  Due to the finite bandwidth of practical wireless systems, one multipath
component can manifest itself as a discrete pulse consisting of multiple taps
in the digital delay domain. This effect is called channel leakage, which
complicates the multipath delay estimation problem. In this paper, we develop a
new algorithm to estimate multipath delays of leaked channels by leveraging the
knowledge of pulse-shaping functions, which can be used to support fine-grained
WiFi sensing applications. Specifically, we express the channel impulse
response (CIR) as a linear combination of overcomplete basis vectors
corresponding to different delays. Considering the limited number of paths in
physical environments, we formulate the multipath delay estimation as a sparse
recovery problem. We then propose a sparse Bayesian learning (SBL) method to
estimate the sparse vector and determine the number of physical paths and their
associated delay parameters from the positions of the nonzero entries in the
sparse vector. Simulation results show that our algorithm can accurately
determine the number of paths, and achieve superior accuracy in path delay
estimation and channel reconstruction compared to two benchmarking schemes.
