  This paper is concerned with the channel estimation problem in multi-user
millimeter wave (mmWave) wireless systems with large antenna arrays. We develop
a novel simultaneous-estimation with iterative fountain training (SWIFT)
framework, in which multiple users estimate their channels at the same time and
the required number of channel measurements is adapted to various channel
conditions of different users. To achieve this, we represent the beam direction
estimation process by a graph, referred to as the beam-on-graph, and associate
the channel estimation process with a code-on-graph decoding problem.
Specifically, the base station (BS) and each user measure the channel with a
series of random combinations of transmit/receive beamforming vectors until the
channel estimate converges. As the proposed SWIFT does not adapt the BS's beams
to any single user, we are able to estimate all user channels simultaneously.
Simulation results show that SWIFT can significantly outperform the existing
random beamforming-based approaches, which use a predetermined number of
measurements, over a wide range of signal-to-noise ratios and channel coherence
time. Furthermore, by utilizing the users' order in terms of completing their
channel estimation, our SWIFT framework can infer the sequence of users'
channel quality and perform effective user scheduling to achieve superior
performance.
