Layered interference alignment: Achieving the total DOF of MIMO X-channels

The K × 2 multiple input multiple output (MIMO) X-channel with constant channel coefficients available at all transmitters and receivers is considered. A new alignment scheme, named layered interference alignment, is proposed in which both vector and real interference alignment techniques are exploited together with joint processing at receiver sides. Data streams, having fractional multiplexing gains, in the desired directions are sent by transmitters to align the interfering signals at receivers efficiently. To decode the intended messages at receivers, a new number theoretic joint processing technique which exploits the availability of several received antennas, is proposed. This processing is backed up by a recent result in the field of Simultaneous Diophantine Approximation, which is introduced in this paper for the firs time. It is shown that incorporating the layered interference alignment is essential to characterize the total DOF of 2 km/ k+1, in the k × 2 m-antenna X-channel.