# Spatial multiplexing

**Spatial multiplexing** (often abbreviated **SM** or **SMX**) is a transmission technique in MIMO wireless communication, Fibre-optic communication and other communications technologies to transmit independent and separately encoded data signals, known as "*streams*". Therefore, the space dimension is reused, or multiplexed, more than one time.

Multiplexing |
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Analog modulation |

Related topics |

## Encoding

### Open-loop approach

In an open-loop MIMO system with transmitter antennas and receiver antennas, the input-output relationship can be described as

where is the vector of transmitted symbols, are the vectors of received symbols and noise respectively and is the matrix of channel coefficients. An often encountered problem in open loop spatial multiplexing is to guard against instance of high channel correlation and strong power imbalances between the multiple streams. One such extension which is being considered for DVB-NGH systems is the so-called *enhanced Spatial Multiplexing (eSM)* scheme.

### Closed-loop approach

A closed-loop MIMO system utilizes Channel State Information (CSI) at the transmitter. In most cases, only partial CSI is available at the transmitter because of the limitations of the feedback channel. In a closed-loop MIMO system the input-output relationship with a closed-loop approach can be described as

where is the vector of transmitted symbols, are the vectors of received symbols and noise respectively, is the matrix of channel coefficients and is the linear precoding matrix.

A precoding matrix is used to precode the symbols in the vector to enhance the performance. The column dimension of can be selected smaller than which is useful if the system requires streams because of several reasons. Examples of the reasons are as follows: either the rank of the MIMO channel or the number of receiver antennas is smaller than the number of transmit antennas.

## See also

- Space–time code
- Space–time trellis code
- WiMAX MIMO
- 3G MIMO
- Fibre-optic communications

## References