Loop Delay Estimation

Loop delay consists of two components that must be resolved independently:

• Integer Delay: Coarse alignment at the sample level, caused by DAC/ADC pipelines, digital filtering, and physical trace lengths
• Fractional Delay: Sub-sample misalignment from analog group delay variations and non-ideal clock synchronization

Integer estimation typically uses cross-correlation peak detection, while fractional alignment requires Farrow structure interpolators or frequency-domain phase slope estimation to achieve sub-sample precision.

The most widely used integer delay estimation technique computes the cross-correlation between the transmitted baseband waveform and the observed feedback signal:

• Peak location of the correlation sequence directly indicates the sample delay
• Robust to moderate noise and nonlinear distortion when the DPD is inactive
• Computationally efficient via FFT-based fast correlation

For wideband mmWave signals, correlation must account for frequency-dependent group delay that can smear the correlation peak and reduce estimation accuracy.

Fractional delay manifests as a linear phase rotation in the frequency domain. Estimation proceeds by:

• Computing the cross-spectrum between reference and feedback signals
• Extracting the phase slope across the signal bandwidth
• Converting the slope to a time delay via Δt = Δφ / (2π · Δf)

This method provides sub-sample resolution without interpolation and is particularly effective for wideband signals where the phase slope is well-defined across many frequency bins.

Initial coarse estimation may leave residual misalignment that degrades DPD linearization. Iterative refinement addresses this:

• Indirect Learning Architecture (ILA) naturally tolerates small delay errors during initial training
• Post-training, the modeled error signal can be cross-correlated with the reference to detect residual skew
• Successive refinement loops converge to sub-sample alignment

This approach is essential in mmWave phased arrays where beam-steering changes the effective electrical path length dynamically.

Modern RFSoC platforms provide built-in mechanisms for loop delay calibration:

• Zynq UltraScale+ RFSoC includes deterministic latency measurement between DAC and ADC paths
• On-chip triggered capture buffers allow simultaneous snapshot of transmit and observe paths
• Hardware timestamps eliminate software-induced jitter from the measurement

These features reduce calibration time from seconds to microseconds, enabling per-packet DPD re-training in burst-mode communication systems.

Loop delay is not static—it drifts with environmental and operational changes:

• Temperature variation: Analog group delay in filters and amplifiers shifts with junction temperature, altering fractional delay by picoseconds to nanoseconds
• PA supply voltage sag: Changes the amplifier's phase response under envelope tracking
• Beam index changes: In phased arrays, each beam direction presents a different effective path length

Robust systems implement periodic re-estimation or delay tracking loops to maintain alignment during continuous operation.

A digital interpolation filter that provides sub-sample time alignment to synchronize the reference and feedback paths. The Farrow structure is the most common implementation, using polynomial-based interpolation to realize a continuously variable delay. Without this, integer-sample alignment leaves a residual timing error that degrades linearization performance, particularly for wideband signals where a fraction of a sample period represents a significant phase error.

A DPD training method that identifies the predistorter by placing it after the power amplifier model in the estimation loop. The ILA avoids the need to compute an explicit inverse model of the PA. However, its accuracy is highly sensitive to loop delay estimation errors; any misalignment between the post-distorter input and the PA output introduces bias into the coefficient extraction, especially in the presence of measurement noise.

An iterative DPD training method that minimizes the error between the desired linear output and the actual PA output. DLA explicitly models the PA characteristic and computes its inverse. This architecture requires precise loop delay alignment because the error signal used for coefficient updates is formed by comparing time-aligned samples. A misalignment of even one sample can cause the iterative solver to diverge or converge to a suboptimal solution.

The robustness of coefficient extraction against ill-conditioned matrices. In the context of loop delay estimation, a poorly aligned feedback signal introduces phase dispersion across the signal bandwidth, which in turn increases the condition number of the autocorrelation matrix used in least-squares estimation. Techniques like ridge regression or Tikhonov regularization are often required to stabilize the solution when residual timing errors cannot be fully eliminated.

The most common method for integer-sample loop delay estimation. It computes the cross-correlation between the transmitted reference and the observed feedback signal. The lag index corresponding to the peak correlation value gives the coarse delay. This technique is robust to nonlinear distortion because the linear component of the signal dominates the correlation peak, but its resolution is limited to one sample period.

An architecture that digitizes the RF signal directly at the carrier frequency using high-speed ADCs, eliminating analog down-conversion stages. This approach simplifies loop delay estimation by removing the variable group delay of analog mixers and filters. In RFSoC platforms, the deterministic latency between the DAC and ADC paths makes the loop delay largely a static, calibratable parameter rather than a dynamic unknown.