Communicating or Computing Over the MAC: Function-Centric Wireless Networks

Distributing data aggregation through multiple access channel (MAC) has been challenging in large wireless networks. In order to tackle the challenge, a computing over the MAC (CP-MAC) scheme has been proposed as a promising communication-computation integrated way for function-centric networks. In this paper, we analyze the performance of the CP-MAC scheme, compared with the traditional communication-computation separated way, i.e., a communicating over the MAC (CM-MAC) scheme. Function-centric wireless networks are considered, where the fusion center (FC) does not need the individual data of each node but only the target function. We begin with the ideal uniform-MAC scenarios, where the CP-MAC scheme is always better than the CM-MAC scheme. Then, practical non-uniform MAC scenarios are studied for both homogeneous networks with Rayleigh fading and heterogeneous networks with a different path loss. Closed-form expressions of the achievable function rate are provided using the asymptotic theory of ordered statistics. It is found that the CP-MAC scheme is not always superior to the CM-MAC scheme. Simulation results are provided to verify and illustrate our derived results.