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} &amp;=
  \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 ?
Singular value decomposition (SVD) is a method of decomposing a matrix into two unitary matrices and a non-negative definite matrix of singular values.

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.