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

This paper theoretically characterizes 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 first design a 2-phase transmission scheme, and then propose a backward/forward cancellation algorithm for decoding. Specifically, we efficiently derive the achievable DoF region from the designed transmission scheme by transformation approach. The main implication of this paper is that for the order-$(K-1)$ messages of $K$-user MIMO broadcast channel, the DoF region with delayed CSIT is larger than the DoF region with no CSIT when $N_2<M$, where $N_1 \le N_2 \le \cdots \le N_K$.