Indirect Learning Architecture (ILA)

The defining mechanism of ILA is the postdistorter, a nonlinear model placed after the power amplifier (PA) in a dedicated training path. This postdistorter is trained to replicate the PA's inverse transfer function by minimizing the error between its output and the predistorter input.

• The postdistorter sees the PA output as its input and the predistorter input as its desired output
• Training uses standard adaptive filtering algorithms like Least Mean Squares (LMS) or Recursive Least Squares (RLS)
• Once training converges, the postdistorter coefficients are directly copied to the predistorter
• This architecture assumes the PA inverse is unique and the postdistorter can accurately model it

ILA operates on a copy-and-paste principle for coefficient transfer. After the postdistorter converges to an optimal solution, its parameters are frozen and transferred to the predistorter in the forward transmission path.

• The predistorter operates in open-loop mode during normal transmission
• No real-time feedback loop exists between PA output and predistorter during operation
• Coefficient updates occur in discrete training intervals, not continuously
• This decoupling simplifies hardware implementation but leaves the system vulnerable to coefficient drift from temperature changes or aging

The ILA training path is susceptible to measurement noise because the postdistorter's desired output—the predistorter input—is assumed to be noise-free, while the postdistorter input contains amplified noise from the PA output observation path.

• The Normalized Mean Squared Error (NMSE) of the postdistorter is biased by observation path noise
• This noise bias causes the estimated coefficients to deviate from the true PA inverse
• The resulting misadjustment degrades linearization performance, particularly for high-order nonlinear terms
• Techniques like Tikhonov regularization can stabilize the solution when the condition number of the data matrix is high

Unlike the Direct Learning Architecture (DLA), ILA does not require an explicit forward model of the power amplifier. The postdistorter directly learns the inverse mapping from observed input-output pairs.

• Eliminates the need for model extraction or behavioral modeling of the PA
• Avoids errors from inaccurate PA forward models that compound in DLA's model inversion step
• The postdistorter implicitly captures all nonlinear and memory effects present in the measured data
• However, this black-box approach provides no insight into the PA's physical characteristics for diagnostics

ILA supports flexible coefficient update strategies to balance computational load and adaptation speed. Training can occur in dedicated time slots or accumulate data over blocks of samples.

• Burst training: Coefficients are updated only during specific training intervals, reducing continuous processing overhead
• Block update: Postdistorter coefficients are recalculated after collecting a batch of samples, using Least Squares Estimation for optimal batch solutions
• Sample-by-sample update: Rare in ILA due to the copy mechanism, but possible with iterative algorithms like Stochastic Gradient Descent (SGD)
• The choice of update mode directly impacts convergence rate and steady-state misadjustment

The architectural separation of training and predistortion paths makes ILA attractive for FPGA-based DPD implementation. The predistorter operates as a static nonlinear filter between coefficient updates.

• The predistorter path requires only a look-up table (LUT) or polynomial evaluator with fixed coefficients
• The computationally intensive training runs on a separate processor or during idle periods
• No high-speed feedback loop is needed during active transmission, reducing timing closure challenges
• This simplicity comes at the cost of inability to track rapid PA characteristic changes during a transmission burst