Computation Over Multi-Access Channels: Multi-Hop Implementation and Resource Allocation

For future wireless networks, enormous numbers of interconnections are required, creating a multi-hop topology and leading to a great challenge on data aggregation. Instead of collecting data individually, a more efficient technique, computation over multi-access channels (CoMAC), has emerged to compute functions by exploiting the signal-superposition property of wireless channels. However, it is still an open problem on the implementation of CoMAC in multi-hop wireless networks considering fading channel and resource allocation. In this paper, we propose multi-layer CoMAC (ML-CoMAC) by combining CoMAC and orthogonal communication to compute functions in the multi-hop network. Firstly, to make the multi-hop network more tractable, we reorganize it into a hierarchical network with multiple layers that consists of subgroups and groups. Then, in the hierarchical network, the implementation of ML-CoMAC is given by computing and communicating subgroup and group functions over layers, where CoMAC is applied to compute each subgroup function and orthogonal communication is adopted for each group to obtain the group function. The general computation rate is derived and the performance is further improved through time allocation and power control. The closed-form solutions to optimization problems are obtained, which suggests that orthogonal communication and existing CoMAC schemes are generalized.