Multi-user downlink resource allocation with per-base station power constraints

The problem of Downlink (DL) sum-rate maximization with required Quality of service (QoS) for a multi-cell, multi-user with per-Base Station (BS) power constraints is solved by an Interior Point Method (IPM). Further, by changing only the objective in the formulation, the problem of DL sum-power minimization with QoS is also solved. For a single-cell, the concept of duality and virtual uplink (VUL) is well understood to solve the DL problem. This cannot be extended to the multi-cell case with per-BS power constraints, also, the total sum-power on the DL and VUL may not be equal as in the single-cell. For a multi-cell, Lagrange-duality is applied to satisfy the power constraints, where the VUL-noise is also an optimization variable. In this paper, the implicit Lagrange-duality in the IPM is used to solve the equivalent VUL problem. With this reformulation, the need to treat VUL-noise as an optimization variable is eliminated. Single-cell duality requirement of equal total sum-power on DL and VUL is also satisfied. Numerical results show that the obtained VUL optimum satisfies the DL constraints thereby satisfying the multi-cell duality.