Gateway User 1 Destination 2 Destination 3 Destination K User 2 User 3 User

This paper is concerned with the performance analysis of a dual-hop random access network where a single gateway is employed to connect a random number of independent users which are hidden from their destination(s). The gateway is an amplify and forward relay, and is the only mean to connect users to their destinations. We develop accurate mathematical models for the multiple access interference which take into account, in addition to the distribution of the number of active users and their random locations, the effects of fading and thermal noise at both the relay and destinations. A new unified mathematical method is developed, which leads to the derivation of new analytical expressions for the overall spectral-efficiency of the dual-hop random access network over Rayleigh and Nakagamim fading channels. The accuracy of the new mathematical results is confirmed by Monte Carlo simulation. The results of this paper can be used to estimate the aggregate throughput of a dual-hop system employing the slotted-Aloha type protocols.