  Consider the joint beamforming and quantization problem in the cooperative
cellular network, where multiple relay-like base stations (BSs) connected to
the central processor (CP) via rate-limited fronthaul links cooperatively serve
the users. This problem can be formulated as the minimization of the total
transmit power, subject to all users' signal-to-interference-plus-noise-ratio
(SINR) constraints and all relay-like BSs' fronthaul rate constraints. In this
paper, we first show that there is no duality gap between the considered
problem and its Lagrangian dual by showing the tightness of the semidefinite
relaxation (SDR) of the considered problem. Then we propose an efficient
algorithm based on Lagrangian duality for solving the considered problem. The
proposed algorithm judiciously exploits the special structure of the
Karush-Kuhn-Tucker (KKT) conditions of the considered problem and finds the
solution that satisfies the KKT conditions via two fixed-point iterations. The
proposed algorithm is highly efficient (as evaluating the functions in both
fixed-point iterations are computationally cheap) and is guaranteed to find the
global solution of the problem. Simulation results show the efficiency and the
correctness of the proposed algorithm.
