Near-Field Spatial Multiplexing

• Near-field spatial multiplexing is a technique that exploits radiative near-field effects to differentiate users by both angle and distance, enhancing channel capacity.
• It uses location-dependent beamfocusing and orthogonal mode synthesis to enable simultaneous transmission to co-directional users separated by range.
• Access schemes and codebook designs like LDMA and NF-SDMA capitalize on extra spatial degrees of freedom to significantly improve sum-rate performance in LoS and hybrid systems.

Searching arXiv for papers on near-field spatial multiplexing and related formulations. arxiv_search: query: "near-field spatial multiplexing location division multiple access near-field beamforming LoS MIMO" max_results: 10 {"query":"near-field spatial multiplexing location division multiple access near-field beamforming LoS MIMO","max_results":10} Near-field spatial multiplexing denotes the use of radiative near-field propagation to create parallel communication modes that are resolved not only by angle but also by distance, and more generally by three-dimensional location. In contrast to classical far-field spatial division multiple access (SDMA), which relies on planar-wave angular orthogonality, large apertures and high carrier frequencies make spherical-wave effects operationally relevant and permit finite-depth beamfocusing, co-directional user separation, and additional spatial degrees of freedom (DoF) in line-of-sight (LoS) and weakly scattering channels (Wu et al., 2022, Ramezani et al., 2022).

1. Propagation regime and electromagnetic basis

Near-field spatial multiplexing arises when array apertures become so large, relative to wavelength and link distance, that the array far-field border

$d_\mathrm{FA}=\frac{2W^2}{\lambda}$

extends into practical service regions. For extremely large aperture arrays (ELAAs), the radiative near-field can reach hundreds of meters or even kilometers, so many users that would previously be modeled in the far field must instead be described by spherical-wave propagation (Ramezani et al., 2022).

This shift changes both channel structure and beamforming. In the far field, the phase across the aperture is approximately linear, wavefronts are planar, and multiplexing is fundamentally angle-driven. In the near field, the path from a user to each antenna differs not only in phase but also in distance, effective aperture, and polarization mismatch. As summarized for ELAA LoS models, near-field-compliant formulations account for differing distances to each antenna, effective aperture variations, and polarization mismatch across the aperture; classical far-field gain and steering models therefore become inaccurate when the user is within the radiative near-field (Ramezani et al., 2022).

A central physical consequence is finite-depth focusing. Unlike a far-field pencil beam, a near-field beam is focused around a spatial region of finite depth. For the ELAA chapter’s matched-filter analysis, the $3$ dB beam depth is finite for focal distances $z<d_\mathrm{FA}/10$ and becomes infinite for $z\ge d_\mathrm{FA}/10$, which marks a transition from range-selective focusing to essentially far-field behavior (Ramezani et al., 2022). This finite depth is the basic mechanism behind range-domain or depth-domain multiplexing.

2. Orthogonality and beamfocusing in the distance domain

The fundamental distinction from classical SDMA is that orthogonality is no longer restricted to angle. The LDMA formulation shows that near-field beam focusing vectors become asymptotically orthogonal even for users at the same angle but at different distances. In particular,

$$\lim_{N\to\infty}\left|\mathbf{b}_\mathrm{L}^H(r_l,\phi)\mathbf{b}_\mathrm{L}(r_m,\phi)\right|=0,\qquad r_l\neq r_m,$$

and the same asymptotic orthogonality extends to the joint angle-distance domain (Wu et al., 2022).

This result directly supports a near-field multiplexing interpretation: users that are inseparable under far-field angle-only steering can become spatially resolvable when their ranges differ sufficiently. The ELAA chapter makes the same point from a beam-geometry perspective: beams focused at distance $d_1$ decay for users at $d_2\neq d_1$, so several beams focused at different depths but along the same angle can serve co-directional users simultaneously and independently (Ramezani et al., 2022). A recurring misconception is that near-field multiplexing is only a sharper version of far-field steering. The cited results indicate a stronger statement: the relevant resource is location-dependent focusing, not merely narrower angular mainlobes (Wu et al., 2022, Ramezani et al., 2022).

An alternative formulation, NF-SDMA, approaches the same problem through beam design rather than directly through user-location codebooks. It proves that beam orthogonality engineered at the transmitter is preserved at any receiver location, from the near field to the far field, and identifies cosine beams as an orthogonal beam family for ULAs and UPAs (Droulias et al., 2024). This establishes a mode-based view of near-field multiplexing: independent communication modes can be synthesized so that orthogonality survives free-space propagation, provided the beam family is chosen appropriately.

3. Access schemes and codebooks

The most explicit multiple-access reinterpretation is location division multiple access (LDMA). LDMA replaces angle-only discrimination by location discrimination, where location is determined by angle and distance. Its operational premise is to exploit extra spatial resources in the distance domain to mitigate inter-user interference in hybrid precoding, and its spherical-domain codebook samples azimuth, elevation, and distance rather than only angle (Wu et al., 2022). The codebook design uses non-uniform distance sampling so that near-field focusing beams remain nearly orthogonal, which makes the scheme compatible with hybrid architectures based on analog phase shifters (Wu et al., 2022).

The performance implications are substantial in scenarios where SDMA is structurally weak. For users aligned at the same angle but separated in range, classical SDMA can serve only one at a time, whereas LDMA can serve all simultaneously with negligible interference in the large-array limit (Wu et al., 2022). In the more detailed simulations reported for the LDMA framework, multipath scenarios showed sum-rate improvements of $60\%$ to $240\%$ over SDMA, and uniformly distributed-user scenarios showed nearly $100\%$ improvement at $3$0 dB (Wu et al., 2023). These results are scenario-specific, but they consistently indicate that the extra distance-domain resolution is not a minor correction.

NF-SDMA provides a complementary codebook perspective. Its cosine-beam construction yields countable sets of mutually orthogonal beams corresponding to same-angle/different-range, same-range/different-angle, and joint angle-range differences, and it includes codebook designs for both multi-element receivers and single-antenna receivers (Droulias et al., 2024). A plausible implication is that LDMA and NF-SDMA are best understood as two formulations of the same near-field resource expansion: one organized around user locations, the other around propagation-invariant orthogonal modes.

Codebook design also appears in channel acquisition. For generalized URAs, an EBRD-aware polar codebook was designed for compressed-sensing channel estimation, with distance sampling constrained by beamdepth and by the effective beamfocusing Rayleigh distance (EBRD). Simulation results report a $3$1 dB NMSE improvement over state-of-the-art methods (Hussain et al., 25 Feb 2026). This links multiplexing and estimation directly: the same geometry that creates additional near-field modes also determines how finely the codebook should sample range.

4. Degrees of freedom, beamdepth, and distance metrics

Several papers recast near-field spatial multiplexing as a DoF problem. The ELAA chapter cites a spatial DoF limit

$3$2

for a planar array of area $3$3, emphasizing that capacity scales with physical aperture area rather than merely with element count (Ramezani et al., 2022). This is consistent with the broader near-field literature: large apertures create more resolvable modes because spherical-wave curvature is observable across the aperture.

A more explicit effective-DoF expression is given for ULA-based MIMO:

$3$4

where $3$5 and $3$6 are the transmit and receive apertures, $3$7 is separation distance, and $3$8 are orientation angles (Hussain et al., 25 Feb 2026). The same work introduces the effective MIMO Rayleigh distance (EMRD),

$3$9

at which EDoF reduces to one, and the maximum spatial multiplexing distance (MSMD),

$z<d_\mathrm{FA}/10$0

with a simplified form $z<d_\mathrm{FA}/10$1 when $z<d_\mathrm{FA}/10$2 and half-wavelength spacing is assumed (Hussain et al., 25 Feb 2026). Experimental measurements with widely spaced phased arrays were reported to match the theoretical EDoF trends and to validate both metrics (Hussain et al., 25 Feb 2026).

For continuous-aperture arrays, the distance-domain DoF has also been analyzed through Hermitian integral operators. In the summarized result for arbitrary continuous-aperture geometry, the distance-domain DoF is predominantly determined by the extreme boundaries of the aperture rather than its detailed interior structure; non-broadside cases are reduced to equivalent broadside cases through projection; and modular arrays can preserve or even increase DoF if they extend those extremes farther under the same total-length constraint (Duong et al., 1 Jul 2025). This suggests that aperture support, not only aperture fill, is a governing variable for distance-domain multiplexing.

Beamdepth and the EBRD provide a complementary, beam-centric characterization. For generalized URAs, the EBRD is defined as the maximum range at which finite-depth beamfocusing is achievable, and beyond it beamdepth becomes infinite and beamfocusing is lost (Hussain et al., 18 Jun 2025). This is important because a narrow beamdepth is not by itself sufficient; the effective near-field volume in which finite-depth focusing exists is equally consequential for multiuser operation.

5. Array geometry, sparsity, polarization, and hybrid architectures

Array geometry strongly shapes near-field multiplexing. For generalized URAs with a fixed number of antennas, a square URA achieves the narrowest beamdepth, but the EBRD is maximized by a wide or tall URA; despite its narrower beamdepth, the square URA may therefore suffer a lower multiuser sum rate because its effective near-field coverage is more constrained (Hussain et al., 18 Jun 2025). In the reported $z<d_\mathrm{FA}/10$3-antenna comparison, a $z<d_\mathrm{FA}/10$4 wide URA achieved $z<d_\mathrm{FA}/10$5 bps/Hz at high SNR, while a $z<d_\mathrm{FA}/10$6 square URA achieved $z<d_\mathrm{FA}/10$7 bps/Hz, yielding a $z<d_\mathrm{FA}/10$8 sum-rate advantage for the elongated geometry (Hussain et al., 18 Jun 2025). A common misconception is accordingly that the most focused geometry is always the best multiplexing geometry; the wide/tall-vs-square comparison shows that EBRD can dominate beamdepth in system-level performance (Hussain et al., 18 Jun 2025).

Sparse arrays exploit a related aperture effect. Sparse MIMO enlarges physical aperture without increasing element count, which can sharpen mainlobes and enlarge the near-field region, thereby increasing effective DoF up to the minimum of the transmit and receive antenna numbers (Wang et al., 2024). The same study reports that sparse MIMO is less likely to experience severe inter-user interference than conventional MIMO in multi-user settings, even though larger-than-half-wavelength spacing introduces grating lobes (Wang et al., 2024). A more implementation-focused result shows that in near-field sparse arrays, grating lobes arise in angle but not in range, and reconfigurable array thinning can leverage this asymmetry (Hussain et al., 25 Feb 2026).

Reconfigurable thinning replaces mechanical movement by switch-based activation of a subset of antennas. Two PSO-based strategies were reported: GTA for grating-lobe suppression and STA for sum-rate maximization. In the summarized simulations, STA matched movable-array performance and reached approximately $z<d_\mathrm{FA}/10$9 of the FULA sum rate using only $z\ge d_\mathrm{FA}/10$0 of the antennas, while GTA was about $z\ge d_\mathrm{FA}/10$1 below STA (Hussain et al., 25 Feb 2026). This indicates that near-field multiplexing gains need not be tied to fully populated apertures, provided the active support is chosen adaptively.

Polarization adds another dimension. For a ULA LoS channel with three orthogonal polarizations at both transmitter and receiver, the near-field channel can support up to three spatial DoF, whereas the far-field maximum tends to two because the channel becomes rank deficient (Agustin et al., 2023). This is a distinct mechanism from range focusing, but it compounds the total modal richness of the near field.

Dynamic hybrid architectures address the power cost of exploiting these modes. A dynamic hybrid beamforming architecture with two independent phase shifters per RF-chain-to-antenna connection was proposed to maximize sum rate while minimizing hardware power consumption; for continuous phase shifters, the WMMSE-TS algorithm was reported to achieve the same performance as the optimal fully digital beamformer even when the number of RF chains equals the number of data streams, while a PLI algorithm addresses discrete phase shifters (Zhang et al., 2023). Near-field multiplexing is therefore not only a propagation problem but also an RF-chain allocation problem.

6. Extensions, demonstrations, and unresolved issues

Near-field spatial multiplexing has been extended beyond direct-array beamforming. In RIS-aided near-field MIMO, channel capacity is achieved by diagonalizing the end-to-end transmitter-RIS-receiver channel and water-filling over the ordered products of the singular values of the two constituent links; the capacity-achieving design requires a non-diagonal RIS reflection matrix, described as a linear, nearly-passive reconfigurable electromagnetic object (EMO) (Bartoli et al., 2022). A closed-form diagonal unit-modulus focusing design was also shown to be exact in paraxial LoS and close to the EMO benchmark in many simulated cases (Bartoli et al., 2022). Closely related IRS deployment work places the IRS in the near field of a sparse BS array to engineer favorable propagation; the summarized simulations report that the expected effective DoF transitions from approximately $z\ge d_\mathrm{FA}/10$2 to the maximum number of users $z\ge d_\mathrm{FA}/10$3 as sparsity and IRS size increase under the proposed deployment criterion (Chen et al., 12 Jan 2026).

Hardware demonstrations have begun to appear. A reconfigurable metasurface gateway fed by orthogonal multi-mode vortex waves converted overlapping vortex modes into distinct near-field focal spots for different users. The reported microwave-chamber and real-time communication experiments used a $z\ge d_\mathrm{FA}/10$4 metasurface, two nested UCA vortex generators, QPSK at $z\ge d_\mathrm{FA}/10$5 GHz, and observed crosstalk suppression greater than $z\ge d_\mathrm{FA}/10$6 dB between spot beams (Zhao et al., 18 Feb 2025). This demonstrates a physically different, but conceptually aligned, route to near-field multiplexing: orthogonal modal generation followed by spatial refocusing.

System integration is also expanding. One letter considers legacy near-field beams as preconfigured spatial resources and superposes additional far-field users through NOMA, showing that coexistence between near-field and far-field communications can be supported and that performance improves with increasing antenna count (Ding et al., 2023). In a grant-free access setting for industrial IoT, an ELAA-based coded random-access architecture exploits near-field spatial clustering; the summarized simulations report support for up to $z\ge d_\mathrm{FA}/10$7 active users per slot with packet loss rate below $z\ge d_\mathrm{FA}/10$8, and for $z\ge d_\mathrm{FA}/10$9 active users with $$\lim_{N\to\infty}\left|\mathbf{b}_\mathrm{L}^H(r_l,\phi)\mathbf{b}_\mathrm{L}(r_m,\phi)\right|=0,\qquad r_l\neq r_m,$$0 replicas the packet loss rate is driven close to $$\lim_{N\to\infty}\left|\mathbf{b}_\mathrm{L}^H(r_l,\phi)\mathbf{b}_\mathrm{L}(r_m,\phi)\right|=0,\qquad r_l\neq r_m,$$1 (Testi et al., 21 Aug 2025). These are not generic limits, but they illustrate that near-field multiplexing can be used as a MAC-layer resource rather than only as a point-to-point PHY phenomenon.

Channel acquisition remains a central difficulty. For UPAs, near-field spatial correlation depends on angle and distance, not on angle alone, and a reduced-subspace least-squares estimator based on a geometry-derived channel subspace was reported to outperform classical LS and approach MMSE performance without requiring full correlation knowledge (Demir et al., 2024). More broadly, the survey-style vision paper identifies channel estimation complexity, codebook and beam-training design, mutual coupling, hardware non-idealities, and the joint exploitation of depth-domain and angular-domain multiplexing as open problems (Ramezani et al., 2023).

Taken together, these results define near-field spatial multiplexing as a generalization of spatial multiplexing from angular resolution to location-aware, aperture-governed mode synthesis. The central theoretical claims are consistent across formulations: spherical-wave propagation creates finite-depth focus, location-dependent orthogonality, and new effective DoF; geometry and aperture support determine how many of these modes are usable; and practical realization depends on codebooks, hybrid architectures, sparse activation, and channel estimation methods that are explicitly near-field aware (Wu et al., 2022, Ramezani et al., 2022).