Performance bound on blind estimation of environmental parameters and radiation source locations with misspecified multipath TOA measurements

Multipath propagation has attracted extensive attention due to its inclusion of environmental information. However, it is difficult to match multipath with the environment without a priori knowledge, making it challenging to exploit multipath. This paper focuses on the performance bound of the estimation problem in a rectangular room. Due to the lack of parameter information of the room in base station (BS), the estimation of environmental parameters and locations of user equipment (UE) distributed in the room are blind estimation problems. Measurements are the time of arrival (TOA) of first-order non-line-of-sight (NLOS) paths and line-of-sight (LOS) path between the BS and UEs, but the specific pairing between NLOS paths and the environment remains unknown. The paper first describes the pairing problem, which causes misspecified multipath TOA measurements, and subsequently derives the likelihood function and the performance bound known as the misspecified Cramer-Rao bound (MCRB) under various pairing conditions. Simulation results demonstrate that only under correct pairings or just a few wrong pairings, the MCRB will significantly less than the other case.