Achievable DoF Regions of Three-User MIMO Broadcast Channel with Delayed CSIT

TL;DR

This paper characterizes the achievable degrees-of-freedom (DoF) regions for the three-user MIMO broadcast channel with delayed CSIT, providing new transmission schemes and a transformation approach to analyze DoF regions for different message orders.

Contribution

It introduces novel transmission schemes for order-2 and order-1 messages and a transformation approach to analyze the achievable DoF region in three-user MIMO broadcast channels with delayed CSIT.

Findings

Complete characterization of order-2 DoF region.

Explicit expression of order-1 DoF region.

Derived sufficient conditions for the proposed DoF region.

Abstract

For the two-user multiple-input multiple-output (MIMO) broadcast channel with delayed channel state information at the transmitter (CSIT) and arbitrary antenna configurations, all the degrees-of-freedom (DoF) regions are obtained. However, for the three-user MIMO broadcast channel with delayed CSIT and arbitrary antenna configurations, the DoF region of order-2 messages is still unclear and only a partial achievable DoF region of order-1 messages is obtained, where the order-2 messages and order-1 messages are desired by two receivers and one receiver, respectively. In this paper, for the three-user MIMO broadcast channel with delayed CSIT and arbitrary antenna configurations, we first design transmission schemes for order-2 messages and order-1 messages. Next, we propose to analyze the achievable DoF region of transmission scheme by transformation approach. In particular, we transform the decoding condition of transmission scheme w.r.t. phase duration into the achievable DoF region w.r.t. achievable DoF, through achievable DoF tuple expression connecting phase duration and achievable DoF. As a result, the DoF region of order-2 messages is characterized and an achievable DoF region of order-1 messages is completely expressed. Besides, for order-1 messages, we derive the sufficient condition, under which the proposed achievable DoF region is the DoF region.