Modeling and Capacity Analysis of Terahertz Channel Based on Beckman-Kirchhoff Scattering Theory

Jinsheng Yang; Lei Zong

doi:10.3788/LOP202259.2301001

Journals >Laser & Optoelectronics Progress >Volume 59 >Issue 23 >Page 2301001 > Article

Laser & Optoelectronics Progress
Vol. 59, Issue 23, 2301001 (2022)

Modeling and Capacity Analysis of Terahertz Channel Based on Beckman-Kirchhoff Scattering Theory

Jinsheng Yang and Lei Zong^*

Author Affiliations

School of Microelectronics, Tianjin University, Tianjin 030072, China

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DOI: 10.3788/LOP202259.2301001 Cite this Article Set citation alerts

Jinsheng Yang, Lei Zong. Modeling and Capacity Analysis of Terahertz Channel Based on Beckman-Kirchhoff Scattering Theory[J]. Laser & Optoelectronics Progress, 2022, 59(23): 2301001 Copy Citation Text

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Abstract

Terahertz (0.1-10 THz) band communication is envisioned as a key technology of future wireless communication because of its technical characteristics, such as super large bandwidth resources and super high communication rates. Herein, ray-tracing techniques and Beckman-Kirchhoff scattering theory are used to modify a unified multi-ray channel model in the terahertz band. The model combines direct, reflection, and scattering, and is supported by experimental data from the literatures. Furthermore, the wideband channel capacity usage is characterized using equal power and water-filling power allocation strategies. The simulation results show that the importance of resource allocation in exploiting the terahertz spectrum due to its extremely high frequency-selectivity. The study will provide some guidance for future research and design of the terahertz communication systems.

Keywords

atmospheric optics and ocean optics Beckman-Kirchhoff scattering theory channel capacity multi-ray channel ray-tracing terahertz

H_{i} (f) = H_{L o S} (f) + H_{R e f} (f) + H_{S c a} (f)

，（1）

H_{S p r} (f) = \frac{c}{4 π f d}

，（2）

H_{A b s} (f) = e x p [- \frac{1}{2} k (f) d]

，（3）

H_{L o S} (f) = H_{S p r} (f) H_{A b s} (f) e x p (- j 2 π f τ_{L o S})

，（4）

H_{R e f} (f) = (\frac{1}{4 π f (r_{1} + r_{2})}) e x p [- \frac{1}{2} k (f) (r_{1} + r_{2})] \cdot R (f) \cdot e x p [- j 2 π f τ_{R e f}]

。（5）

R (f) = Γ \cdot e^{- \frac{g}{2}} = Γ \cdot e x p (- \frac{8 π^{2} f σ^{2} c o s^{2} θ_{i}}{c^{2}})

，（6）

\begin{matrix} R_{T E} (f) = \frac{c o s θ_{i} - \sqrt[]{\frac{ε_{2}}{ε_{1}} - s i n^{2} θ_{i}}}{c o s θ_{i} + \sqrt[]{\frac{ε_{2}}{ε_{1}} - s i n^{2} θ_{i}}} \cdot e^{- \frac{g}{2}} = \\ - (1 + \frac{- 2 c o s θ_{i}}{c o s θ_{i} + \sqrt[]{\frac{ε_{2}}{ε_{1}} - s i n^{2} θ_{i}}}) \cdot e^{- \frac{g}{2}} \approx - (1 + \frac{- 2 c o s θ_{i}}{\sqrt[]{\frac{ε_{2}}{ε_{1}} - 1}}) \cdot \\ e^{- \frac{g}{2}} \approx - e x p (\frac{- 2 c o s θ_{i}}{\sqrt[]{\frac{ε_{2}}{ε_{1}} - 1}}) \cdot e^{- \frac{g}{2}} \end{matrix}

；（7）

R_{T M} (f) = \frac{\frac{ε_{2}}{ε_{1}} c o s θ_{i} - \sqrt[]{\frac{ε_{2}}{ε_{1}} - s i n^{2} θ_{i}}}{\frac{ε_{2}}{ε_{1}} c o s θ_{i} + \sqrt[]{\frac{ε_{2}}{ε_{1}} - s i n^{2} θ_{i}}} \cdot e^{- \frac{g}{2}} \approx - e x p (\frac{- 2 (\frac{ε_{2}}{ε_{1}}) c o s θ_{i}}{\sqrt[]{\frac{ε_{2}}{ε_{1}} - 1}}) \cdot e^{- \frac{g}{2}}

。（8）

\begin{array}{l} H_{S c a} (f) = (\frac{1}{4 π f (s_{1} + s_{2})}) e x p [- \frac{1}{2} k (f) (s_{1} + s_{2})] \cdot \\ S (f) \cdot e x p [- j 2 π f τ_{S c a}] \end{array}

，（9）

E_{s} = (1 + Γ) E_{i n}

，（10）

ρ = \frac{E_{S}}{E_{r}}

，（11）

E_{r} = \frac{j k A c o s θ_{i} e^{j k r}}{π r}

，（12）

E_{S} = \frac{2 A c o s θ_{i}}{λ r} ρ

。（13）

g = k^{2} σ^{2} {(c o s θ_{1} + c o s θ_{2})}^{2}

，（14）

ρ_{\infty} = \{\begin{matrix} e^{- \frac{g}{2}} \sqrt[]{ρ_{0}^{2} + \frac{π L^{2} F^{2}}{L_{x} L_{y}} \sum_{m = 1}^{\infty} \frac{g^{m}}{m! m} e x p [\frac{- (u_{x}^{2} + u_{y}^{2}) L^{2}}{4 m}]}, g ≪ 1 \\ \sqrt[]{\frac{π L^{2} F^{2}}{L_{x} L_{y} v_{z}^{2} σ^{2}} \sum_{m = 1}^{\infty} \frac{g^{m}}{m! m} e x p [\frac{- (u_{x}^{2} + u_{y}^{2}) L^{2}}{4 u_{z}^{2} σ^{2}}]}, g ≫ 1 \end{matrix}

，（15）

ρ_{0} = s i n c (v_{x} L_{x}) \cdot s i n c (v_{y} L_{y}),

（16）

v_{x} = k (s i n θ_{1} - s i n θ_{2} c o s θ_{3})

，（17）

v_{y} = k (s i n θ_{2} s i n θ_{3})

，（18）

v_{z} = - \sqrt[]{ε_{2} / ε_{1}} k (c o s θ_{1} + c o s θ_{2})

，^（19）

F^{2} = c o s θ_{1}

。（20）

P_{t o t} = P_{s p e c u l a r} + P_{s c a t t e r i n g}

。（21）

ρ_{s p e c u l a r f i n i t e}^{2} = Γ^{2} \cdot e^{- g}

，（22）

R (f) = Γ \cdot e^{- \frac{g}{2}}

，（23）

S (f) = \{\begin{matrix} Γ \cdot e^{- \frac{g}{2}} \cdot \sqrt[]{\frac{π L^{2} c o s θ_{1}}{L_{x} L_{y}} \sum_{m = 1}^{\infty} \frac{g^{m}}{m! m} e x p [\frac{- (u_{x}^{2} + u_{y}^{2}) L^{2}}{4 m}]}, g ≪ 1 \\ Γ \cdot \sqrt[]{\frac{π L^{2} c o s θ_{1}}{L_{x} L_{y} v_{z}^{2} σ^{2}} \sum_{m = 1}^{\infty} \frac{g^{m}}{m! m} e x p [\frac{- (u_{x}^{2} + u_{y}^{2}) L^{2}}{4 u_{z}^{2} σ^{2}}]}, g ≫ 1 \end{matrix}

。（24）

H_{i} (f) = \{\begin{array}{l} (\frac{1}{4 π f d}) e x p [- \frac{1}{2} k (f) d] \cdot e x p [- j 2 π f τ_{L o S}], d i r e c t \\ [\frac{1}{4 π f (r_{1} + r_{2})}] e x p [- \frac{1}{2} k (f) (r_{1} + r_{2})] \cdot R_{\frac{T E}{T M}} (f) \cdot e x p (- j 2 π f τ_{R e f}), r e f l e c t i o n \\ [\frac{1}{4 π f (s_{1} + s_{2})}] e x p [- \frac{1}{2} k (f) (s_{1} + s_{2})] \cdot S (f) \cdot e x p (- j 2 π f τ_{S c a}), s c a t t e r i n g \end{array}

。（25）

C = Δ f_{i} l o g_{2} [1 + \frac{{|H_{i}|}^{2} P_{i}}{Δ f_{i} S_{N} (f_{i})}]

，（26）

Jinsheng Yang, Lei Zong. Modeling and Capacity Analysis of Terahertz Channel Based on Beckman-Kirchhoff Scattering Theory[J]. Laser & Optoelectronics Progress, 2022, 59(23): 2301001

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