Orthogonal Beam-Focusing With Planar Arrays for Multiple Access in Near-Field Communications

Far-field multiple access techniques, such as space division multiple access (SDMA), leverage the angular orthogonality of beams in the far-field to serve multiple users with minimum interference. Recent approaches to extend this idea into the near-field involve the use of uniform planar arrays (UPAs) to generate focused beams that are able to achieve orthogonality only asymptotically, i.e. for infinitely large transmitter sizes. Gaining access to strictly zero beam correlations with transmitters of finite size could therefore lead to the full suppression of interference in the near-field, boosting the multiple access to unprecedented performance levels. In this work, we propose the use of circular, instead of the widely used rectangular, UPAs to generate focused beams that have strictly zero correlations. We demonstrate analytically that such beams satisfy the orthogonality condition for finite-size transmitters, thus offering a multitude of communication modes for multiple access in the near-field. We prove theoretically that focused beam orthogonality, defined in terms of the inner product of beam-focusing steering vectors, guarantees that the maximum of one beam is co-located with nulls of all other beams, similarly to how the angular orthogonality of classical far-field SDMA guarantees interference suppression. Based on this property, we propose codebook designs for near-field SDMA (NF-SDMA), which we evaluate in different scenarios. Our simulation results verify that the spectral efficiency of NF-SDMA schemes based on the proposed beams can be significantly higher than that achieved by focused beams generated with rectangular arrays.