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This study investigates power‐domain non‐orthogonal multiple access based wireless information exchange process. The investigation considers a dual‐hop non‐regenerative full‐duplex wireless one‐way relaying networks in the system model, where the source terminal transmits two different types of information and subtracts the interference signal at the destination by using successive interference cancellation technique. The outage probability, error probability, achievable rate, and ergodic rate of the considered system is analytically derived. In addition, optimum power allocation coefficients and relay terminal position are determined using the optimization techniques. Monte‐Carlo simulation results validate the analytical and asymptotic derivations. The derived analytical expressions are found closely in agreement with the system level numerical results.