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In this paper, we analyze the performance of multi-hop transmission systems that employ amplify-and-forward relays over a Rayleigh fading environment in the presence of a Poisson field of interferers. The interference model considers the effect of spatial distribution of co-channel interferers in the vicinity of the relays and the destination node. Using a tight upper bound on the end-to-end signal-to-interference ratio, a closed-form expression for the system outage probability is derived. Moreover, a lower bound for the average symbol error rate of general modulations, the exact average bit error rate (BER) of binary modulations and the average channel capacity are presented in the form of single-fold integrals that can be reliably evaluated numerically, whereas closed-form results are obtained for a special case of the dual-hop relaying system. Finally, asymptotic expressions for the system outage probability and the end-to-end BER are derived which provide useful insights regarding the factors affecting the performance of the considered system. The novel expressions can be used to show the impact of interference model parameters such as the transmit power, path loss exponent, and spatial density of interferers on the performance of multi-hop wireless systems. Simulation results are further provided to demonstrate the accuracy of the analytical expressions.