Near-field orthogonality and cosine beams for near-field space division multiple access in 6G communications and beyond

Spatial division multiple access (SDMA), a powerful method routinely applied in multi-user multiple-input multiple-output (MIMO) communications, relies on the angular orthogonality of beams in the far field, to distinguish multiple users at different angles. Yet, with the gradual shift of wireless connectivity to the near-field of large radiating apertures, the applicability of classical SDMA becomes questionable. Therefore, to enable near-field multiple access, it is necessary to design beams that have the desired orthogonality in the near-field. In this work, we propose the concept of near-field space division multiple access (NF-SDMA), to enable SDMA in the near-field. We demonstrate analytically that the orthogonality of beams is preserved at any location of the receiver, from the near-field to the far-field of the transmitter. By judicious design, we select the family of cosine beams and we prove that they satisfy the orthogonality condition, offering a multitude of communication modes in the near-field. We demonstrate how the correlation of beams generated with uniform linear arrays (ULAs) is extended to uniform planar arrays (UPAs) in a straightforward and insightful manner. To test our analytical findings, we propagate the designed beams numerically, and we measure their orthogonality both at the transmitter and the receiver. We verify that the orthogonality of the proposed beams is successfully retrieved at a receiver that resides in the near-field of the transmitter, and is also robust to displacements of the receiver. Based on our findings, we propose codebook designs for NF-SDMA that are applicable for receivers with many elements and even with single antennas.