Pulse Shape-Aided Multipath Parameter Estimation for Fine-Grained WiFi Sensing

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 parameter estimation. In this study, we propose a new algorithm to estimate multipath parameters, including delay, angle of arrival (AOA), and angle of departure (AOD) of leaked channels. This is accomplished by leveraging the knowledge of pulse shaping functions, a technique that can be applied to enhance the precision of WiFi sensing. More specifically, we formulate the channel impulse response (CIR) between a transmit and a receive antenna as a linear combination of a set of overcomplete basis vectors, each corresponding to a different delay. Considering the limited number of paths in physical environments, we formulate the multipath parameter estimation as a group sparse recovery problem. We develop a two-stage approach based on variational expectation maximization (VEM) to solve the formulated problem. In the first stage, we estimate the sparse vectors and determine the number of physical paths and their associated delay parameters from the positions of the nonzero entries. In the second stage, we use Newton's method to estimate the AOA and AOD of each path. The Cramér-Rao lower bound (CRLB) for multipath parameter estimation is derived for performance evaluation. Simulation results show that our algorithm can achieve superior estimation accuracy in multipath parameters compared to two benchmarking schemes and approach the CRLB.