Sample-by-Sample Update

The core mechanism relies on stochastic gradient descent (SGD) applied at the sample level. For each new complex baseband sample pair (input and observed output), the instantaneous gradient of a cost function—typically the squared error magnitude—is computed. The predistorter coefficients are then adjusted by a small step in the negative gradient direction. This eliminates the latency associated with block accumulation, allowing the system to track thermal memory effects and dynamic power supply variations within microseconds.

A critical design tension exists between convergence rate and steady-state misadjustment. A larger step size (learning rate) enables rapid acquisition of the PA's inverse characteristic during abrupt operational changes, such as a sudden carrier frequency hop. However, this amplifies gradient noise, causing the coefficients to jitter around the Wiener optimum. This excess error manifests as residual error vector magnitude (EVM) and incomplete adjacent channel power ratio (ACPR) suppression.

The arithmetic budget per sample is strictly bounded by the system's sampling rate. For a 100 MHz 5G NR carrier, the update must complete within 10 nanoseconds. This mandates highly optimized, low-latency implementations:

• Look-Up Table (LUT) Adaptation: Updating a single LUT entry based on the instantaneous input magnitude.
• Simplified Polynomials: Using a memory polynomial with a very small number of taps.
• LMS Variants: Employing the simplest Least Mean Squares update, avoiding matrix inversions required by Recursive Least Squares (RLS).

Continuous, uncorrelated updates make the system susceptible to coefficient drift in the absence of persistent excitation. If the input signal has a low peak-to-average power ratio (PAPR) for an extended period, the gradient estimates become biased, and coefficients can wander toward unstable regions. Mitigation strategies include Tikhonov regularization (leakage) in the update equation, which gently biases coefficients toward zero, and periodic re-centering based on a more robust, slower background block update loop.

The primary advantage over block update or burst training methods is the ability to track non-stationary distortion in real-time. This is critical for compensating thermal memory effects where the PA's gain and phase shift vary with the instantaneous die temperature. As the envelope power fluctuates, the sample-by-sample update continuously re-linearizes the transmitter, preventing spectral regrowth spikes that occur when a static predistorter lags behind the PA's changing thermal state.

Sample-by-sample updating is the natural execution mode for a closed-loop Direct Learning Architecture (DLA). In DLA, the error is formed directly between the desired ideal signal and the actual PA output. This instantaneous error drives the coefficient update without the intermediate step of training a separate postdistorter as in Indirect Learning Architecture (ILA). The result is a single, unified adaptive loop that directly minimizes the in-band and out-of-band distortion power.