On Achievable Degrees of Freedom for the Frequency-Selective K-User Interference Channel in the Presence of an Instantaneous Relay

In this paper, we study the degrees of freedom (DoF) of the frequency-selective K-user interference channel in the presence of an instantaneous relay (IR) with multiple receive and transmit antennas. We investigate two scenarios based on the IR antennas' cooperation ability. First, we assume that the IR receive and transmit antennas can coordinate with each other, where the transmitted signal of each transmit antenna can depend on the received signals of all receive antennas, and we derive an achievable DoF for this model. In our interference alignment scheme, we divide receivers into two groups, called clean and dirty receivers. We design our scheme such that a part of the message of clean receivers can be demultiplexed at the IR. Thus, the IR can use these message streams for interference cancelation at the clean receivers. Next, we consider an IR, whose antennas do not have coordination with each other, where the transmitted signal of each transmit antenna only depends on the received signal of its corresponding receive antenna, and we derive an achievable DoF for it. We show that the achievable DoF decreases considerably compared with the coordinated case. In both of these models, our schemes achieve the maximum K DoFs, if the number of transmit and receive antennas is more than a finite threshold.