A closed-form upper bound of the sum rate of blind interference alignment and its application to control of the number of active users

Blind interference alignment (B-IA) achieves the optimal degrees of freedom (DoF) in multiple-input single-output (MISO) broadcast channels (BC) when the number of users goes infinity. However, supporting infinite number of users requires to infinite length of symbol extension that is infeasible in practical systems, and maximizing DoF does not guarantee sum rate maximization especially at the low and medium SNR regime. In this paper, we derive the sum rate upper bound of B-IA schemes of [1] and [2] as a closed-form expression. Using the closed-form upper bound, we determine the sub-optimal number of active users for a given SNR and the total number of users in the system. Numerical results show that the upper bound captures the optimal number of active users well, and that controlling number of active users enhances the sum rate performance of the B-IA schemes.