Minimum Overhead Beamforming and Resource Allocation in D2D Edge Networks

Device-to-device (D2D) communications is expected to be a critical enabler of distributed computing in edge networks at scale. A key challenge in providing this capability is the requirement for judicious management of the heterogeneous communication and computation resources that exist at the edge to meet processing needs. In this paper, we develop an optimization methodology that considers the network topology jointly with device and network resource allocation to minimize total D2D overhead, which we quantify in terms of time and energy required for task processing. Variables in our model include task assignment, CPU allocation, subchannel selection, and beamforming design for multiple-input multiple-output (MIMO) wireless devices. We propose two methods to solve the resulting non-convex mixed integer program: semi-exhaustive search optimization, which represents a ``best-effort'' at obtaining the optimal solution, and efficient alternate optimization, which is more computationally efficient. As a component of these two methods, we develop a novel coordinated beamforming algorithm which we show obtains the optimal beamformer for a common receiver characteristic. Through numerical experiments, we find that our methodology yields substantial improvements in network overhead compared with local computation and partially optimized methods, which validates our joint optimization approach. Further, we find that the efficient alternate optimization scales well with the number of nodes, and thus can be a practical solution for D2D computing in large networks.