The Feasibility of Interference Alignment for MIMO Interfering Broadcast-Multiple-Access Channels

The feasibility conditions of interference alignment (IA) are analyzed for interfering broadcast-multiple-access channels in which one cell operates as downlink but the other cell operates as uplink. Under a general multiple-input and multiple-output antenna configuration, a necessary condition and a sufficient condition for one-shot linear IA are established, i.e., linear IA without symbol or time extension. In various example networks of interest, the optimal sum degrees of freedom (DoFs) are characterized by the derived necessary condition and sufficient condition. For symmetric DoF within each cell, a sufficient condition is established in a more compact expression, which yields the necessary and sufficient condition for a class of symmetric DoFs. An iterative construction of transmit and receive beamforming vectors is further proposed, which provides a specific beamforming design satisfying one-shot IA. Simulation results demonstrate that the proposed IA not only achieves larger DoF, but also significantly improves the sum rate over the single-cell operation in the practical signal-to-noise ratio regime.