LUT AM-PM

The LUT AM-PM stores complex phase rotation factors indexed by instantaneous input envelope magnitude. As the power amplifier's phase shift varies with drive level—particularly near compression—the LUT applies an inverse phase rotation to the baseband signal before the PA. This pre-distortion cancels the AM-PM conversion, preserving the modulation constellation and preventing error vector magnitude (EVM) degradation. Typical GaN Doherty amplifiers exhibit 5-15 degrees of AM-PM distortion that must be corrected across the entire dynamic range.

In practical implementations, the AM-PM LUT is rarely standalone—it forms the imaginary component of a complex-gain LUT architecture. Each table entry stores a single complex value where:

• Magnitude provides AM-AM correction (gain expansion)
• Phase provides AM-PM correction (phase rotation) This unified complex multiplication applies both corrections simultaneously in one operation, minimizing computational latency. The combined correction factor is computed as G_complex = G_AM * e^(j*φ_PM) where G_AM is the amplitude correction and φ_PM is the phase correction.

The AM-PM LUT is addressed using the instantaneous signal envelope magnitude |x(n)|, quantized to a finite number of bins. Key indexing considerations include:

• Uniform spacing: Equal power steps across the dynamic range, simple but inefficient near compression
• Non-uniform spacing: Higher bin density in the gain compression region where AM-PM conversion changes most rapidly
• Address calculation: The quantized magnitude directly maps to a memory address, typically using the upper bits of the digitized envelope for hardware efficiency Typical implementations use 256-1024 entries to balance memory footprint against correction accuracy.

AM-PM LUT coefficients are updated iteratively using gradient-based adaptation algorithms that minimize the phase error between the desired and actual PA output. The LMS (Least Mean Square) algorithm provides simple, low-complexity updates:

• Error signal: Phase difference between input reference and feedback
• Update rule: φ_k(n+1) = φ_k(n) - μ * e_phase(n) * x*(n)
• Step size μ: Controls convergence speed vs. steady-state jitter For faster convergence, RLS (Recursive Least Squares) offers superior tracking at the cost of higher computational complexity, particularly valuable during rapid temperature or bias changes.

Discrete LUT entries introduce quantization error when the input envelope falls between stored indices. Interpolation techniques mitigate this:

• Linear interpolation: Computes weighted average between two adjacent phase values, reducing error by 6-10 dB
• Polynomial interpolation: Uses multiple neighboring entries for higher-order curve fitting
• Cubic spline interpolation: Provides smooth phase transitions with continuous first derivatives Without interpolation, quantization error manifests as spectral regrowth in adjacent channels. Linear interpolation typically adds only 1-2 clock cycles of latency in FPGA implementations while significantly improving ACLR performance.

Power amplifier AM-PM characteristics drift with junction temperature and device aging, requiring continuous LUT adaptation. Key mechanisms include:

• Thermal memory effects: Slow phase drift due to die heating over milliseconds to seconds
• Bias voltage variation: Supply fluctuations alter the PA's operating point and phase response
• GaN trapping effects: Charge trapping in gallium nitride devices causes long-term phase shifts Adaptive LUT architectures track these variations by continuously updating phase coefficients based on the real-time feedback error signal, maintaining linearization performance across environmental and operational changes without requiring recalibration.

A unified table architecture that stores a single complex-valued coefficient per entry to simultaneously correct both amplitude (AM-AM) and phase (AM-PM) distortion. Unlike separate AM-AM and AM-PM tables, the complex-gain approach applies a single complex multiplication to the input signal, inherently handling the interaction between gain expansion and phase rotation. This reduces memory access overhead and simplifies the datapath in FPGA implementations.

The amplitude-to-amplitude correction counterpart that compensates for the power amplifier's nonlinear gain compression curve. While AM-PM corrects phase rotation, AM-AM addresses the magnitude distortion where output power fails to track input power linearly. The two corrections are physically coupled in the PA—gain compression and phase shift both intensify as the transistor approaches saturation—but are often stored in separate LUTs for independent adaptation granularity.

The process of mapping an input signal's instantaneous power or magnitude to a specific memory address within the predistortion look-up table. For AM-PM correction, the index is typically derived from the envelope squared (I² + Q²) to avoid costly square-root operations. The indexing function must cover the full dynamic range of the signal, with careful attention to address overflow at peak power levels to prevent memory access violations.

A mathematical technique for estimating predistortion values between discrete table entries to reduce quantization error and improve linearization accuracy. For AM-PM correction, linear interpolation between adjacent phase values prevents phase discontinuities that would cause spectral regrowth. Higher-order interpolation (e.g., cubic) can further smooth the phase correction surface but increases computational complexity in real-time hardware.

An iterative adaptation algorithm that minimizes the mean squared error between the desired and actual amplifier output to recursively update LUT coefficients. For AM-PM correction, the LMS algorithm computes the phase error from the feedback signal and adjusts only the addressed table entry proportionally to the step size. This gradient-based approach ensures stable convergence of the phase correction values without requiring matrix inversion.

The spacing between adjacent entries in a look-up table, determining the resolution of the predistortion function across the input signal dynamic range. For AM-PM correction, insufficient granularity in regions of rapid phase variation (typically near the amplifier's compression point) leads to stair-step phase errors and residual distortion. Non-uniform spacing allocates higher density where the phase curve is steepest.