A preprint on near-field multiple-input, multiple-output (MIMO) communications reports a beamforming design that came close to the rate of a full singular-value decomposition (SVD) benchmark while using much less reported CPU time in simulations. The advantage became more apparent as the number of transmitter antennas increased. The study focuses on a dual-UPA system and combines a geometry-based boundary between near-field and far-field operation with a lower-dimensional channel calculation.
Geometry sets the boundary
The method starts with the physical geometry of the arrays. It sets antenna positions with planar and z coordinates, then calculates the Euclidean distance between every transmit-receive antenna pair. To turn those distances into a usable criterion, the derivation uses a Taylor expansion and writes each pairwise distance as a center-to-center distance plus horizontal and vertical correction terms. The analysis then compares the near-field calculation with the far-field planar-wave approximation.
The paper gives a sufficient near-field-to-far-field boundary as d0 ≥ π(DT + DR)^2/(4λϕ̄). Read in ordinary terms, it increases with the combined transmitter and receiver apertures squared and decreases with wavelength and the phase-difference threshold. Because it is sufficient, the expression is presented as a condition tied to the chosen phase-difference limit, not as a universal measured cutoff for every array.
In simulations using the same threshold ϕ̄ = π/8, the 90 GHz case produced the largest reported boundary distance and the 30 GHz case the smallest. The boundary also rose with transmitter antenna count and was larger for smaller thresholds. At the stated threshold, it matched the conventional Rayleigh distance.
A smaller route to beamforming
For the beamforming calculation, the near-field channel is written as γ0(Hy ⊗ Hx), a Kronecker product of lower-dimensional vertical and horizontal component matrices. The design then performs two low-dimensional SVDs and follows them with water-filling power allocation across the streams. The calculation is intended to preserve the channel structure needed for rate analysis without carrying out one SVD on the full channel matrix.
The numerical evaluation compares it with full-dimensional SVD using water-filling, full-dimensional SVD using equal power, and far-field SVD based on a planar-wave channel. Against those references, the proposed Kronecker-SVD design approached the water-filled full-dimensional result and outperformed the equal-power and far-field schemes. The authors interpret this as indicating that the geometric decomposition preserves the main near-field channel structure, while water-filling is needed for efficient allocation across streams.
The paper reports full-dimensional SVD complexity as O(Mx My Nx Ny min(Mx My, Nx Ny)), while Kronecker-SVD is given as O(Mx Nx min(Mx, Nx) + My Ny min(My, Ny)). In effect, the proposed calculation replaces one full-dimensional decomposition with two lower-dimensional decompositions. The CPU comparison showed much less reported CPU time for the proposed design, with a larger advantage as transmitter antenna count increased.
What the simulations establish
The main numerical setting used a 60 GHz carrier, wavelength 0.005 metres, half-wavelength spacing at both ends, a 40 by 40 transmit array, a 16 by 16 receive array, four data streams and maximum transmit power of 10 dBm. This is a modeling study built from analytical geometry, channel models and numerical configurations rather than participant data. No over-the-air validation is reported in the supplied analysis.
The evidence has clear limits. The boundary is a sufficient, upper-bound-based result, but the supplied analysis does not quantify how conservative it is. The rate and CPU comparisons are qualitative in the reviewed material: they give the reported ordering and scaling trend, but no numerical rates, runtimes, repeated-run variability or inferential uncertainty. The simulations therefore support conclusions within the stated dual-UPA model, but do not establish that the same behavior will hold for other array geometries, channel conditions or hardware.
Publication note
The manuscript is listed as arXiv:2608.25510v1 [eess.SP], dated 26 Aug 2026, and the supplied record identifies it as a preprint. It reports support from two Shaanxi provincial funding programs, Grants 24JK0674 and 2025JC-YBQN-889.
Paper data and sources
Original title: Near-Field Dual-UPA Communications: A Generalized Geometric Approach
Authors: Li Zheng, Xing Hao, Ziru Chen et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text