILA circumvents direct inverse modeling by swapping the input and output of the PA model during training. The postdistorter is trained on the PA's output as input and the PA's input as the target, effectively learning the inverse without explicitly inverting a complex non-linear function.

The prerequisite step for ILA where an accurate behavioral model of the PA is created. This model replicates the non-linear transfer function of the amplifier and is used to generate the training data for the postdistorter. The fidelity of the ILA solution is fundamentally bounded by the accuracy of this forward model, making it a critical dependency in the overall linearization chain.

Two distinct adaptation strategies for ILA-based DPD:

• Offline Training: Coefficients are identified using dedicated training sequences in a controlled environment before live operation. Suitable for static PA characteristics.
• Online Training: Coefficients are continuously updated during live transmission by capturing feedback from the PA output. Essential for tracking time-varying non-linearity due to thermal and load effects.

A behavioral model frequently used as the basis function set within ILA. GMP extends the standard memory polynomial by including cross-terms between the signal and its lagging or leading envelope values. This captures complex memory effects that simpler models miss. In ILA, the GMP structure is applied identically to both the forward PA model and the postdistorter, ensuring structural consistency during coefficient copying.