  In view of noteworthy communications performance improvements for future
B5G/6G (such as cognitive Internet of Things, space-ground integration network
and so on), cooperative communications (CC) diversity with relays selection
algorithms have been extensively studied to significantly improve
communications quality, but so far there is still a lot of potential
optimization work with CC schemes. In this paper, in the light of NP-hard
problem of subsets relays selection, further studies for theorems of relays
subsets with K-layers power allocation standard have been put forward to
explore better performance in B5G/6G cognitive IoT (Internet of Things)
networks, we propose unified layers-based optimized mobile relays subsets
algorithms for full-duplex (FD) non-orthogonal multiple access (NOMA) to
greatly improve transmission rate. After revealing and taking into account
fundamental properties of relays, such as mobile relays nodes state, relays
locations, fading characteristics and so on, optimized FD-NOMA algorithm based
on these relays features has been presented to improve transmission validity,
and a related series of relays subsets theorems have been derived and proved,
then minimum upper bound of maximum transmission rates has been estimated to
reveal two-way balanced optimal transmission conclusion for FD-NOMA. In
general, proposed general and optimized algorithm can be used in multiple
future cooperative communications scenarios in B5G/6G networks such as
cognitive IoT. Simulations results show that proposed scheme has several times
transmission rates than other classical relays selection algorithms
