  This paper investigates a multiuser millimeter-wave (mmWave) uplink system in
which each user is equipped with a multi-antenna fluid antenna system (FAS)
while the base station (BS) has multiple fixed-position antennas. Our primary
objective is to maximize the system capacity by optimizing the transmit
covariance matrices and the antenna position vectors of the users jointly. To
gain deeper insights, we commence by deriving upper bounds and approximations
for the maximum capacity. Then we delve into the capacity maximization problem.
Beginning with the simple scenario of a single user equipped with a
single-antenna FAS, we reveal that a closed-form optimal solution exists when
there are only two propagation paths between the user and the BS. In the case
where multiple propagation paths are present, a near-optimal solution can be
obtained through a one-dimensional search method. Expanding our focus to
multiuser cases, where users are equipped with either single- or multi-antenna
FAS, we show that the original capacity maximization problems can be
reformulated into distinct rank-one programmings. Then, we propose alternating
optimization algorithms to deal with the transformed problems. Simulation
results indicate that FAS can improve the capacity of the multiple access (MAC)
system greatly, and the proposed algorithms outperform all the benchmarks.
