We discuss the background of PU^{2}RC before describing the history of PU^{2}RC.

## Features for the implementation of MU-MIMO Edit

In general, MU-MIMO schemes consist of precoding, feedback and scheduling features. Fundamental requirements for each features are described in the following subsections.

### Precoding Edit

To transmit different information for multiple users simultaneously, MU-MIMO systems perform precoding at the transmitter. Precoding can be implemented as either a linear precoding form, $ \mathbf{x} = \mathbf{W} \mathbf{s} $, or a nonlinear precoding form, $ \mathbf{x} = \mathbf{W}(\mathbf{s}) $. We focus linear precoding because of computational simplicity and implementation possibility. For linear precoding, it is assumed that the precoding matrix is given by $ \mathbf{W} = [\mathbf{w}_1, \mathbf{w}_2, \ldots, \mathbf{w}_K] $ where $ \mathbf{w}_k $ is the precoding vector for user $ k $. The received signal at user $ k $ is then given by

- $ \mathbf{y}_k = \mathbf{H}_k \mathbf{W} \mathbf{s} + \mathbf{n}_k $

where $ \mathbf{H}_k $ is the channel matrix of user $ k $ and $ \mathbf{s} $ is the transmit information vector of the selected users.

### Feedback Edit

The precoding matrix $ \mathbf{W} $ is generated based on the downlink channel information, fed back from users. The feedback signaling can contains either direct channel information (usually by scalar quantization) or codebook index (usually by vector quantization). While the direct channel information approach is simple but requires high-rate feedback, the codebook based approach is relatively complicated but requires low-rate feedback.

### Scheduling Edit

## Backgoud Edit

For high definition multimedia services, high spectral efficiency is necessary for the next generation cellular networks. MIMO can be a candidate solution to achieve high spectral efficiency. However, SU-MIMO has a limitation for mobile devices because of a form factor since SU-MIMO requires multiple antennas at both BS and UEs. Multiple antennas at the base station is feasible relative to those at UEs. MU-MIMO can achieve a multiplexing gain proportional to the number of transmit antennas at BS even with a single antenna at UEs by multiuser precoding techniques at the transmitter. For high performance precoding, it is necessary to have accurate channel knowledge at the transmitter, which is burden some for the uplink channel, as well as to use the complex precoding algorithm for the optimal performance. Since high amount of feedback signaling can reduce the uplink throughput, a low amount feedback MU-MIMO scheme is needed for mobile communication systems. We propose the PU2RC strategy which can achieve high performance with low feedback overhead and low precoding complexity by the use of combination of user scheduling in a wireless packet basis cellular network. We further investigate a precoding algorithm and a user scheduling method for the variable feedback scenario using a new performance measure for feedback systems.

## History Edit

Including ZF Beamforming, a set of multiuser beamforming, or multiuser multiple-input and multiple-output (MU-MIMO), schemes has been actively discussed in the wireless cellular standards including 3GPP LTE/LTE-A and IEEE 802.16m [X]. At the expense of uplink loss by feedback signaling, multiuser beam-forming can offer significant system throughput enhancement compared to conventional single user multistream beamforming, or single user MIMO (SU-MIMO), schemes even when a single receiver antenna is equipped at each UE [X]. Per-User Unitary Rate Control (PU2RC) is the cellular network initiative of multiuser beamforming implementation. PU2RC effectively utilizes both multiuser precoding and scheduling to enhance the system throughput performance in the multiple antenna cellular standards [X]. PU2RC uses the feedback information codebook consisting of $ 2^B − \log_2 M $ unitary matrices where $ 2^B $ is the number of total precoding vectors in the codebook and $ M $ is the number of transmit antennas [X]. After each UE feeds back the preferred matrix index (PMI), the relative preferred vector index (PVI) in the selected preferred matrix and the channel quality information based on the PMI and PVI information to the BS, the BS selects maximum throughput users for each PVI and the best PMI based on the selected users so as to transmit multiple streams for multiple users.