Complex-Gain LUT

Unlike dual-table architectures that separate gain and phase correction, a Complex-Gain LUT stores a single complex coefficient (I + jQ) per index. This inherently couples amplitude expansion with phase rotation, matching the physical behavior of power amplifiers where compression and phase shift occur simultaneously. The complex multiplication applies both corrections in one operation, reducing computational latency in the predistortion path.

The LUT is indexed by the instantaneous input signal magnitude (|x(n)|) or squared magnitude (|x(n)|²). A quantizer maps the continuous envelope value to a discrete address. Key design parameters include:

• LUT Granularity: Spacing between adjacent entries
• Addressing Range: Normalized to the signal's peak-to-average ratio
• Non-Uniform Spacing: Higher density in compression regions for improved accuracy

The predistorter applies correction via a single complex multiply: x_pd(n) = x(n) × LUT(|x(n)|). This operation:

• Scales the magnitude to counteract gain compression
• Rotates the phase to cancel AM-PM conversion
• Preserves the original signal's spectral characteristics when properly converged Hardware implementations often use a single complex multiplier in the transmit datapath.

Coefficients are updated using the complex error signal between the desired output and the attenuated PA feedback. Common adaptation algorithms include:

• Complex LMS: Updates each entry proportionally to the conjugate of the error
• Complex RLS: Provides faster convergence at higher computational cost
• Secant-based methods: For direct inverse estimation without explicit model extraction The adaptation rate must balance tracking speed against steady-state noise.

To mitigate LUT quantization error, interpolation between adjacent entries is employed. Common techniques:

• Linear interpolation: Simple, low-latency, sufficient for smooth nonlinearities
• Cubic interpolation: Higher accuracy for rapidly varying gain curves
• Farrow structure: Efficient hardware implementation of polynomial interpolation Interpolation allows smaller LUT sizes while maintaining ACLR performance.

In real-time systems, a Ping-Pong LUT architecture uses two identical memory banks. While one bank actively predistorts the transmit signal, the adaptation engine updates the other in the background. A synchronized switch occurs after convergence, ensuring zero glitching or transient spectral regrowth during coefficient updates. This is critical for live traffic in 5G NR base stations.