On the Degrees of Freedom of the Compound MIMO Broadcast Channels with Finite States

Understand

Multiple-antenna broadcast channels with $M$ transmit antennas and $K$ single-antenna receivers is considered, where the channel of receiver $r$ takes one of the $J_r$ finite values.

• It is assumed that the channel states of each receiver are randomly selected from $\mathds{R}^{M\times 1}$ (or from $\mathds{C}^{M\times 1}$).
• It is shown that no matter what $J_r$ is, the degrees of freedom (DoF) of $\frac{MK}{M+K-1}$ is achievable.
• The achievable scheme relies on the idea of interference alignment at receivers, without exploiting the possibility of cooperation among transmit antennas.