Feedback in the K-user interference channel.

We consider the scalar K-user Gaussian interference channel (IC) with feedback, where channel coefficients are fixed over time and frequency. We focus on two feedback models: (1) each receiver feeds back its received signal to all the transmitters and (2) functions of the received signals are fed back through a backward IC. We show that the feedback degrees-of-freedom (fdof) of the first model is K/2 if the global channel matrix is invertible. For the second feedback model, we show that fdof - 3/2 is achievable for the 3-user IC. Then, we show how nontrivial fdof can be achieved for the K-user IC, when the global channel matrix belongs to a specific spectral family of matrices. Our achievable schemes are linear and require a finite number of signal-space dimensions, contrasting the asymptotic interference alignment by Cadambe et al. and the real interference alignment by Motahari et al. Another consequence of feedback is that it can strictly increase the degrees-of-freedom for some classes of ICs.