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Channel Capacity of Near-Field Line-of-Sight Multiuser Communications

Boqun Zhao, Chongjun Ouyang, Xingqi Zhang, Yuanwei Liu

TL;DR

Theoretical and numerical results are presented and compared with far-field communications to demonstrate that the NF capacity of these three channels converges to finite values rather than growing unboundedly as the number of array elements increases.

Abstract

The channel capacity of near-field (NF) communications is characterized by considering three types of line-of-sight multiuser channels: i) multiple access channel (MAC), ii) broadcast channel (BC), and iii) multicast channel (MC). For NF MAC and BC, closed-form expressions are derived for the sum-rate capacity as well as the capacity region under a two-user scenario. These results are further extended to scenarios with an arbitrary number of users. For NF MC, closed-form expressions are derived for the two-user channel capacity and the capacity upper bound with more users. Further insights are gleaned by exploring special cases, including scenarios with infinitely large array apertures, co-directional users, and linear arrays. For comparison, the MAC and BC sum-rates achieved by typical linear combiners and precoders are also analyzed. Theoretical and numerical results are presented and compared with far-field communications to demonstrate that: i) the NF capacity of these three channels converges to finite values rather than growing unboundedly as the number of array elements increases; ii) the capacity of the MAC and BC with co-directional users can be improved by using the additional range dimensions in NF channels to reduce inter-user interference (IUI); and iii) the MC capacity benefits less from the NF effect compared to the MAC and BC, as multicasting is less sensitive to IUI.

Channel Capacity of Near-Field Line-of-Sight Multiuser Communications

TL;DR

Theoretical and numerical results are presented and compared with far-field communications to demonstrate that the NF capacity of these three channels converges to finite values rather than growing unboundedly as the number of array elements increases.

Abstract

The channel capacity of near-field (NF) communications is characterized by considering three types of line-of-sight multiuser channels: i) multiple access channel (MAC), ii) broadcast channel (BC), and iii) multicast channel (MC). For NF MAC and BC, closed-form expressions are derived for the sum-rate capacity as well as the capacity region under a two-user scenario. These results are further extended to scenarios with an arbitrary number of users. For NF MC, closed-form expressions are derived for the two-user channel capacity and the capacity upper bound with more users. Further insights are gleaned by exploring special cases, including scenarios with infinitely large array apertures, co-directional users, and linear arrays. For comparison, the MAC and BC sum-rates achieved by typical linear combiners and precoders are also analyzed. Theoretical and numerical results are presented and compared with far-field communications to demonstrate that: i) the NF capacity of these three channels converges to finite values rather than growing unboundedly as the number of array elements increases; ii) the capacity of the MAC and BC with co-directional users can be improved by using the additional range dimensions in NF channels to reduce inter-user interference (IUI); and iii) the MC capacity benefits less from the NF effect compared to the MAC and BC, as multicasting is less sensitive to IUI.
Paper Structure (47 sections, 17 theorems, 103 equations, 13 figures)

This paper contains 47 sections, 17 theorems, 103 equations, 13 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Channel Model
  4. Signal Models for Multiuser Communications
  5. MAC
  6. BC
  7. MC
  8. Multiple Access Channel
  9. Near-Field Capacity of the Two-User Case
  10. Sum-Rate Capacity
  11. Capacity Region
  12. Comparison with the FF Capacity
  13. Comparison with Linear Combiners
  14. Optimal Linear Combining
  15. Maximal-Ratio Combining
  16. ...and 32 more sections

Key Result

Lemma 1

When the SIC decoding order $1\rightarrow2$ is adopted, the rates of the UTs are, respectively, given by For the decoding order $2\rightarrow1$, we have

Figures (13)

  • Figure 1: Illustration of the array geometry.
  • Figure 2: Illustration of the ULA.
  • Figure 3: $\Gamma_{{\mathsf{ul}},\ell}$ versus $M$ for different combiners with $(\theta_1,\phi_1)=(\frac{\pi}{3},\frac{2\pi}{3})$ and the other parameter settings given in Section \ref{['numerical']}.
  • Figure 4: Illustration of the BC and dual MAC capacity regions.
  • Figure 5: $\Gamma_{{\mathsf{dl}},\ell}$ versus $M$ for different precoders with $(\theta_1,\phi_1)=(\frac{\pi}{3},\frac{2\pi}{3})$ and the other parameter settings given in Section \ref{['numerical']}.
  • ...and 8 more figures

Theorems & Definitions (28)

  • Lemma 1
  • Theorem 1
  • Corollary 1
  • Remark 1
  • Remark 2
  • Corollary 2
  • Corollary 3
  • Remark 3
  • Lemma 2
  • Corollary 4
  • ...and 18 more