Indirect Learning Architecture (ILA)

The ILA operates in an open-loop configuration during training, meaning the predistorter's output does not feed back into the coefficient estimation process. Instead, a separate postdistorter block is placed after the power amplifier (PA). The training algorithm minimizes the error between the postdistorter's output and the PA's input signal. This decoupling simplifies the training process by avoiding the complexities of a closed-loop system, but it relies on the critical assumption that the nonlinear blocks are commutable.

The core mechanism of ILA is the copy principle. A neural network is first trained as a postdistorter to invert the PA's nonlinear characteristics. Once the postdistorter's weights converge, they are directly copied to the predistorter block, which is placed before the PA. This assumes that the optimal inverse function identified at the output is identical to the optimal inverse function required at the input. This assumption holds perfectly for static nonlinearities but can introduce errors in systems with strong memory effects.

The mathematical validity of the ILA rests on the commutability of the nonlinear blocks. The architecture assumes that the cascade of the predistorter (P) and the power amplifier (PA) is equivalent to the cascade of the PA and the postdistorter (P). In practice, this is an approximation. For a PA with significant memory effects, the linear time-invariant (LTI) dynamics do not commute with the static nonlinearity, making the postdistorter a suboptimal copy for the predistorter. This limitation drives the need for more complex architectures like the Direct Learning Architecture (DLA).

The ILA training loop uses a specific signal routing. The original baseband signal, x(n), is transmitted through the PA to generate the distorted output, y(n). The postdistorter neural network takes y(n)/G (where G is the linear gain) as its input and produces an estimate of the original signal, z(n). The error signal e(n) = x(n) - z(n) is used to update the network's weights via backpropagation. This architecture is inherently stable during training because it is not part of the transmission chain.

The ILA is widely used for its simplicity and stability. Since the training loop is isolated from the transmission path, it cannot become unstable during coefficient extraction. It is an excellent choice for offline model extraction in a laboratory setting using captured waveform data. The architecture is straightforward to implement with standard supervised learning frameworks, making it a common baseline for comparing more advanced neural network predistorter topologies like RVTDNNs or CVNNs.

A key weakness of the ILA is its sensitivity to measurement noise. The postdistorter is trained to invert a noisy version of the PA's output. When the trained weights are copied to the predistorter, the model can inadvertently learn to compensate for the noise profile of the training data, leading to noise enhancement in the transmitted signal. Furthermore, the commutability assumption breaks down for wideband signals with strong memory effects, resulting in degraded Adjacent Channel Leakage Ratio (ACLR) performance compared to closed-loop methods.

The first stage of the ILA process where a neural network is trained to act as a postdistorter—placed after the PA—to linearize the combined system output. This network learns the inverse of the PA's nonlinear transfer function.

• Training data: PA input-output pairs with the output as network input
• Objective: Minimize error between postdistorter output and PA input
• Output: A trained inverse model ready for copying to the predistorter position

The critical theoretical premise underlying ILA: that the order of a nonlinear predistorter and a nonlinear power amplifier can be swapped without changing the overall system output. This allows the postdistorter to be copied directly to the predistorter position.

• When valid: Memoryless nonlinearities or systems with mild memory effects
• When violated: Strong PA memory effects break commutability
• Consequence of violation: Residual distortion remains after ILA training
• Mitigation: Augmented ILA with iterative refinement loops

ILA separates the process into two distinct phases: model extraction (training the postdistorter) and model copy (transferring weights to the predistorter). This contrasts with DLA, which trains the predistorter directly in its operational position.

• Extraction phase: Offline or online training of the inverse model
• Copy phase: Weight transfer with no additional training required
• Benefit: Simplifies training by avoiding closed-loop instability
• Limitation: Copy fidelity depends on commutation assumption validity

While standard ILA uses a fixed copied predistorter, adaptive variants incorporate online learning to periodically retrain the postdistorter and update the predistorter copy. This tracks time-varying PA behavior due to temperature drift, aging, and channel changes.

• Trigger mechanisms: Performance degradation thresholds or timed intervals
• Update strategy: Background postdistorter retraining with atomic weight transfer
• Challenge: Ensuring stability during live coefficient updates
• Implementation: Common in FPGA-based DPD with dual-buffer coefficient tables

A supervised learning approach closely related to ILA where a neural network is trained to imitate the input-output mapping of an ideal predistorter generated by an offline reference model. The trained clone is then deployed as the operational predistorter.

• Teacher model: High-complexity offline optimizer (e.g., indirect learning with full Volterra)
• Student model: Lightweight neural network suitable for real-time inference
• ILA connection: Both use a two-stage train-then-deploy paradigm
• Advantage: Decouples training complexity from inference latency constraints