  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.
