Degrees-of-freedom for the 4-user SISO interference channel with improper signaling

It has been recently shown that for the 3-user single-input single-output (SISO) interference channel with constant channel coefficients, a maximum of 1.2 degrees-of-freedom (DoF) are achievable using linear interference alignment schemes when improper (a.k.a. asymmetric) Gaussian signaling is applied. In this paper, we study the 4-user SISO interference channel and provide inner and outer bounds for the total number of DoF achievable for this channel. We prove that at least 4/3 DoF are achievable for the 4-user channel using also linear interference alignment techniques and improper signaling. A simple converse proof shows that no more than 8/5 DoF are achievable for this scheme. Simulation results seem to indicate that the inner bound is in fact tight for this channel, and serve to illustrate the sum-rate improvement with respect to time division multiple access (TDMA) techniques.