Capacity Maximization of Uplink with Fluid Antenna System at Both Ends

This paper investigates the capacity performance of an uplink fluid antenna system (FAS), in which the base station (BS) is equipped with multiple fluid antennas and each user has a single fluid antenna. We aim to maximize the capacity of the system by optimizing the transmit power, and the user and BS antenna positions. Beginning with simple cases where the number of paths or the number of BS antennas is small, we reveal that the capacity is independent of the antenna positions. Then we give an upper bound on the capacity for the case where the BS has a single fluid antenna. After that, we show that in the optimal case, all users should transmit at the maximum power. Moreover, we propose an alternative algorithm to iteratively optimize the antenna positions at the BS and user sides. When keeping the user antenna positions fixed, the BS antenna positions are updated alternatively using a discrete exhaustive search in the single-user case. By transforming the capacity maximization problem into a difference-of-convex (DC) form, the majorization-minimization (MM) algorithm can also be applied to jointly optimize the BS antenna positions when there is a single user in the system. For the multiuser scenario, the antenna positions at the BS side are optimized utilizing the gradient descent method. We show that the user antenna positions can also be optimized using the discrete exhaustive search or the MM algorithm. Simulation results show that FAS can greatly improve the system capacity compared to traditional fixed-position antenna systems.