Non-Uniform LUT

Unlike uniform tables with fixed intervals, non-uniform LUTs employ variable spacing between adjacent entries. The spacing is compressed in the gain compression region near saturation, where the amplifier's AM-AM and AM-PM characteristics change most rapidly. In the linear region, spacing expands to conserve memory. This adaptive resolution ensures that the LUT granularity is proportional to the local derivative of the amplifier's transfer function, minimizing LUT interpolation error without increasing total table size.

The core mechanism is a companding function that maps the uniform input signal envelope to a non-uniform address space. Common implementations include:

• μ-law and A-law companding: Borrowed from telephony, these logarithmic functions densely pack entries at high amplitudes.
• Polynomial-based warping: Custom polynomials fitted to the amplifier's gain curve derivative.
• Piecewise linear segmentation: Dividing the dynamic range into segments with different linear slopes. This mapping is applied before LUT addressing, effectively acting as a pre-distortion of the index itself.

A non-uniform LUT achieves equivalent linearization performance to a much larger uniform table. For example, a 64-entry non-uniform table with μ-law spacing can match the adjacent channel leakage ratio (ACLR) improvement of a 256-entry uniform table. This 4:1 compression ratio directly reduces FPGA block RAM utilization and power consumption. The trade-off is increased complexity in the LUT addressing logic, which must compute the companding function in real-time or use a small secondary mapping table.

When using LMS LUT update algorithms, the adaptation must account for the non-uniform spacing. Standard LMS assumes equal step sizes; applying it directly causes uneven convergence rates. Solutions include:

• Normalized LMS: Scaling the step size inversely proportional to the local entry density.
• Interpolation-aware adaptation: Distributing the error update to multiple neighboring entries based on interpolation weights.
• Virtual uniform adaptation: Performing coefficient updates in a virtual uniform space, then resampling to the non-uniform grid. These techniques ensure stable LUT convergence across all power levels.

Implementing non-uniform LUTs in FPGA-based DPD requires careful pipelining. The companding function can be implemented via:

• Piecewise linear approximation: Using a small number of comparators and multipliers for real-time warping.
• Pre-computed mapping ROM: A small uniform LUT that translates the quantized input magnitude to the non-uniform address.
• CORDIC-based logarithmic conversion: For μ-law implementations, leveraging existing CORDIC hardware. The LUT interpolation block (typically linear or quadratic) must also operate on the non-uniformly spaced entries, requiring the local spacing value as an additional input.

Doherty amplifier optimization particularly benefits from non-uniform LUTs. The Doherty architecture exhibits a sharp gain compression inflection point at the transition from the carrier to peaking amplifier (typically 6 dB back-off). A non-uniform LUT can concentrate entries precisely around this AM-AM and AM-PM discontinuity, while using sparse spacing elsewhere. This targeted resolution is critical for correcting the complex nonlinearity of wideband signal linearization in modern 5G base stations, where Doherty PAs are ubiquitous.

Defines the spacing between adjacent entries across the input signal dynamic range. In a uniform LUT, this spacing is constant, leading to wasted resolution in linear regions and insufficient resolution in compression. Non-uniform granularity reallocates entries to match the amplifier's gain curve derivative, placing more points where the AM-AM and AM-PM characteristics change most rapidly.

The residual nonlinearity that occurs when the true predistortion function falls between stored table entries. Non-uniform LUTs directly target this error source by increasing entry density in high-curvature regions. Key factors affecting interpolation error:

• Linear interpolation between widely-spaced entries in compression zones
• Polynomial interpolation complexity vs. accuracy trade-offs
• Quantization error compounding at the table output

Controls the speed at which table coefficients are updated in response to changing amplifier characteristics. Non-uniform LUTs introduce an additional adaptation consideration: entries in densely-populated regions may converge at different rates than those in sparse regions. The LMS LUT update algorithm must account for variable entry spacing to maintain uniform convergence behavior across the table.

Techniques for reducing total stored coefficients to minimize memory footprint and power consumption. A non-uniform LUT is itself a form of intelligent compression—achieving equivalent or superior linearization accuracy with fewer total entries than a uniform table. Additional compression strategies include:

• LUT partitioning into sub-tables with independent spacing
• Sparse indexing with interpolation between active entries
• Logarithmic spacing for signals with high peak-to-average power ratios

The two fundamental distortion components stored in a predistortion LUT. AM-AM correction compensates for gain compression at high input power, while AM-PM correction addresses input-power-dependent phase shift. Non-uniform LUTs allocate the highest entry density precisely where these curves exhibit their steepest slopes—typically in the gain compression region near the amplifier's 1 dB compression point.