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

TL;DR

This paper characterizes the degrees-of-freedom region for order-(K-1) messages in a K-user MIMO broadcast channel with delayed CSIT, revealing larger DoF regions than with no CSIT under certain antenna configurations.

Contribution

It provides a new theoretical characterization of the DoF region with delayed CSIT for arbitrary antenna setups, including a novel transmission scheme and outer bounds.

Findings

The DoF region with delayed CSIT exceeds that with no CSIT when N_2 < M.

A 2-phase transmission scheme achieves the derived DoF region.

The DoF outer region is established using a Genie-bound approach.

Abstract

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 $N_1 \le N_2 \le \cdots \le N_K$.