Performance Bounds of Ranging Precision in SPAD-Based dToF LiDAR

LiDAR with direct time-of-flight (dToF) technology based on single-photon avalanche diode detectors (SPADs) has been widely adopted in various applications. However, a comprehensive theoretical understanding of its fundamental ranging performance bounds-particularly the degradation caused by pile-up effects due to system dead time and the potential benefits of photon-number-resolving detectors-remains incomplete and has not been systematically established in prior work. In this work, we present the first theoretical derivation of the Cramér-Rao lower bound (CRLB) for dToF systems explicitly accounting for dead time effects, generalize the analysis to SPADs with photon-number-resolving capabilities, and further validate the results through Monte Carlo simulations and maximum likelihood estimation. Our analysis reveals that pile-up not only reduces the information contained within individual ToF but also introduces a previously overlooked statistical coupling between distance and photon flux rate, further degrading ranging precision. The derived CRLB enables the determination of the optimal optical photon flux, laser pulse width (with FWHM of ≈0.56τ), and ToF quantization resolution that yield the best achievable ranging precision, showing that an optimal precision of approximately 0.53τ/N remains theoretically achievable, where τ is TDC resolution and N is the number of laser pulses. The analysis further quantifies the limited performance improvement enabled by increased photon-number resolution, which exhibits rapidly diminishing returns. Overall, these findings establish a unified theoretical framework for understanding the fundamental limits of SPAD-based dToF LiDAR, filling a gap left by earlier studies and providing concrete design guidelines for the selection of optimal operating points.