principle
The received CSI can be expressed as:
CSI ( f , t ) = A noise ( f , t ) e − j θ offset ( f , t ) ( H s ( f ) + H d ( f , t ) ) CSI(f , t)=A_{\text {noise }}(f, t) e^{-j \theta_{\text {offset }}(f, t)}\left(H_{s}(f)+H_{ d}(f, t)\right)CS I ( f ,t)=Anoise (f,t)e−jθoffset (f,t)(Hs(f)+Hd(f,t))
其中， A noise A_{\text {noise }} Anoise is the amplitude noise, θ offset \theta_{\text {offset }}ioffset is the random phase offset, H s ( f ) H_{s}(f)Hs( f ) is a static component,H d ( f , t ) H_{d}(f, t)Hd(f,t ) is the dynamic component
The conjugate multiplication of CSI can be expressed as:
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 ) ) \begin{aligned} &H_{c m}(f, t)=C S I_{1}(f, t) \overline{C S I_{2}(f, t)}\\ &=\left(A_{\text {noise }}(f, t) e^{-j \theta_{\text {offset }}(f, t)}\left(H_{s 1}(f)+H_{d 1}(f, t)\right)\right) \overline{\left(A_{\text {noise }}(f, t) e^{-j \theta_{\text {offset }}(f, t)}\left(H_{s 2}(f)+H_{d 2}(f, t)\right)\right)}\\ &=\left(A_{\text {noise }}(f, t) e^{-j \theta_{\text {offset }}(f, t)}\left(H_{s 1}(f)+H_{d 1}(f, t)\right)\right)\left(A_{\text {noise }}(f, t) e^{j \theta_{\text {offset }}(f, t)} \overline{\left(H_{s 2}(f)+H_{d 2}(f, t)\right)}\right)\\ &=A_{\text {noise }}(f, t)^{2}\left(H_{s 1}(f)+H_{d 1}(f, t)\right)\left(\overline{H_{s 2}(f)}+\overline{H_{d 2}(f, t)}\right)\\ &=A_{\text {noise }}(f, t)^{2}(\underbrace{H_{s 1}(f) \overline{H_{s 2}(f)}}_{(1)}+\underbrace{H_{s 1}(f) \overline{H_{d 2}(f, t)}}_{\text {(2) }}+\underbrace{\overline{H_{s 2}(f)} H_{d 1}(f, t)}_{\text {(3) }}+\underbrace{\left.H_{d 1}(f, t) \overline{H_{d 2}(f, t)}\right)}_{\text {(4) }}\\ &\approx A_{\text {noise }}(f, t)^{2}\left(H_{s 1}(f) \overline{H_{s 2}(f)}+H_{s 1}(f) \overline{H_{d 2}(f, t)}+\overline{H_{s 2}(f)} H_{d 1}(f, t)\right) \end{aligned} Hcm(f,t)=CSI1(f,t)CSI2(f,t)=(Anoise (f,t)e−jθoffset (f,t)(Hpage 1(f)+Hd 1(f,t)))(Anoise (f,t)e−jθoffset (f,t)(Hs 2(f)+Hd 2(f,t)))=(Anoise (f,t)e−jθoffset (f,t)(Hpage 1(f)+Hd 1(f,t)))(Anoise (f,t)ejθoffset (f,t)(Hs 2(f)+Hd 2(f,t)))=Anoise (f,t)2(Hpage 1(f)+Hd 1(f,t))(Hs 2(f)+Hd 2(f,t))=Anoise (f,t)2((1) Hpage 1(f)Hs 2(f)+(2) Hpage 1(f)Hd 2(f,t)+(3) Hs 2(f)Hd 1(f,t)+(4) Hd 1(f,t)Hd 2(f,t))≈Anoise (f,t)2(Hpage 1(f)Hs 2(f)+Hpage 1(f)Hd 2(f,t)+Hs 2(f)Hd 1(f,t))
Among them, (1) is a time-invariant term; (4) is weak compared to (2) and (3) and can be ignored; (2) and (3) are time-varying, and (3) contains the interesting Dopp Le shift, while (2) contains an arithmetically opposite number, which may produce ambiguous Doppler velocity estimates.
shortcoming
- A disadvantage of conjugate multiplication based DFS extraction methods is the amplified noise. It can be seen from the formula that the conjugate multiplication operation eliminates the CSI phase offset, but further amplifies the CSI amplitude noise.
- Another disadvantage of conjugate multiplication based DFS extraction methods is that they must use heuristics to deal with ambiguous speed issues. WiDance [1] selects the antennas and carefully assigns the order of the antennas in the conjugate multiplication to ensure correct estimation. DopplerMUSIC [2] amplifies the CSI magnitude of one antenna and reduces the CSI magnitude of the other antenna to alleviate ambiguity. Although the above approaches work to a certain extent, ambiguity remains a challenge in practice.
references
[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