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Multiple access for near-field communications: SDMA or LDMA?

Zidong Wu, Linglong Dai

arXiv:2208.06349v6eess.SP

TL;DR

Classical SDMA for massive MIMO relies on far-field angular separation and therefore does not fully exploit near-field distance-domain resources in ELAA systems. The paper proposes LDMA with near-field beam focusing, proves distance-domain asymptotic orthogonality, and develops spherical-domain codebooks; analysis and simulations show improved spectrum efficiency over SDMA.

  • Problem

    Classical hybrid-precoding SDMA relies on far-field angular orthogonality and does not fully exploit the additional distance-domain spatial resources available in near-field ELAA communications.

  • Method

    LDMA uses near-field location-dependent beam-focusing vectors, distance-domain asymptotic orthogonality, and spherical-domain codebooks to serve users at different angles and distances.

  • Results

    LDMA achieves asymptotically interference-free spectrum efficiency as antenna counts increase and outperforms classical SDMA in linear and uniformly distributed multi-user scenarios.

  • Takeaways & Limitations

    Near-field distance focusing provides an additional spatial dimension for hybrid-precoding multi-user access beyond classical angular SDMA.

Abstract

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Spatial division multiple access (SDMA) is essential to improve the spectrum efficiency for multi-user multiple-input multiple-output (MIMO) communications. The classical SDMA for massive MIMO with hybrid precoding heavily relies on the angular orthogonality in the far field to distinguish multiple users at different angles, which fails to fully exploit spatial resources in the distance domain. With the dramatically increasing number of antennas, the extremely large-scale antenna array (ELAA) introduces additional resolution in the distance domain in the near field. In this paper, we propose the concept of location division multiple access (LDMA) to provide a new possibility to enhance spectrum efficiency compared with classical SDMA. The key idea is to exploit extra spatial resources in the distance domain to serve different users at different locations (determined by angles and distances) in the near field. Specifically, the asymptotic orthogonality of near-field beam focusing vectors in the distance domain is proved, which reveals that near-field beam focusing is able to focus signals on specific locations with limited leakage energy at other locations. This special property could be leveraged in hybrid precoding to mitigate inter-user interferences for spectrum efficiency enhancement. Moreover, we provide the spherical-domain codebook design method for LDMA communications with the uniform planar array, which provides the sampling method in the distance domain. Additionally, performance analysis of LDMA is provided to reveal that the asymptotic optimal spectrum efficiency could be achieved with the increasing number of antennas. Finally, simulation results verify the superiority of the proposed LDMA over SDMA in different scenarios.

I. INTRODUCTION

As ELAA systems move communications into the near field, classical far-field SDMA cannot fully exploit distance-domain spatial resources. The paper proposes LDMA, using near-field beam focusing and distance-domain orthogonality to improve multi-user spectrum efficiency.

  • I. INTRODUCTION: ELAA systems use thousands of antennas to pursue major spectrum-efficiency gains, but increasing antenna counts also raises power consumption and hardware costs.The paper motivates an alternative to relying only on more antennas for thinner beams and interference suppression.
  • I. INTRODUCTION: Classical SDMA distinguishes users primarily through angularly directed beams, while hybrid precoding must address constant-modulus constraints and can require complex optimization.Beam-steering approaches reduce complexity, but their spatial discrimination is mainly directional in the far field.
  • B. Our Contributions: LDMA serves users at different locations by using near-field energy-focusing vectors that exploit both angle and distance as spatial resources.This adds distance-domain focusing to the angular separation used by classical SDMA.
  • B. Our Contributions: As antenna counts grow, near-field beams focusing on the same angle but different distances become asymptotically orthogonal under the Fresnel approximation.This property provides theoretical support for distinguishing users through distance-domain focusing in large arrays.
  • B. Our Contributions: A 3D near-field codebook for uniform planar arrays is proposed to use the additional distance-domain orthogonality in practical LDMA precoding.The codebook supplies a spherical-domain sampling method for near-field beam design.
  • B. Our Contributions: As the number of antennas tends to infinity, LDMA spectrum efficiency can approach interference-free scenarios, and simulations verify superiority over classical SDMA.The reported analysis and simulations support LDMA as another possibility for spectrum-efficiency enhancement in hybrid precoding.

B. Far-Field Channel Model

Far-field channels use planar-wave steering vectors determined by spatial angles, whereas ELAA near-field channels require spherical-wave beam focusing that depends on both angle and distance.

  • Far-Field Channel Model: Far-field steering vectors depend on transmitting or receiving angles for a fixed array structure.
  • Near-Field Channel Model: As antenna counts increase, the Rayleigh distance expands, making spherical-wave modeling necessary across much of the cell.A 3200-antenna array can have a Rayleigh distance of about 200 meters.
  • Near-Field Channel Model: Near-field beam focusing vectors encode signal energy at locations indexed by distance and spatial angles.
  • Near-Field Channel Model: The UPA near-field phase is coupled across its two axes, unlike the separable far-field UPA steering vector.
  • Near-Field Channel Model: Near-field channels can distinguish users at the same angle but different distances, unlike far-field channels based on planar waves.

III. ANALYSIS OF ASYMPTOTIC ORTHOGONALITY OF NEAR-FIELD BEAM FOCUSING VECTORS

Near-field beam focusing vectors become orthogonal in distance and angle-distance domains as antenna counts grow, extending far-field angular orthogonality and supporting simultaneous transmissions.

  • ULA Systems: Near-field beam focusing vectors with the same angle and different distances become asymptotically orthogonal for ULA systems.
  • ULA Systems: At 30 GHz, correlation between focusing vectors at (5 m, π/6) and (15 m, π/6) significantly decreases as antenna count increases.The Fresnel-based approximation closely matches the accurate correlation.
  • ULA Systems: ULA focusing vectors corresponding to any different angles or distances are asymptotically orthogonal as antenna count increases.
  • ULA Systems: This 2D orthogonality generalizes far-field angular orthogonality and limits interference between waves arriving from different angles or distances.
  • ULA Systems: The distance-domain orthogonality provides a basis for distinguishing users by location and developing LDMA for simultaneous transmissions.

B. Analysis of UPA Systems

For UPA systems, near-field focusing vectors at the same elevation and azimuth but different distances become asymptotically orthogonal, with one sufficiently large array dimension enough to guarantee the property.

  • Analysis of UPA Systems: UPA focusing vectors with the same elevation and azimuth but different distances are asymptotically orthogonal as the number of antennas increases.
  • Analysis of UPA Systems: The asymptotic analysis assumes the near-field approximation remains valid, although the near-field assumption eventually fails as antenna count tends to infinity.
  • Analysis of UPA Systems: The UPA result is stronger than the corresponding ULA case because a very large N1 or N2 can guarantee orthogonality between different focusing vectors.
  • Analysis of UPA Systems: Improved spatial orthogonality in UPA communications limits interference from waves radiated toward different locations.

IV. NEAR-FIELD LOCATION DIVISION MULTIPLE ACCESS SCHEME

LDMA uses near-field beam focusing to serve users at distinct locations, exploiting distance-domain resolution alongside angular separation. The section develops a spherical-domain UPA codebook that samples angles and distances while retaining compatibility with hybrid analog precoding.

  • LDMA scheme: LDMA uses location-dependent near-field focusing vectors as analog precoders for users at different angles and distances.This contrasts with far-field SDMA, which primarily exploits angular beam steering.
  • Codebook design: Near-field codebook design must add radius sampling because far-field DFT codebooks sample only elevation and azimuth angles.The UPA design also addresses quadratic distance-dependent terms in the near-field model.
  • Codebook design: Neglecting the bilinear quadratic term causes at most 5% beamforming loss when communication distance exceeds 7.24 m for a 256 × 16 UPA at 30 GHz.The approximation simplifies UPA codebook design while introducing limited loss under the stated threshold and system parameters.
  • Codebook design: The spherical-domain codebook uses analytical beam correlations to perform non-uniform distance sampling for beams sharing the same direction.The distance correlation decreases with the sampling parameter, allowing a predefined correlation threshold to guide sampling density.
  • Codebook design: For a 64 × 64 UPA at 30 GHz, the designed codebook characterizes near-field sampling locations and has constant-modulus vectors suitable for analog phase shifters.The codebook is therefore directly applicable to hybrid-precoding multiuser MIMO systems.

C. LDMA Communication Procedure

The LDMA communication procedure combines near-field codebook-based beam selection, equivalent-channel estimation, and digital precoding. It supports parallel uplink and downlink transmissions through hybrid precoding.

  • Communication procedure: LDMA comprises initial access, uplink equivalent-channel estimation, and uplink/downlink data transmission.The procedure is illustrated as a three-stage communication process.
  • Digital precoding: Digital combiners and precoders are designed from the effective channel using WMMSE or zero-forcing methods.This digital stage follows analog beam selection and channel estimation.
  • Initial access: During initial access, beam sweeping selects a codeword for each user, and the selected codewords form the analog precoder.Each user reports its beam decision after beam determination.
  • Scope: The proposed procedure is not the only LDMA realization; alternative near-field channel estimation, beam sweeping, and precoding methods can also be incorporated.This leaves the LDMA concept compatible with multiple implementation choices.

V. PERFORMANCE ANALYSIS

The performance analysis examines whether LDMA approaches interference-free capacity and whether its distance-domain resolution improves spectrum efficiency over SDMA when users share a direction.

  • Performance analysis: The analysis evaluates asymptotic capacity and spectrum-efficiency gains in a same-direction multi-user scenario.The second scenario uses linearly distributed users to expose LDMA’s distance-domain advantage.
  • Performance analysis: LDMA is analyzed as a means to exploit spatial resources beyond the angular domain used by classical far-field SDMA.The analysis focuses on the additional resolution provided by near-field beam focusing.
  • Performance analysis: The section investigates whether increasing antenna count enables LDMA to approach ideal spectrum efficiency without multi-user interference.This provides the theoretical basis for comparing LDMA with SDMA.

A. Asymptotic Capacity of Single-path Channel

For single-path channels, the analysis derives LDMA spectrum efficiency under idealized assumptions and studies its asymptotic capacity and same-direction user separation. It also gives an approximate upper bound for linearly distributed users.

  • A. Asymptotic Capacity of Single-path Channel: The single-path analysis assumes perfect channel state information, an infinite analog codebook, equal power allocation, and zero-forcing digital precoding.These assumptions allow the spectrum efficiency to be expressed through the near-field focusing-vector matrix.
  • A. Asymptotic Capacity of Single-path Channel: As the number of antennas N tends to infinity, LDMA spectrum efficiency approaches the ideal interference-free capacity with probability one.The result follows from the asymptotic orthogonality of near-field beams.
  • B. Linear Distribution Analysis: LDMA’s distance-domain resolution can distinguish single-path users located at the same angle, motivating analysis of linearly distributed users.This is the spatial distinction that separates LDMA from classical SDMA in the considered setting.
  • B. Linear Distribution Analysis: The three-user linear-distribution analysis assumes single-path channels, high SNR, negligible non-adjacent interference, and zero-forcing digital precoding.The resulting expression is therefore tied to these stated modeling assumptions.
  • B. Linear Distribution Analysis: The resulting spectrum-efficiency expression is an approximate upper bound because non-adjacent-user interference is neglected.The paper denotes the practical relationship as R ≲ R_aub.

VI. SIMULATION RESULTS

The simulations evaluate LDMA in a single-cell near-field communication scenario with multiple single-antenna UEs served by an ELAA base station. They use 30 GHz half-wavelength spacing and consider both ULA and UPA arrays.

  • The evaluation considers multiple single-antenna UEs served by one ELAA-equipped base station in a single-cell scenario.
  • The carrier frequency is 30 GHz, with half-wavelength antenna spacing of d = λ/2 = 0.5 cm.
  • The simulations use a 512-element ULA and a 256×16-element UPA.

A. Linear Distribution Scenario for ULA Systems

The simulations compare LDMA with classical far-field SDMA across linear and uniform user distributions, channel conditions, antenna sizes, and UPA configurations. LDMA consistently achieves higher spectrum efficiency, with gains attributed to distance-domain orthogonality and near-field beamforming.

  • Linear Distribution Scenario for ULA Systems: Even randomly distributed UEs with LDMA outperform far-field SDMA when the number of UEs is not very large.Under linear placement, far-field SDMA supports only one UE because the single-path channels share the same steering vector.
  • Linear Distribution Scenario for ULA Systems: At SNR = 20 dB, WMMSE-based LDMA achieves about 60% and ZF-based LDMA about 240% performance gain over their SDMA counterparts in a multipath ULA scenario.The comparison uses K = 4 UEs, L = 5 NLoS paths, and both ZF and WMMSE digital precoding.
  • Conclusions: LDMA gains originate from extra distance-domain orthogonality and higher near-field beamforming gain compared with far-field beamforming.Distance-domain orthogonality accommodates more users with limited interference, while near-field focusing can increase beamforming gain.
  • Uniform Distribution Scenario for ULA Systems: At SNR = 20 dB, WMMSE-based LDMA achieves nearly 90% higher spectrum efficiency than classical WMMSE-based SDMA for uniformly distributed UEs.The uniform-distribution setting uses K = 10 UEs, five NLoS paths, and locations spanning a 4–100 m radius range and −π/3 to π/3 angles.
  • Performance Under Different System Parameters: LDMA and SDMA both lose spectrum efficiency as the number of NLoS paths increases, while LDMA remains superior to SDMA.The decrease is attributed to match-filter-based analog precoding, which favors sparse channel models.
  • Performance Under Different System Parameters: LDMA always outperforms SDMA across different Rician κ values, and spectrum efficiency increases with κ because the LoS component becomes stronger.
  • Performance Under Different System Parameters: As the antenna array grows from 64 to 512 elements, far-field SDMA deteriorates whereas near-field LDMA slightly improves.The reported trend is associated with stronger near-field effects and improved interference management from near-field focusing beams.
  • Performance of UPA Systems: For a 256 × 16 UPA at SNR = 20 dB, LDMA gains about 150% and 50% over ZF-based SDMA under linear and uniform UE distributions, respectively.The spherical-domain codebook also outperforms a same-size uniform-sampling near-field codebook.

APPENDIX A PROOF OF COROLLARY 2

The proof establishes that the correlation between near-field beam focusing vectors converges to zero for distinct locations. It handles separate cases according to whether the distance-domain coefficient η2 is zero.

  • The correlation of focusing vectors for distinct locations is expressed using the coefficients η1 and η2.The locations are characterized by range and angle, and the derivation substitutes the summation with an integral approximation.
  • When η2 ≠ 0, the correlation bound is derived through a variable substitution and Fresnel-function limits.
  • When η2 = 0, the distinct-location assumption ensures different angles, and the correlation still converges to zero.

APPENDIX C PROOF OF LEMMA 4

The proof derives an integral approximation for the correlation of beam focusing vectors aimed at the same direction but different distances. Fresnel-function properties then yield the limiting correlation expression.

  • The two-dimensional summation is approximated by an integral after substituting the antenna-index variables and using the stated index ranges.
  • Fresnel-function properties reduce the resulting integrations to the expression involving G(β1)G(β2), completing the proof.The proof also uses the diagonal effective channel structure under the matched focusing analog precoder and ZF digital precoding.

APPENDIX E PROOF OF COROLLARY 3

The proof establishes asymptotic orthogonality of distinct near-field beam-focusing vectors, yielding B^HB=I with probability one as the antenna count grows. It then analyzes correlation-dependent spectrum efficiency and shows it is maximized by minimizing the common adjacent-user correlation.

  • Asymptotic orthogonality: As the number of antenna elements tends to infinity, B^HB converges to the identity matrix with probability one under uniformly distributed user locations.This follows from the asymptotic orthogonality of different beam-focusing vectors in the distance domain.
  • Spectrum-efficiency analysis: Spectrum efficiency is determined by the diagonal elements of (B^HB)^-1, which are derived using the beam-correlation terms g1 and g2.The derivation substitutes these diagonal elements into the spectrum-efficiency expression and applies a high-SNR approximation.
  • Two-user optimization: For two users, symmetry and convexity show that the point where g1(x) equals g2(x) is a local maximum of the spectrum-efficiency objective.The derivative vanishes at the symmetric point because g1(x)=g2(r0−x) and g1 is monotonically decreasing.
  • Multiple-user analysis: For multiple linearly distributed users, the correlation matrix is tridiagonal with adjacent-user correlation δ, enabling a recurrence-based expression for its inverse diagonal elements.Positive semidefiniteness requires |δ|^2≤1, ensuring the recurrence roots are real.
  • Multiple-user optimization: The inverse diagonal elements increase monotonically with |δ|, so spectrum efficiency is maximized when the adjacent-user correlation is minimized across all K users.The minimizing configuration is expressed as the minimum achievable maximum adjacent-user correlation over the user distances.
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