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 ?

  • $\begingroup$ 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. $\endgroup$
    – AlexTP
    Sep 19, 2019 at 11:14

1 Answer 1


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.

Channel decomposition via SVD.


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