IEEE Signal Processing - May 2018 - 75

minor environmental perturbations and affects CSIs only slightly, the periodic pattern of breathing embedded in the CSI time
series is very distinct and can be extracted with high fidelity.

simplicity, we assume that breathing affects only multipath 1
and the gain of multipath 1 takes the form of [44]
g 1 (t) = g 1 # c 1 +

CSI model in the presence of breathing
To better understand the impact of breathing on CSI values, let
us start with a time-varying CSI (CFR) model without environmental perturbations as
(k)

h F (t) =

L

/ g , e -j2

r

d,
mk

+ e (k) (t),

(19)

, =1

where k ! V and V denotes the set of usable subcarriers with
a total of N sub usable subcarriers, L is the total number of multipaths, g , is the complex gain of multipath ,, d , is the length of
multipath ,, and m k is the wavelength of subcarrier k given by
m k = C/ ( fc (k/N DFT Ts)) . Here, fc is the carrier frequency, c is
the speed of light, Ts is the sampling interval given as Ts = 1/B
where B is the baseband bandwidth of the Wi-Fi signals, and
N DFT is the size of the discrete Fourier transform. The function
e (k) (t) is the thermal noise on subcarrier k at time t. Without
environmental perturbations, the multipath gains and delays are
time invariant.
With breathing, one or more multipath gains and delays
become time varying and introduce periodic variations into
the CSI values. Figure 18 demonstrates an example of how
breathing affects CSI values received on Wi-Fi devices. For

Dd 1 sin i sin 2rb t + z -},
` 60
jm
d1

(20)

where g1 and d1 are the gain and path length for multipath
1 in a static environment, Dd 1 is the additional positional
displacement of multipath 1 caused by breathing, } is the pathloss exponent, i is the angle between the subject and the
impinging EM wave, b is the breathing rate measured in
breaths per minute, and z is the initial breathing phase. Given
that d 1 & Dd 1, g 1 (t) can be approximated by the time-invariant
multipath gain g1.
Meanwhile, breathing affects the phase of multipath 1 by
changing its path length d 1 (t) , expressed as
d 1 (t) = d 1 + Dd 1 sin i sin ` 2rb t + z j .
60

(21)

Substituting (19) and (21) into (18), we have
d1

(k)

h F (t) = g 1 e -j2r m k e -j2r
L

Dd 1 sin i sin ` 2rb t +z j
60
mk

d,

+ / g , e -j2r m k + e (k) (t) .

(22)

, =2

Subcarrier Index

CSI Amplitude

Dynamic

0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02

10
20
30
40
50
60
70
80
90
100
110
10

LOS

20 30 40
Time (s)

50

60

CSI Phase

Subcarrier Index

Static

3

10
20
30
40
50
60
70
80
90
100
110

2
1
0
-1
-2
-3
10

20

30 40
Time (s)

50

60

FIGURE 18. The impact of breathing on CSIs.
IEEE Signal Processing Magazine

|

May 2018

|

75



Table of Contents for the Digital Edition of IEEE Signal Processing - May 2018

Contents
IEEE Signal Processing - May 2018 - Cover1
IEEE Signal Processing - May 2018 - Cover2
IEEE Signal Processing - May 2018 - Contents
IEEE Signal Processing - May 2018 - 2
IEEE Signal Processing - May 2018 - 3
IEEE Signal Processing - May 2018 - 4
IEEE Signal Processing - May 2018 - 5
IEEE Signal Processing - May 2018 - 6
IEEE Signal Processing - May 2018 - 7
IEEE Signal Processing - May 2018 - 8
IEEE Signal Processing - May 2018 - 9
IEEE Signal Processing - May 2018 - 10
IEEE Signal Processing - May 2018 - 11
IEEE Signal Processing - May 2018 - 12
IEEE Signal Processing - May 2018 - 13
IEEE Signal Processing - May 2018 - 14
IEEE Signal Processing - May 2018 - 15
IEEE Signal Processing - May 2018 - 16
IEEE Signal Processing - May 2018 - 17
IEEE Signal Processing - May 2018 - 18
IEEE Signal Processing - May 2018 - 19
IEEE Signal Processing - May 2018 - 20
IEEE Signal Processing - May 2018 - 21
IEEE Signal Processing - May 2018 - 22
IEEE Signal Processing - May 2018 - 23
IEEE Signal Processing - May 2018 - 24
IEEE Signal Processing - May 2018 - 25
IEEE Signal Processing - May 2018 - 26
IEEE Signal Processing - May 2018 - 27
IEEE Signal Processing - May 2018 - 28
IEEE Signal Processing - May 2018 - 29
IEEE Signal Processing - May 2018 - 30
IEEE Signal Processing - May 2018 - 31
IEEE Signal Processing - May 2018 - 32
IEEE Signal Processing - May 2018 - 33
IEEE Signal Processing - May 2018 - 34
IEEE Signal Processing - May 2018 - 35
IEEE Signal Processing - May 2018 - 36
IEEE Signal Processing - May 2018 - 37
IEEE Signal Processing - May 2018 - 38
IEEE Signal Processing - May 2018 - 39
IEEE Signal Processing - May 2018 - 40
IEEE Signal Processing - May 2018 - 41
IEEE Signal Processing - May 2018 - 42
IEEE Signal Processing - May 2018 - 43
IEEE Signal Processing - May 2018 - 44
IEEE Signal Processing - May 2018 - 45
IEEE Signal Processing - May 2018 - 46
IEEE Signal Processing - May 2018 - 47
IEEE Signal Processing - May 2018 - 48
IEEE Signal Processing - May 2018 - 49
IEEE Signal Processing - May 2018 - 50
IEEE Signal Processing - May 2018 - 51
IEEE Signal Processing - May 2018 - 52
IEEE Signal Processing - May 2018 - 53
IEEE Signal Processing - May 2018 - 54
IEEE Signal Processing - May 2018 - 55
IEEE Signal Processing - May 2018 - 56
IEEE Signal Processing - May 2018 - 57
IEEE Signal Processing - May 2018 - 58
IEEE Signal Processing - May 2018 - 59
IEEE Signal Processing - May 2018 - 60
IEEE Signal Processing - May 2018 - 61
IEEE Signal Processing - May 2018 - 62
IEEE Signal Processing - May 2018 - 63
IEEE Signal Processing - May 2018 - 64
IEEE Signal Processing - May 2018 - 65
IEEE Signal Processing - May 2018 - 66
IEEE Signal Processing - May 2018 - 67
IEEE Signal Processing - May 2018 - 68
IEEE Signal Processing - May 2018 - 69
IEEE Signal Processing - May 2018 - 70
IEEE Signal Processing - May 2018 - 71
IEEE Signal Processing - May 2018 - 72
IEEE Signal Processing - May 2018 - 73
IEEE Signal Processing - May 2018 - 74
IEEE Signal Processing - May 2018 - 75
IEEE Signal Processing - May 2018 - 76
IEEE Signal Processing - May 2018 - 77
IEEE Signal Processing - May 2018 - 78
IEEE Signal Processing - May 2018 - 79
IEEE Signal Processing - May 2018 - 80
IEEE Signal Processing - May 2018 - 81
IEEE Signal Processing - May 2018 - 82
IEEE Signal Processing - May 2018 - 83
IEEE Signal Processing - May 2018 - 84
IEEE Signal Processing - May 2018 - 85
IEEE Signal Processing - May 2018 - 86
IEEE Signal Processing - May 2018 - 87
IEEE Signal Processing - May 2018 - 88
IEEE Signal Processing - May 2018 - 89
IEEE Signal Processing - May 2018 - 90
IEEE Signal Processing - May 2018 - 91
IEEE Signal Processing - May 2018 - 92
IEEE Signal Processing - May 2018 - 93
IEEE Signal Processing - May 2018 - 94
IEEE Signal Processing - May 2018 - 95
IEEE Signal Processing - May 2018 - 96
IEEE Signal Processing - May 2018 - 97
IEEE Signal Processing - May 2018 - 98
IEEE Signal Processing - May 2018 - 99
IEEE Signal Processing - May 2018 - 100
IEEE Signal Processing - May 2018 - 101
IEEE Signal Processing - May 2018 - 102
IEEE Signal Processing - May 2018 - 103
IEEE Signal Processing - May 2018 - 104
IEEE Signal Processing - May 2018 - 105
IEEE Signal Processing - May 2018 - 106
IEEE Signal Processing - May 2018 - 107
IEEE Signal Processing - May 2018 - 108
IEEE Signal Processing - May 2018 - 109
IEEE Signal Processing - May 2018 - 110
IEEE Signal Processing - May 2018 - 111
IEEE Signal Processing - May 2018 - 112
IEEE Signal Processing - May 2018 - 113
IEEE Signal Processing - May 2018 - 114
IEEE Signal Processing - May 2018 - 115
IEEE Signal Processing - May 2018 - 116
IEEE Signal Processing - May 2018 - 117
IEEE Signal Processing - May 2018 - 118
IEEE Signal Processing - May 2018 - 119
IEEE Signal Processing - May 2018 - 120
IEEE Signal Processing - May 2018 - 121
IEEE Signal Processing - May 2018 - 122
IEEE Signal Processing - May 2018 - 123
IEEE Signal Processing - May 2018 - 124
IEEE Signal Processing - May 2018 - 125
IEEE Signal Processing - May 2018 - 126
IEEE Signal Processing - May 2018 - 127
IEEE Signal Processing - May 2018 - 128
IEEE Signal Processing - May 2018 - 129
IEEE Signal Processing - May 2018 - 130
IEEE Signal Processing - May 2018 - 131
IEEE Signal Processing - May 2018 - 132
IEEE Signal Processing - May 2018 - Cover3
IEEE Signal Processing - May 2018 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201809
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201807
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201805
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201803
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201801
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1117
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0917
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0717
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0517
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0317
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0117
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1116
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0916
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0716
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0516
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0316
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0116
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1115
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0915
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0715
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0515
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0315
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0115
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1114
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0914
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0714
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0514
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0314
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0114
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1113
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0913
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0713
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0513
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0313
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0113
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1112
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0912
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0712
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0512
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0312
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0112
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1111
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0911
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0711
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0511
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0311
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0111
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1110
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0910
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0710
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0510
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0310
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0110
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1109
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0909
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0709
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0509
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0309
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0109
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1108
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0908
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0708
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0508
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0308
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0108
https://www.nxtbookmedia.com