Blind interference alignment over homogeneous 3-user 2 × 1 broadcast channel

This paper studies the blind interference alignment (BIA) in a homogeneous 3-user 2 × 1 broadcast channel (BC). In a homogeneous BC, each link connecting the transmitter and a user undergoes independent fading with identical coherence time. BIA refers to the implementation of interference alignment with no need of CSIT. It is shown in our early work [1] that, BIA can be easily accomplished in a homogeneous 2-user 2 × 1 BC with no requirement of using time-frequency extension, or mounting an extra antenna to each single-antenna receiver. In this paper, we extend the idea to a homogeneous 3-user 2 × 1 BC. We show that, if the three homogeneous 2 × 1 links satisfy certain offset condition, a homogeneous 3-user 2 × 1 BC can be completely decomposed into finite-time channel blocks, and each of which is BIA-feasible. By using a new technique that is different with the one in our early work, we prove a sufficient condition for a homogeneous 3-user 2 × 1 BC to be completely decomposable, i.e., to be suitable for BIA to achieve the optimal 3/2 DoF. We further study a multi-user 2 × 1 broadcast network, in which there are K ≥ 3 homogeneous users and their coherence time offsets are independently and uniformly distributed. We show that, if K ≥ 15, a 2-antenna transmitter can find, with more than 99% certainty, three users to form a BIA-feasible 3-user BC and achieve the optimal 3/2 DoF with no need of CSIT.