# Spatial multiplexing

Spatial multiplexing

Spatial multiplexing 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

:$mathbf\left\{N_s\right\}=min\left(N_t,N_r\right)$

if a linear receiver is used. This means that $N_s$ streams can be transmitted in parallel, leading to a $N_s$ increase of the spectral efficiency (the number of bits per second and per Hz that can be transmitted over the wireless channel).

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:$mathbf\left\{y\right\}=mathbf\left\{Hx\right\}+mathbf\left\{n\right\}$ where $mathbf\left\{x\right\} = \left[x_1, x_2, ldots, x_\left\{N_t\right\}\right] ^T$ is the $N_t imes 1$ vector of transmitted symbols, $mathbf\left\{y,n\right\}$ are the $N_r imes 1$ vectors of received symbols and noise respectively and $mathbf\left\{H\right\}$ is the $N_r imes N_t$ matrix of channel coefficients.

Closed-loop approach

In a closed-loop MIMO system the input-output relationship with a closed-loop approach can be described as:$mathbf\left\{y\right\}=mathbf\left\{HWs\right\}+mathbf\left\{n\right\}$ where $mathbf\left\{s\right\} = \left[s_1, s_2, ldots, s_\left\{N_s\right\}\right] ^T$ is the $N_s imes 1$ vector of transmitted symbols, $mathbf\left\{y,n\right\}$ are the $N_r imes 1$ vectors of received symbols and noise respectively, $mathbf\left\{H\right\}$ is the $N_r imes N_t$ matrix of channel coefficients and $mathbf\left\{W\right\}$ is the $N_t imes N_s$ linear precoding matrix.

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

History

* Single-user MIMO
** Bell Laboratories Layered Space-Time (BLAST), Gerard. J. Foschini (1996)
** Per Antenna Rate Control (PARC), Varanasi, Guess (1998), Chung, Huang, Lozano (2001)
** Selective Per Antenna Rate Control (SPARC), Ericsson (2004)
*Multi-user MIMO: Samsung, Qualcomm, Ericsson, TI, Huawei, Philipse, Alcatel-Lucent, Freescale, et al.
** PU2RC allows the network to allocate each antenna to the different user which is not considered in single-user MIMO scheduling. Instead of a physical antenna, the network can transmit a user date through a codebook based spatial beam, i.e., a virtual antenna. The efficient user scheduling such as pairing spatially distinguishable users with codebook based spatial beams are additionally used for the simplification of wireless networks in terms of additionally required wireless resource and complex protocol modification.
* Enhanced multiuser MIMO
** Employ advanced decoding techniques
** Employ advanced precoding techniques

ee also

*MIMO, 3G MIMO and WIMAX MIMO
*Space–time code
*Space–time trellis code
*Precoding

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