Look-Up Table Model

LUT models operate on instantaneous input envelope only, mapping the current signal magnitude to a complex gain value. The table is indexed by quantized amplitude or power:

• Indexing parameter: |x(n)| or |x(n)|²
• Stored value: Complex gain G(|x|) = AM-AM + j·AM-PM correction
• Output generation: y(n) = x(n) · LUT[|x(n)|]

This single-dimensional lookup eliminates all multiply-accumulate operations beyond the final complex multiplication, achieving single-cycle throughput in hardware implementations.

The fundamental limitation of basic LUT models is the absence of memory effects. The output depends solely on the current input sample:

• Cannot capture thermal memory (sub-millisecond to second timescales)
• Cannot model electrical memory from bias networks and matching circuits
• Cannot represent trapping effects in GaN HEMT devices

This makes pure LUT models suitable only for narrowband signals where the signal bandwidth is much smaller than the amplifier's memory bandwidth. For wideband 5G signals, memory effects become dominant and degrade LUT linearization performance.

LUT performance is governed by amplitude quantization granularity. The input envelope range is divided into discrete bins:

• Uniform spacing: Equal-width bins across the amplitude range
• Non-uniform spacing: Higher density in nonlinear regions (compression zone)
• Typical table sizes: 64–1024 entries for practical implementations
• Interpolation: Linear or cubic interpolation between entries reduces quantization error

Quantization noise from insufficient table resolution manifests as residual spectral regrowth. The optimal table size balances linearization accuracy against memory footprint in FPGA BRAM or ASIC register files.

LUT coefficients must adapt to track PA characteristic drift due to temperature, aging, and frequency changes. Common adaptation approaches include:

• Direct learning: Compare PA output to desired signal, update LUT via LMS gradient descent
• Indirect learning: Identify post-distorter coefficients, copy to predistorter LUT
• Linear interpolation update: Modify only adjacent table entries to maintain smoothness
• Bulk table reload: Complete table replacement during idle slots or guard intervals

Adaptation convergence speed must exceed the rate of PA characteristic change. Temperature-compensated LUTs store multiple tables indexed by measured junction temperature.

Two fundamental LUT mapping strategies exist for predistortion:

Complex Gain LUT:

• Stores single complex gain value per amplitude bin
• Output: x_pd(n) = x(n) · G(|x(n)|)
• Compact storage, single complex multiply

I/Q Mapping LUT:

• Stores separate I and Q predistortion values per amplitude bin
• Output: x_pd(n) = LUT_I[|x|] + j·LUT_Q[|x|]
• Direct mapping, no multiplication required

The complex gain approach dominates modern implementations due to its compatibility with Cartesian transmitter architectures and simpler adaptation mathematics.

To overcome the memoryless limitation, multidimensional LUTs incorporate additional indexing dimensions:

• 2D LUT: Indexed by |x(n)| and |x(n-1)| to capture first-order memory
• Envelope derivative LUT: Indexed by |x(n)| and d|x|/dt for thermal tracking
• Frequency-indexed LUT: Separate tables for different carrier frequencies
• Power-indexed LUT: Tables indexed by average power level for envelope tracking systems

These extensions bridge the gap between pure LUT simplicity and memory polynomial accuracy, though at the cost of exponentially growing storage requirements with each added dimension.