Discrete relay beamforming for broadcasting with relay selection

In this paper, broadcast beamforming problem is considered in relay-assisted wireless networks. Two-phase relay communication is adopted. In the first phase, a source transmits common information to multiple relays which use amplify-and-forward relay protocol. Each relay multiplies its received signal by a complex weight and transmits it to the receivers. The amplitudes and phases of complex relay weights are chosen from discrete sets in order to decrease overhead for the feedback channel. Relay selection is employed in order to decrease network complexity. Nonlinear optimization problem is converted to a linear form suitable for mixed integer linear programming. The optimum solution can be found using branch-and-cut method.