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

We investigate multiuser uplink communications from multiple single-antenna users to a base station (BS), which is equipped with multiple fluid antennas (FAs) and adopts zero-forcing receivers to decode multiple signals. We aim to optimize antennas’ 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 antennas’ positions at the BS. 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 antennas’ positions in our proposed design, the total transmit power of all users can be decreased significantly as compared to competitive benchmarks.