On the degrees of freedom of the compound MISO broadcast channels with finite states
Mohammad Ali Maddah-Ali · 2010
We consider compound multiple-antenna broadcast channels with M transmit antennas and K single-antenna receivers, where the channel of receiver r takes one of Jrcomplex vectors. We show that for any finite Jr, the degrees of freedom (DoF) of MK/M+K-1 is achievable. It is in contrary to the commonly believed conjecture that the DoF collapses to one for large Jr's. We also establish the optimality of this result, where Jr≥ M, r = 1, ..., K. The achievable scheme relies on using a number theoretic approach of interference alignment, and ignoring the possibility of cooperation among the transmit antennas. Moreover, we show that if Jr's for some of the users are relatively small, then both transmit cooperation and interference alignment are needed. Unlike the conventional schemes, here the transmit precoders are not full rank.