The generalized degrees of freedom (GDoF) of the two-user multiple-input multiple-output interference channel is studied under the assumption of delayed channel state information at the transmitters. In particular, with M antennas at each transmitter and N antennas at each receiver, and in the non-trivial case when M N (with the case of M N not needing any CSIT), new lower and upper bounds on the symmetric GDoF are obtained that are parameterized by α, which links the interference-to-noise ratio (INR) and the signalto-noise ratio (SNR) at each receiver via INR = SNRα. A new upper bound for the symmetric GDoF is obtained by maximizing abound on the weighted sum rate, which in turn is obtained from a combination of genie-aided side-information and an extremal inequality. The maximum weighted sum rate in the high SNR regime is shown to occur when the transmit covariance matrix at each transmitter is full rank. An achievability scheme is developed that is based on block-Markov encoding and backward decoding, and which incorporates channel statistics through interference quantization and digital multicasting. This symmetric GDoF lower bound is maximized separately for different ranges of α, by optimizing the transmit power levels in the achievability scheme separately in the very weak [0 ≤ α ≤ (1/2)], weak [(1/2) <; α ≤ 1], and strong (α 1) interference regimes. The lower and upper bounds coincide when α ≥ [(r + 1)/(r + 2)], where r = min(2, M/N), thus characterizing the symmetric GDoF completely for strong interference and a range of values of weak interference. It is also shown that treating interference as noise is strictly sub-optimal from a GDoF perspective even when the interference is very weak.

The generalized degrees of freedom (GDoF) region of the multiple-input multiple-output (MIMO) Gaussian Z-interference channel with an arbitrary number of antennas at each node is established under the assumption of delayed channel state information at transmitters (CSIT). The GDoF region is parameterized by α, which links the interference-to-noise ratio (INR) to the signal-to-noise ratio (SNR) via INR = SNRα. A new outer bound for the GDoF region is established by maximizing a bound on the weighted sum-rate of the two users, which in turn is obtained by using a combination of genie-aided side-information and an extremal inequality. The maximum weighted sum-rate in the high SNR regime is shown to occur when the transmission covariance matrix of the interfering transmitter has full rank. An achievability scheme based on block-Markov encoding and backward decoding is developed which uses interference quantization and digital multicasting to take advantage of the channel statistics of the cross-link, and the scheme is separately shown to be GDoF-optimal in both the weak (α ≤ 1) and strong (α > 1) interference regimes. This is the first complete characterization of the GDoF region of any interference network with delayed CSIT, as well as the first such GDoF characterization of a MIMO network with delayed CSIT and arbitrary number of antennas at each node. For all antenna tuples, the GDoF region is shown to be equal to or larger than the degrees of freedom (DoF) region over the entire range of α, which leads to a V-shaped maximum sum-GDoF as a function of α, with the minimum occurring at α = 1. The delayed CSIT GDoF region and the sum-DoF are compared with their counterparts under perfect CSIT, thereby characterizing all antenna tuples and ranges of α for which delayed CSIT is sufficient to achieve the perfect CSIT GDoF region (or sum-DoF). It is also shown that treating interference as noise is not, in general, GDoF-optimal for the MIMO Z-IC, even in the weak interference regime.

The degrees of freedom (DoF) region for three users and the sum and symmetric DoF for K users are obtained for the multiple-input multiple-output cyclic Z-interference channel with M transmit antennas and N receive antennas at each user pair under the separate assumptions of perfect and delayed channel state information at the transmitters (CSIT). New communication schemes based on interference alignment are developed and are shown to be DoF-optimal for all choices of the number of antennas. The maximum sum-DoF scales linearly with the number of users for both perfect and delayed CSIT.

The degrees of freedom (DoF) region is obtained for the 3-user symmetric multiple-input multiple-output cyclic Z-interference channel with M transmit antennas and N receive antennas at each user-pair under the separate assumptions of perfect and delayed channel state information at the transmitter (CSIT). New communication schemes based on interference alignment are developed and are shown to be DoF-optimal for all choices of the number of antennas. For both perfect and delayed CSIT, the new schemes are shown to outperform those for the 2-user Z-interference channel in terms of sum DoF.

The degrees of freedom (DoF) region of the two-user multiple-input multiple-output (MIMO) interference channel is established under hybrid CSIT models in which there is some combination of instantaneous, delayed or no channel state information at the transmitters (CSIT) of each of the four channel matrices. In a standard version of this hybrid CSIT model, there is delayed CSIT at one transmitter and instantaneous CSIT at the other transmitter of incoming channel matrices at their respective unpaired receivers. The DoF regions for this standard model is established and, moreover, it is shown to be applicable to a large class of hybrid CSIT models. In so doing, a new DoF-optimal achievable scheme based on a combination of transmit beamforming and interference alignment is developed. Conditions are obtained on the numbers of antennas at each of the four terminals such that the DoF region under hybrid CSIT is equal to that under (a) instantaneous CSIT and (b) delayed CSIT. It is also demonstrated that by alternating between constituent hybrid CSIT states it is possible to obtain synergistic DoF benefits.