LUT Quantization Error

The fundamental error source arising from representing continuous predistortion gain values with a finite number of bits in each LUT entry. Each coefficient is rounded to the nearest representable level, introducing a quantization noise floor that propagates through the transmitter chain.

• Error magnitude: ±0.5 LSB (least significant bit) for ideal rounding
• Spectral impact: Broadband noise floor elevation in adjacent channels
• Bit-width trade-off: Each additional bit improves SNR by approximately 6 dB
• Typical resolution: 10-16 bits for wireless infrastructure applications

Distortion caused by mapping continuous input envelope values to a finite set of discrete table addresses. The spacing between adjacent LUT entries determines how coarsely the nonlinear predistortion curve is sampled.

• Coarse granularity: Misses sharp gain compression transitions near saturation
• Fine granularity: Increases memory footprint and power consumption
• Non-uniform spacing: Concentrates entries in high-compression regions
• Typical table sizes: 64-4096 entries depending on signal bandwidth and PA characteristics

The remaining uncorrected nonlinearity after applying linear or polynomial interpolation between adjacent LUT entries. While interpolation smooths the predistortion response, it cannot perfectly reconstruct the underlying continuous function.

• Linear interpolation: First-order approximation, residual error proportional to second derivative of predistortion curve
• Polynomial interpolation: Higher-order fits reduce error but increase computational latency
• Error concentration: Highest in regions of rapid gain curvature change
• Mitigation: Increased table density in high-curvature regions

The compounding of quantization errors when multiple signal processing stages each introduce discrete amplitude rounding. Errors from LUT coefficient quantization combine with ADC/DAC quantization in the feedback path and digital signal path.

• Error accumulation: RMS sum of uncorrelated quantization noise sources
• Feedback path impact: ADC quantization limits observable error correction accuracy
• DAC resolution: Transmit DAC quantization adds output distortion beyond LUT errors
• System-level budgeting: Total quantization budget must be allocated across all digital stages

The complex interaction between multi-dimensional LUT addressing and quantization error. When memory taps are included, quantization noise from each dimension multiplies through the nonlinear predistortion function, creating cross-term distortion products.

• Dimension scaling: Error grows with number of memory taps
• Coefficient correlation: Quantization errors in adjacent taps can constructively interfere
• Stability concern: Quantization can introduce limit cycles in adaptive loops
• Mitigation: Joint optimization of bit-width across all dimensions

The specific mechanism by which LUT quantization error causes adjacent channel leakage. The quantization noise floor is not purely white—it interacts with the modulated signal to produce nonlinear spectral spreading that degrades ACLR (Adjacent Channel Leakage Ratio).

• Noise shaping: Quantization error spectrum colored by signal statistics
• ACLR degradation: Typically 1-3 dB per bit reduction below optimal
• Critical metric: Regulatory masks require ACLR below -45 dBc for most standards
• Compensation: Dithering techniques can whiten quantization noise spectrum