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Independent Component Analysis is a computational method for separating a multivariate signal into multiple independent components
When applied to MIMO communications, ICA can be described as a computational method for estimating the mixed variable matrix and the transmitted signal by observing only the observed signal.
For simplicity, we assume that noise is not considered, and the estimation of 𝑿 is based on the directly observable 𝑺 with respect to equation (2-2).
The estimate of the transmitted signal 𝑿 ̂ can be expressed as Equation 4 using the weight matrix 𝑾^𝑯.
The components 𝑥_𝑚 [𝑘] of the transmission matrix 𝑿 follow a discrete distribution, but when H is multiplied and several independent signals are mixed, their probability density distribution approaches a Gaussian distribution by the central limit theorem.
When 𝒘_𝑚 is adjusted so that the non-zero element of the vector composed by 〖𝒘_𝑚〗^𝑯 𝑯 becomes one, the central limit theorem does not hold and the discrete distribution of the transmitted symbols appears as is .
In other words, when 𝒘𝒘_𝑚 is determined so that the non-Gaussianity of 〖𝒘_𝑚〗^𝑯𝑺 is maximized, 𝒙 ̂_𝑚 can be considered one independent component and BSS is realized [4].
Thus, independent component analysis can be considered as a problem of searching for the direction with the maximum non-Gaussianity.
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IEEE/ICACT20230070 Slide.06
[Big Slide]