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On the Impact of Reactive Region on the Near-Field Channel Gain

Chongjun Ouyang, Zhaolin Wang, Boqun Zhao, Xingqi Zhang, Yuanwei Liu

TL;DR

This work analyzes near-field channel gain with both radiating and reactive EM components, deriving new expressions for SPD and CAP arrays and performing asymptotic analysis as aperture size grows. It demonstrates that the reactive region introduces only small, rapidly decaying corrections to the gain, with asymptotic gains G_eva^upa and G̃_eva^upa approaching their radiating counterparts G_rad^upa and G̃_rad^upa as distance increases. The results, applicable to UPAs and ULAs and linked by the occupancy factor μ_oc, show the reactive region has negligible impact on near-field performance even for infinite apertures, aligning with energy-conservation expectations. The findings provide theoretical justification for neglecting evanescent-wave effects in practical near-field design and offer closed-form asymptotic expressions to quantify the limits of reactive-region influence. These insights are relevant for the design of extremely large aperture arrays at high frequencies in near-field regimes and for validating energy-transfer predictions in NFC scenarios.

Abstract

The near-field channel gain is analyzed by considering both radiating and reactive components of the electromagnetic field. Novel expressions are derived for the channel gains of spatially-discrete (SPD) and continuous-aperture (CAP) arrays, which are more accurate than conventional results that neglect the reactive region. To gain further insights, asymptotic analyses are carried out in the large aperture size, based on which the impact of the reactive region is discussed. It is proved that for both SPD and CAP arrays, the impact of the reactive region on near-field channel gain is negligible, even as the array aperture size approaches infinity.

On the Impact of Reactive Region on the Near-Field Channel Gain

TL;DR

This work analyzes near-field channel gain with both radiating and reactive EM components, deriving new expressions for SPD and CAP arrays and performing asymptotic analysis as aperture size grows. It demonstrates that the reactive region introduces only small, rapidly decaying corrections to the gain, with asymptotic gains G_eva^upa and G̃_eva^upa approaching their radiating counterparts G_rad^upa and G̃_rad^upa as distance increases. The results, applicable to UPAs and ULAs and linked by the occupancy factor μ_oc, show the reactive region has negligible impact on near-field performance even for infinite apertures, aligning with energy-conservation expectations. The findings provide theoretical justification for neglecting evanescent-wave effects in practical near-field design and offer closed-form asymptotic expressions to quantify the limits of reactive-region influence. These insights are relevant for the design of extremely large aperture arrays at high frequencies in near-field regimes and for validating energy-transfer predictions in NFC scenarios.

Abstract

The near-field channel gain is analyzed by considering both radiating and reactive components of the electromagnetic field. Novel expressions are derived for the channel gains of spatially-discrete (SPD) and continuous-aperture (CAP) arrays, which are more accurate than conventional results that neglect the reactive region. To gain further insights, asymptotic analyses are carried out in the large aperture size, based on which the impact of the reactive region is discussed. It is proved that for both SPD and CAP arrays, the impact of the reactive region on near-field channel gain is negligible, even as the array aperture size approaches infinity.
Paper Structure (11 sections, 6 theorems, 35 equations, 5 figures)

This paper contains 11 sections, 6 theorems, 35 equations, 5 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. SPD Arrays
  4. CAP Arrays
  5. SPD Arrays
  6. Analysis of the Channel Gain
  7. Impact of the Reactive Region
  8. Uniform Linear Array
  9. CAP Arrays
  10. Numerical Results
  11. Conclusion

Key Result

Theorem 1

When the BS is equipped with an SPD array, the channel gain is given by where ${\mathcal{H}}=\{\left.(x,z)\right|-\frac{M_x\varepsilon}{2}\leq x\leq\frac{M_x\varepsilon}{2},-\frac{M_z\varepsilon}{2}\leq z\leq\frac{M_z\varepsilon}{2}\}$.

Figures (5)

  • Figure 1: Illustration of the EM field.
  • Figure 2: Illustration of an SPD array and a CAP array.
  • Figure 3: Channel gains of SPD and CAP arrays.
  • Figure 4: Channel gain ratio.
  • Figure 5: The inscribed and circumscribed disks of the rectangular region ${\mathcal{H}}=\{\left.(x,z)\right|\frac{M_x\varepsilon}{-2}\leq x\leq\frac{M_x\varepsilon}{2},\frac{M_z\varepsilon}{-2}\leq z\leq\frac{M_z\varepsilon}{2}\}$.

Theorems & Definitions (13)

  • Theorem 1
  • Theorem 2
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Corollary 1
  • Remark 5
  • Remark 6
  • Theorem 3
  • ...and 3 more