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

Abstract

Most of the existing research on degrees-of-freedom (DoF) with imperfect channel state information at the transmitter (CSIT) assume the messages are private, which may not reflect reality as the two receivers can request the same content. To overcome this limitation, we consider hybrid private and common messages. We characterize the optimal DoF region for the two-user multiple-input multipleoutput (MIMO) broadcast channel with hybrid messages and imperfect CSIT. We establish a three-step procedure for the DoF converse to exploit the utmost possible relaxation. For the DoF achievability, since the DoF region has a specific three-dimensional structure w.r.t. antenna configurations and CSIT qualities, by dividing CSIT qualities into cases, we check the existence of corner point solutions, and then design a hybrid messages-aware rate-splitting scheme to achieve them. Besides, we show that to achieve the strictly positive corner points, it is unnecessary to split the private messages into unicast and multicast parts because the allocated power for the multicast part should be zero. This implies that adding a common message can mitigate the rate-splitting complexity of private messages.

The DoF region of two‐user MIMO broadcast channel with delayed imperfect‐quality CSIT

“…Thus, order-2 symbols, which are desired by two receivers, are construct at the transmitter and transmitted in this phase. It should be highlighted that in contrast to the existing design [2][3][4][5][6][7][8][9][10], our novelty is to configure the duration of Phase-III, amount of symbols transmitted in Phase-I and II, according to CSIT quality. The details of the transmission scheme are elaborated below.…”

“…It can be seen that $$\alpha _i = 1$$ represents delayed CSIT, and $$\alpha _i = 0$$ represents no CSIT. As [2–10], the CSI at receivers are perfect and global, namely each receiver has $$\mathcal {H}_i^n,\forall i$$.…”

“…For the three‐user MIMO broadcast channel with delayed CSIT, the complete DoF region is unclear, where the latest progress on this problem can be found in [4–6]. The DoF region of order‐$$(K-1)$$ messages, which are desired by $$K-1$$ receivers, for the K ‐user MIMO broadcast channel with delayed CSIT was characterized in [7].…”

“…The achievability proof is through a novel transmission scheme design. In contrast to [2][3][4][5][6][7][8][9][10], the duration of each phase and the amount of transmitted symbols are configured based on the imperfection of delayed CSIT. The derived DoF region shows that the DoF region with delayed imperfect-quality CSIT lies between the DoF region with no CSIT and the DoF region with delayed CSIT.…”

The DoF Region of Two-User MIMO Broadcast Channel with Delayed Imperfect-Quality CSIT

“…For the three-user MIMO broadcast channel with delayed CSIT, the complete DoF region is unclear, where the latest progress on this problem can be found in [3,4,5]. The DoF region of order-(K − 1) messages, which are desired by K − 1 receivers, for the K-user MIMO broadcast channel with delayed CSIT was characterized in [6].…”