Look-Up Table (LUT) DPD

The core mechanism of LUT DPD is a direct mapping from instantaneous input signal magnitude to a stored complex gain correction factor. The input signal's envelope |x(n)| is quantized into discrete bins, each addressing a unique memory location containing a pre-computed complex multiplication coefficient. This coefficient simultaneously corrects both AM-AM distortion (gain compression) and AM-PM distortion (phase rotation) introduced by the power amplifier. The predistorter multiplies the incoming baseband sample by the retrieved complex value, effectively applying the inverse of the amplifier's static non-linear transfer function before the signal reaches the PA.

LUT DPD is fundamentally designed to address memoryless non-linearity—distortion that depends solely on the current input sample, not on past values. This makes it highly effective for narrowband signals where the PA's bandwidth is much larger than the signal bandwidth, and thermal memory effects are negligible. The technique excels at correcting the classic soft compression curve of Class AB amplifiers and the severe gain inflection points of Doherty power amplifiers operating near saturation. However, as signal bandwidth increases in modern 5G and satellite communications, pure LUT approaches struggle because the PA's output becomes dependent on previous symbols, introducing memory effects that a static table cannot capture.

The performance of LUT DPD is critically dependent on table resolution—the number of discrete amplitude bins. A coarse table with few entries introduces quantization noise and stair-step discontinuities in the predistortion function, generating unwanted intermodulation products. Conversely, an excessively fine table increases memory footprint and adaptation time without proportional linearization gains. Typical implementations use 64 to 1024 entries with non-uniform spacing, where bins are denser in regions of rapid gain variation (near compression points) and sparser in linear regions. Advanced designs employ linear interpolation between adjacent bins to smooth the correction surface and reduce required table depth.

LUT coefficients are populated through an offline or online training process that characterizes the PA's non-linear transfer function. In the indirect learning architecture, a training sequence is transmitted, the PA output is captured and normalized, and the complex gain error at each amplitude bin is computed by comparing the ideal linear output to the actual distorted output. The inverse of this error becomes the stored correction value. Online adaptation continuously updates table entries using a feedback receiver to track changes due to temperature drift, device aging, and antenna load mismatch. The adaptation rate must balance tracking speed against stability—too fast an update can cause oscillation, while too slow fails to compensate for dynamic environmental changes.

LUT DPD offers the lowest computational complexity of any DPD architecture, making it ideal for cost-sensitive and power-constrained applications. The predistortion operation reduces to a single complex multiply per sample after the address calculation. Address generation requires computing the signal magnitude √(I² + Q²), which can be approximated using the CORDIC algorithm or simplified magnitude estimators to avoid expensive square-root operations. Total latency is typically a few clock cycles, enabling use in real-time wideband systems. This efficiency comes at the cost of linearization performance—LUT DPD typically achieves 5-10 dB less ACLR improvement compared to memory polynomial or neural network approaches when applied to wideband signals with significant memory effects.

To address the limitations of one-dimensional amplitude-only indexing, multi-dimensional LUT architectures extend the indexing scheme to include additional signal parameters. A 2D LUT indexes by both instantaneous amplitude and its derivative or by amplitude and a lagging envelope value, capturing first-order memory effects. 3D LUTs add further dimensions such as the amplitude of a delayed sample or the signal's instantaneous frequency. These extensions bridge the gap between pure static LUTs and full behavioral models like the Generalized Memory Polynomial, offering improved linearization for moderate-bandwidth signals while retaining much of the implementation simplicity. The trade-off is exponential growth in table size—a 2D table with 64 bins per dimension requires 4096 entries.

The primary non-linearity that LUT DPD is designed to correct. AM-AM distortion describes the non-linear relationship between the input signal's instantaneous amplitude and the output signal's amplitude, manifesting as gain compression at high power levels.

• LUTs store complex gain values that are the exact inverse of the measured AM-AM curve.
• Correction is purely amplitude-dependent, ignoring phase dynamics.
• Effective only for memoryless or quasi-memoryless power amplifiers.

The phase-domain counterpart to AM-AM distortion. AM-PM distortion occurs when the phase shift introduced by the power amplifier varies as a function of the instantaneous input amplitude.

• A standard LUT addresses this by storing complex-valued correction coefficients (I and Q) rather than scalar gains.
• The LUT simultaneously corrects amplitude compression and phase rotation at each index point.
• Severe AM-PM conversion often indicates the presence of memory effects, which a static LUT cannot fully compensate.

The fundamental limitation of static LUT-based DPD. Memory effects refer to the dependence of a power amplifier's current output on past input values, caused by:

• Thermal dynamics: Transistor junction temperature changes with signal history.
• Bias network impedance: Low-frequency envelope currents modulate the supply.
• Trapping effects: Charge capture and release in semiconductor materials.

A pure LUT has no mechanism to model these temporal dependencies, leading to residual distortion in wideband signals where memory effects dominate.

The process of dynamically updating LUT entries to track time-varying amplifier behavior. Without adaptation, a static LUT becomes inaccurate due to:

• Temperature drift during operation.
• Aging of the transistor over its lifecycle.
• Load mismatch from antenna impedance changes.

Adaptation typically uses a least mean squares (LMS) or recursive least squares (RLS) algorithm to update individual LUT bins based on the error between the desired and observed output.

The successor model that addresses LUT limitations. The GMP extends the basic memory polynomial by including cross-terms between the signal and its lagging or leading envelope values.

• Captures complex memory effects that a static LUT cannot.
• Serves as the baseline behavioral model against which neural network DPD is benchmarked.
• Represents the transition from memoryless LUT correction to full Volterra series-based dynamic linearization.

A common identification method used to populate LUT coefficients. In ILA, the predistorter parameters are estimated by:

1. Swapping the input and output of the power amplifier model.
2. Training a post-distorter that, when placed after the PA, produces a linear output.
3. Copying the post-distorter coefficients directly into the predistorter LUT.

This avoids the need to compute a direct inverse model, but assumes commutability that fails when significant memory effects are present.