In this paper, we characterize the degrees-of-freedom (DoF) region of order-$(K-1)$ messages for the $K$-user multiple-input multiple-output (MIMO) broadcast channel with delayed channel state information at the transmitter (CSIT) and arbitrary antenna configurations, where the transmitter has $M$ antennas and the receiver $i=1,2,\cdots,K$ has $N_i$ antennas. For the converse, we first derive the DoF region of order-$(K-1)$ messages for the $K$-user MIMO broadcast channel with no CSIT and arbitrary antenna configurations with the aid of the proposed Genie-bound, and then establish the DoF outer region. For the achievability, we design the transmission scheme, and propose the backward/forward cancellation algorithm for decoding. Concisely, we derive the achievable DoF region from the designed transmission scheme by transformation approach. Our results indicate that, for order-$(K-1)$ messages of the $K$-user MIMO broadcast channel, the DoF region with delayed CSIT is larger than the DoF region with no CSIT when $N_2<M$, where $N_1 \le N_2 \le \cdots \le N_K$.
翻译：在本文中,我们用“K-K--1”为“K-K-1”为“K-K-1”为“K-K-1”为“K-”用户多投入多产出广播频道(MIIMO)”提供的信息,在“发报机”(CSIT)和“任意天线配置”上提供延迟的频道状态信息,在“DOF外区域”中,发射机拥有“M”天线和接收器$=1,2,\cdddots,K$为“N_i”天线。反之,我们首先为“K-1”为“K-”为“K-”为“K-”为“K-1”为“MIMIMO”用户无“C-K-$”广播频道提供“K-K-”信息,然后在“GENIT-T-M”的帮助下,建立“DOF”外部区域。为了可实现目的,我们设计了“M2\“C-M”区域,我们从设计中的“C-N_“C-M”“C_”延迟区域。我们用“C_“C_$”为“C_“C_”的“C_“C_”为“C_“C_”的“C_”表示”区域,因为“D_“D_“C_”为“C_”的“C_“D_”的“C_”“D_“D_”为“D_“C_“D_”的“Z”的“Z”的“Z”的“D”的“Z”表示“Z”区域,我们“Z”的“D”表示“D”的“D”表示“Z”表示“D_“D_“D’区域”的“Z”的“Z”为”为“D_“D_“D_“Z”区域”的“Z”的“Z”的“D_“Z”的“Z”的“Z”为”为”的“D_”表示“S_“D_“D_”的“D_”表示,因为“C_“S_“D_“S_“S_“D_“S_”区域”区域”为“S”为“D_“D
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