Degrees of Freedom Region of the (M,N_1,N_2) MIMO Broadcast Channel with Partial CSIT: An Application of Sum-set Inequalities Based on Aligned Image Sets
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The degrees of freedom (DoF) region is characterized for the 2-user multiple input multiple output (MIMO) broadcast channel (BC), where the transmitter is equipped with M antennas, the two receivers are equipped with N_1 and N_2 antennas, and the levels of channel state information at the transmitter (CSIT) for the two users are parameterized by β_1, β_2, respectively. The achievability of the DoF region was established by Hao, Rassouli and Clerckx, but no proof of optimality was heretofore available. The proof of optimality is provided in this work with the aid of sum-set inequalities based on the aligned image sets (AIS) approach.
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