Migrating computational intensive tasks from mobile devices to more resourceful cloud servers is a promising technique to increase the computational capacity of mobile devices while saving their battery energy. In this paper, we consider an MIMO multicell system where multiple mobile users (MUs) ask for computation offloading to a common cloud server. We formulate the offloading problem as the joint optimization of the radio resources-the transmit precoding matrices of the MUs-and the computational resources-the CPU cycles/second assigned by the cloud to each MU-in order to minimize the overall users' energy consumption, while meeting latency constraints. The resulting optimization problem is nonconvex (in the objective function and constraints). Nevertheless, in the single-user case, we are able to compute the global optimal solution in closed form. In the more challenging multiuser scenario, we propose an iterative algorithm, based on a novel successive convex approximation technique, converging to a local optimal solution of the original nonconvex problem. We then show that the proposed algorithmic framework naturally leads to a distributed and parallel implementation across the radio access points, requiring only a limited coordination/signaling with the cloud. Numerical results show that the proposed schemes outperform disjoint optimization algorithms.
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