  Compressive approaches provide a means of effective channel high resolution
channel estimates in millimeter wave MIMO systems, despite the use of analog
and hybrid architectures. Such estimates can also be used as part of a joint
channel estimation and localization solution. Achieving good localization
performance, though, requires high resolution channel estimates and better
methods to exploit those channels. In this paper, we propose a low complexity
multidimensional orthogonal matching pursuit strategy for compressive channel
estimation based by operating with a product of independent dictionaries for
the angular and delay domains, instead of a global large dictionary. This leads
to higher quality channel estimates but with lower complexity than
generalizations of conventional solutions. We couple this new algorithm with a
novel localization formulation that does not rely on the absolute time of
arrival of the LoS path and exploits the structure of reflections in indoor
channels. We show how the new approach is able to operate in realistic 3D
scenarios to estimate the communication channel and locate devices in an indoor
simulation setting.
