Fluid Antennas-Enabled Multiuser Uplink: A Low-Complexity Gradient Descent for Total Transmit Power Minimization

TL;DR

This work addresses energy-efficient multiuser uplink by equipping the base station with a movable-antenna array and decoding via zero-forcing. It reformulates the transmit-power minimization under rate constraints as minimizing $f({\bf x})=\sum_{i=1}^M 1/\lambda_i\{ {\bf\Omega}^{-1}{\bf H}({\bf x})^H {\bf H}({\bf x}) \}$, and solves it with a projected gradient descent whose gradient is obtained in closed form through eigen-decomposition. The key contributions are the closed-form gradient enabling low-complexity iterations and the demonstrated power reductions relative to RPA, FPA, and MMSE benchmarks under LoS and Rician fading. The approach is computationally efficient and well-suited for real-time FA position optimization, offering practical path to energy-efficient multiuser uplink systems.

Abstract

We investigate multiuser uplink communication from multiple single-antenna users to a base station (BS), which is equipped with a movable-antenna (MA) array and adopts zero-forcing receivers to decode multiple signals. We aim to optimize the MAs' positions at the BS, to minimize the total transmit power of all users subject to the minimum rate requirement. After applying transformations, we show that the problem is equivalent to minimizing the sum of each eigenvalue's reciprocal of a matrix, which is a function of all MAs' positions. Subsequently, the projected gradient descent (PGD) method is utilized to find a locally optimal solution. In particular, different from the latest related work, we exploit the eigenvalue decomposition to successfully derive a closed-form gradient for the PGD, which facilitates the practical implementation greatly. We demonstrate by simulations that via careful optimization for all MAs' positions in our proposed design, the total transmit power of all users can be decreased significantly as compared to competitive benchmarks.

Figures (5)

• Figure 1: Illustration of the system model.
• Figure 2: Feasible movement region for each FA.
• Figure 3: Computational complexity of the proposed design and the original definition based method.
• Figure 4: The convergence behavior of the proposed PGD method.
• Figure 5: Average total transmit power versus (a) $N$; (b) $L$; (c) $K$.