基於 WiFi 通道狀態資訊的跌倒偵測系統研究及改進

93  Download (0)

Full text

(1)

國立臺灣大學電機資訊學院電信工程學研究所 碩士論文

Graduate Institute of Communication Engineering College of Electrical Engineering and Computer Science

National Taiwan University Master Thesis

基於 WiFi 通道狀態資訊的跌倒偵測系統研究及改進

A Study on a Device-Free Fall Detection System Based on WiFi Channel State Information and its Improvement

吳易錡 Yi-Chi Wu

指導教授:謝宏昀 博士 Advisor: Hung-Yun Hsieh, Ph.D.

中華民國 111 年 9 月

September 2022

(2)

doi:10.6342/NTU202203973

致謝

秋風蕭蕭,金風送爽,剎那間研究所的 700 多個日子已過,台北依舊是時 代的繁榮,暖陽依舊是那樣的燦爛,人們依舊是如此的熟悉。如今驪歌響起,

高興但不捨,高興能在研究所期間領悟了許多道理、學會了好多知識、得到了 眾多有誼;不捨鳥語花香的校園、燈火輝煌的城市。

感謝父母在我徬徨無助時給予我關心及鼓勵,願意傾聽我的苦水和牢騷,

在我遭遇挫折或不順心時,給我建議並當我最強大的後盾,讓我可以專心於學 習和研究。感謝謝宏昀教授在研究上提供我許多想法以及建議,在每一次的報 告討論中都可以明白研究的核心及重點,讓我可以一步步成功整合研究並完成 論文。感謝一起畢業的學長和同學,很慶幸這一路上有你們的陪伴,讓我在這 趟旅程中不會感受到孤獨。感謝這屆的同學,平常的嘻笑玩鬧已成回憶,時間 仍不斷的流逝,期許你們都能盡快完成這趟旅程,踏上下班列車。感謝實驗室 的學弟,讓我感受到實驗室的熱情,希望你們都可以向自己的目標邁進。

時光荏苒,曲終人散,這趟旅程將到終點站,而等待我的是下個嶄新的旅 途。縱使有多麼的感傷也得離別,再見了台大,再見了熟悉的人們,再見了台 北,期待未來有朝一日與你們的相聚。

2022/09/24 吳易錡筆

(3)

摘要

跌倒運動檢測是近年來學術和應用領域最引人注目的人體運動檢測,因為 跌倒是現代社會老年人致命健康威脅的主要原因,甚至可能導致死亡。由於跌 倒會產生比一般日常運動更高的速度,我們使用速度資訊來檢測跌倒運動。速 度資訊非常適用於在有偌大速度差異運動中的跌倒檢測,例如走路和跌倒。然 而,我們很難只用速度來區分有速度差別不顯著的運動,例如跌倒和奔跑。因 此,我們設計了一種新穎的跌倒檢測系統,該系統利用基於通道狀態信息 (CSI) 功率響應的自相關函數(autocorrelation function, ACF)的速度資訊以 及機器學習模型的集成方法實現。首先,我們使用 PicoScenes 平台從常見的 WiFi 信號中收集 PHY 層細粒度的 CSI。在接收到 CSI 信號後,我們設計了一 種新的第一局部谷值演算法來尋找 CSI 功率響應的自相關函數(ACF)的第一局 部谷值的位置。然後,藉由該位置計算出速度資訊。結果表明,我們通過演算 法估計的速度具有代表性,因為估計的速度幾乎與實際速度成正比。因此,我 們利用此速度資訊進行後續跌倒偵測,並將其視為二元分類任務,因為只有兩 類數據:有跌倒和無跌倒。為了完成二元分類,我們在速度資訊上使用機器學 習模型的檢查點集成方法的擴展,該模型可以區分有細微速度差別的運動,特 別是對於卷積神經網絡(CNN)。使用此系統性能可以提高 29% 且誤判率可以降 低 30.5%。最終,我們將此系統應用於多人環境,準確率為 90% 且精確度可以 到達 94%。

(4)

doi:10.6342/NTU202203973

ABSTRACT

Fall motion detection is the most high-profile human motion detection in aca- demic and industrial regions in recent years since fall is the leading cause of fatal health threats for elders in modern society that can even give rise to death. Since fall leads to a higher speed than general daily motions, we employ speed informa- tion to detect fall motion. The speed works well on fall detection in the motions with a huge difference in speed, such as walking and falling. Nevertheless, it is impossible to use only speed to distinguish the motions with a slight difference in speed, such as falling and running. Therefore, we design a novel fall detection system leveraging a machine learning model with the ensemble method and speed information based on the autocorrelation function (ACF) of Channel State Infor- mation (CSI) power response. First, we collect PHY layer fine-grained CSI from ubiquitous WiFi signals with the PicoScenes platform. After receiving the CSI signal, we design a new first local valley algorithm to find the location of the first local valley of the autocorrelation function (ACF) of CSI power response. Then, the speed information is calculated from this location. The result shows that our estimated speed by the algorithm is representative since the estimated speed is almost proportional to the real speed. Thus, we leverage this speed information for the following fall detection and regard it as a binary classification task since there are only two classes of data: fall class and no fall class. To accomplish binary classification, we perform the machine learning model with the extension of the checkpoint ensemble techniques on the speed information, which can distinguish the motions with a slight difference in speed, especially for the Convolutional Neu- ral Network (CNN). The performance is improved by 29% and the false alarm rate is decreased by 30.5%. Eventually, we apply it to the multi-person environment.

The accuracy is 90% and the precision reaches 94%.

ii

(5)

TABLE OF CONTENTS

ABSTRACT . . . . ii

LIST OF TABLES . . . vi

LIST OF FIGURES . . . vii

CHAPTER 1 INTRODUCTION . . . . 1

CHAPTER 2 BACKGROUND AND RELATED WORK . . . . 5

2.1 Introduction of Motion Detection . . . 5

2.2 WiFi Signals . . . 6

2.2.1 Received Signal Strength (RSS) and Received Signal Strength Indicator (RSSI) . . . 6

2.2.2 Channel State Information (CSI) . . . 6

2.2.3 Comparison and Conclusion . . . 7

2.3 CSI Tool . . . 8

2.3.1 Linux 802.11n CSI Tool . . . 8

2.3.2 PicoScenes . . . 9

2.4 CSI Phase Offsets . . . 11

2.5 Fall Motion Detection Techniques . . . 12

2.5.1 Wearable Sensor-based Approaches . . . 12

2.5.2 Ambient-based Approaches . . . 13

2.5.3 Vision-based Approaches . . . 13

2.5.4 Radio-Frequency (RF)-based Approaches . . . 13

2.6 WiFi-based Fall Motion Detection . . . 14

CHAPTER 3 SYSTEM MODEL . . . . 16

3.1 System Design . . . 16

3.2 Data Collection . . . 17

3.3 Speed Estimation . . . 20

3.4 Fall Detection . . . 21

3.4.1 Sliding Window . . . 21

(6)

doi:10.6342/NTU202203973

TABLE OF CONTENTS iv

CHAPTER 4 SPEED ESTIMATION . . . . 23

4.1 ACF of CSI Power Response . . . 23

4.1.1 Statistical Theory of EM Waves in a Rich-scattering En- vironment . . . 23

4.1.2 Received Electric Field of EM Waves . . . 27

4.1.3 CSI Power Response and Its ACF . . . 27

4.1.4 The Relationship between the First Local Valley of Differ- ential ACF and the Speed . . . 29

4.2 First Local Valley Algorithm . . . 32

4.2.1 First Local Valley . . . 32

4.2.2 The Complexity of the Function . . . 33

4.2.3 Smoothing Method . . . 35

4.2.4 Topographic Prominence . . . 38

4.2.5 First Local Valley Algorithm . . . 40

4.3 Motion Detection Methods . . . 40

4.3.1 Overview . . . 40

4.3.2 ACF of CSI power response . . . 41

4.4 Modified Speed Estimation Algorithm . . . 42

4.5 Acceleration . . . 44

CHAPTER 5 FALL DETECTION . . . . 45

5.1 Sliding Window . . . 45

5.2 Machine Learning Model for Binary Classification . . . 47

5.2.1 Target Problem . . . 47

5.2.2 Binary Cross Entropy . . . 48

5.2.3 Fully Connected Neural Network (FCNN) Model . . . 49

5.2.4 1-D Convolutional Neural Network (CNN) Model . . . . 50

5.3 Extension of the Checkpoint Ensemble . . . 52

CHAPTER 6 PERFORMANCE EVALUATION . . . . 55

6.1 Experimental Setup . . . 55

6.1.1 Experimental Environment . . . 55

6.1.2 Parameters Setting . . . 56

(7)

TABLE OF CONTENTS v

6.1.3 Motion Dataset . . . 57

6.1.4 Metrics . . . 57

6.2 Speed Evaluation . . . 57

6.3 Motion Evaluation . . . 60

6.3.1 Threshold Method . . . 60

6.3.2 Datasets . . . 63

6.3.3 Preprocessing . . . 63

6.3.4 Original Method . . . 64

6.3.5 Novel Method . . . 65

6.3.6 Ablation Study . . . 74

6.4 Multi-person Environment . . . 74

CHAPTER 7 CONCLUSION AND FUTURE WORK . . . . . 79

REFERENCES . . . . 81

(8)

doi:10.6342/NTU202203973

LIST OF TABLES

1 Comparison of recent CSI-based indoor fall detection systems . . 15 2 Layers of the FCNN model . . . 50 3 Layers of the CNN1D model . . . 52 4 Ablation study . . . 74

vi

(9)

LIST OF FIGURES

1 The overview of RSS and CSI. . . 8

2 The interface of Linux 802.11n CSI tool. . . 9

3 The interface of PicoScenes platform. . . 10

4 Overview of system architecture. . . 16

5 PicoScenes information on the receiver. . . 18

6 Part of the converted and arranged csv file. . . 19

7 CSI amplitude data. . . 19

8 Speed information after speed estimation. . . 20

9 Optimal speed information after motion detection. . . 20

10 The aboriginal run motion data. . . 21

11 The run motion data with sliding window. . . 22

12 The process of fall detection. . . 22

13 The block of speed estimation. . . 23

14 Theoretical spatial ACF from [12]. . . 26

15 Differential spatial ACF from [12]. . . 26

16 First local valley in differential spatial ACF from [12]. . . 32

17 Spatial ACF. . . 33

18 Curve fitting problem. . . 34

19 The results of spectral smoothing. . . 37

20 Spectral smoothing with different values of smooth_fraction. . . . 37

21 The first local valley may be different from the first local minimum. 38 22 The topographic prominence. . . 39

23 The result of valley detection by topographic prominence. . . 39

24 The effect of the first value in the differential ACF. . . 43

25 Final speed information in different motions of algorithm 4. . . . 43

26 Speed and acceleration of run motion. . . 44

27 The block of fall detection. . . 45

28 The aboriginal run motion data. . . 46

(10)

doi:10.6342/NTU202203973

LIST OF FIGURES viii

29 The run motion data with sliding window. . . 47

30 The architecture of FCNN model. . . 49

31 The architecture of CNN model. . . 51

32 Ensemble method. . . 54

33 The transmitter and the receiver in the environment. . . 55

34 The overall research environment in room 521. . . 56

35 The walking environment. . . 58

36 The location of walk motion. . . 59

37 The relationship between the measured speed and the real speed. 60 38 Scatter figure of walk and fall motion. . . 61

39 Scatter figure of walk, fall, and run motion. . . 61

40 The implementation of original method. . . 62

41 The confusion matrix of original method. . . 64

42 Original method. . . 65

43 The confusion matrix of FCNN model. . . 66

44 FCNN model. . . 67

45 The confusion matrix of CNN model. . . 68

46 CNN model on run motion. . . 68

47 Different results of CNN model. . . 69

48 CNN model with checkpoint ensemble on a series of motions. . . . 70

49 The confusion matrix of CNN model with checkpoint ensemble method. . . 71

50 The wrong results of our novel method. . . 72

51 The windows of fall and run motion. . . 73

52 The confusion matrix of CNN model with checkpoint ensemble in the multi-person environment. . . 76

53 The results of CNN model with checkpoint ensemble on walk-and- fall motion. . . 77

54 The results of CNN model with checkpoint ensemble on run-and- fall motion. . . 78

(11)

CHAPTER 1

INTRODUCTION

Fall motion is a behavior that is a common but often overlooked cause of in- jury. In Taiwan, around one in six adults over 65 will have at least one fall a year in 2017, and the second highest accident injury causes of death over 65 years old elderly is falls, which is preceded only by traffic accidents [1]. In addition, the Cen- ter for Disease Control and Prevention (CDC) indicates that more than one out of four older people falls each year and one out of five falls leads to a serious injury such as broken bones or head injury [2]. Most falls do not result in serious in- jury among young people. However, according to the research, 80% injury-related hospitalizations over age 65 come from falls [3], and nearly 3 million older people in the world are treated in emergency departments for fall injuries [2]. Addition- ally, fall leads to 53.9% minor injuries and 27.3% serious injuries, including bone fractures (like wrist, arm, ankle, and hip fractures), bone dislocations, visceral injuries, head injury, traumatic brain injury (TBI), etc. Most importantly, falls can give rise to severe head injuries that might lead to hemiplegia, paralysis, and even death if the older people ignore it or don’t see the doctor immediately. After experiencing a fall, it might cause post-fall syndrome (PFS), fallophobia, and fear of falling to an elder in the future [3]. These fears could cause older people to cut down on their everyday activities. When a person is less active, they become weaker, increasing their chances of falling [2]. Thus, fall is one of the significant health threats and impediments for elders around the world; timely and reliable fall motion detection is crucial for alleviating the injury and sequela effects of fall.

As fall motion is one of the most dangerous motions, there are many methods to detect fall motion. In earlier studies, the mainstream technologies are ambient device-based, wearable sensor-based, and visible camera-based. In ambient device- based [4] [5], it implants the sensors in the monitoring environment so that the environment information can be used as the metric of fall motion, for example, the vibration of the floor. However, ambient device-based might usually cause unnecessary false alarms. In wearable sensor-based [6] [7], the sensors are worn on the person in the monitoring environment, but it is inconvenient for people to carry the custom-made devices all day. In visible camera-based [8] [9], the high-resolution camera must be installed in the monitoring environment, so an image processing algorithm for scene recognition can be performed on a series of recorded images. Nonetheless, the camera watches the people in the environment

(12)

doi:10.6342/NTU202203973 2

like a hawk, which leads to a privacy problem. Besides, the camera is sensitive to light, so visible camera-based does not operate in dim and dark surroundings.

Due to the limitations in the earlier research, we perform WiFi signals to detect fall motion. Compared with the above-mentioned fall detection solutions, the ad- vantages of WiFi signals are device-free, privacy preserving, light unaffecting, and Non-Line-Of-Sight nature. If there is a fall motion in the environment of interest, the WiFi signals are interfered with by the motion. Then, we leverage the distorted signals to detect the motions since different activities cause different interferences.

To obtain the useful distorted signals, we observe the Channel State Information (CSI), which is the PHY layer information of wireless signals. In CSI data, it is fine-grained information that can capture the information of multiple propagation paths in the time domain. In addition, we employ PicoScenes platform [10] to col- lect CSI data. PicoScenes platform is the most novel CSI collected platform, which was released in August 2021. In this platform, we can operate on all-format, all- channel, and all-bandwidth packets by widespread and common Network Interface Cards (NIC), such as AX210, AX200, QCA9300, and IWL5300, compared with common Linux 802.11n CSI Tool [11], which only operates on 802.11 n protocol, fixed bandwidth, and IWL5300 NIC.

Since fall motion is a quick activity in daily life compared with general motions, such as walk, sit, stand, ..., the speed of a motion seems to be a useful and feasible feature to detect fall motion. Based on the speed information, we can classify the motions; for instance, if the speed is slow, the motion may be a walk motion; if the speed is fast, the motion might be a fall motion. Thus, we employ WiSpeed [12]

to estimate the speed of the motion by the statistical theory of EM waves in a rich-scattering environment. In WiSpeed, it can classify the fall motion from the walk, stand up, sit down, and pick up motions, which are the motions with a large difference in speed. Nevertheless, there are two imperfections in WiSpeed. First, it proposed a peak identification algorithm to estimate the speed indirectly, but the algorithm is ambiguous and obscure. Furthermore, it does not describe the relationship between the estimated speed and the real speed, so we do not know the efficacy and accuracy of the algorithm. Second, if there is a run motion in the environment, it is a false alarm in WiSpeed since it only uses the speed threshold method for classification that the speed of run and fall motions are all over the threshold. That is to say, WiSpeed cannot deal with the motions with a slight difference in speed.

Therefore, to improve the first weakness, we design a first local valley algo- rithm by the complexity of the function and the spectral smoothing method. The

(13)

3

algorithm can effectively find the location of the first local valley, which can in- directly estimate the speed. After performing the algorithm, the estimated speed is usable and available for the following research since the relationship between the estimated speed and the real speed is close to proportional that represents the algorithm can obtain the almost real speed of a moving object. In addition, to solve the second shortcoming, we perform the machine learning model for bi- nary classification that one class is fall motion, and the other is no fall motion.

We employ the Fully Connected Neural Network (FCNN) model first, which can roughly classify the two class motion and the motions with a slight difference in speed. The accuracy is only 82% and precision is 87% since it is a simple clas- sification method. Next, we perform the Convolutional Neural Network (CNN) model [13]. This model can classify the two class motion and the motions with a slight difference in speed more accurately since it can extract useful features by convolutional layers. With the run motion, the CNN model has 88% accuracy and 93% precision compared with 65% in WiSpeed and 82% and 87% in the FCNN model. Furthermore, as there is little randomness in the model, we employ an extended version of the checkpoint ensemble method to obtain the advantages of all best models and result in better outcomes by a majority vote. After using the CNN model with the extension of the checkpoint ensemble method, the accuracy reaches 94% and precision reaches 96%. Eventually, we move our system into a multi-person environment. Since our system obtains the highest speed among the objects in a multi-person environment, it can still detect fall motion correctly.

The accuracy of fall detection in a multi-person environment is about 90% and the precision is about 94%.

In summary, the main contributions of this work are as follows:

1. We use the first local valley algorithm to find the location of the first local valley, which can indirectly estimate the speed with this important location.

First, we calculate the complexity of the function; and then, we smooth the function by spectral smoothing with Fourier Transform based on the complexity. After employing the algorithm, we find that the relationship between the estimated speed and the true speed is a direct ratio, which means that our estimated speed has a certain accuracy, i.e., our estimated speed can effectively represent the almost real speed. In contrast, the speed and algorithm in WiSpeed are unclear and ambiguous, so we cannot explic- itly know the relationship and accuracy between the estimated speed and the real speed.

2. We perform the machine learning models to classify the motions, such as the FCNN and CNN models. In these models, we can get better results

(14)

doi:10.6342/NTU202203973 4

than WiSpeed, especially for the CNN model since it can extract useful and valuable features automatically with the convolutional layer. Additionally, as there is some randomness in the machine learning models, we perform the extension of the checkpoint ensemble method to obtain the benefits of the best models and output better results by a majority vote. In conclusion, we employ the machine learning model with the extension of the checkpoint ensemble method for classification, which has better classification results and can cope with the motions with a slight difference in speed. On the contrary, WiSpeed only leverages a simple threshold method to classify the motions that the faster speed is fall motion and the slower speed is viewed as no fall motion. In this method, it cannot deal with the motions with a slight difference in speed, such as run and fall motion, since the speeds of these motions are similar to each other so the threshold method would classify them into the same class.

(15)

CHAPTER 2

BACKGROUND AND RELATED WORK

2.1 Introduction of Motion Detection

Detection is a process to detect what we want to detect by some tools. If we’d like to detect human motion, it is known as human motion detection. If we want to detect different material objects, it is called object detection. It is called human presence detection if we prefer to detect anyone in the region of interest. We are interested in human motion detection, which is usually employed in three main daily life applications.

1. Smart home: This application can detect how long people sit or stay in a fixed position. If people have been seated for a long time, it will notify them to stand up and limber up their muscles and joints. In addition, if people work out or exercise at home, it can detect and record how many times squats, push-ups, sit-ups, and so forth, which makes it easy for people to work out and exercise at home.

2. Home care: In this application, it can accomplish the recognition of dan- gerous or life-threatening movements and activities, such as fall motion or motion of hitting the head, because people are prone to internal bleeding or other serious problems of falling to the ground, especially the elderly may have fractures or more severe body injuries when they fall. Over and above that, these motions can even cause death. As a result, when these activities happen, it must notify the family members immediately.

3. Home security: In this application, it can be realized that there is no one at home by the book during the work and class period. If there is any movement or activity detected at home, it will first distinguish whether it is a person or a pet. If it is a pet, its movement will be ignored. If it is a person, it will notify the family members, ask them to pay attention, and watch out for intrusion or burglary.

In conclusion, Motion detection is a groundbreaking technology because we can know the different motions without seeing them directly. With this powerful technology, the smart home, home care, and home security applications can be accomplished perfectly.

(16)

doi:10.6342/NTU202203973

2.2. WIFI SIGNALS 6

2.2 WiFi Signals

In WiFi fall motion detection or generally WiFi human motion recognition, the transmitter sends the wireless signals to the receiver. Before arriving at the receiver, the wireless signal would be distorted, modulated, and interfered by hu- man motion. We can simply classify human motion by differentiating the received distorted signals with similarity functions or machine learning models. Recently, the researchers almost employ Received Signal Strength (RSS) or Channel State Information (CSI) signal from WiFi commodity devices as the above wireless sig- nal to detect different motions by the signal distortion and interference. The following sections explain these two WiFi signals separately.

2.2.1 Received Signal Strength (RSS) and Received Signal Strength Indicator (RSSI)

Received Signal Strength (RSS) belongs to the MAC layer information of wire- less communication protocol, which characterizes the total received power of all propagation paths and is coarse-grained information. In an everyday environment, there are multiple signals transmitted paths from a transmitter to a receiver. The summed value of power received over all paths is [14]

V = XN

i=1

∥ Vi ∥ e−jθ, (2.1)

where Vi and θi are the amplitude and phase of the ith multipath component and N is the total number of multipath components. RSS is the above received total power V in decibels (dB):

R = 10 log2(∥ V ∥2). (2.2)

After obtaining RSS, the Received Signal Strength Indicator (RSSI) is only a value range conversion from RSS since the value range of RSS is usually negative, which is inconvenient for practical applications and RSSI can transform the nega- tive value of RSS to positive. Therefore, some papers prefer to exploit RSSI. From Equation (2.2), RSS is the superimposition of multipath components, which can- not explicitly describe each path component’s characteristic, called coarse-grained information. As a result, RSS or RSSI is not capable of coping with the multipath effect and the indoor environment’s temporal dynamics.

2.2.2 Channel State Information (CSI)

Channel State Information (CSI) belongs to the PHY layer information of wireless communication protocol, which characterizes the channel performance

(17)

2.2. WIFI SIGNALS 7

with the amplitude and phase for subcarrier frequency fk measured at time t0 in an OFDM-based communication system, such as WiFi, LTE, 5G, etc., and is fine- grained information. Compared with RSS, which is a summation of all paths that is incapable of dealing with the multipath effect, Channel Impulse Response (CIR) can fully characterize the individual paths, which can describe the multipath effect of the wireless channel and denote as [14]

h(τ ) = XN

i=1

αie−jθiδ(τ − τi), (2.3) where αi, θi, and τi are the amplitude attenuation, phase shift, and time delay of the ith multipath component, respectively. δ(τ ) is the Dirac delta function which represents that each impulse is a delayed multipath component with the corre- sponding amplitude and phase. In the frequency domain, we can also perform Channel frequency response (CFR) to describe multipath transmission by ampli- tude, frequency, and phase frequency which is the Fourier Transforms from CIR, shown as below:

H(fk, t0) =∥ H(fk, t0)∥ ej∠H(fk,t0), (2.4) where fk and t0 are the central frequency of subcarrier k and measured time.

∠H(fk, t0) is the phase of CFR. Actually, CSI is the K sampled version of CFR, formulated as below:

H(fk, t0) =∥ H(fk, t0)∥ ej∠H(fk,t0), k = 1,· · · , K. (2.5) From Equation (2.5), CSI comes from CIR and CFR, so it can accurately distinguish each multiple propagation path in the time domain, called fine-grained information, which represents that CSI is capable of handling the multipath effect effectively.

2.2.3 Comparison and Conclusion

From the previous sections, the relationship, process, and equations of RSS and CSI signals are shown in Figure 1

(18)

doi:10.6342/NTU202203973

2.3. CSI TOOL 8

WiFi signals

CFR RSSI

CIR RSS

CSI

value range conversion

FT

sampled version

𝑉 = ෍

𝑖=1 𝑁

𝑉𝑖𝑒−𝑗𝜃𝑖 R = 10 log2( 𝑉2)

ℎ 𝜏 = ෍

𝑖=1 𝑁

𝛼𝑖𝑒−𝑗𝜃𝑖𝛿(𝜏 − 𝜏𝑖)

𝐻 𝑓𝑘, 𝑡0 = 𝐻 𝑓𝑘, 𝑡0 𝑒𝑗𝐻 𝑓𝑘,𝑡0

𝐻 𝑓𝑘, 𝑡0 = 𝐻 𝑓𝑘, 𝑡0 𝑒𝑗𝐻 𝑓𝑘,𝑡0, 𝑘 = 1~𝐾

Superimposition of multipath signals

Discrimination of multipath characteristics Capture the multipath effect Fine-grained Fail to capture the multipath effect Coarse-grained (MAC layer)

(PHY layer)

Each impulse represents a delayed multipath component

Figure 1: The overview of RSS and CSI.

2.3 CSI Tool

2.3.1 Linux 802.11n CSI Tool

Before any CSI platform releasing, all researchers only perform RSS or RSSI signal to implement WiFi sensing applications. Nevertheless, Section 2.2.1 has some shortcomings of the RSS signal, merely capturing total power at the receiver.

Compared with RSS, CSI is another better choice for WiFi sensing since it can display the multipath effect and contains channel information between each pair of transmit-receive antennas at the level of the individual subcarrier. The first and earliest CSI platform is Linux 802.11n CSI tool [11], released by Daniel Halperin et al..

Linux 802.11n CSI tool [11] uses the Intel WiFi Wireless Link 5300 NIC with three antennas to implement the CSI data collection and works on the ancient Ubuntu 14.04 as the operating system. The Intel 5300 NIC reports CSI for 30 groups of subcarriers, spread evenly among the 56 subcarriers of a 20MHz channel or the 114 subcarriers in a 40MHz channel, which is about one group for every two subcarriers at 20 MHz or one in 4 at 40 MHz, namely, this platform can only obtain 30 subcarriers regardless of the bandwidth or other conditions.

Linux 802.11n CSI tool was released in 2011, which is far from today. This platform is fast, simple, and convenient for implementing WiFi sensing research.

Still, the limitation of the number of subcarriers and the firmly fixed characteristic allows it to lose its importance and be replaced by other platforms by degrees.

(19)

2.3. CSI TOOL 9

That is the primary reason why we abandon it to exploit another platform.

We have employed the sensing system with TP-LINK TL-WDR7500 wireless router as the access point (AP) and the Linux 802.11n CSI tool on the Dell PP39L notebook (2.53 GHz Intel Core 2 Duo Processor and 4 GB RAM) equipped with off-the-shelf Intel WiFi Wireless Link 5300 NIC with Ubuntu 14.04 as the monitor- ing point (MP) to collect the CSI data, which is .dat file. The operated interface is illustrated in the following figure.

Figure 2: The interface of Linux 802.11n CSI tool.

2.3.2 PicoScenes

In previous CSI platforms, such as Linux 802.11n CSI tool, Atheros CSI tool, and Nexmon CSI tool, all of them are inflexibility in some perspectives. For example, first, they are only able to support particular hardware, such as IWL 5300, AR9580, and bcm4366c0 NIC respectively. Additionally, they are limited to some specific configurations, which can only operate on 20/40 MHz bandwidth and on IEEE 802.11n/ac protocol. Eventually, all of them cannot support the latest hardware (AX200/AX210 NIC) and deployment (IEEE 802.11ax protocol) to obtain more channel information. In conclusion, they are a little bit outdated;

however, fortunately, there is an newest CSI platform to accomplish the flexible and robust characteristics, i.e., PicoScenes [10], released by Zhiping Jiang et al..

PicoScenes [10] is a versatile and powerful platform for CSI-based WiFi sens- ing research. It helps researchers overcome two barriers in WiFi sensing research:

inadequate hardware features and insufficient measurement software functional- ity. From a hardware viewpoint, it supports the most CSI-extractable hardware,

(20)

doi:10.6342/NTU202203973

2.3. CSI TOOL 10

including commercial off-the-shelf (COTS) WiFi NICs and software defined radio (SDR) devices, such as AX210/AX200/QCA9300/IWL5300 and all models of the USRP, respectively. From a software standpoint, it features the live CSI plot, various low-level controls, and packet injection in all formats and all bandwidths, which promises a fixed-rate CSI measurement.

There are many advantages of PicoScenes. It is the first and currently the only platform to support multi-NIC concurrent CSI measurement and public-available 802.11ax-format CSI measurement. In addition, it is a super easy installation with auto-update support. We can install PicoScenes on Ubuntu 20.04 in just three simple steps: downloading a KB-size .deb file, double-clock installing it, and finally installing the platform via the popular apt install approach. At last, it supports most models of CSI-extractable hardware. It currently supports the AX210, AX200, QCA9300, IWL5300 NIC, and the USRP-based SDR devices, which is the broadest hardware platform in the world.

We have implemented the sensing system with the PicoScenes on ASUS S500SA computer (2.9 GHz Intel Core i5-10400 Processor, 8GB RAM, GeForce GT1030 2GB) equipped with commodity AX200 NIC with Ubuntu 20.04 as the trans- mitter (TX) and the PicoScenes on Gigabyte Aorus 15G notebook (2.3-5.1 GHz Intel Core i7-10875H Processor, 16GB RAM, GeForce RTX-2060 GDDR6 8GB) equipped with commodity AX200 NIC with Ubuntu 20.04 as the receiver (RX) to collect the CSI data, which is .csi file. The operated interface is shown as follows.

Figure 3: The interface of PicoScenes platform.

(21)

2.4. CSI PHASE OFFSETS 11

2.4 CSI Phase Offsets

In CSI information, there is amplitude and phase information in each subcar- rier. However, in CSI phase information, as a result of hardware imperfection, non-synchronized clock, delayed packets, and so forth, it suffers from several off- sets and distortions [15], [16], [17], [18] which leads phase data to be noisy and interfered. We introduce and list general phase offsets in the following part. Thus, in our research, we only employ CSI amplitude data that is less distorted than CSI phase data.

• Carrier Frequency Offset (CFO): It is the difference between the carrier frequency of the transmitted signal and the one measured at the receiver, i.e., the carrier frequency of the transmitter and receiver are not perfectly matched, because both are generated from non-synchronized Local Oscil- lators (LOs) whose frequency offset is independently shifting and varying over time due to hardware imperfection. Consequently, the phase of all CSI subcarriers will suffer from a temporal (time-varying) phase offset ϕCF O.

• Sampling Frequency Offset (SFO): The SFO of the transmitter and the receiver exhibit an offset since the ADC clocks of the transmitter and the receiver are non-synchronized and imperfection; both will drift separately.

Therefore, each received signal will experience a time-varying delay offset (time shift) with respect to the transmitted signal. In the frequency domain, the offset is represented in the CSI phase as an additional phase rotation proportional to subcarrier index (sub-channel) m, denoted as τSF O.

• Packet Detection Delay (PDD): After an OFDM symbol passes through the down-conversion and ADC sampling, the receiver estimates the packet boundary of the OFDM symbol by using correlation detection or energy detection. The estimated packet boundary may include a delay offset, i.e., a delay is a time required to recover and determine the transmitted modulated symbols from the received signal. Similar to SFO, this delay exhibits in the frequency domain as another additional phase rotation proportional to subcarrier index (sub-channel) m, named as τP DD.

• Phase-locked loop Phase Offset (PPO): Phase-locked loop circuit is respon- sible for generating a center frequency for both transmitter and receiver. As both are using different chips, it will also individually create and start some random initial phases when the WiFi NIC is initialized, causing phase dif- ference to the received OFDM symbol, i.e., each time when the transmitter and the receiver start to operate, random initial phases are generated, and the such initial phase difference is known as PPO ϕ .

(22)

doi:10.6342/NTU202203973

2.5. FALL MOTION DETECTION TECHNIQUES 12

• Phase Ambiguity (PA): It is the phase difference between two receiving antennas. Recent work validates a so-called four-way phase ambiguity ex- istence in Intel WiFi Wireless Link 5300 NIC when working on 2.4 GHz, which can lead the phase difference to be θ, θ + π2, θ− π2, θ − π. As for Atheros 9380 NIC, it is similar to discovering a two-way phase ambiguity.

It expresses as ϕP A.

On the basis of five phase offsets, they can be categorized into time domain and frequency domain phase rotation error. CFO, PPO, and PA are phase offset errors in the time (temporal) domain. They would have identical values across the subcarriers in each receiving antenna when time changes, i.e., they are subcarrier independent. In contrast, SFO and PDD are phase offset errors in the frequency domain. They would change their values as changing in time, i.e., they are sub- carrier dependent. To summarize, different subcarriers in each spatial stream will display the same phase offset values of CFO, PPO, and PA but different phase offset values of SFO and PDD. Thus, the total phase offsets of subcarrier m in the received signal ϕof f set,m can be modeled as a summation of these five offsets in the following [15]

ϕof f set,m= −2πm(τSF O+ τP DD)

T + ϕCF O+ ϕP P O + ϕP A, (2.6) where T is the OFDM symbol time.

2.5 Fall Motion Detection Techniques

Currently, there are mainly four existing solutions for human sensing, recogni- tion, and detection, especially for fall motion detection: wearable sensor-based ap- proaches, ambient-based approaches, vision-based approaches, and radio-frequency (RF)-based approaches. The first is a device-based approach, and the last three are device-free approaches.

2.5.1 Wearable Sensor-based Approaches

Wearable sensor-based approaches are to hold some specific devices or wear some special devices with embedded sensors to detect the motion and activity of the human who wears them. The embedded sensors include accelerometers, gyroscopes, barometric sensors, ECG sensors, smartphones, and magnetometers to reveal the wearer’s motion. In [6] and [7], they use some kinds of sensors to capture some information (e.g., velocity, acceleration, blood pressure, etc.) of the human for fall motion detection. However, there are some drawbacks, including always-on-body requirement (e.g., carrying a specialized device all the time is

(23)

2.5. FALL MOTION DETECTION TECHNIQUES 13

inconvenient and cumbersome, especially for some elders.), and battery problems (e.g., the batteries in the device need to be changed frequently.).

2.5.2 Ambient-based Approaches

Ambient-based approaches exploit multiple dedicated devices with sensors im- planted in the environment of interest to obtain the ambient information to detect the motion and activity of the human when the human is closed to them. The ambient information includes audio noise (acoustic sensor), floor vibration sensor, bed sensor, and pyroelectric IR sensor. In [4] and [5], they employ devices with specific sensors installed in the environment to capture the proximity ambient in- formation of the human closed to them for fall motion detection. Nevertheless, shortcomings emerge in these approaches. For instance, installed requirements (e.g., special devices equipped with sensors need to be installed in the environ- ment beforehand.) and false alarm problems (e.g., the other sources which cause the same effect in the environment, such as falling objects, would lead to the large portion of false alarms).

2.5.3 Vision-based Approaches

Vision-based approaches use cameras or depth cameras like Kinect deployed in the monitoring environment of interest to capture images or videos to detect the motion and activity of the human who is Line-Of-Sight and in the clear field of view. The cameras capture the snapshot of human motions and activities, and then computer vision methods and machine learning model are performed to discern the motions. In [8] and [9], they apply computer vision algorithms to analyze the captured images and video sequences of the human for fall motion detection.

Unfortunately, these approaches have some limitations, such as the Line-Of-Sight requirement (e.g., it cannot detect through the presence of obstacles, like walls and doors.), the lighting requirement (e.g., it is difficult to work in a dark or dim environment.), and privacy intrusion (e.g., it cannot be installed in some specific positions such as bathroom and bedroom.)

2.5.4 Radio-Frequency (RF)-based Approaches

Due to the limitations of the aforementioned fall detection approaches, the contactless, device-free, privacy preserving, low deployment cost, light unaffecting, and Non-Line-Of-Sight nature allow the Radio-frequency (RF)-based approaches to become much more popular in recent years, such as the Doppler radar, Blue- tooth and WiFi signals. In RF-based systems, the transmitter sends the wireless signals to the receiver. The different human motions in the environment can

(24)

doi:10.6342/NTU202203973

2.6. WIFI-BASED FALL MOTION DETECTION 14

cause different distortions and interferences in the received signals. By analyzing the distorted signals at the receiver, the different distorted signals can be mapped to the different human activities. RSS and CSI of WiFi signals discussed in Sec- tion 2.2 are usually used for wireless signals. In recent research, CSI is superior in implementing human motion detection and sensing since it is fine-grained infor- mation that can obtain more channel information compared with a coarse-grained RSS. In [19], [20], [21], and [22], they leverage CSI information received by WiFi commodity devices to extract some useful and important features for fall motion detection.

2.6 WiFi-based Fall Motion Detection

Fall is one of the most dangerous motions in daily life. The most common ap- proach to detect fall motion is WiFi-based fall motion detection, which is related to Radio-Frequency (RF)-based approaches in Section 2.5.4, due to the character- istics of device-free, privacy preserving, and Non-Line-Of-Sight nature. In recent years, there has been some research on WiFi-based fall motion detection.

In WiFall [19], it is the first WiFi-based fall motion detection paper. It only takes the amplitude of CSI for activity classification and uses the weighted moving average filter for denoising. To obtain the activity region, it performs anomaly detection aiming to detect the anomaly change in wireless signal, which repre- sents the motion region. Lastly, a Support Vector Machine (SVM) is used for motion classification. The accuracy is 87%. However, in WiFall, it can only be implemented in a single-person environment and Line-Of-Sight (LOS) environ- ment. Besides, the system can only perform four predefined activities (i.e., walk, sit, stand up, fall).

In RT-Fall [21], it leverages CSI amplitude and phase difference across different subcarriers and streams and uses a 1-D linear interpolation algorithm, band-pass filter, and segmentation for data preprocessing. It extracts eight features from CSI amplitude and phase difference for activity classification, including the normal- ized standard deviation (STD), the median absolute deviation (MAD), the offset of signal strength, interquartile range (IR), signal entropy, the velocity of signal change, the TimeLag, and the power decline ratio (PDR). At last, it performs an SVM classifier with the above features to classify fall motion from other mo- tions (e.g., standing, walking, running/jogging, jumping, sitting down, getting up from a chair/bed, lying down, picking up an object, answering the phone, eating, performing an exercise like a push-up, ...)) that the accuracy is 91%. Nonethe- less, in RT-Fall, it can only be implemented in a single-person environment and Line-Of-Sight (LOS) environment, which is the same as WiFall.

(25)

2.6. WIFI-BASED FALL MOTION DETECTION 15

In WiSpeed [12], it exploits the statistical theory of electromagnetic (EM) waves in the rich-scattering environment to establish a relationship between the autocorrelation function (ACF) of CSI power response (the square of the magni- tude of CSI) and the speed of moving object. After performing WiSpeed, it can obtain the speed and acceleration of the motion, such as falling down, standing up, sitting down, and picking up. It can use the threshold method to distinguish fall motion because its speed and acceleration change is the maximum of four motions. The accuracy is 95%. However, it can only be implemented in a single- person environment. Additionally, it can merely classify the motions with a large difference in speed, such as fall and walk motions. If the speeds of motions are similar, e.g., fall and run motions, it cannot operate successfully.

In DeFall [22], it takes the same statistical theory of electromagnetic (EM) waves in a rich-scattering environment of WiSpeed to obtain the speed and ac- celeration of the motion. Moreover, it employs the band-relased segmental locally normalized dynamic time-wraping (SLNDTW) technique to localize an event’s start and end points since there might exist redundant segments of other motions, such as walking and sitting down, before or after the fall event, including stand- then-fall and walk-then-fall. Then it performs dynamic time-wraping (DTW) distance to detect whether the event is a fall motion or not. The accuracy is 96%.

Although it can be implemented in a multi-person environment (two people) and Non-Line-Of-Sight environment, it can still merely classify the motions with a large difference in speed, which is the same as WiSpeed. Last but not least, the above references are listed in Table 1.

Table 1: Comparison of recent CSI-based indoor fall detection systems

Name CSI Feature Accuracy Limitation

WiFall [19] amplitude 87%

single person, LOS between Tx and Rx, performing predefined activities RT-Fall [21] amplitude,

phase 91% single person,

LOS between Tx and Rx WiSpeed [12] amplitude 95%

single person, motions with a large

difference in speed DeFall [22] amplitude 96% motions with a large

difference in speed

(26)

doi:10.6342/NTU202203973

CHAPTER 3

SYSTEM MODEL

3.1 System Design

Data Collection Speed Estimation Fall Detection

Motion Detection Machine Learning

Model Extension of

Checkpoint Ensemble

First Local Valley Algorithm ACF of CSI power

response

Sliding Window

Figure 4: Overview of system architecture.

In Figure 4, it is our system architecture. First of all, we collect the CSI data of motion by the PicoScenes platform in the environment of interest. Next, we estimate the speed of motion from the previously collected CSI data. To estimate the speed, we calculate the autocorrelation function (ACF) of CSI power response and perform a first local valley algorithm to find the location of the first local valley since the speed is concerned about this crucial location. Moreover, we employ the motion detection method to detect the motion region, which can remove the redundancy region (no motion region) of the speed. At last, we want to distinguish the fall motion from the calculated speed. Before classifying the motions, we apply a sliding window to the speed since it corresponds to real time analysis. Then, we take the window data as the input training data into the machine learning model with the ensemble method to implement the fall motion detection because this task can be regarded as a binary classification problem. In the following contents, we are going to introduce each block in Figure 4 and its

16

(27)

3.2. DATA COLLECTION 17

technology.

3.2 Data Collection

As we have discussed the CSI tool in section 2.3, we are going to perform the PicoScenes platform to collect CSI data. Compared with the Linux 802.11n CSI tool, PicoScenes can operate on the specific channel and bandwidth to reduce interference from other devices since most wireless devices operate on a 2.4GHz channel, such as Bluetooth, Zigbee, wireless keyboard and mouse. Thus, we em- ploy the PicoScenes platform on the two computers. Each of them is equipped with Intel AX200 NIC with two antennas; one computer is the transmitter, the other is the receiver. The transmission link channel works on Wireless LAN (WLAN) 5 GHz channel 40 with a carrier frequency of 5.2 GHz and a channel bandwidth of 20 MHz in the IEEE 802.11ac protocol, so it can obtain a total of 57× 2 × 2 subcarriers, where 2 is the number of the antenna on the transmitter and receiver and 57 is the size that FFT size in the 20 MHz bandwidth of IEEE 802.11ac protocol removes the number of guard subcarriers which are against interference from adjacent channels or sub-channels (64− 7 = 57). Additionally, the sampling rate, also called transmission speed, sets to 1500 Hz. After receiving the data, we can get the .csi file named concatenating input, motion, and the motion index, e.g., input_fall_1.csi and input_walk_5.csi. In the file, there is a lot of useful information, such as device information which is device type ID (AX200), packet protocol (802.11ac), the number of transmit and receive Space-Time Streams (2), etc., channel information which are channel bandwidth (20 MHz), carrier fre- quency (5.2 GHz), the number of OFDM subcarriers (57), and so on, and CSI information which is CSI data, CSI magnitude data, and CSI phase data, shown in figure 5. However, this type of file cannot do a follow-up analysis since it cannot be opened directly. Therefore, we need to perform the data conversion to extract the applicable information in the .csi file.

(28)

doi:10.6342/NTU202203973

3.2. DATA COLLECTION 18

Figure 5: PicoScenes information on the receiver.

Now, we have received a .csi file from the data collection block and need to extract the information in the file. There are two tools, PicoScenes MATLAB Toolbox (PMT) [23] and PicoScenes Python Toolbox (PPT) [24], to implement it. As PPT is easy to use, high scalability, and faster parsing than the PMT implementation, we apply it to parse the received frame structure. The data structures of the raw parsing packets are all listed in [25]. In the packet, there are many structures and variables, such as StandardHeader, which is the 802.11 MAC header of source and destination, RxSBasic, which is the received information, e.g., device ID, channel bandwidth, carry frequency, ..., RxExtraInfo, MVMExtra, BasebandSignals, and so on. The most vitally important information to us is the CSI segment which includes CSI data, CSI magnitude data, and CSI phase data.

As a consequence, we perform PPT to extract CSI information from the CSI segment into a .csv file, which arranges CSI information as that the 1st column is the timestamp, the 2nd to 229th columns are the amplitudes of 57 subcarriers from 4 streams, and the 230th to 457th columns are the phases of 57 subcarriers from 4 streams, shown in figure 6, which only captures a part of .csv file and the first column in the figure is the timestamp.

(29)

3.2. DATA COLLECTION 19

Figure 6: Part of the converted and arranged csv file.

After transforming the .csi file into the .csv file, it can be plotted in Figure 7 based on the amplitude data, which is one of the 2nd to 229th columns in the .csv file. Specially, we only perform the CSI amplitude data and discard the CSI phase data in our system, since there are many offsets and distortions in phase data, such as Carrier Frequency Offset, Sampling Frequency Offset, Packet Detection Delay, etc., discussed in Section 2.4.

(a) CSI amplitude of fall motion. (b) CSI amplitude of run motion.

Figure 7: CSI amplitude data.

(30)

doi:10.6342/NTU202203973

3.3. SPEED ESTIMATION 20

3.3 Speed Estimation

To obtain the speed information, we adopt the statistical theory of EM waves in a rich-scattering environment [26], which exists uncountable static and dynamic scatterers distributing randomly in the space that are assumed to be diffusive and can reflect the encroaching EM waves toward all directions that can break LOS (Light-Of-Sight) restriction. First, we need to calculate the autocorrelation function (ACF) of CSI power response, which is related to the speed of a moving object. Then, we perform the first local valley algorithm to find the location of the first local valley of ACF of CSI power response since the speed is the location of the first local valley of theoretical spatial ACF divided by this location. By taking the location of the first local valley, we can calculate the corresponding speed of the dynamic scatterers. Figure 8 shows the speed estimation results based on the above techniques.

(a) Speed of fall motion. (b) Speed of run motion.

Figure 8: Speed information after speed estimation.

However, there is redundant speed information in no motion region since there is noise in the environment, as shown in Figure 8. We apply the motion detection method by ACF of CSI power response to settle the problem. If there is a motion, the ACF is greater than 0 when the value on the time domain is close to 0. In Figure 9, it is the result of the motion detection method, which can remove the redundancy region effectively.

(a) Speed of fall motion. (b) Speed of run motion.

Figure 9: Optimal speed information after motion detection.

(31)

3.4. FALL DETECTION 21

3.4 Fall Detection

3.4.1 Sliding Window

In Figure 10, it is the result of run motion after performing the speed esti- mation. We prefer to apply the sliding window on it because the sliding window is more corresponding to the real time analysis. Thus, we merely preserve the windows that the maximum speed in them is greater or equal to vmac=x, which is the minimum speed of fall motion, and the others are discarded that can reduce the computation load and time, which is displayed in Figure 11.

Figure 10: The aboriginal run motion data.

After obtaining the sliding window data, we take it as the input data for the following task. We transform the fall motion detection task into a binary classification problem since we only need to classify which motion is a fall or no fall.

In order to solve the binary classification, we perform machine learning models, but we will get a little bit different results from each training process. Thus, we employ an extension of the checkpoint ensemble method, which is an extended version of the checkpoint ensemble method that is to averaging the predictions from checkpoint of the best models with a series of training processes, to obtain the benefits of the best models so that the result of the machine learning model with the ensemble method would be better than the original machine learning model that we will discuss in the following sections.

(32)

doi:10.6342/NTU202203973

3.4. FALL DETECTION 22

Figure 11: The run motion data with sliding window.

Ultimately, in Figure 12, it is our process of fall detection. Input data is the window data and the fall motion technique is the machine learning model with the extension of the checkpoint ensemble method. After the process, it will output the results: Fall or No Fall.

Fall

No Fall

Input Data Fall Detection

x[2]

x[3]

x[1]

p[1]

p[2]

Figure 12: The process of fall detection.

(33)

CHAPTER 4

SPEED ESTIMATION

We are going to exploit the statistical theory of electromagnetic (EM) waves in the rich-scattering environment to establish a relationship between the auto- correlation function (ACF) of CSI power response (the square of the magnitude of CSI) and the speed of the moving object. After building the relationship, we can obtain the speed information of the monitoring object, shown in Figure 13.

Data Collection Fall Detection

Machine Learning

Model Extension of

Checkpoint Ensemble Sliding Window

Speed Estimation

Motion Detection First Local Valley

Algorithm ACF of CSI power

response

Figure 13: The block of speed estimation.

4.1 ACF of CSI Power Response

4.1.1 Statistical Theory of EM Waves in a Rich-scattering Environ- ment

Most research on motion detection usually performs a multipath propagation model which has a direct path (Light-Of-Sight, LOS) and indirect paths (Non- Light-Of-Sight, NLOS). The detected efficacy of a direct path is better than in- direct paths that might affect the performance of indirect paths, called the LOS restriction. As a result, to provide excellent performance on both direct and in- direct paths, we adopt the rich-scattering statistical model [12] of EM waves for

(34)

doi:10.6342/NTU202203973

4.1. ACF OF CSI POWER RESPONSE 24

motion detection. In this model, there are uncountable static and dynamic scat- terers distributing randomly in the space that are assumed to be diffusive and can reflect the encroaching EM waves toward all directions to break the LOS restriction.

4.1.1.1 Scattered Electric Field of EM Waves

Buildings and rooms can be viewed as reverberation cavities/chambers in that they exhibit internal multipath propagations [27]. Thus, in an indoor environment or a reverberation chamber, also called mode stirred or mode-tune chamber, we send an EM wave from transmitter to receiver, which can be viewed as a plane wave. At this time, the received electric field ⃗Ei(t, f ) of ith scatterer at time t, where f is the frequency of transmitted EM wave, can be denoted as the integral of plane waves over all real angles as follows [26]:

E⃗i(t, f ) = Z

F (θ)e⃗ i⃗k·⃗vitdθ = Z

0

Z π 0

F (α, β)e⃗ i⃗k·⃗vitsin αdαdβ, (4.1) where solid angle θ is shorthand for the elevation and azimuth angles, α and β, and dθ = sin αdαdβ, ⃗vi is the speed of ith scatterer, ⃗k is the wavenumber with direction which can be replaced as ⃗k = −k(ˆx sin α cos β + ˆysin α sin β + ˆzcos α), and ⃗F (θ) is the angular spectrum.

4.1.1.2 Autocorrelation Function (ACF) of EM Waves

Now, we start to derive the autocorrelation function (ACF) for the total com- plex electric field in a reverberation chamber to observe the relationship between the speed of ith scatterer and ACF. The ACF is a function of the two field points at different two time points with a time difference τ . It can be defined as [26]

ρE

i(τ, f ) = q ⟨ ⃗Ei(0, f ), ⃗Ei(τ, f )⟩

⟨| ⃗Ei(0, f )|2⟩⟨| ⃗Ei(τ, f )|2

. (4.2)

The numerator in Equation (4.2) is the correlation function (or mutual coherence function), which has been used to describe wave propagation in random media [28]. Moreover, in probability, the ACF is the autocovariance function divided by variance or the normalized autocovariance function, denoted as

ρEi(τ, f ) = q ⟨ ⃗Ei(0, f )− ⟨ ⃗Ei(0, f )⟩, ⃗Ei(τ, f )− ⟨ ⃗Ei(τ, f )⟩⟩

⟨| ⃗Ei(0, f )− ⟨ ⃗Ei(0, f )⟩ |2⟩⟨| ⃗Ei(τ, f )− ⟨ ⃗Ei(τ, f⟩ |2

. (4.3)

The numerator in Equation (4.3) is the autocovariance function and the denomi- nator is the variance.

(35)

4.1. ACF OF CSI POWER RESPONSE 25

Without loss of generality, as the moving directions of all the dynamic scat- terers are approximately the same, we can choose z-axis as the moving direction, time 0 at the origin and time τ on the z-axis:

t0 = 0 and t1 = τ. (4.4)

Therefore, the z component of the electric field is [29]

E⃗iz(t, f ) = Z

sin α ⃗Fα(θ)ei⃗k·⃗vitdθ. (4.5) With Equation (4.2) and (4.5), the ACF of z component of ith scatterer is [29]

ρE

iz(τ, f ) = 3 (kviτ )2

hsin(kviτ )

kviτ − cos(kviτ ) i

. (4.6)

Furthermore, the x or y component of the electric field are the same because the moving direction is the z-axis which is perpendicular to the x-axis and y-axis. As a result, the x or y component of the electric field is shown as below [28]

E⃗ix(t, f ) = ⃗Eiy(t, f ) = Z



cos α cos β ⃗Fα(θ)− sin β ⃗Fβ(θ)



ei⃗k·⃗vitdθ. (4.7) With Equation (4.2) and (4.7), the ACF of x or y component of ith scatterer is [28]

ρE

ix(τ, f ) = ρE

iy(τ, f ) = 3 2

hsin(kviτ )

kviτ 1 (kviτ )2

sin(kviτ )

kviτ − cos(kviτ )

i

. (4.8) Currently, we have obtained the ACF of each component of ith scatterer, and we’d like to observe the theoretical spatial ACF derived from the temporal ACF for the speed estimation in the following section.

4.1.1.3 Theoretical Spatial ACF

Now, we have derived the autocorrelation function (ACF) of each component in Equation (4.6) and (4.8), so the equations of theoretical spatial ACFs can be replaced by Equation (4.6) and (4.8) as follows, where distance d = viτ and wavenumber k = λ.

ρEix(d, f ) = ρEiy(d, f ) = 3 2

hsin(λd)

λ d 1

(λd)2

sin(λ d)

λd − cos(2π λ d)

i

, (4.9)

ρEiz(d, f ) = 3 (λd)2

hsin(λd)

λ d − cos(2π λ d)

i

. (4.10)

If we assume the unit of d is λ (d in λ unit), the Equations (4.9) and (4.10) become

ρEix(d, f ) = ρEiy(d, f ) = 3 2

hsin(2πd)

2πd 1

(2πd)2

sin(2πd)

2πd − cos(2πd)i

, d in λ (4.11)

(36)

doi:10.6342/NTU202203973

4.1. ACF OF CSI POWER RESPONSE 26

ρEiz(d, f ) = 3 (2πd)2

hsin(2πd)

2πd − cos(2πd)i

, d in λ (4.12)

Based on Equations (4.11) and (4.12), the theoretical spatial ACFs are shown as Figure 14 and 15, where ∆ρ(n)(τ ) is the derivative of ρ(n)(τ ), i.e., (n)(τ ).

Figure 14: Theoretical spatial ACF from [12].

Figure 15: Differential spatial ACF from [12].

Figure

Updating...

References

Related subjects :