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Active reconfigurable intelligent surface (ARIS) is a promising way to compensate for multiplicative fading attenuation by amplifying and reflecting event signals to selected users. This paper investigates the performance of ARIS assisted non-orthogonal multiple access (NOMA) networks over cascaded Nakagami- fading channels. The effects of hardware impairments (HIS) and reflection coefficients on ARIS-NOMA networks with imperfect successive interference cancellation (ipSIC) and perfect successive interference cancellation (pSIC) are considered. More specifically, we develop new precise and asymptotic expressions of outage probability and ergodic data rate with ipSIC/pSIC for ARIS-NOMA-HIS networks. According to the approximated analyses, the diversity orders and multiplexing gains for couple of non-orthogonal users are attained in detail. Additionally, the energy efficiency of ARIS-NOMA-HIS …