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The system outage probability of a mobile-relay-based two-way amplify-and-forward (AF) relaying system is investigated. Independently but not necessarily identically distributed N*Nakagami-m fading is adopted to provide a realistic description of the mobile-to-mobile (M2M) channel. By slightly adjusting the integral region, concise and generalised closed-form lower and upper bounds are obtained, providing valuable insight into practical system designs. Simulation results highlight the derived expressions and show that the lower bound can act as a tight closed-form outage probability expression.