Time Alignment

Time alignment must achieve fractional sample accuracy—often on the order of picoseconds for wideband signals. Integer-sample alignment is insufficient because a misalignment of even 0.1 samples introduces a frequency-dependent phase error that masquerades as memory effect, corrupting the extracted model coefficients.

• Achieved through Farrow interpolators or polyphase filter banks
• Typical requirements: alignment to within 1/64th to 1/256th of a sample period
• Residual timing jitter directly degrades Adjacent Channel Leakage Ratio (ACLR) after linearization

The most common alignment technique computes the cross-correlation between the reference and feedback signals. The lag index corresponding to the peak correlation value provides an integer-sample delay estimate.

• Works robustly even with nonlinear distortion present in the feedback signal
• Parabolic or sinc interpolation around the correlation peak refines the estimate to sub-sample precision
• Computationally efficient when implemented via Fast Fourier Transform (FFT) using the cross-correlation theorem

The loop delay encompasses the total propagation latency through the digital-to-analog converter, modulator, power amplifier, coupler, demodulator, and analog-to-digital converter. This delay must be measured and compensated before model extraction.

• Can span hundreds to thousands of sample periods in wideband systems
• Temperature variations cause delay drift that requires periodic re-estimation
• Separate from phase offset, which must be corrected independently after time alignment

For high-precision applications, a two-stage process is employed: coarse alignment via cross-correlation followed by iterative fine alignment using the model extraction algorithm itself.

• The Normalized Least Mean Squares (NLMS) filter can inherently track small timing errors
• Iterative methods minimize the post-distortion error as a function of fractional delay
• Essential for mmWave and massive MIMO systems where phase coherence across channels is critical

In a Direct Learning Architecture (DLA), time alignment is performed continuously within the adaptation loop. The predistorter output must be aligned with the observed PA output to compute the true error signal.

• Misalignment introduces bias in the gradient estimate used for coefficient updates
• Real-time alignment tracking compensates for thermal drift in analog components
• Often implemented with a dedicated delay-locked loop in FPGA-based DPD systems

Even minor timing errors produce systematic degradation in Normalized Mean Squared Error (NMSE) and spectral regrowth prediction accuracy. A misalignment of 0.5 samples can increase NMSE by 10 dB or more.

• Misalignment manifests as spurious memory effects in the extracted model
• Causes ill-conditioning of the regression matrix during coefficient estimation
• Validated by observing the constellation diagram for rotation and spreading after alignment