Interference Management of Analog Function Computation in Multicluster Networks

Computation over multiple access channels (CoMAC) has been proposed to solve the problem of spectrum scarcity in wireless networks, which combines communication and computation efficiently using the superposition property of wireless channels. In this paper, we consider a multi-cluster CoMAC network, whose performance is affected by the inter-cluster interference and the non-uniform fading. To minimize the sum mean squared error of signals aggregated at different fusion centers (FCs), we propose a transceiver design for multi-cluster CoMAC. Specifically, we adopt a uniform-forcing transmitter design to formulate the receiver design as a quadratic sum-of-ratios problem with nonconvex quadratic constraints. Then, we propose a branch-and-bound algorithm to find its optimal solution with a given error tolerance. To solve the problem in a decentralized way, we develop a distributed algorithm based on the primal decomposition theory. Each subproblem is solved by using the successive convex approximation method. Further combining Lagrange duality, we derive the optimal solution structure of each subproblem, based on which we can find the solution with lower complexity. Simulation results demonstrate the effectiveness of the proposed distributed transceiver design.