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 $\beta _{1}, \beta _{2}$ , 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.

中文翻译：

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具有部分 CSIT 的 (M;N1;N2) MIMO 广播信道的自由度区域：基于对齐图像集的和集不等式的应用

自由度 (DoF) 区域的特征在于 2 用户多输入多输出 (MIMO) 广播信道 (BC)，其中发射机配备有 百万美元 天线，两个接收器都配备 $N_{1}$ 和 $N_{2}$ 两个用户的发射机 (CSIT) 信道状态信息电平参数化为 $\beta _{1}, \beta _{2}$ ， 分别。自由度区域的可实现性是由 Hao、Rassouli 和 Clerckx 建立的，但迄今为止还没有最优性的证据。在这项工作中，借助基于对齐图像集 (AIS) 方法的和集不等式，提供了最优性的证明。