A Systematic Approach for Interference Alignment in CSIT-less Relay-Aided X-Networks

The degrees of freedom (DoF) of an X-network with M transmit and N receive nodes utilizing interference alignment with the support of $J$ relays each equipped with $L_j$ antennas operating in a half-duplex non-regenerative mode is investigated. Conditions on the feasibility of interference alignment are derived using a proper transmit strategy and a structured approach based on a Kronecker-product representation. The advantages of this approach are twofold: First, it extends existing results on the achievable DoF to generalized antenna configurations. Second, it unifies the analysis for time-varying and constant channels and provides valuable insights and interconnections between the two channel models. It turns out that a DoF of $\nicefrac{NM}{M+N-1}$ is feasible whenever the sum of the $L_j^2 \geq [N-1][M-1]$.