NOMA-Enhanced Computation Over Multi-Access Channels

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 channels (CoMAC) provides an intelligent solution by computing a desired function over the air based on the signal-superposition property of wireless channels. 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 (RB). The corresponding achievable rate is derived based on sub-function superposition, which prevents a vanishing computation rate for large numbers of nodes. We further study the limiting case when the number of nodes goes to infinity. An exact expression of the rate is derived that provides a lower bound on the computation rate. Compared with existing CoMAC, the NOMA-based CoMAC not only achieves a higher computation rate but also provides an improved non-vanishing rate. Furthermore, the diversity order of the computation rate is derived, which shows that the system performance is dominated by the node with the worst channel gain among these sub-functions in each RB.