LUT Interpolation Error

The spacing between adjacent table entries directly limits correction accuracy. Coarse granularity increases interpolation error, especially in regions of high AM-AM curvature near compression. Error scales approximately with the square of the spacing for linear interpolation.

• Sparse tables: Smaller memory footprint but higher residual distortion
• Dense tables: Better accuracy at the cost of increased FPGA BRAM utilization
• Non-uniform spacing: Concentrates entries in high-gradient regions to optimize the accuracy-memory trade-off

The mathematical complexity of the interpolation function determines how well it approximates the true predistortion curve between stored points.

• Nearest-neighbor: Zero-order hold introduces significant quantization error and spectral artifacts
• Linear interpolation: First-order approximation; error is proportional to the second derivative of the predistortion function
• Polynomial (cubic/Lagrange): Higher-order fits reduce error in smooth regions but can introduce Runge's phenomenon oscillations near discontinuities
• Spline interpolation: Minimizes curvature discontinuities at table boundaries

Wideband signals expose the limitations of memoryless LUT architectures. When the signal bandwidth exceeds the amplifier's memory effect time constant, the instantaneous envelope alone cannot capture the full nonlinear dynamics.

• Narrowband signals: Memoryless LUT with interpolation is often sufficient
• Wideband 5G signals: Require multi-dimensional LUTs with memory taps; interpolation error compounds across dimensions
• Memory depth mismatch: Using insufficient memory taps causes interpolation to fit the wrong underlying function, increasing out-of-band emissions

The intrinsic nonlinearity shape of the power amplifier determines interpolation difficulty. Sharp gain compression knees and rapid phase expansion regions create high second-derivative zones where linear interpolation fails.

• Soft compression: Gradual curvature is well-approximated by linear interpolation
• Hard clipping / Doherty combining: Abrupt transitions require dense table spacing or higher-order interpolation
• GaN vs. LDMOS: Different semiconductor technologies exhibit distinct curvature profiles affecting interpolation error distribution across the input power range

In adaptive LUT systems, interpolation error is not purely static. Real-time coefficient updates introduce stochastic jitter that interacts with the interpolation process.

• LMS step size trade-off: Large step sizes accelerate convergence but inject noise that interpolation can amplify
• Gradient misalignment: Noisy coefficient estimates cause the interpolated surface to fluctuate, creating time-varying residual distortion
• Ping-pong buffer switching: Transitions between active and update tables can cause momentary interpolation discontinuities if not synchronized with the signal envelope

Finite word-length effects in hardware implementation introduce quantization error at multiple stages: input envelope quantization, coefficient storage precision, and interpolation arithmetic rounding.

• Envelope quantization: Coarse ADC resolution for the indexing signal misaligns the lookup address
• Coefficient bit-depth: Insufficient fixed-point precision for stored complex gains introduces granular noise
• Interpolator rounding: Truncation in multiply-accumulate operations creates limit cycles and spurious tones
• Error floor: Combined quantization effects set a hard lower bound on achievable linearization performance independent of table size

The mathematical technique used to estimate predistortion values between discrete table entries. Linear interpolation calculates a weighted average of the two nearest stored coefficients, while higher-order polynomial interpolation fits a curve through multiple adjacent points. The choice of interpolation method directly determines the magnitude of the interpolation error—the residual distortion remaining after correction. Linear interpolation is computationally efficient but introduces larger errors in regions of high amplifier nonlinearity, whereas cubic spline interpolation reduces error at the cost of increased computational complexity.

The spacing between adjacent entries in a look-up table, defining the resolution of the predistortion function. Finer granularity reduces interpolation error by storing more coefficients, but increases memory requirements and power consumption. Key trade-offs include:

• Coarse granularity: Lower memory footprint, higher interpolation error, potential spectral regrowth
• Fine granularity: Reduced error, improved ACLR, larger silicon area
• Non-uniform spacing: Concentrates entries in high-compression regions where the amplifier gain curve changes most rapidly

The distortion introduced by representing continuous predistortion functions with a finite number of discrete amplitude levels within each table entry. This error compounds with interpolation error to form the total residual nonlinearity. Quantization error is determined by the bit-width of stored coefficients—typical implementations use 12-16 bits for the complex gain values. Insufficient bit depth creates staircase artifacts in the correction signal, generating unwanted spectral components that degrade adjacent channel leakage ratio performance.

A post-processing filter applied across adjacent look-up table entries to remove adaptation noise and prevent discontinuous coefficient transitions. Smoothing directly addresses interpolation error by ensuring that the stored function is inherently continuous and differentiable. Common techniques include:

• Moving average filtering across neighboring entries
• Polynomial curve fitting to enforce smoothness constraints
• Regularization during adaptation to penalize abrupt coefficient changes Without smoothing, even accurate individual entries can produce large interpolation errors when the underlying function contains sharp discontinuities.

A look-up table with variable spacing between entries, allocating higher density in regions of rapid amplifier gain compression. This architecture directly minimizes interpolation error by concentrating computational resources where the predistortion function exhibits the highest curvature. In the linear region of the power amplifier, entries can be widely spaced with negligible error. In the compression region near saturation, dense spacing captures the sharp gain roll-off. Non-uniform addressing logic uses a companding function to map input envelope values to memory addresses, optimizing error distribution across the entire dynamic range.

The number of sequential historical signal samples used in conjunction with the instantaneous index to address a multi-dimensional predistortion look-up table. Memory effects in power amplifiers—caused by thermal dynamics, bias circuit time constants, and charge trapping—mean that the optimal predistortion coefficient depends on past signal values as well as the present envelope. Multi-dimensional LUTs reduce interpolation error by capturing these memory-dependent nonlinearities, but exponentially increase storage requirements. A 2D LUT with depth-2 memory and 256 envelope bins requires 65,536 stored coefficients.