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In this paper, the synergy of combining the edge and central cloud computing is studied in heterogeneous cellular networks (HetNets). Multi-antenna small base stations (SBSs) equipped with edge cloud servers offer computing services for user equipment (UEs) proximally, whereas a macro base station (MBS) provides central cloud computing services for UEs via wireless multiple-input multiple-output (MIMO) backhaul allocated to their associated SBSs. With task processing latency constraints for UEs, the network energy consumption is minimized through jointly optimizing the cloud selection, the UEs' transmit powers, the SBSs' receive beamformers, and the SBSs' transmit covariance matrices. A mixed integer and non-convex optimization problem is formulated, and a decomposition algorithm is proposed to obtain a tractable solution iteratively. The simulation results confirm that great performance improvement …