Retrospective interference alignment for interference channels with delayed feedback

We deal with interference channels with (i) delayed channel state information at the transmitter (CSIT), and (ii) delayed output feedback at the receiver and no CSIT. We extend the algorithm by Maleki et al. [8] for M = 3 users to any M ≥ 3 under the constraint that all the transmitter/receiver pairs are active simultaneously. We propose a retrospective interference alignment algorithm achieving M2/(M2−1) degrees of freedom (DoF) in the case (i) and an algorithm attaining [M/2]M/([M/2](M−1) + 1) DoF in the case (ii). However, larger DoF — 9/8 in (i) and 6/5 in (ii) — are easily achievable, for any M, when orthogonal channels (e.g. in time, frequency, etc.) are shared by triplets of transmitter/receiver pairs, and within each subchannel the algorithm by Maleki et al. [8] is applied. Hence, our work suggests that, for all M and both in the case (i) and in the case (ii), the strategy maximizing the DoF entails that three transmitter/receiver pairs are simultaneously active on the same channel.