Performance Bounds of Ranging Precision in SPAD-Based dToF LiDAR

Abstract: Lidar with direct time-of-flight (dToF) technology based on single-photon avalanche diode detectors (SPAD) has been widely adopted in various applications. However, a comprehensive theoretical understanding of its fundamental ranging performance limits--particularly the degradation caused by pile-up effects due to system dead time and the potential benefits of photon-number-resolving architectures--remains incomplete. In this work, the Cramer-Rao lower bound (CRLB) for dToF systems is theoretically derived accounting for dead time effects, generalized to SPAD detectors with photon-number-resolving capabilities, and are further validated through Monte Carlo simulations and maximum likelihood estimation. Our results reveal that pile-up not only reduces the information contained within individual ToF but also introduces statistical coupling between distance and photon flux rate, further degrading ranging precision. The derived CRLB is used to determine the optimal optical photon flux, laser pulse width, and ToF quantization resolution that yield the best achievable ranging precision. The analysis further quantifies the limited performance improvement enabled by increased photon-number resolution, which exhibits rapidly diminishing returns. These findings provide theoretical guidance for the design of dToF systems and the selection of their optimal operating points.