Multicast relay beamforming through dual approach

We consider physical layer multicasting in an amplify-and-forward multi-antenna relay network. Assuming each relay antenna has individual power budget, our objective is to design the relay processing matrix to minimize the maximum individual antenna power for a given received SNR target at each destination. As the problem is NP-hard, we propose an approximate solution by solving the problem in the Lagrange dual domain. Through this Lagrange dual approach, we reveal a prominent structure, which enables us to derive a semi-closed form expression for the relay processing matrix that depends on a set of dual variables. These dual variables can be determined through an efficient semi-definite programming formulation. Compared with the traditional semi-definite relaxation (SDR) approach, the proposed solution has much lower computational complexity. Furthermore, it produces the optimal solution if such solution can be extracted from the SDR approach. Thus, the proposed solution can serve as a good alternative to the SDR approach, for the performance and complexity trade-off.