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Future networks are expected to connect an enormous number of nodeswirelessly using wide-band transmission. This brings great challenges. To avoidcollecting a large amount of data from the massive number of nodes, computationover multi-access channel (CoMAC) is proposed to compute a desired functionover the air utilizing the signal-superposition property of MAC. Due tofrequency selective fading, wide-band CoMAC is more challenging and has neverbeen studied before. In this work, we propose the use of orthogonal frequencydivision multiplexing (OFDM) in wide-band CoMAC to transmit functions in asimilar way to bit sequences through division, allocation and reconstruction offunction. An achievable rate without any adaptive resource allocation isderived. To prevent a vanishing computation rate from the increase of thenumber of nodes, a novel sub-function allocation of sub-carriers is derived.Furthermore, we formulate an optimization problem considering power allocation.A sponge-squeezing algorithm adapted from the classical water-filling algorithmis proposed to solve the optimal power allocation problem. The improvedcomputation rate of the proposed framework and the corresponding allocation hasbeen verified through both theoretical analysis and simulation.

Computation over Wide-Band MAC: Improved Achievable Rate through Sub-Function Allocation