Predistorter Synthesis

The most straightforward synthesis method involves mathematically inverting the extracted power amplifier (PA) model. For a Hammerstein model (static nonlinearity followed by linear filter), the inverse is a Wiener model (linear filter followed by static nonlinearity). This analytical inversion is exact for block-structured models but becomes intractable for complex Generalized Memory Polynomial (GMP) structures, requiring numerical approximation instead.

The ILA avoids explicit model inversion by placing a copy of the predistorter in a feedback path. The architecture trains a postdistorter to minimize the error between the PA output and the desired linear output. Once converged, the postdistorter's coefficients are copied directly to the predistorter. This method is robust to measurement noise but assumes the PA is invertible and that the postdistorter-to-predistorter copy is valid.

In a DLA, the predistorter coefficients are updated directly by minimizing the error between the desired signal and the actual PA output. This requires a model of the PA to compute the gradient of the error with respect to the predistorter parameters. The DLA is more computationally intensive than the ILA but can achieve superior performance because it optimizes the true linearization objective without the copy assumption.

The pth-order inverse is a foundational Volterra theory concept. For a nonlinear system, the pth-order inverse is a system that, when cascaded with the original, cancels all nonlinearities up to order p. In DPD synthesis, a finite-order approximation of the exact inverse is constructed by cascading lower-order inverse kernels. This provides a systematic, though computationally demanding, path to predistorter design.

Synthesized predistorters are highly susceptible to numerical instability, especially with high-order polynomials. Basis function orthogonalization (e.g., using QR decomposition or Principal Component Analysis) is critical during coefficient extraction. Without it, the regression matrix becomes ill-conditioned, leading to wildly oscillating predistorter gain functions that amplify noise and fail to linearize the PA at signal peaks.

Synthesis is not a one-time offline operation. Modern transmitters use online training algorithms like Recursive Least Squares (RLS) to continuously update the predistorter. This closed-loop synthesis adapts to thermal memory effects, aging, and channel frequency changes. The synthesis engine must balance convergence speed against computational latency to maintain linearity during dynamic transmission scenarios.

An adaptive architecture where the predistorter is placed before the PA, and the error between the desired input and the actual PA output is used to update the predistorter coefficients directly.

• Key Advantage: Theoretically finds the exact inverse of the PA.
• Challenge: Requires the PA model to be identifiable and invertible.
• Process: The error signal is computed in the time domain and fed to an adaptation algorithm that adjusts the predistorter.

A widely used architecture where a postdistorter is first trained to model the inverse of the PA, and its coefficients are then copied to the predistorter.

• Process: The PA output is used as the input to a postdistorter block, which is trained to produce the PA input.
• Advantage: Avoids the need for explicit PA model inversion; the adaptation is a standard system identification problem.
• Assumption: Relies on the commutability of the nonlinear blocks, which holds for memoryless systems but can introduce bias with memory effects.

A theoretical framework for synthesizing a predistorter by cascading a Volterra model of the PA with its exact inverse, truncated to a specific nonlinear order.

• Concept: If a PA is modeled by a Volterra series up to order P, its p-th order inverse can be analytically derived.
• Limitation: The complexity of the inverse grows rapidly with order and memory depth, making it impractical for high-order, wideband systems.
• Usage: Primarily a theoretical benchmark rather than a practical implementation strategy.

The core identification step in the Indirect Learning Architecture where a nonlinear model is fitted to map the PA output signal back to the PA input signal.

• Input: The attenuated and downconverted PA output (y).
• Target: The original PA input (x).
• Algorithm: Standard system identification techniques like Least Squares (LS) or Recursive Least Squares (RLS) are used to find the postdistorter coefficients.
• Result: The coefficient vector defining the inverse nonlinear characteristic.

A control-theoretic approach that synthesizes the predistortion signal by iteratively refining the input waveform over repeated transmissions of the same signal.

• Mechanism: The error from the previous transmission is used to compute a correction to the input signal for the next iteration.
• Benefit: Can achieve perfect linearization without an explicit PA model.
• Constraint: Requires a repetitive signal and a stationary PA characteristic over the iteration period, making it suitable for test and measurement but not dynamic traffic.

The hardware-accelerated process of solving for predistorter coefficients within the strict latency constraints of a live transmission system.

• Hardware: Typically implemented on FPGAs or dedicated DSP cores.
• Algorithms: Uses numerically efficient methods like QR Decomposition (QRD) or optimized RLS variants.
• Pipeline: Involves capturing a data buffer, constructing the basis function matrix, solving the normal equations, and updating the predistorter LUTs or polynomial evaluators in a continuous loop.