arXiv:2610.08973v1 Announce Type: new Abstract: This paper investigates a reconfigurable intelligent surface (RIS)-assisted backscatter non-orthogonal multiple access (NOMA) network operating as the secondary system of an underlay cognitive radio network. A multi-antenna base station serves several user clusters through the RIS, each containing a backscatter device (BD). We maximise the weighted sum rate of the secondary network by jointly optimising the transmit beamformers and the RIS reflection matrix, subject to the power budget, the interference-temperature limit and minimum rate requirements. The non-convex problem is solved by alternating optimisation, using semidefinite relaxation and sequential rank-one constraint relaxation. Interference-normalised user ordering makes the successive interference cancellation constraints redundant. A closed-form equal-rate power split is derived; it agrees closely with simulation and costs about 4.5% of the sum rate. Supporting the BDs reduces the NOMA sum rate by 8.7% relative to a no-BD design, while a larger BD reflection coefficient raises the backscatter rate with little NOMA loss.