Power Scaling Law of Superdirective Multi-User Beamforming in Compact Arrays

Traditional antenna arrays with a half-wavelength spacing between elements are capable of achieving a power gain proportional to the number of antennasM. Superdirective antenna arrays, however, leverage smaller antenna spacing to approach an achievable power gain ofM2, which could provide a significant performance improvement to the spectral efficiency in wireless communication systems. In this paper, we study the power scaling law of superdirective beamforming in multi-user communication systems using a uniform linear array (ULA). First, we extend superdirective precoding from single-user to multi-user multipath scenarios. Employing the basis of Legendre polynomials, we prove that the scaling laws of both the power gain and signal-to-interference-plus-noise ratio (SINR) are betweenMandM2, whereM2is achieved in the end-fire direction. To further enhance user power gains and effectively manage interference, we formulate and solve an optimization problem that maximizes the directivity gain while nullifying interference to other users. We demonstrate that this scheme can significantly improve spectral efficiency in multi-user settings, even when antenna spacing approaches zero. Moreover, we address the narrow directivity bandwidth issue, showing that the directivity of superdirective arrays decreases sharply as the frequency moves away from the center frequency, necessitating the use of multi-carrier technology to overcome this limitation. Simulation results verify the proposed power scaling law and show significant improvements in spectral efficiency with our proposed methods compared to a traditional antenna array with half-wavelength spacing.