Blind Interference Alignment (BIA) schemes create and exploit channel coherence patterns without the knowledge of channel realizations at transmitters, while beamforming schemes rely primarily on channel knowledge available to the transmitters without regard to channel coherence patterns. In order to explore the compatibility of these disparate ideas and the possibility of synergistic gains, this work studies the Degrees of Freedom (DoF) of the 2-user${(M_{1}\times N_{1})(M_{2}\times N_{2})}$Multiple-Input Multiple-Output (MIMO) Interference Channel (IC) where Transmitter 1 is equipped with reconfigurable antennas and has no channel knowledge, while Transmitter 2 has partial channel knowledge but no reconfigurable antennas. Taking a fundamental dimensional analysis perspective, the main question is to identify which antenna configurations allow synergistic DoF gains. The main results of this work are two-fold. The first result identifies antenna configurations where both reconfigurable antennas and partial channel knowledge are individually beneficial, as those where$M_{1}< N_{1}< \min (M_{2},N_{2})$. The second result shows that synergistic gains exist in each of these settings, over the best known solutions that rely on either reconfigurable antennas or partial channel knowledge alone. Coding schemes that jointly exploit partial channel knowledge and reconfigurable antennas emerge as a byproduct of the analysis.

The Generalized Degrees of Freedom (GDoF) of the two user interference channel are characterized for all parameter regimes under the assumption of finite precision channel state information at the transmitters (CSIT), when a limited amount of (half-duplex or full-duplex) cooperation is allowed between the transmitters in the form of π DoF of shared messages. In all cases, the number of over-the-air bits that each cooperation bit buys is shown to be equal to either 0, 1, 1/2 or 1/3. The most interesting aspect of the result is the 1/3 slope, which appears only under finite precision CSIT and strong interference, and as such has not been encountered in previous studies that invariably assumed perfect CSIT. Indeed, the achievability and converse for the parameter regimes with 1/3 slope are the most challenging aspects of this work. In particular, the converse relies on non-trivial applications of Aligned Images bounds.

The Generalized Degrees of Freedom (GDoF) of the two user interference channel are characterized for all parameter regimes under the assumption of finite precision channel state information at the transmitters (CSIT), when a limited amount of cooperation is allowed between the transmitters in the form of π DoF of shared messages. In all cases, the number of over-the-air bits that each cooperation bit buys is shown to be equal to either 0, 1, 1/2 or 1/3.

For the $K=2$ user MISO BC, i.e., the wireless broadcast channel where a transmitter equipped with $K=2$ antennas sends independent messages to $K=2$ receivers each of which is equipped with a single antenna, the generalized degrees of freedom (GDoFs) region are characterized for arbitrary channel strength and channel uncertainty levels for each of the channel coefficients. The result is extended to K>2 users under additional restrictions which include the assumption of symmetry.

In order to gain new insights into multiple-input- multiple-output (MIMO) interference networks, the optimality of Σk=1KMk/2 (half the cake per user) degrees of freedom is explored for a K-user MIMO interference channel where the cross-channels have arbitrary rank constraints, and the kth transmitter and receiver are equipped with Mkantennas each. The result consolidates and significantly generalizes results from prior studies by Krishnamurthy et al., of rank-deficient interference channels where all users have M antennas; and by Tang et al., of full rank interference channels where the kth user pair has Mkantennas. The broader outcome of this paper is a novel class of replication-based outer bounds for arbitrary rank-constrained MIMO interference networks where replicas of existing users are added as auxiliary users and the network connectivity is chosen to ensure that any achievable scheme for the original network also works in the new network. The replicated network creates a new perspective of the problem, so that even simple arguments such as user cooperation become quite powerful when applied in the replicated network, giving rise to stronger outer bounds, than when applied directly in the original network. Remarkably, the replication-based bounds are broadly applicable not only to MIMO interference channels with arbitrary rank-constraints, but much more broadly, even beyond Gaussian settings.

By introducing a novel outer bound, we find Σk=1kMk/2 degrees of freedom (half the cake per user) for a K-user multiple-inputmultiple-output (MIMO) interference channel (IC) where the cross-channels have arbitrary rank constraints, and the kthtransmitter and receiver are equipped with Mkantennas each. The result consolidates and significantly generalizes results from prior studies by Krishnamurthy et al., of rank-deficient interference channels where all users have M antennas; and by Tang et al., of full rank interference channels where the kthuser pair has Mkantennas.