  Radio localization is a key enabler for joint communication and sensing in
the fifth/sixth generation (5G/6G) communication systems. With the help of
multipath components (MPCs), localization and mapping tasks can be done with a
single base station (BS) and single unsynchronized user equipment (UE) if both
of them are equipped with an antenna array. However, the antenna array at the
UE side increases the hardware and computational cost, preventing localization
functionality. In this work, we show that with Doppler estimation and MPCs,
localization and mapping tasks can be performed even with a single-antenna
mobile UE. Furthermore, we show that the localization and mapping performance
will improve and then saturate at a certain level with an increased UE speed.
Both theoretical Cram\'er-Rao bound analysis and simulation results show the
potential of localization under mobility and the effectiveness of the proposed
localization algorithm.
