The Degrees of Freedom Regions of Two-User and Certain Three-User MIMO Broadcast Channels with Delayed CSIT

TL;DR

This paper characterizes the degrees of freedom regions for two-user and certain three-user MIMO broadcast channels with delayed channel state information, providing tight bounds and an interference alignment scheme for optimal performance.

Contribution

It derives a tight outer-bound for the DoF region of general K-user MIMO BCs with delayed CSIT and develops an interference alignment scheme for specific cases.

Findings

Outer-bound for the DoF region of K-user MIMO BCs with delayed CSIT

Exact DoF region characterization for two-user MIMO BCs

Achievable scheme using interference alignment for certain three-user MIMO BCs

Abstract

The degrees of freedom (DoF) region of the fast-fading MIMO (multiple-input multiple-output) Gaussian broadcast channel (BC) is studied when there is delayed channel state information at the transmitter (CSIT). In this setting, the channel matrices are assumed to vary independently across time and the transmitter is assumed to know the channel matrices with some arbitrary finite delay. An outer-bound to the DoF region of the general $K$-user MIMO BC (with an arbitrary number of antennas at each terminal) is derived. This outer-bound is then shown to be tight for two classes of MIMO BCs, namely, (a) the two-user MIMO BC with arbitrary number of antennas at all terminals, and (b) for certain three-user MIMO BCs where all three receivers have an equal number of antennas and the transmitter has no more than twice the number of antennas present at each receivers. The achievability results are obtained by developing an interference alignment scheme that optimally accounts for multiple, and possibly distinct, number of antennas at the receivers.