  5G mmWave MIMO systems enable accurate estimation of the user position and
mapping of the radio environment using a single snapshot when both the base
station (BS) and user are equipped with large antenna arrays. However, massive
arrays are initially expected only at the BS side, likely leaving users with
one or very few antennas. In this paper, we propose a novel method for
single-snapshot localization and mapping in the more challenging case of a user
equipped with a single-antenna receiver. The joint maximum likelihood (ML)
estimation problem is formulated and its solution formally derived. To avoid
the burden of a full-dimensional search over the space of the unknown
parameters, we present a novel practical approach that exploits the sparsity of
mmWave channels to compute an approximate joint ML estimate. A thorough
analysis, including the derivation of the Cram\'er-Rao lower bounds, reveals
that accurate localization and mapping can be achieved also in a MISO setup
even when the direct line-of-sight path between the BS and the user is severely
attenuated.
