We consider theories and technologies for a multiuser MIMO system with limited feedback downlink channel state information.

## Game theory on the limited feedback systemEdit

If a user feedback $ B $ bits to the base station, is the feedback signaling beneficial directly to the performance of that user? If the base station strongly coordinates all users in a networks not to happen a selfish behavior, it is general to regard your feedback signaling directly related to your performance. Once we assume that users can select the number of feedback bits by himself, we must investigate the possibility of the selfish behavior in the limited feedback systems.

If one user occupys whole the uplink channel for his feedback signaling, other users can not load their feedback information even if feedback signaling is crucial to their performance. The possible solution to this situation is that the basestation sets up the number of feedback bits for each user in a constant value regardless channel states of different users.

## Two User MU-MIMO Systems with Zero-forcing BeamformingEdit

In the section, we explore two user multi-user MIMO systems to investigate the possibility of the selfish behavior and protection methods. Two user systems are treated for the analytical simplicity. The beamforming weight vector of user 2 will be determined with respect to the quantized feedback channel vector of user 1 without referring his own channel vector and vice versa. The transmit signal is then given by

- $ \mathbf{x} = \mathbf{w}_1 s_1 + \mathbf{w}_2 s_2 $

where $ \mathbf{w}_1 $ is orthogonal to the channel vector of user 2 and $ \mathbf{w}_2 $ is orthogonal to the channel vector of user 1. The received signal at the user 1 is give by

- $ y_1 = \mathbf{h}_1^H( \mathbf{w}_1 s_1 + \mathbf{w}_2 s_2) + n_1 $

If the number of feedback bits at user 1 increase, the inner product of $ \mathbf{h}_1 $ and $ \mathbf{w}_2 $ goes to more zero.