LUT Interpolation

Interpolation directly mitigates LUT Quantization Error by generating intermediate values between coarsely spaced table entries. Without interpolation, the predistorter approximates the continuous inverse nonlinearity with a staircase function, producing spectral regrowth and residual distortion. Linear interpolation reduces this error proportionally to the square of the LUT Granularity, while higher-order polynomial interpolation achieves even greater suppression of out-of-band emissions.

The most common hardware-friendly method computes a correction value as a weighted average of two adjacent Complex-Gain LUT entries. Given an input envelope value falling between index k and k+1, the interpolated coefficient is: LUT[k] + α(LUT[k+1] - LUT[k]), where α is the fractional offset. This requires one real multiplier and two adders per I/Q path, making it ideal for FPGA-Based DPD Implementation with minimal resource overhead.

Higher-order interpolation uses multiple neighboring table entries to fit a polynomial curve through the stored coefficients. Common approaches include:

• Quadratic interpolation: Uses 3 adjacent points for parabolic fitting
• Cubic spline interpolation: Ensures continuous first and second derivatives across segment boundaries
• Lagrange interpolation: Provides exact fit through all selected points These methods reduce LUT Interpolation Error more aggressively than linear techniques but increase computational latency and DSP block consumption.

LUT Interpolation Error represents the residual nonlinearity after estimation and is bounded by the second derivative of the predistortion function. The error magnitude scales with the square of the LUT Step Size for linear interpolation and with the cube for quadratic methods. In Wideband Signal Linearization, where the predistortion function exhibits rapid variation due to Thermal Memory Effect Compensation, insufficient interpolation order manifests as elevated Adjacent Channel Leakage Ratio (ACLR).

Interpolation introduces a fundamental design trade-off between LUT Granularity and computational complexity:

• Fine granularity + no interpolation: Larger memory footprint, simpler addressing logic
• Coarse granularity + linear interpolation: Reduced memory, minimal latency increase
• Coarse granularity + cubic interpolation: Smallest memory, highest DSP utilization For mmWave Digital Predistortion with multi-GHz bandwidths, linear interpolation with optimized Non-Uniform LUT spacing often provides the optimal balance of ACLR performance and power consumption.

Interpolation operates on coefficients produced by LMS LUT Update or other Coefficient Estimation Algorithms. During Online Training Algorithms, interpolation smooths the effective predistortion surface, preventing abrupt transitions that cause LUT Gain Compression discontinuities. However, interpolation can mask individual entry errors during LUT Training, potentially slowing LUT Convergence if the adaptation algorithm cannot distinguish between interpolation artifacts and true coefficient misalignment.

The fundamental distortion floor caused by representing a continuous predistortion function with a finite number of discrete amplitude levels. Quantization error manifests as spectral regrowth and an elevated noise floor, directly limiting the achievable Adjacent Channel Leakage Ratio (ACLR).

• Arises from the finite bit-depth of stored coefficients
• Reduced by increasing LUT word length (e.g., from 12-bit to 16-bit)
• Interacts with interpolation error to define total linearization accuracy

The spacing between adjacent entries in a look-up table, determining the resolution of the predistortion function across the input signal dynamic range. Coarse granularity increases interpolation error, while fine granularity consumes more memory.

• Uniform spacing: equal step size across all power levels
• Non-uniform spacing: higher density in gain compression regions
• Trade-off: memory footprint vs. correction accuracy

The simplest interpolation method that estimates intermediate predistortion values by drawing a straight line between two adjacent LUT entries. Computationally efficient but introduces linear interpolation error in regions of high amplifier nonlinearity.

• Requires only one multiply-add operation per dimension
• Assumes linear behavior between stored points
• Inadequate for wideband signals with strong memory effects

A higher-order estimation technique that fits a polynomial curve through multiple adjacent LUT entries to approximate the predistortion function. Polynomial interpolation significantly reduces residual error in highly nonlinear amplifier regions.

• Lagrange interpolation: exact fit through N+1 points
• Cubic spline: smooth piecewise polynomials with continuous derivatives
• Higher computational cost but superior ACLR improvement

A post-processing filter applied across adjacent look-up table entries to remove adaptation noise and prevent spectral regrowth caused by discontinuous coefficient transitions. Smoothing ensures the predistortion function is continuous and differentiable.

• Moving average filters reduce random coefficient jitter
• Low-pass filtering prevents high-frequency distortion artifacts
• Critical after online adaptation before coefficients go live

A look-up table architecture with variable spacing between entries, allocating higher density in regions of rapid amplifier gain compression to optimize correction accuracy. This approach minimizes interpolation error without increasing total memory.

• Companding: logarithmic or mu-law spacing mimics amplifier characteristics
• Adaptive partitioning: entry density tracks the derivative of the AM-AM curve
• Reduces interpolation error by up to 6 dB compared to uniform spacing