  Channel state information (CSI) at the base station (BS) is crucial to
achieve beamforming and multiplexing gains in multiple-input multiple-output
(MIMO) systems. State-of-the-art limited feedback schemes require feedback
overhead that scales linearly with the number of BS antennas, which is
prohibitive for $5$G massive MIMO. This work proposes novel limited feedback
algorithms that lift this burden by exploiting the inherent sparsity in double
directional (DD) MIMO channel representation using overcomplete dictionaries.
These dictionaries are associated with angle of arrival (AoA) and angle of
departure (AoD) that specifically account for antenna directivity patterns at
both ends of the link. The proposed algorithms achieve satisfactory channel
estimation accuracy using a small number of feedback bits, even when the number
of transmit antennas at the BS is large -- making them ideal for $5$G massive
MIMO. Judicious simulations reveal that they outperform a number of popular
feedback schemes, and underscore the importance of using angle dictionaries
matching the given antenna directivity patterns, as opposed to uniform
dictionaries. The proposed algorithms are lightweight in terms of computation,
especially on the user equipment side, making them ideal for actual deployment
in $5$G systems.
