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Fast-Fading Channel and Power Optimization of the Magnetic Inductive Cellular Network

Honglei Ma, Erwu Liu, Zhijun Fang, Rui Wang, Yongbin Gao, Wenjun Yu, Dongming Zhang

Abstract

The cellular network of magnetic Induction (MI) communication holds promise in long-distance underground environments. In the traditional MI communication, there is no fast-fading channel since the MI channel is treated as a quasi-static channel. However, for the vehicle (mobile) MI (VMI) communication, the unpredictable antenna vibration brings the remarkable fast-fading. As such fast-fading cannot be modeled by the central limit theorem, it differs radically from other wireless fast-fading channels. Unfortunately, few studies focus on this phenomenon. In this paper, using a novel space modeling based on the electromagnetic field theorem, we propose a 3-dimension model of the VMI antenna vibration. By proposing ``conjugate pseudo-piecewise functions'' and boundary $p(x)$ distribution, we derive the cumulative distribution function (CDF), probability density function (PDF) and the expectation of the VMI fast-fading channel. We also theoretically analyze the effects of the VMI fast-fading on the network throughput, including the VMI outage probability which can be ignored in the traditional MI channel study. We draw several intriguing conclusions different from those in wireless fast-fading studies. For instance, the fast-fading brings more uniformly distributed channel coefficients. Finally, we propose the power control algorithm using the non-cooperative game and multiagent Q-learning methods to optimize the throughput of the cellular VMI network. Simulations validate the derivation and the proposed algorithm.

Fast-Fading Channel and Power Optimization of the Magnetic Inductive Cellular Network

Abstract

The cellular network of magnetic Induction (MI) communication holds promise in long-distance underground environments. In the traditional MI communication, there is no fast-fading channel since the MI channel is treated as a quasi-static channel. However, for the vehicle (mobile) MI (VMI) communication, the unpredictable antenna vibration brings the remarkable fast-fading. As such fast-fading cannot be modeled by the central limit theorem, it differs radically from other wireless fast-fading channels. Unfortunately, few studies focus on this phenomenon. In this paper, using a novel space modeling based on the electromagnetic field theorem, we propose a 3-dimension model of the VMI antenna vibration. By proposing ``conjugate pseudo-piecewise functions'' and boundary distribution, we derive the cumulative distribution function (CDF), probability density function (PDF) and the expectation of the VMI fast-fading channel. We also theoretically analyze the effects of the VMI fast-fading on the network throughput, including the VMI outage probability which can be ignored in the traditional MI channel study. We draw several intriguing conclusions different from those in wireless fast-fading studies. For instance, the fast-fading brings more uniformly distributed channel coefficients. Finally, we propose the power control algorithm using the non-cooperative game and multiagent Q-learning methods to optimize the throughput of the cellular VMI network. Simulations validate the derivation and the proposed algorithm.
Paper Structure (21 sections, 7 theorems, 55 equations, 12 figures, 2 tables, 1 algorithm)

This paper contains 21 sections, 7 theorems, 55 equations, 12 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Antenna Vibration Modeling
  3. The Modeling
  4. MI Fast-Fading Gain
  5. Statistical Characteristics of VMI Fast-fading Gain
  6. General Distribution Vibration Model
  7. Gaussian Road Roughness Model
  8. Outage probability
  9. Power Control Optimization Algorithm With Multiagent Q-Learning
  10. Network Modeling
  11. Problem Transformation
  12. Design Multiagent Q-Learning Algorithm
  13. Numerical Evaluation
  14. CDF of VMI fast-fading gain
  15. Expectation of VMI fast-fading gain
  16. ...and 6 more sections

Key Result

Lemma 1

(Concavity): The functions $J_{b,i+}(X_i)$ and $J_{b,i-}(X_i)$ are convex and concave for $\phi_i \in [0, \frac{\pi}{2}\!+\!k\pi]$, respectively. Conversely, the functions $J_{b,i+}(X_i)$ and $J_{b,i-}(X_i)$ are concave and convex for $\phi_i \in [-\frac{\pi}{2}\!-\!k\pi, 0]$, respectively.

Figures (12)

  • Figure 1: Antenna vibration modeling for the channel from BS $b$ to VU $i$, $\theta_i \in [-90^\circ,90^\circ]$ is the angle of the antenna vibration, $\phi\in[-180^\circ, 180^\circ]$ represents the antenna background orientation, $X_i$ is the AVI.
  • Figure 2: Equivalent circuit model for the channel from BS to VU $i$.
  • Figure 3: Example of a CVMC network.
  • Figure 4: Received SNR under a VMI fast-fading channel. Suppose the vehicle is traveling away from the BS at a speed of 3 m/s along an underground road inclined at a $30^\circ$ angle.
  • Figure 5: CDF values of VMI fast-fading gain with different average AVIs.
  • ...and 7 more figures

Theorems & Definitions (11)

  • Definition 1
  • Lemma 1
  • Lemma 2
  • Definition 2
  • Theorem 1
  • Theorem 2
  • Proposition 1
  • Remark 1
  • Definition 3
  • Proposition 2
  • ...and 1 more