Achieving low-power wide coverage and good spectral efficiency is one of the main objectives of next-generation wireless communication. Non-Orthogonal Multiple Access (NOMA)-assisted Ambient Backscatter Communication (AmBC) has proven to be capable of offering great spectral efficiency at low power. In contrast, Intelligent Reflecting Surface (IRS) has proven to be capable of improving coverage. Consequently, efforts have been made to integrate those technologies. However, thorough model development and analysis are necessary to benefit from such coexistence. In this study, we analyze the performance of a Power Domain (PD)-NOMA-enabled base station acting as a source in a multiple-user IRS-assisted AmBC system. The main approach we take is to use PD-NOMA to send a signal from the base station to the IRS that has both modulated (with a primary message) and unmodulated carrier components. In addition to relaying the primary message, the IRS will then send its (secondary) message to user devices utilizing the unmodulated carrier and Binary Phase-shift Keying (BPSK). Then, using a Band Pass Filter (BPF) and Successive Interference Cancellation (SIC), the user devices decode their respective messages from the received signals. To obtain further understanding, we derived novel closed-form expressions for the Outage Probabilities (OPs) and also provided asymptotic assessments of the OPs. Our results show that raising the IRS element count enhances the OPs. Additionally, devices' outage performance is impaired due to the imperfections in SIC. Furthermore, we found that a device's OP rises as the power allocation factor increases. Lastly, we found that the NOMA-based IRS-assisted system outperforms OMA-based systems in terms of outages. |