Design of downlink beamformer for real-time and non-real-time services

We study the downlink beamformer design problem considering different real-time requirements of users. The problem is formulated mathematically as a non-convex optimization problem. The objective is to maximize the minimum signal to interference plus noise ratio (SINR) of the non-real-time service users, considering the SINR constraints of the real-time users and the total transmission power constraint. We carefully study the feasibility conditions for the original non-convex optimization problem. The results provide both theoretical and physical insights into the beamformer design problem. After a series of equivalence and relaxation of the original problem, the solution can be found via bisection feasibility checking and solving a set of geometric programming (GP) problems obtained from randomization. Combining the feasibility checking algorithm and the randomization procedure, we have our algorithm for computing the beamforming vector. Numerical results are provided for illustration.