Temperature-Compensated LUT

Unlike a standard 1-D or 2-D LUT that maps only instantaneous amplitude or amplitude and envelope derivative, a temperature-compensated LUT adds a third dimension: the device's thermal state.

• Indexing variables typically include |x(n)|, |x(n-1)|, and a quantized junction temperature estimate
• The thermal dimension captures the slow-varying quiescent bias shift caused by self-heating
• This structure directly addresses the fact that a PA's AM-AM and AM-PM curves are not static but drift with thermal impedance dynamics

The accuracy of the compensation depends entirely on the quality of the thermal state variable fed into the LUT indexer. Direct junction measurement is rarely practical, so estimation techniques are employed.

• Direct sensing: On-die temperature diodes or thermistors provide a voltage proportional to junction temperature
• Model-based estimation: A real-time thermal convolution of the transmit power envelope with a pre-characterized Foster or Cauer thermal model predicts junction temperature
• Power integration: A simple moving average of |x(n)|^2 approximates the low-pass filtered thermal response for narrowband signals

Populating a 3-D LUT through direct measurement at every temperature bin is impractical. Instead, interpolation and adaptive update mechanisms are critical.

• Multi-linear interpolation between adjacent temperature and amplitude bins smooths the correction surface
• Selective bin update: Only the LUT entries corresponding to the current operating region (amplitude and temperature) are updated via LMS or RLS algorithms
• Thermal tracking loops slowly adjust coefficients in the background, decoupled from the fast amplitude-dependent adaptation, to track ambient temperature drift and aging

The primary engineering trade-off is between LUT size and compensation accuracy. Adding a thermal dimension exponentially increases storage requirements.

• A 128-amplitude × 8-temperature bin LUT requires 1024 complex coefficients, manageable in modern FPGA BRAM
• Non-uniform quantization allocates more bins to the temperature range where the PA's characteristics change most rapidly (e.g., near quiescent bias threshold shifts)
• Compression techniques such as polynomial fitting within temperature segments can reduce storage at the cost of interpolation logic complexity

A key benefit of temperature-compensated LUTs is their ability to correct thermal-induced spectral asymmetry, which memoryless or purely electrical-memory models cannot address.

• Thermal memory creates a dispersive phase response that skews the upper and lower sidebands differently
• By indexing phase correction coefficients against the thermal state, the LUT can apply asymmetric phase pre-distortion
• This directly improves ACLR in the adjacent channels, particularly for signals with high peak-to-average power ratios that induce significant self-heating cycles

Temperature-compensated LUTs are especially critical for Gallium Nitride (GaN) power amplifiers, where thermal effects are tightly coupled with charge trapping phenomena.

• GaN current collapse (trapping) is thermally activated, creating a slow-memory effect that modulates gain as a function of both temperature and bias history
• A temperature-indexed LUT can jointly compensate for the thermal AM-AM distortion and the trap-related gain sag
• The thermal time constants in GaN-on-SiC devices (typically 100 µs to 10 ms) align well with the update rates achievable in FPGA-based LUT adaptation engines