LUT Smoothing

LUT smoothing removes abrupt jumps between adjacent table entries that arise from independent coefficient adaptation. Without smoothing, these discontinuities introduce high-frequency spectral components that cause adjacent channel leakage. The smoothing filter enforces a continuity constraint across the predistortion function, ensuring that neighboring entries transition smoothly. This is particularly critical in high-granularity LUTs where independent adaptation noise creates microscopic stair-step artifacts in the correction curve.

Discontinuous LUT entries act as impulse-like distortion sources that generate spectral regrowth into adjacent channels. Smoothing applies a low-pass filtering effect across the table index dimension, attenuating high-frequency coefficient variations that would otherwise modulate the transmitted signal. The result is improved Adjacent Channel Leakage Ratio (ACLR) without requiring additional linearization bandwidth. Typical implementations achieve 3-5 dB ACLR improvement by eliminating adaptation-induced coefficient noise.

The simplest and most common smoothing technique applies a sliding window average across adjacent LUT entries:

• Window size: Typically 3-7 entries, balancing noise reduction against distortion correction accuracy
• Uniform weighting: Equal weights for all entries within the window
• Implementation: Convolution of the LUT coefficient vector with a rectangular kernel
• Computational cost: Minimal, requiring only addition and division operations per entry

This method effectively removes zero-mean adaptation noise while preserving the underlying predistortion function shape.

Advanced smoothing employs local polynomial regression to fit a smooth curve through noisy LUT entries:

• Linear interpolation: First-order polynomial fit between adjacent entries, eliminating step discontinuities
• Savitzky-Golay filtering: Least-squares polynomial fit within a sliding window, preserving higher-order features
• Spline interpolation: Cubic or higher-order splines ensure C² continuity across the entire table
• Adaptive order selection: Higher polynomial orders in gain compression regions where the predistortion curve changes rapidly

This approach preserves intentional nonlinear correction while removing stochastic adaptation artifacts.

Smoothing intensity must adapt to operating conditions to balance noise suppression against correction fidelity:

• High SNR conditions: Lighter smoothing preserves fine predistortion detail when adaptation noise is minimal
• Low SNR conditions: Stronger smoothing prevents noise amplification during poor feedback quality
• Convergence-dependent: Maximum smoothing during initial adaptation, gradually reduced as the LUT converges
• Region-dependent: Stronger smoothing in low-probability amplitude regions where sparse updates create noisy estimates

Adaptive smoothing prevents over-smoothing that would degrade linearization performance in well-trained table regions.

Real-time LUT smoothing in FPGA or ASIC implementations requires careful architectural design:

• Ping-pong buffering: Smoothing operates on the inactive buffer while the active buffer performs predistortion
• Pipeline stages: Multi-cycle smoothing operations pipelined to maintain throughput at sample rates exceeding 491.52 MHz for 5G NR
• Memory bandwidth: Smoothing reads multiple adjacent entries simultaneously, requiring multi-port memory or caching
• Fixed-point precision: Smoothing arithmetic must preserve coefficient accuracy while preventing overflow in accumulation stages

Efficient hardware smoothing typically adds less than 2% additional logic resources to the overall DPD implementation.

A mathematical technique for estimating predistortion values between discrete table entries to reduce quantization error. While LUT smoothing operates across adjacent coefficients to remove adaptation noise, interpolation operates within a single index interval to calculate the exact correction value for an input that falls between two stored entries.

• Linear interpolation connects two adjacent points with a straight line
• Polynomial interpolation uses higher-order curves for smoother transitions
• Cubic spline interpolation minimizes curvature discontinuities

Without interpolation, the predistorter output exhibits stair-step discontinuities that generate spectral regrowth. Combined with smoothing, interpolation ensures both intra-entry and inter-entry continuity.

The distortion introduced by representing continuous predistortion functions with a finite number of discrete amplitude levels. Quantization error manifests as granular noise in the correction signal, creating a noise floor that limits achievable adjacent channel leakage ratio (ACLR).

• Amplitude quantization affects coefficient precision (typically 10-16 bits)
• Index quantization determines how finely the input envelope is divided
• Combined effect produces both in-band EVM degradation and out-of-band spectral regrowth

LUT smoothing directly mitigates the index quantization component by blending adjacent entries, effectively increasing the perceived resolution without increasing memory. This is critical for low-cost FPGA implementations where memory resources are constrained.

The speed at which look-up table coefficients are updated, controlling the trade-off between tracking agility and steady-state noise. A high adaptation rate enables rapid tracking of thermal memory effects and supply voltage variations, but introduces coefficient jitter that appears as phase noise.

• Fast adaptation (μ > 0.1): Tracks rapid envelope changes, high residual noise
• Slow adaptation (μ < 0.01): Low steady-state noise, poor transient tracking
• Variable step-size: Adapts μ based on error signal magnitude

LUT smoothing acts as a low-pass filter on the adaptation process, allowing designers to use faster adaptation rates for tracking while filtering out the resulting high-frequency coefficient noise before it reaches the predistorter output.

The spacing between adjacent entries in a look-up table, determining the resolution of the predistortion function across the input signal dynamic range. Uniform granularity allocates equal spacing across the entire range, while non-uniform granularity concentrates entries in regions of rapid gain compression.

• Coarse granularity (64-128 entries): Low memory, high interpolation error
• Fine granularity (512-1024 entries): High accuracy, increased power consumption
• Optimal granularity balances ACLR requirements against hardware constraints

LUT smoothing effectively increases the perceived granularity by blending adjacent entries, enabling equivalent performance with fewer physical table entries. This is particularly valuable in massive MIMO systems where hundreds of predistorters must operate simultaneously.

The comprehensive approach to reducing adjacent channel leakage and improving ACLR through linearization techniques. Spectral regrowth occurs when nonlinear amplification spreads signal energy into adjacent frequency bands, violating regulatory emission masks defined by 3GPP and FCC standards.

• ACLR targets: Typically -45 dBc for 5G NR base stations
• Regrowth mechanisms: AM-AM compression, AM-PM conversion, memory effects
• Mitigation hierarchy: Crest factor reduction → DPD → LUT smoothing → filtering

LUT smoothing addresses the discontinuity-induced regrowth component that persists even after conventional DPD. Abrupt transitions between adjacent LUT entries create broadband spectral artifacts that smoothing eliminates through coefficient averaging.

The state where iterative adaptation algorithms have minimized the error signal to a stable residual level, indicating the look-up table accurately models the inverse amplifier nonlinearity. Convergence time is a critical specification for systems that must rapidly re-linearize after channel switching or temperature changes.

• LMS convergence: Typically 100-1000 iterations depending on step size
• RLS convergence: Faster (10-50 iterations) but higher computational cost
• Convergence criteria: Error vector magnitude (EVM) below threshold for N consecutive iterations

LUT smoothing is applied post-convergence as a final cleanup stage. It removes the small-amplitude coefficient oscillations that persist around the converged values, preventing these residual fluctuations from modulating the transmitted signal and generating close-in phase noise.