Interference Alignment and Degrees of Freedom of the Two-User X Channel with an Instantaneous Relay
In this paper we investigate the sum degrees of freedom (DoF) of multiple unicasts in a wireless network. With 2 source nodes, 2 destination nodes, there are a total of 4 independent unicast sessions (messages), one from each source to each sink node (this setting is also known as an X network), and also there is a delay-free relay working in full-duplex mode helping the transmissions from the source to destination nodes. For such a channel setting, we prove that 5/3 DoF is achievable almost surely for time-varying/frequency-selective channels, based on the ideas of aligned interference neutralization, linear forwarding and interference alignment. Also, the achievable scheme can be easily translated to the rational alignment scheme for the network with constant-values channel coefficients. In addition, we provide an intuition for the 5/3 DoF result from the perspective of counting the number of linear equations and variables.