Intelligent Reflecting Surfaces (IRS) have revolutionized wireless communication systems through their adaptive reconfiguration of the radio propagation environment. This paper compares an IRS-assisted non-orthogonal multiple access (NOMA) system and a relay-assisted NOMA system. The investigation delves into the impact of the number of IRS elements on the performance of a two-user NOMA system. A dynamic power allocation scheme is proposed based on the number of IRS elements. Specifically, analytical investigations reveal the range, upper, and lower bounds of power allocation coefficients. The asymptotic values of these bounds are also determined. Furthermore, an optimization problem is formulated to maximize the sum-rate while considering individual minimum rate constraints. The minimum number of passive reflecting elements required by the IRS is determined to meet the minimum target data rates for both users. Analytical calculations determine the optimal number of IRS elements, minimizing total power consumption. Simulation results confirm the superiority of the IRS over the decode-and-forward relay approach.
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