This paper considers the quality-of-service (QoS)-based joint beamforming and compression design problem in the downlink cooperative cellular network, where multiple relay-like base stations (BSs), connected to the central processor via rate-limited fronthaul links, cooperatively transmit messages to the users. The problem of interest is formulated as the minimization of the total transmit power of the BSs, subject to all users' signal-to-interference-plus-noise ratio (SINR) constraints and all BSs' fronthaul rate constraints. In this paper, we first show that there is no duality gap between the considered joint optimization problem and its Lagrangian dual by showing the tightness of its semidefinite relaxation (SDR). Then, we propose an efficient algorithm based on the above duality result for solving the considered problem. The proposed algorithm judiciously exploits the special structure of an enhanced Karush-Kuhn-Tucker (KKT) conditions of the considered problem and finds the solution that satisfies the enhanced KKT conditions via two fixed point iterations. Two key features of the proposed algorithm are: (1) it is able to detect whether the considered problem is feasible or not and find its globally optimal solution when it is feasible; (2) it is highly efficient because both of the fixed point iterations in the proposed algorithm are linearly convergent and evaluating the functions in the fixed point iterations are computationally cheap. Numerical results show the global optimality and efficiency of the proposed algorithm.

翻译：本文考虑下行协作蜂窝网络中基于服务质量（QoS）的联合波束赋形与压缩设计问题，其中多个类似于中继的基站（BS）通过速率受限的前传链路连接至中央处理器，协作向用户传输消息。该优化问题被表述为在所有用户信干噪比（SINR）约束和所有基站前传速率约束下，最小化基站总发射功率。首先，通过证明半定松弛（SDR）的紧性，本文证明了所考虑的联合优化问题与其拉格朗日对偶之间不存在对偶间隙。随后，基于上述对偶结果，提出一种求解该问题的高效算法。该算法巧妙利用了所考虑问题增强型卡鲁什-库恩-塔克（KKT）条件的特殊结构，并通过两个不动点迭代求解满足增强KKT条件的解。该算法的两个关键特性为：（1）能够检测所考虑问题是否可行，并在可行时找到全局最优解；（2）效率极高，因算法中的两个不动点迭代均为线性收敛，且不动点迭代中的函数评估计算成本较低。数值结果验证了所提算法的全局最优性与高效性。