﻿ 一种基于菲涅尔区的免穿戴呼吸检测模型 A Device-Free Breathing Detection Model Based on Fresnel Zone

Hans Journal of Wireless Communications
Vol.08 No.03(2018), Article ID:25272,10 pages
10.12677/HJWC.2018.83010

A Device-Free Breathing Detection Model Based on Fresnel Zone

Yu Gu, Bowen Liu, Jinhai Zhan

University of Technology, Hefei Anhui

Received: May 13th, 2018; accepted: May 29th, 2018; published: Jun. 5th, 2018

ABSTRACT

Detecting breathing with wireless signal has been proved to be feasible, but there are still some problems that should be improved. For example, the experiment usually requires a large space. Also, the experiment is vulnerable to environmental factors like surrounding people’s activities. This paper analyzes and compares the radius of the Fresnel Zone in different directions mathematically. We have built an optimization model for the antenna setting exploring of the classic path loss model in free space propagation and the characteristics of electromagnetic field of antennas. The results of our experiments show that the WI-BD model based on Fresnel Zone is feasible. The change range of channel state information can reach 4 - 8 dB, and the model has several significant advantages: Firstly, it effectively reduces the size of the space required by the experiments; Secondly, we can directly get the best radius of Fresnel Zone; Lastly, we can adjust the distance between the antennas to get the best performance.

Keywords:Fresnel Zone, Channel State Information, Respiratory Rate, Line Of Sight, Reflected Signal, External Antenna

1. 引言

2. 模型的理论准备

2.1. 菲涅尔区模型

$|\stackrel{⇀}{\text{AM}}|+|\stackrel{⇀}{\text{MB}}|={L}_{1}+i×\frac{\lambda }{2},i\in {N}^{*}$ (1)

${r}_{i}^{x}=\left(\left({L}_{1}+i×\frac{\lambda }{2}\right)-{L}_{1}\right)/2=i×\frac{\lambda }{4}$ (2)

${r}_{i}^{y}=\frac{1}{4}\sqrt{{\left({L}_{1}+i×\frac{\lambda }{2}\right)}^{2}-{\left({L}_{1}\right)}^{2}}$ (3)

Figure 1. Signal propagation model in LOS environment

Figure 2. The section of Fresnel zone

Figure 3. The change of Fresnel zone radius

2.2. 自由空间传播损耗计算

$\text{PL}=32.5+\mathrm{lg}\left(F\right)+\mathrm{lg}\left(D\right)$ (4)

WIFI信号的载波频率固定不变，因此F为常量。于是结合公式(4)可知，传播距离D越大，路径损耗越高。经过计算，大约传播距离增加一倍，信号能量强度衰减6 dB。

2.3. 常见WIFI天线物理特征

3. 实验设定的理论分析

$\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1$ (5)

$k=-\frac{{b}^{2}x}{{a}^{2}y}=\frac{b}{a}\mathrm{cot}\left(\theta \right)$ (6)

${k}_{m}=-\frac{\sqrt{{m}^{2}{\lambda }^{2}+8mc\lambda }}{4c+m\lambda }\mathrm{cot}\left(\theta \right)$ (7)

${k}_{m-1}=-\frac{\sqrt{{\left(m-1\right)}^{2}{\lambda }^{2}+8\left(m-1\right)c\lambda }}{4c+\left(m-1\right)\lambda }\mathrm{cot}\left(\theta \right)$ (8)

$M=4c+m\lambda$$N={m}^{2}{\lambda }^{2}+8mc\lambda$ ，代入公式(7)和公式(8)，则有：

$\frac{{k}_{m}}{{k}_{m-1}}=\frac{\sqrt{N}}{M}/\left(\frac{\sqrt{N-\left(2m-1\right){\lambda }^{2}-8c\lambda }}{M-\lambda }\right)$ (9)

$相位差=\frac{呼吸位移}{菲涅尔区半径}×\text{π}$ (10)

Figure 4. The distance change of common focus ellipse

Table 1. Antenna spacing and detection area radius (unit: cm)

4. WI-BD模型简介及验证

4.1. WI-BD模型简介

WI-BD模型的具体结构如图5所示。

Figure 5. The structure of WI-BD model

1) 初始化。任意选择第k子载波进行差分处理，生成差分序列 $\Delta {I}_{k}^{1},\cdots ,\Delta {I}_{k}^{p}$

2) 合并单调区间。令 $t=1$$P=0$$Q=0$ ；将差分序列中相邻同为正或同为负的数值合并成一个区间，以区间累加值 $\Delta {m}_{i}$ 以及合并数值个数 $\Delta {n}_{i}$ 表示第i区间，可得累加值序列 $\Delta {m}_{1},\cdots ,\Delta {m}_{r}$ 和计数序列 $\Delta {n}_{1},\cdots ,\Delta {n}_{r}$

3) 若t小于r，从位置t开始，在累加值序列中找到第一个大于给定阈值 ${A}_{1}$$\Delta {m}_{a}$ 作为吸气阶段起始位置；否则退出算法。

4) 从 $s=a$ 开始，尝试累加 $\Delta {m}_{s}$$\Delta {n}_{s}$ ，若s等于r，则退出算法；若在b处有 $\Delta {m}_{s}$ 的累加值大于 ${M}_{1}$ ，且 $\Delta {n}_{s}$ 的累加值不大于 ${N}_{1}$ ，则认为找到吸气阶段，更新 $t=b+1$ ，若P为0，则 $P=b$ ，否则；否则， $t=t+1$ ，转3)。

5) 若t小于r，从位置t开始，在累加值序列中找到第一个小于给定阈值 ${A}_{2}$$\Delta {m}_{c}$ 作为呼气阶段起始位置；否则退出算法。

6) 从 $s=c$ 开始，尝试累加 $\Delta {m}_{s}$$\Delta {n}_{s}$ ，若s等于r，则退出算法；若在d处有 $\Delta {m}_{s}$ 的累加值小于 ${M}_{2}$ ，且 $\Delta {n}_{s}$ 的累加值不大于 ${N}_{2}$ ，则认为找到呼气阶段，更新 $t=d+1$ ；否则 $P=0$$t=t+1$ ，转3)。

7) 若P为0，则 $P=Q$ ，转3)。

8) 累计 $\Delta {n}_{P}$$\Delta {n}_{Q-1}$ ，记为S。则有 ${F}_{v}=60f/S$ ，更新 $P=Q$$t=t+1$ ，转3)。

4.2 模型验证

WI-BD模型与其他基于WIFI信号的呼吸检测对比如表2所示，很明显本文所述模型在多个方面具有显著的优势。本文已证明天线间距显著影响有效检测范围，且不同方向上菲涅尔区半径存在差异性，因此认为本文所述模型在经过调整后可用于多人模式下呼吸检测，未来工作中将进一步予以探索。

(a) 平卧睡姿 (b) 侧卧睡姿

Figure 6. The Experimental arrangement of supine posture and lateral decubitus posture

(a) 降噪前 (b) 降噪后

Figure 7. De-noising treatment of respiratory data

Figure 8. The change of instantaneous respiratory frequency

Table 2. The comparison of respiratory detection models based on WIFI signal (unit: dB)

5. 结束语

A Device-Free Breathing Detection Model Based on Fresnel Zone[J]. 无线通信, 2018, 08(03): 87-96. https://doi.org/10.12677/HJWC.2018.83010

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