IEEE Signal Processing - May 2018 - 76

The first term on the right-hand side of H k (t) in (22) can
be decomposed into an infinite summation according to the
Jacobi-Anger expansion [45], given as

e

-j2r

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

+3

=

mk

/

(-1) m J m (o k) e jm

2rb t jmz
60 e
,

(23)

m =-3

where o k = 2r sin iDd 1 /m k and J m (x) is the mth-order Bessel
function with argument x.
In practice, J m (o k) decays rapidly for m $ 2, given typical values of o k, and H k (t) can be approximated as
d1

+1

2rb

h F (t) . g 1 e -j2r m k / (-1) m J m (o k) e jm 60 t e jmz
m =-1
1444444444
42
44444444443
(k)
(k)

S ( t)

L

d,

+ / g , e -j2r m k + e (k) (t),
=2
1, 44
42
4443
(k)

(24)

I

where S (k) (t) stands for the useful signal for breathing monitoring on subcarrier k and I (k) represents the time-invariant
part due to the static environment and is regarded as the inter(k)
ference. Notice that the dynamic model of h F (t) shown in
(24) can be easily extended to multiperson cases.

Breathing monitoring using CSI values
As breathing introduces periodic variations into the CSI time
series, to extract the breathing rate, we can calculate the pairwise complex-valued TRRS between any two CSI values in
the time series, which encapsulates variations of both CSI
amplitudes and phases, given as
N sub

TR (h F, i, h F, m) =

/ h F,i [k] h )F,m [k] e -j(

Experimental results

~ * + l * k)

k =1

h F, i
i, m = 1, 2, f, N ,

2

h F, j

2

(25)
(k)

92.6

90

99.1

99.57

96.35

94.5

99.45

Accuracy (%)

95

99.51

where N is the number of CSI vectors and h F, i = {h F, i} k ! V =
[h F, i [1], g, h F, i [N sub]] is the CSI vector composed by all

100

85
80

1

2

3
4
5
Number of People

6

7

FIGURE 19. The accuracy with multiple people under the NLOS scenario.
76

of the subcarriers received at the ith time instance. We
introduce ~ * and l * in (25) to remove the initial and linear
phase distortions.
The TRRS matrix R includes all of the pairwise TRRS
values. Assuming a total of N CSI vectors, the (i, m)th entry
of the N × N TRRS matrix R is given by R i, m, as shown
in (25).
After this, the breathing rates can be extracted from the
TRRS matrix via a spectral analyzer, e.g., based on the RootMUSIC algorithm [46]. If we denote the 2N - 2 complex roots
by zt = {zt 1, zt 2, zt 3, f, zt 2N -2}, then one can choose p out of
the N - 1 complex roots closest to the unit circle, where p is
the signal subspace dimension. The breathing rate estimation
can be formulated as bt i = 60 # ^\zt i 2rTsh, i = 1, 2, f, p,
where Ts is the sampling interval and \ (x) is the operator that
extracts the phase from the complex argument x.
In reality, breathing rates are limited to a finite range
[b min, b max], since a person cannot breathe extremely quickly or slowly. Thus, we sift the breathing rate estimations
bt = [bt 1, bt 2, f, bt p] by discarding those outside the range of
[b min, b max] , which leads to bu = [bt r1, bt r2, f, bt r p], where pl is
the number of the remaining complex roots and ri is the index
of the ith remaining estimation.
For CSIs measured on N chl Wi-Fi channels and with N link
antenna links, the set bu can be written as the union of the
estimated breathing rates calculated on all Wi-Fi channels
and antenna links, i.e., bu =, sN=link1 , Nf =chl1 bu (s, f), where bu (s, f) is the
breathing rate estimation obtained on the sth antenna link and
fth Wi-Fi channel.
We can also extend the breathing rate estimation to a multiperson breathing monitoring case by running a clustering
algorithm, e.g., affinity propagation [47], on the estimated
breathing rates [81].

We evaluated the performance of the breathing monitoring
system by comparing the breathing rate estimations against
the ground truths. To obtain the ground truths, each participant
synchronized his or her breathing with a metronome.
Up to seven people were invited into a conference room,
with two devices placed under NLOS for breathing monitoring.
Figure 19 summarizes the performance accuracy, which shows
that an accuracy of 99.1%, when K = 7, and a mean accuracy of
97.3% averaging over all seven cases were achieved.

Related works and comparisons
As discussed in the previous sections, if one can create a large
effective bandwidth with the aid of either antenna or frequency
diversity, there will be large enough multipaths available to
enable many cutting-edge IoT applications that are independent
of the carrier frequency. Our experimental results showed that the
CSI obtained using Wi-Fi chips with antenna diversity can render
meaningful radio analytics. With more bandwidth possibly available in fifth generation, and thus more multipaths observed, one
can expect even better performance. In addition, it is possible to
implement these IoT applications with even just one antenna.

IEEE Signal Processing Magazine

|

May 2018

|



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

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