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Consider the joint beamforming and quantization problem in the cooperativecellular network, where multiple relay-like base stations (BSs) connected tothe central processor (CP) via rate-limited fronthaul links cooperatively servethe users. This problem can be formulated as the minimization of the totaltransmit power, subject to all users' signal-to-interference-plus-noise-ratio(SINR) constraints and all relay-like BSs' fronthaul rate constraints. In thispaper, we first show that there is no duality gap between the consideredproblem and its Lagrangian dual by showing the tightness of the semidefiniterelaxation (SDR) of the considered problem. Then we propose an efficientalgorithm based on Lagrangian duality for solving the considered problem. Theproposed algorithm judiciously exploits the special structure of theKarush-Kuhn-Tucker (KKT) conditions of the considered problem and finds thesolution that satisfies the KKT conditions via two fixed-point iterations. Theproposed algorithm is highly efficient (as evaluating the functions in bothfixed-point iterations are computationally cheap) and is guaranteed to find theglobal solution of the problem. Simulation results show the efficiency and thecorrectness of the proposed algorithm.

Efficiently and Globally Solving Joint Beamforming and Compression Problem in the Cooperative Cellular Network via Lagrangian Duality