Multi-Band Indirect Learning Architecture (MB-ILA)

MB-ILA operates by placing a post-distorter in a feedback path that processes the attenuated and downconverted PA output. The coefficients of this post-distorter are adapted using an error signal formed by comparing the post-distorter output to the original baseband input. This architecture transforms the nonlinear inverse modeling problem into a linear-in-parameters system identification task, enabling the use of standard adaptive filtering algorithms such as Least Mean Squares (LMS) or Recursive Least Squares (RLS) without requiring a direct model inversion of the PA.

Once the post-distorter coefficients converge to an acceptable error floor, they are directly copied to the predistorter in the forward transmission path. This assumes that the post-distorter and predistorter are structurally identical and that the PA is operating in a quasi-static regime. The copy operation is typically performed during a training frame or idle period to avoid introducing transient distortion into the live signal. This decoupling of training and linearization paths is the defining characteristic of the indirect learning architecture.

In MB-ILA, the error signal used for adaptation is computed independently for each frequency band after digital downconversion and channel filtering of the PA output. For a dual-band system, two distinct error signals are formed:

• Band 1 Error: e₁(n) = y₁(n) - x₁(n)
• Band 2 Error: e₂(n) = y₂(n) - x₂(n) where y₁(n) and y₂(n) are the post-distorter outputs and x₁(n), x₂(n) are the original baseband inputs. This per-band error formulation allows the 2D-DPD model coefficients to be updated to jointly minimize distortion in both bands while inherently accounting for cross-band intermodulation products.

Unlike Direct Learning Architecture (DLA), which requires an explicit PA behavioral model for backpropagation, MB-ILA is model-agnostic with respect to the PA. The adaptation loop directly observes the actual PA output, making the coefficient estimation inherently robust to model inaccuracies, thermal drift, and aging effects. The primary trade-off is that the post-distorter is trained on the PA's output, which contains measurement noise and potential ADC quantization errors, requiring sufficient averaging or filtering in the adaptation algorithm.

MB-ILA requires periodic insertion of dedicated training frames during which the coefficient copy operation occurs. This introduces a spectral efficiency overhead, as these frames cannot carry user data. In modern 5G NR systems, this overhead is minimized by aligning training with synchronization signal blocks (SSB) or using cyclic prefix (CP) periods for coefficient updates. Advanced implementations employ smooth coefficient transition techniques, such as linear interpolation between old and new coefficient sets, to prevent abrupt changes in the predistorter transfer function that could violate adjacent channel leakage ratio (ACLR) masks.

MB-ILA is compatible with any multi-band behavioral model that is linear in its coefficients, including:

• 2D Memory Polynomial (2D-MMP)
• Multi-Band Generalized Memory Polynomial (MB-GMP)
• 2D Look-Up Table (2D-LUT) with linear interpolation The architecture places no restriction on the predistorter structure beyond linearity in parameters, allowing designers to select the model that best balances linearization performance against FPGA resource utilization. The post-distorter and predistorter must share the identical model structure and basis function set.