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# Spatial multiplexing

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 Title: Spatial multiplexing Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Spatial multiplexing

Spatial multiplexing (often abbreviated SM or SMX) is a transmission technique in MIMO wireless communication to transmit independent and separately encoded data signals, so-called streams, from each of the multiple transmit antennas. Therefore, the space dimension is reused, or multiplexed, more than one time.

If the transmitter is equipped with N_t antennas and the receiver has N_r antennas, the maximum spatial multiplexing order (the number of streams) is,

N_s=\min(N_t, N_r)\!

if a linear receiver is used. This means that N_s streams can be transmitted in parallel, ideally leading to an N_s increase of the spectral efficiency (the number of bits per second and per Hz that can be transmitted over the wireless channel). The practical multiplexing gain can be limited by spatial correlation, which means that some of the parallel streams may have very weak channel gains.

## Contents

• Encoding 1
• Open-loop approach 1.1
• Closed-loop approach 1.2
• References 3

## Encoding

### Open-loop approach

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

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

where \mathbf{x} = [x_1, x_2, \ldots, x_{N_t}]^T is the N_t\times 1 vector of transmitted symbols, \mathbf{y,n} are the N_r \times 1 vectors of received symbols and noise respectively and \mathbf{H} is the 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

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

where \mathbf{s} = [s_1, s_2, \ldots, s_{N_s}]^T is the N_s\times 1 vector of transmitted symbols, \mathbf{y,n} are the N_r\times 1 vectors of received symbols and noise respectively, \mathbf{H} is the N_r\times N_t matrix of channel coefficients and \mathbf{W} is the N_t\times N_s linear precoding matrix.

A precoding matrix \mathbf{W} is used to precode the symbols in the vector to enhance the performance. The column dimension N_s of \mathbf{W} can be selected smaller than N_t which is useful if the system requires 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.