Power Minimization for Fluid Antenna-Assisted Downlink Non-Orthogonal Multiple Access Systems

The fluid antenna (FA) has recently gained prominence as a promising technique for reconfiguring wireless channels by adjusting its position within a finite space. In this paper, we study a downlink FA-assisted non-orthogonal multiple access (NOMA) system, where the base station (BS) is equipped with multiple fixed-position antennas to serve users and each user is equipped with a single FA. Our goal is to minimize the total transmit power at the BS by jointly optimizing the beamforming vectors and the positions of the FAs at the users under the constraint of the minimum achievable rate for each user. To tackle the formulated non-convex problem, alternating optimization is applied, where the transmit beamforming optimization is performed by using the semi-definite relaxation (SDR) technique. A novel sub-optimal optimization based on the fractional programming (FP) technique and projected gradient descent (PGD) method is proposed for designing the positions of the FAs. Then, the proposed method for solving the positions of the FAs is implemented in the single-input single-output (SISO) special scenario. Thanks to the simplicity of the SISO scenario, we derive a closed-form expression for the transmit power coefficients concerning the positions of the FAs at the users, which inspires us to develop a PGD-based low-complexity algorithm. Furthermore, our investigation reveals valuable insights into the SISO FA-assisted NOMA system. Simulation results demonstrate that the proposed algorithms significantly reduce the transmit power in both SISO and multiple-input single-output (MISO) scenarios compared to benchmark schemes.