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With the advent of 5G and the need for energy-efficient massively connected wireless networks, in this work, we consider an energy harvesting (EH) based multi-relay downlink cooperative non-orthogonal multiple access (NOMA) system with practical constraints. The base station serves NOMA users with the help of decode-and-forward based multiple EH relays, where relays harvest the energy from the base station's radio frequency. A relay is selected from the multiple -relays by using a partial relay selection protocol. The system is considered to operate in half-duplex mode over a generalized independent and identical Nakagami fading channel. The closed-form expression of outage probability and ergodic rate are derived for users, under the assumption of imperfect channel state information (CSI) and imperfect successive interference cancellation (SIC) at the receiver node. Expression of outage …