Optimal Antenna Configuration Filtering and Joint Power Control in Fluid Antenna Multiple Access Networks

In this work, we study a fluid antenna multiple access (FAMA) system, where a base station (BS) with multiple fluid antennas is responsible for the communication service supply to multiple users also equipped with fluid antennas. We concentrate on the optimal joint antenna configuration and resource allocation design, where the transmit power control is jointly optimized with the antenna configuration including BS antenna assignment and port selection at all activated fluid antennas. The large number of discrete variables needed for antenna configuration makes the joint optimization very challenging. To address these challenges without loss of optimality, we develop in this work a novel methodology for globally optimal FAMA designs. We first focus on FAMA throughput maximization while taking user fairness into account and accordingly formulate a mixed-integer nonlinear problem. To facilitate the optimal design, we characterize the optimal power control with given antenna configuration, which enables us to build up a system of equations and inequalities (SEI) tailored for examining the achievability of any throughput level. A fixpoint-based approach is subsequently proposed for effectively inferring the solvability of established SEI, as well as the throughput achievability. Leveraging the proposed fixpoint-based inference approach, we develop an efficient iterative algorithm for the optimal antenna configuration filtering, where all nonoptimal configuration candidates are efficiently filtered and removed via fixpoint inspections. The optimal power control associated with the optimal antenna configuration finalizes the globally optimal FAMA design. Afterwards, we extend the whole design methodology to a scenario requesting energy efficiency maximization, achieving globally optimal energy-efficient FAMA design. Finally, the obtained FAMA solutions are examined via numerical simulations, verifying the global optimality and spotlighting the high benefits of considering joint antenna configuration and power control in FAMA.