**Figure:**

**configuration of single-user digital precoder for**

**millimeter**

**Wave massive MIMO system**

Precoding and combining are two excellent ways to send and receive signals over a multi-antenna communication process, respectively (i.e., * MIMO antenna communication*). The channel matrix is the basis of both the precoding and combining matrices. Precoding matrices are typically used on the transmitter side and combining matrixes on the receiving side. The two matrices allow us to generate multiple simultaneous data streams between the transmitter and receiver. The nature of the data streams is also orthogonal. That helps decrease or cancel (theoretically) interference between any two data streams.

The channel matrix is first properly diagonalized. Diagonalization is the process of transforming any matrix into an equivalent diagonal matrix, where all of the diagonal elements are non-zero and all of the other elements are zeros. Let me explain an example,

**H**=

2 0 2

0 1 2

0 1 0

*(*

**H**= Channel Matrix)**y = h*x + n**

**D**.

**D**=

**y = D*x + n**

**y1**h11 0 0

**x1**

**y2 =**0 h22 0

***x2 + n**

**y3**0 0 h33

**x3**

**y1 = h11*x1 + n**

**y2 = h22*x2 + n**

**y3 = h33*x3 + n**

If the combining matrix is** W **and the precoding matrix is **F**.

**F*H*W = D**

When the precoding **F** matrix is used on the TX side and the **W** matrix is combined on the RX side.

## Summary:

In an environment with many scatterers, modern wireless communication systems use * spatial multiplexing* to increase data flow within the system. To transmit multiple data streams over the channel, a set of precoding and combining weights is derived from the channel matrix. Then, each data stream can be independently retrieved. Magnitude and phase terms are included in these weights, which are frequently utilized in digital communication.

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