Network coordinated beamforming with per-cell power constraints

This paper considers transmit beamforming optimization problem for a multi-cell downlink channel with multiple transmit antennas at the base-station. In contrast to the conventional sum-power constraint on the transmit antennas, this paper adopts a per-cell power constraint, which is more realistic in practical implementations. Assuming that the second-order statistics of the channel coefficients are available, this paper investigates the optimization problem of minimizing the total transmission power with individual signal-to-interference-plus-noise ratio (SINR) constraint and per-cell transmission power constraint using Lagrangian duality theory. It is shown that with the approach of Lagrangian duality, the downlink beamforming problem with per-cell power constraint can be transformed into a dual uplink minimax problem with an uncertain noise, and the uplink-downlink duality gives rise to efficient numerical algorithm for solving the downlink per-cell beamforming problem.