Real interference alignment for vector channels

We present a real interference alignment technique for multiple-input multiple-output (MIMO) networks. This technique is based on a theorem due to Dirichlet and Khintchine for simultaneous Diophantine approximation and uses the outputs of all the antennas at the receiver simultaneously for decoding, instead of using them in an antenna-by-antenna basis. This allows us to forgo asymptotic real interference alignment for several multi-user scenarios such as the two-user MIMO interference channel with confidential messages and the two-user MIMO multiple access wiretap channel.