The Generalized Degrees-of-Freedom Region of the Two-User MIMO Broadcast Channel With Delayed CSIT

In this paper, we characterize the generalized degrees-of-freedom (GDoF) region of the two-user <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(M,N_{1},N_{2})$ </tex-math></inline-formula> multiple-input multiple-output (MIMO) broadcast channel with delayed channel state information at the transmitter (CSIT), where there are one transmitter with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> antennas and two receivers with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{1}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{2}$ </tex-math></inline-formula> antennas, respectively. Under delayed CSIT, different from the existing converse approaches in the multiple-input single-output (MISO) GDoF and MIMO degrees-of-freedom (DoF) models, we incorporate new components into traditional approaches for this MIMO GDoF converse. For the achievability, we generalize the existing MISO achievable scheme. Our result reveals how the channel strength and antenna configuration impact the GDoF region of the two-user MIMO broadcast channel with delayed CSIT. Furthermore, the extension of our converse to a GDoF outer region of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -user MIMO broadcast channel with delayed CSIT is also provided.