In order to overcome the non-transition issue of the conventional reconfigurable intelligent surface, a signal enhancement algorithm based on non-orthogonal multiple access networks is proposed, aided by simultaneous-transmitting-and-reflecting reconfigurable intelligent surfaces. By utilizing the omni property of the simultaneous-transmitting-and-reflecting reconfigurable intelligent surface, it is possible to serve multiple users on both sides simultaneously. Since the direct signal and the reflected signals through simultaneous-transmitting-and-reflecting reconfigurable intelligent surface can be coherent, and by utilizing the Riemannian conjugate gradient algorithm, the signal power level of non-orthogonal multiple access users can be significantly boosted by the proposed signal enhancement based algorithm. As a result, the outage probability is decreased and the transmission rate performance is enhanced. Simulation results show that an improvement of 3.6 bit / (s· Hz) spectral efficiency is observed in the random phase shift scenario, compared to the scenario without simultaneous-transmitting-and-reflecting reconfigurable intelligent surface. Furthermore, an extra 2.3 bit / (s· Hz) gain on the spectral efficiency can be obtained when the proposed Riemannian conjugate gradient algorithm is employed, which validates the superiority of the proposed algorithm.