Orthogonal Beams and Codebook Design for Near-Field Space-Division Multiple Access in 6G Systems

Space 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. Recently proposed near-field multiple access schemes employ focused beams, which achieve orthogonality only asymptotically with respect to the transmitter size. Hence, a multiple access scheme based on beams with strictly zero near-field correlation is still missing. In this work we propose a novel technique, to enable SDMA in the near-field. By judicious design, we select the family of cosine beams and we prove that they satisfy the orthogonality condition for finite-size transmitters, offering in the near-field a multitude of communication modes, implemented by beams that can co-exist without interference. 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 and, 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. We also 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. Based on our findings, we propose codebook designs for near-field space division multiple access (NF-SDMA) that are applicable for receivers with many elements and even with single antennas.