  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.
