  Millimeter wave (mmWave) systems will likely employ directional beamforming
with large antenna arrays at both the transmitters and receivers. Acquiring
channel knowledge to design these beamformers, however, is challenging due to
the large antenna arrays and small signal-to-noise ratio before beamforming. In
this paper, we propose and evaluate a downlink system operation for multi-user
mmWave systems based on compressed sensing channel estimation and conjugate
analog beamforming. Adopting the achievable sum-rate as a performance metric,
we show how many compressed sensing measurements are needed to approach the
perfect channel knowledge performance. The results illustrate that the proposed
algorithm requires an order of magnitude less training overhead compared with
traditional lower-frequency solutions, while employing mmWave-suitable
hardware. They also show that the number of measurements need to be optimized
to handle the trade-off between the channel estimate quality and the training
overhead.
