# 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

37 Related Articles

### 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

### Cooperative diversity

**group cooperative relay**

Cooperative diversity

### Space–time code

**space–time codingspace-time codingSpace Time Code (STC)**

Space–time code

### Space–time trellis code

Space–time trellis 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.