In the cooperative cellular network, relay-like base stations are connected to the central processor (CP) via rate-limited fronthaul links and the joint processing is performed at the CP, which thus can effectively mitigate the multiuser interference. In this paper, we consider the joint beamforming and compression problem with per-antenna power constraints in the cooperative cellular network. We first establish the equivalence between the considered problem and its semidefinite relaxation (SDR). Then we further derive the partial Lagrangian dual of the SDR problem and show that the objective function of the obtained dual problem is differentiable. Based on the differentiability, we propose two efficient projected gradient ascent algorithms for solving the dual problem, which are projected exact gradient ascent (PEGA) and projected inexact gradient ascent (PIGA). While PEGA is guaranteed to find the global solution of the dual problem (and hence the global solution of the original problem), PIGA is more computationally efficient due to the lower complexity in inexactly computing the gradient. Global optimality and high efficiency of the proposed algorithms are demonstrated via numerical experiments.

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