On the Optimality of Opportunistic Interference Alignment in 3-Transmitter MIMO Interference Channels

In this paper, we propose opportunistic interference alignment (OIA) for three-transmitter multiple-input multipleoutput (MIMO) interference channels (ICs). In the proposed OIA scheme, each transmitter has its own user group that consists of K users, and each transmitter opportunistically selects the user whose received interference signals are most aligned. Thus, three-transmitter MIMO IC is opportunistically constructed by three transmitters and their selected users. Contrary to conventional IA, perfect channel information for all of the interference links is not required at the transmitter. Each user just needs to feed back one scalar value in the proposed OIA scheme. When the number of receive antennas is NR (with NR = 2M ) and the number of transmit antennas is NT (with NT ≥ M ), we prove that each transmitter can achieve M degrees of freedom (DoF) as the number of users in each group goes to infinity (K → ∞), in comparison with the 2M 3 DoF known to be achievable in the three-transmitter M × 2M MIMO IC. We also show that the user scaling K ∝ PαM2 enables the network to achieve M DoF per transmitter where P is transmit power, and α is the relative path loss of the interfering channel in decibels. The computational complexity of the proposed OIA scheme is analyzed and compared with conventional user selection schemes.