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.

Spatial multiplexing

2xSMX or STC+2xMRC

Encoding

Open-loop approach

In an open-loop MIMO system with ${\displaystyle N_{t}}$ transmitter antennas and ${\displaystyle N_{r}}$ receiver antennas, the input-output relationship can be described as

${\displaystyle \mathbf {y} =\mathbf {Hx} +\mathbf {n} }$

where ${\displaystyle \mathbf {x} =[x_{1},x_{2},\ldots ,x_{N_{t}}]^{T}}$ is the ${\displaystyle N_{t}\times 1}$ vector of transmitted symbols, ${\displaystyle \mathbf {y,n} }$ are the ${\displaystyle N_{r}\times 1}$ vectors of received symbols and noise respectively and ${\displaystyle \mathbf {H} }$ is the ${\displaystyle N_{r}\times N_{t}}$ 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

${\displaystyle \mathbf {y} =\mathbf {HWs} +\mathbf {n} }$

where ${\displaystyle \mathbf {s} =[s_{1},s_{2},\ldots ,s_{N_{s}}]^{T}}$ is the ${\displaystyle N_{s}\times 1}$ vector of transmitted symbols, ${\displaystyle \mathbf {y,n} }$ are the ${\displaystyle N_{r}\times 1}$ vectors of received symbols and noise respectively, ${\displaystyle \mathbf {H} }$ is the ${\displaystyle N_{r}\times N_{t}}$ matrix of channel coefficients and ${\displaystyle \mathbf {W} }$ is the ${\displaystyle N_{t}\times N_{s}}$ linear precoding matrix.

A precoding matrix ${\displaystyle \mathbf {W} }$ is used to precode the symbols in the vector to enhance the performance. The column dimension ${\displaystyle N_{s}}$ of ${\displaystyle \mathbf {W} }$ can be selected smaller than ${\displaystyle N_{t}}$ which is useful if the system requires ${\displaystyle N_{s}(\neq N_{t})}$ 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

• 3G MIMO
• Space–time code
• Space–time trellis code
• WiMAX MIMO

References