  Massive Multiple-Input Multiple-Output (massive MIMO) is a variant of
multi-user MIMO in which the number of antennas at each Base Station (BS) is
very large and typically much larger than the number of users simultaneously
served. Massive MIMO can be implemented with Time Division Duplexing (TDD) or
Frequency Division Duplexing (FDD) operation. FDD massive MIMO systems are
particularly desirable due to their implementation in current wireless networks
and their efficiency in situations with symmetric traffic and delay-sensitive
applications. However, implementing FDD massive MIMO systems is known to be
challenging since it imposes a large feedback overhead in the Uplink (UL) to
obtain channel state information for the Downlink (DL). In recent years, a
considerable amount of research is dedicated to developing methods to reduce
the feedback overhead in such systems. In this paper, we use the sparse spatial
scattering properties of the environment to achieve this goal. The idea is to
estimate the support of the continuous, frequency-invariant scattering function
from UL channel observations and use this estimate to obtain the support of the
DL channel vector via appropriate interpolation. We use the resulting support
estimate to design an efficient DL probing and UL feedback scheme in which the
feedback dimension scales proportionally with the sparsity order of DL channel
vectors. Since the sparsity order is much less than the number of BS antennas
in almost all practically relevant scenarios, our method incurs much less
feedback overhead compared with the currently proposed methods in the
literature, such as those based on compressed-sensing. We use numerical
simulations to assess the performance of our probing-feedback algorithm and
compare it with these methods.
