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.

## Channel Quality Calculation Edit

the original single user single stream beamforming system feeds back

- $ \mathrm{CQI}_{\mathrm{SU},m} = \mathrm{SNR} |\mathbf{h}_m^H \mathbf{w}_m|^2 $

while the channel quality information for user $ m $ in the PU^{2}RC system is given by

- $ \mathrm{CQI}_{\mathrm{MU},m} = \frac{\frac{\mathrm{SNR}}{M} |\mathbf{h}_m^H \mathbf{w}_m|^2} {1+\frac{\mathrm{SNR}}{M} \sum_{l \neq M} |\mathbf{h}_m^H \mathbf{w}_l|^2} $
- $ = \frac{||\mathbf{h}_m||^2 \cos^2( \angle \mathbf{h}_m, \mathbf{w}_m)} {\frac{M}{\mathrm{SNR}} + \sum_{l \neq M} ||\mathbf{h}_m||^2 \cos^2( \angle \mathbf{h}_m, \mathbf{w}_l)} $
- $ \geq \frac{||\mathbf{h}_m||^2 \cos^2( \angle \mathbf{h}_m, \mathbf{w}_m)} {\frac{M}{\mathrm{SNR}} + ||\mathbf{h}_m||^2 (1 - \cos^2( \angle \mathbf{h}_m, \mathbf{w}_m))} $

where $ \mathbf{h}_m $ is the channel vector and $ \mathbf{w}_m $ is the beamforming vector.

## Receive Combining Weights Edit

We compare three receive combining methods which are expected SINR combining method^{[1]}, the quantization based combining (QBC) method, and the eigen-mode combining method, where the expected SINR is investigated also by Matteo Trivellato.

When SNR is high, the expected SINR method becomes similar to the eigen-mode method because noise is more dominant than interference. When SNR is low, the expected SINR combining method becomes the QBC method because interference is more dominant than noise.

## References Edit

- ↑ M. Trivellato, H. Huang, and F. Boccardi, “Antenna Combining and Codebook Design for the MIMO Broadcast Channel with Limited Feedback,” (invited paper), in Proc. Asilomar Conference on Signals, Systems, and Computers 2007, Pacific Grove, USA, Nov. 2007.