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We study the degrees of freedom (DoF) of the multiple-input multiple-outputX-channel (MIMO XC) with delayed channel state information at the transmitters(delayed CSIT), assuming linear coding strategies at the transmitters. Wepresent two results: 1) the linear sum DoF for MIMO XC with general antennaconfigurations, and 2) the linear DoF region for MIMO XC with symmetricantennas. The converse for each result is based on developing a novelrank-ratio inequality that characterizes the maximum ratio between thedimensions of received linear subspaces at the two multiple-antenna receivers.The achievability of the linear sum DoF is based on a three-phase strategy, inwhich during the first two phases only the transmitter with fewer antennasexploits delayed CSIT in order to minimize the dimension of its signal at theunintended receiver. During Phase 3, both transmitters use delayed CSIT to sendlinear combinations of past transmissions such that each receiver receives asuperposition of desired message data and known interference, thussimultaneously serving both receivers. We also derive other linear DoF outerbounds for the MIMO XC that, in addition to the outer bounds from the sum DoFconverse and the proposed transmission strategy, allow us to characterize thelinear DoF region for symmetric antenna configurations.

Linear Degrees of Freedom of the MIMO X-Channel with Delayed CSIT