Degrees of freedom of SIMO X channel

In this study, the authors mainly study the degrees of freedom (DoFs) of M × N user single input multiple output (SIMO) (or multiple input single output (MISO)) X channels, in which the channel coefficients are drawn from a continuous distribution and data-sharing among users are unavailable. First, the authors establish an outer bound of DoFs for multiple-in multiple-out (MIMO) X channel, which is tighter than those in previous work. For SIMO X channel with R antennas at each user, the authors prove that the DoFs is [ MNR /( M + NR − R )], which is achieved by symbol extension and interference alignment. As the transmitters and receivers are interchangeable in the network considered, the authors obtain corresponding results for MISO X channel. Finally, the authors generalise our result to MIMO X channel with R antennas at each user, and show that its DoFs is [ MNR /( M + N − 1)].