K-user MIMO X network system with perfect interference alignment

In wireless X networks where all transmitters send the independent messages to all receivers, the theoretical degrees of freedom (DOF) and interference alignment (IA) scheme for its achievability are given by Cadambe and Jafar. However, IA scheme for wireless X network may be infeasible in practice unless the transmitters have the perfect channel information. In addition, if the transmitter with single antenna uses time-varying channel coefficients as a beamforming vector, the infinite channel extension is required to achieve the theoretical DOF of wireless X networks with perfect IA scheme. In this paper, we consider K-user MIMO X network where K transmitters and K receivers have M antennas each. While the beamforming vectors have been constructed with multiple channel uses over multiple time slot in the earlier work, we consider the beamforming vectors constructed only by a spatial signature over unit time. Accordingly the channel information at the transmitters can be available instantaneously. Then we propose the perfect IA scheme with no channel extension. Based on our sum-rate analysis and the simulation results, we confirm that our proposed scheme can achieve MK/2 DOF which is quite close to the theoretical degrees of freedom region of wireless X networks.