Sub-Function Superposition for Computation Over NOMA

Massive numbers of nodes will be connected in future wireless networks. This brings great difficulty to collect a large amount of data. Instead of collecting the data individually, computation over multi-access channel (CoMAC) provides an intelligent solution by computing a desired function over the air based on the signal-superposition property of wireless channel. To improve the spectrum efficiency in conventional CoMAC, we propose the use of non-orthogonal multiple access (NOMA) for functions in CoMAC. The desired functions are decomposed into several sub-functions, and multiple sub-functions are selected to be superposed over each resource block. The corresponding achievable rate is derived based on sub-function superposition, which prevents a vanishing computation rate for large numbers of nodes. Compared with the existing CoMAC works, the NOMA-based CoMAC not only achieves a higher computation rate, but also provides an improved non-vanishing rate.