  In this paper, we analyze the two-node joint clock synchronization and
ranging problem. We focus on the case of nodes that employ time-to-digital
converters to determine the range between them precisely. This specific design
choice leads to a sawtooth model for the captured signal, which has not been
studied before from an estimation theoretic standpoint. In the study of this
model, we recover the basic conclusion of a well-known article by Freris,
Graham, and Kumar in clock synchronization. More importantly, we discover a
surprising identifiability result on the sawtooth signal model: noise improves
the theoretical condition of the estimation of the phase and offset parameters.
To complete our study, we provide performance references for joint clock
synchronization and ranging using the sawtooth signal model by presenting an
exhaustive simulation study on basic estimation strategies under different
realistic conditions. With our contributions in this paper, we enable further
research in the estimation of sawtooth signal models and pave the path towards
their industrial use for clock synchronization and ranging.
