接收到的CSI可以表示为:
C
S
I
(
f
,
t
)
=
A
noise
(
f
,
t
)
e
−
j
θ
offset
(
f
,
t
)
(
H
s
(
f
)
+
H
d
(
f
,
t
)
)
C S I(f, t)=A_{\text {noise }}(f, t) e^{-j \theta_{\text {offset }}(f, t)}\left(H_{s}(f)+H_{d}(f, t)\right)
CSI(f,t)=Anoise (f,t)e−jθoffset (f,t)(Hs(f)+Hd(f,t))
其中,
A
noise
A_{\text {noise }}
Anoise 是幅度噪声 ,
θ
offset
\theta_{\text {offset }}
θoffset 是随机相位偏移,
H
s
(
f
)
H_{s}(f)
Hs(f)是静态分量,
H
d
(
f
,
t
)
H_{d}(f, t)
Hd(f,t)是动态分量
CSI的共轭相乘可以表示为:
H
c
m
(
f
,
t
)
=
C
S
I
1
(
f
,
t
)
C
S
I
2
(
f
,
t
)
‾
=
(
A
noise
(
f
,
t
)
e
−
j
θ
offset
(
f
,
t
)
(
H
s
1
(
f
)
+
H
d
1
(
f
,
t
)
)
)
(
A
noise
(
f
,
t
)
e
−
j
θ
offset
(
f
,
t
)
(
H
s
2
(
f
)
+
H
d
2
(
f
,
t
)
)
)
‾
=
(
A
noise
(
f
,
t
)
e
−
j
θ
offset
(
f
,
t
)
(
H
s
1
(
f
)
+
H
d
1
(
f
,
t
)
)
)
(
A
noise
(
f
,
t
)
e
j
θ
offset
(
f
,
t
)
(
H
s
2
(
f
)
+
H
d
2
(
f
,
t
)
)
‾
)
=
A
noise
(
f
,
t
)
2
(
H
s
1
(
f
)
+
H
d
1
(
f
,
t
)
)
(
H
s
2
(
f
)
‾
+
H
d
2
(
f
,
t
)
‾
)
=
A
noise
(
f
,
t
)
2
(
H
s
1
(
f
)
H
s
2
(
f
)
‾
⏟
(
1
)
+
H
s
1
(
f
)
H
d
2
(
f
,
t
)
‾
⏟
(2)
+
H
s
2
(
f
)
‾
H
d
1
(
f
,
t
)
⏟
(3)
+
H
d
1
(
f
,
t
)
H
d
2
(
f
,
t
)
‾
)
⏟
(4)
≈
A
noise
(
f
,
t
)
2
(
H
s
1
(
f
)
H
s
2
(
f
)
‾
+
H
s
1
(
f
)
H
d
2
(
f
,
t
)
‾
+
H
s
2
(
f
)
‾
H
d
1
(
f
,
t
)
)
其中,(1)是时不变项;(4)相较于(2)(3)很弱,可以忽略;(2)和(3)是时变的,(3)包含感兴趣的多普勒频移,而(2)包含一个算术上相反的数字,这可能会产生模棱两可的多普勒速度估计。
[1] Inferring motion direction using commodity wi-fi for interactive exergames
[2] Indotrack: Device-free indoor human tracking with commodity wifi
本文参考 WiTraj: Robust Indoor Motion Tracking with WiFi Signals