MIMO/SDMA and Beyond are discussed. MIMO has been considered as important technology to enhance the performance of wireless communication systems.

## Introduction Edit

We start with discussion on the definition of MIMO. MIMO represents various multiple antenna technologies in a wide sence, and represents only multiple-input and multiple-output (MIMO) antenna technology in a narrow sence.

The employment of multiple antennas at wireless equipments can improve the performance of signal transmission and reception in wireless systems. The throughput performance of MIMO systems is enhanced almost proportional to the minimum of transmission and reception antennas embedded at at terminal.

## System Model Edit

### MIMO MAC Edit

*Main article: MIMO MAC*

## MIMO Edit

*Main article: MIMO*

### Precoding Edit

*Main article: Precoding*

### Single User Beamforming Edit

Single user beamforming is beamforming for one user in a network where multiple antennas is applied at the access point (AP) (or at the transmitter). The performance of single user beamforming can be represented by the system throughput. For downlink channels, we consider the duality property between the uplink and downlink channels. If the perfect channel status information is available at the AP, the achievable throughput of the downlink beamforming system can be given by

- $ C_\mathrm{perfect} = \log_2( 1 + P ||\mathbf{h}||^2) $

where $ P $ is the transmit power and $ \mathbf{h} $ is the downlink beamforming channel.

## SDMA Edit

### Transmit Beamforming Edit

*Main article: Transmit Beamforming*

- Digital feedback single-user beamforming is a beamforming technology that transmit a single user from the base station.

### Zero-forcing Beamforming Edit

*Main article: Zero-forcing Beamforming*

Zero-forcing Beamforming (ZF-BF) transmits or receives date to the direction of the desired users and nulls out the direction of undesired users or interference users, respectively. The concept of interference users can be used for equivalent meaning to undesired users in the transmitting mode.

### Limited Feedback Edit

To apply Zeroforcing Beamforming (ZF-BF) at the transmitter for multiuser wireless networks, the downlink channel states information (CSI) for whole candidate users should be available at the transmitter. Moreover, the accuracy of channel state information at the transmitter (CSIT) must increase according to average signal-to-noise ratio of the downlink channel, assuming the every candidate users are located at the same distance from the BS.

#### Digital FeedbackEdit

*Main article: Digital Feedback*

#### Analog FeedbackEdit

Feedback can be implemented as analog signaling so that no quantization processing is not used.

### Intelligent Beamforming Edit

#### KASSPER Approach Edit

## Multiuser Scheduling for Feedback Beamformig SystemsEdit

*Main article: Multiuser Scheduling for Feedback Beamformig Systems*

Both multiuser scheduling and feedback beamforming require the overhead signal feedback. Therefore, the combination of two scheme is a complex problem in terms of the feedback resource allocation. If the number of users is smaller than the number of transmit antennas, the base station can transmit the signals to all users without user selection. When the number of users is larger than the number of transmit antennas, the base station will select a set of users for transmission. Assume that the set of all user denoted as $ A $ and the cardinality of $ A $ is $ K $. The size of the selected user set is less than or equal to the number of transmit antennas, i.e., $ |S| \leq M $ where $ M $ is the number of transmit antennas and $ S \in A $ is the set of the selected users.

## Cooperative Wireless Networks Edit

### Relaying Strategies Edit

#### Amplify-and-Forward Edit

#### Decode-and-Forward Edit

#### Compress-and-Forward Edit

*Main article: Compress and forward*

The compress-and-forward strategy allows the relay node to compress the received signal before transmitting it to the destination node, where the Wyner-Ziv coding has been known as the optimal compression algorithm.

## Shannon Theory 2.0 Edit

*Main article: Shannon Theory 2.0*

### Theoretical Approach vs. Experimental ApproachEdit

*Main article: Theoretical Approach vs. Experimental Approach*

## Basic Mathematical Theorem for Performance Analysis Edit

### Jensen's inequality Edit

### Tailor Serious Edit

### Lagrange Multiplier and KKT Conditions Edit

- Lagrange multiplier is a mathematical tool to optimize the condition with some subjective.

## Personal Thesis Edit

We include on-going personal thesis for discussion.

### J. S. Kim, Limited Feedback MIMO/SDMA Edit

*Main article: Limited Feedback MIMO/SDMA*

In this thesis, we discuss effective limited Feedback MIMO/SDMA schemes in terms of the system performance.

### J. S. Kim, On the performance of digital feedback beamforming systems Edit

This paper discusses net spectral efficiency for digital feedback beamforming systems in complex wireless networks. Contrary to SISO cellular networks, MIMO, multiuser beamforming, cooperative relay networks can be seen as complex wireless networks because the signal complexity of such cellular networks substantially higher than simple cellular networks where the link to link channel is of main interest.