Achievable Sum Rate and Degrees of Freedom of Opportunistic Interference Alignment in MIMO Interfering Broadcast Channels

In this paper, the sum rate of opportunistic interference alignment (OIA) is analyzed in multiple-input-multiple-output interfering broadcast channels. The alignment metric upon which users are scheduled is based on the chordal distance between certain interfering subspaces at each receiver, and the closed-form expressions for the rates of the scheduled users are derived. Furthermore, we show that for a system in which each user has $N$ receive antennas and the $j$ th base station transmits $d_{j}$ data streams, where $\sum _{j=1}^{I}d_{j}={N}+1$ and ${N}\ge 2$ , the rate for each user can be approximated by the mean of a Gumbel random variable. Further analysis reveals that if the number of users in cell $i$ scales as $\rho ^{\alpha }$ , where $\rho $ is the normalized transmit power and $\alpha \in [{0,1}]$ , then cell $i$ can achieve $\alpha d_{i}$ degrees of freedom. The simulation results confirm the validity of the theoretical analysis and the accuracy of the approximation. Thus, the sum rate analysis provided herein is an effective performance evaluation method for multi-cell OIA.