Precoding

limited feedback precodinglinear precoding
Precoding is a generalization of beamforming to support multi-stream (or multi-layer) transmission in multi-antenna wireless communications.wikipedia
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Multi-user MIMO

MU-MIMOmulti-userMulti-user MIMO (MU-MIMO)
In multi-user MIMO, the data streams are intended for different users (known as SDMA) and some measure of the total throughput (e.g., the sum performance or max-min fairness) is maximized.
Examples of advanced transmit processing for MIMO BC are interference aware precoding and SDMA-based downlink user scheduling.

Beamforming

beam formingbeamformerAntenna beamforming
Precoding is a generalization of beamforming to support multi-stream (or multi-layer) transmission in multi-antenna wireless communications.
3G evolution — LTE/UMB: Multiple-input multiple-output (MIMO) precoding based beamforming with partial Space-Division Multiple Access (SDMA)

Spatial correlation

spatially correlatedspatially uncorrelated
In spatially correlated environments, the long-term channel statistics can be combined with low-rate feedback to perform multi-user precoding.
The idea is that if the propagation channels between each pair of transmit and receive antennas are statistically independent and identically distributed, then multiple independent channels with identical characteristics can be created by precoding and be used for either transmitting multiple data streams or increasing the reliability (in terms of bit error rate).

Dirty paper coding

Pre-cancellation of estimated interferenceSpatial interference cancellation codingTomlinson-Harashima Precoding
Nonlinear precoding is designed based on the concept of dirty paper coding (DPC), which shows that any known interference at the transmitter can be subtracted without the penalty of radio resources if the optimal precoding scheme can be applied on the transmit signal.
The technique consists of precoding the data in order to cancel the interference.

Multi-objective optimization

multiobjective optimizationmulti-objectivecost function
This can be viewed as a multi-objective optimization problem where each objective corresponds to maximization of the capacity of one of the users.
Multi-user MIMO techniques are nowadays used to reduce the interference by adaptive precoding.

Zero-forcing precoding

zero-forcing
Linear precoding strategies include maximum ratio transmission (MRT), zero-forcing (ZF) precoding, and transmit Wiener precoding There are also precoding strategies tailored for low-rate feedback of channel state information, for example random beamforming.
Precoding

MIMO

multiple-input multiple-outputmultiple-input and multiple-outputmultiple-input multiple-output communications
Precoding is a generalization of beamforming to support multi-stream (or multi-layer) transmission in multi-antenna wireless communications.
MIMO can be sub-divided into three main categories: precoding, spatial multiplexing (SM), and diversity coding.

IEEE 802.11n-2009

n802.11n802.11b/g/n
802.11n
The transmitter and receiver use precoding and postcoding techniques, respectively, to achieve the capacity of a MIMO link.

Spatial multiplexing

multiple data streamsspatial demultiplexingSpatial multiplex coding
Spatial multiplexing
where is the N_s\times 1 vector of transmitted symbols, are the N_r\times 1 vectors of received symbols and noise respectively, \mathbf{H} is the matrix of channel coefficients and \mathbf{W} is the linear precoding matrix.

Space-division multiple access

SDMAspace division multiple accessSpace Division Multiple Access (SDMA)
In multi-user MIMO, the data streams are intended for different users (known as SDMA) and some measure of the total throughput (e.g., the sum performance or max-min fairness) is maximized.

Channel state information

channel estimationchannel knowledgeCSI
Linear precoding strategies include maximum ratio transmission (MRT), zero-forcing (ZF) precoding, and transmit Wiener precoding There are also precoding strategies tailored for low-rate feedback of channel state information, for example random beamforming. In point-to-point systems, some of the benefits of precoding can be realized without requiring channel state information at the transmitter, while such information is essential to handle the inter-user interference in multi-user systems. The precoding strategy that maximizes the throughput, called channel capacity, depends on the channel state information available in the system.

Narrowband

narrow-bandnarrownarrow band
Most classic precoding results assume narrowband, slowly fading channels, meaning that the channel for a certain period of time can be described by a single channel matrix which does not change faster.

Fading

shadowingfading channelfrequency-selective fading
Most classic precoding results assume narrowband, slowly fading channels, meaning that the channel for a certain period of time can be described by a single channel matrix which does not change faster.

Orthogonal frequency-division multiplexing

OFDMorthogonal frequency division multiplexingCOFDM
In practice, such channels can be achieved, for example, through OFDM.

Channel capacity

capacitydata capacityinformation capacity
The precoding strategy that maximizes the throughput, called channel capacity, depends on the channel state information available in the system.

Singular value decomposition

SVDsingular-value decompositionsingular values
If the channel matrix is completely known, singular value decomposition (SVD) precoding is known to achieve the MIMO channel capacity.

Feedback

feedback loopfeedback loopsfeedback mechanism
Linear precoding strategies include maximum ratio transmission (MRT), zero-forcing (ZF) precoding, and transmit Wiener precoding There are also precoding strategies tailored for low-rate feedback of channel state information, for example random beamforming.

Scheduling (computing)

schedulingschedulerscheduling algorithm
Furthermore, there might be more users than data streams, requiring a scheduling algorithm to decide which users to serve at a given time instant.

Signal-to-noise ratio

signal to noise ratioSNRsignal-to-noise
Zero-forcing precoding may even achieve the full multiplexing gain, but only provided that the accuracy of the channel feedback increases linearly with signal-to-noise ratio (in dB).

Vector quantization

VQvector quantisation.VQA
Quantization and feedback of channel state information is based on vector quantization, and codebooks based on Grassmannian line packing have shown good performance.

Signal-to-interference-plus-noise ratio

signal-to-interference and noise ratio (SINR)signal-to-interference-and-noisesignal-to-interference-plus-noise
The signal-to-interference-and-noise ratio (SINR) at user k becomes

Space–time code

space–time codingspace-time codingSpace Time Code (STC)
Space–time code

David J. Love

While at UT Austin, Love worked alongside Robert Heath Jr. to pioneer MIMO feedback strategies (limited feedback precoding), a form of which is currently found in IEEE 802.11 WLAN, Wimax cellular, and LTE cellular standards, especially Grassmannian beamforming.