Joint Space Decomposition-and-Synthesis Approach and Achievable DoF Regions for $K$ -User MIMO Interference Channels

The paper proposes a new approach of joint space decomposition-and-synthesis (JSDS) for deriving achievable degree-of-freedom (DoF) region by interference alignment without symbol extension for K-user MIMO interference channel. Solving the interference alignment problem is to find the precoders that align desired signal and interference with disjoint subspaces at receivers. A related property of these precoders is that the solution range for each one of them is a union of linear spaces, termed transmit spaces. Based on this property, the JSDS approach is developed to derive transmit spaces that fulfill alignment conditions. From this approach, achievable DoF regions for 2 and 3-user interference channels are obtained. The region for the 2-user channel is shown to coincide with the existing result of the DoF capacity of the channel. For the K-user (K > 3) case, inner as well as outer bounds are given.