Superdirectivity-enhanced Multi-user Wireless Communications: Power Scaling Law and Interference-nulling Precoding

Traditional multiple-input multiple-output (MIMO) systems exhibit power gains that are proportional to the number of antennas M. By contrast, a superdirective array has the potential to attain the power gain proportional to $M^{2}$, which may lead to great improvements in spectral efficiency. However, few early studies explore the superdirectivity in multi-user wireless communications. In this paper, we conduct a detailed study on the topic. Firstly, we extend the superdirective precoding from single-user scenarios to multi-user multipath scenarios. Utilizing the Legendre polynomials basis, we prove that the scaling laws of both the power gain and the signal-to-interference-plus-noise ratio (SINR) are between $\mathcal{O}(M)$ and $\mathcal{O}\left(M^{2}\right)$, where $\mathcal{O}\left(M^{2}\right)$ is achieved at the end-fire direction. We reveal that, for a fixed-aperture compact antenna array without considering ohmic loss and impedance mismatch loss, the power gain keeps growing with the increasing number of antennas. Furthermore, we propose a Multi-user Interference-Nulling Superdirective (MINS) precoding scheme to maximize user power gains while eliminating interference. Simulation results verify the proposed power scaling law and show significant improvements in spectral efficiency using our methods compared to the traditional MIMO.