# What does the physical meaning of $\mathbf{U} \Sigma \ \mathbf{V}^{*}$ in the MIMO system?

SVD is a method to cancel the interference in MIMO system,we often do the SVD of channel as below

\begin{align} \mathbf{H} &= \mathbf{U} \ \Sigma \ \mathbf{V}^{T} \\ % \end{align}

So $$\mathbf{U}$$ means the beamforming direction of receiver? and $$\mathbf{V}$$ means the beamforming direction of transmitter? and the singular value in the diagonal of $$\Sigma$$ means the gain of channel ?Why can we use this to decrease or cancel the noise ?

• How do you define beamforming "direction"? I mean beamforming itself is the whole process from preprocessing $V$ to post processing $U$, and this is the only thing matters. For other questions, you can follow the answer of Peter K. – AlexTP Sep 19 '19 at 11:14

In the context of MIMO communications, the $$\mathbf{H}$$ matrix defines the channel; it doesn't specify anything directly about the transmitter or the receiver.
This paper has the following diagram which shows one interpretation of the $$\mathbf{U}$$ and $$\mathbf{V}$$ matrices. The SVD allows the channel to be decomposed into several parallel paths, with no crosstalk between them. 