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This paper theoretically characterizes the degrees-of-freedom (DoF) region oforder-$(K-1)$ 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 theconverse, we first derive the DoF region of order-$(K-1)$ messages for the$K$-user MIMO broadcast channel with no CSIT and arbitrary antennaconfigurations with the aid of the proposed Genie-bound, and then establish theDoF outer region. For the achievability, we first design a 2-phase transmissionscheme, and then propose a backward/forward cancellation algorithm fordecoding. Specifically, we efficiently derive the achievable DoF region fromthe designed transmission scheme by transformation approach. The mainimplication of this paper is that for the order-$(K-1)$ messages of $K$-userMIMO broadcast channel, the DoF region with delayed CSIT is larger than the DoFregion with no CSIT when $N_2<M$, where $N_1 \le N_2 \le \cdots \le N_K$.

The DoF Region of Order-(K-1) Messages for the K-user MIMO Broadcast Channel with Delayed CSIT