LUT Indexing

The most fundamental indexing method where the instantaneous envelope magnitude |x(n)| of the complex baseband input signal is computed and quantized to form the memory address. This scalar index maps directly to a single-entry complex-gain correction factor. The address calculation is typically Address = floor(|x(n)| / Step_Size), creating a one-dimensional table that corrects static AM-AM and AM-PM distortion but ignores memory effects.

Uses the instantaneous input power |x(n)|² rather than magnitude to generate the table address. This provides a non-uniform spacing in terms of magnitude, naturally allocating higher resolution in the compression region where the amplifier's gain curve changes most rapidly. Power indexing is computationally efficient as it avoids a square-root operation and better matches the physical origin of nonlinearity in semiconductor junctions.

Extends the address space to include delayed signal samples to compensate for memory effects. A 2D LUT uses the current magnitude |x(n)| and a previous magnitude |x(n-1)| as row and column indices. This creates an N×N matrix of coefficients that captures first-order memory. Higher-dimensional indexing with additional taps increases correction fidelity but causes exponential growth in memory requirements, often mitigated by LUT partitioning or sparse interpolation.

Uniform indexing divides the input dynamic range into equal-amplitude steps, simplifying hardware addressing but wasting resolution in linear regions. Non-uniform indexing uses variable step sizes—typically derived from a companding function like μ-law or a signal-dependent PDF—to concentrate entries where the amplifier's gain derivative is steepest. This optimizes correction accuracy for a fixed table size and is essential for signals with high peak-to-average power ratios.

Hardware indexing logic must handle signals exceeding the LUT's designed dynamic range. Saturation logic clamps the address to the maximum valid index when the input envelope exceeds the table's upper bound, preventing memory access violations. Underflow near zero magnitude is typically handled by forcing the lowest address. Proper normalization of the input signal to match the table's span is critical to avoid clipping-induced spectral regrowth.

When LUT interpolation is employed, the indexing logic must output not only the base address but also the fractional offset between adjacent entries. For linear interpolation, the indexer computes Address_Base = floor(Normalized_Input) and Fraction = Normalized_Input - Address_Base. The predistorter then reads coefficients at Address_Base and Address_Base+1, blending them using the fraction. This dramatically reduces quantization error without increasing table size.

The hardware logic that calculates the memory address for a look-up table entry based on the quantized input signal magnitude and optional memory tap indices. The addressing scheme directly determines access latency and hardware complexity.

• Maps instantaneous envelope power to a binary address
• Incorporates memory depth taps for multi-dimensional tables
• Must handle overflow conditions when signal exceeds normalized range
• Typically implemented via simple bit-shifting of the magnitude word

The process of scaling the input signal envelope to match the predefined dynamic range of the look-up table indexing scheme. Proper normalization prevents address overflow and ensures the full table depth is utilized.

• Scales instantaneous power to fit within [0, 1] or fixed-point equivalent
• Prevents clipping of high-power samples at maximum address
• Ensures low-power signals don't waste addressable range
• Normalization factor must track average power variations in adaptive systems

The spacing between adjacent entries in a look-up table, determining the resolution of the predistortion function across the input signal dynamic range. Finer granularity improves correction accuracy at the cost of increased memory.

• Uniform spacing: equal step size across all power levels
• Non-uniform spacing: higher density in compression regions
• Trade-off: 256 entries may achieve -50 dBc ACLR; 512 entries may reach -55 dBc
• Granularity directly impacts quantization error magnitude

A look-up table with variable spacing between entries, allocating higher density in regions of rapid amplifier gain compression to optimize correction accuracy. This approach maximizes linearization performance for a given memory budget.

• Dense spacing near 1 dB compression point where nonlinearity accelerates
• Coarse spacing in linear region where correction is minimal
• Requires companding function to map uniform input to non-uniform addresses
• Reduces total entries by 30-50% versus uniform table for equivalent ACLR

The number of sequential historical signal samples used in conjunction with the instantaneous index to address a multi-dimensional predistortion look-up table. Memory depth captures the power amplifier's long-term memory effects caused by thermal and bias network dynamics.

• 1D table: instantaneous envelope only (memoryless correction)
• 2D table: current sample + one delayed sample
• 3D table: addresses short-term thermal memory and electrical memory
• Total addresses = (envelope bins) × (memory depth dimensions)
• Typical depth of 2-3 taps for GaN Doherty amplifiers

The distortion introduced by representing continuous predistortion functions with a finite number of discrete amplitude levels within the look-up table. Quantization error manifests as residual nonlinearity and elevated spectral regrowth.

• Amplitude quantization: finite bit-width of stored coefficients (typically 12-16 bits)
• Address quantization: finite number of table entries (envelope resolution)
• Error floor typically 5-10 dB below the uncorrected distortion
• Mitigated by LUT interpolation between adjacent entries