The integration of pinching antenna systems with non-orthogonal multiple access (NOMA) has emerged as a promising technique for future 6G applications. This paper is the first to investigate power minimization for NOMA-assisted pinching antenna systems utilizing multiple dielectric waveguides. We formulate a total power minimization problem constrained by each user's minimum data requirements, addressing a classical challenge. To efficiently solve the non-convex optimization problem, we propose an iterative algorithm. Furthermore, we demonstrate that the interference function of this algorithm is standard, ensuring convergence to a unique fixed point. Numerical simulations validate that our developed algorithm converges within a few steps and significantly outperforms benchmark strategies across various data rate requirements. The results also indicate that the minimum transmit power, as a function of the interval between the waveguides, exhibits an approximately oscillatory decay with a negative trend.

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