This paper is concerned with the performance of a gateway connecting a group of independent users to their destinations and employ the random slotted- Aloha type protocol. The users are isolated from their destinations and the only way to communicate with their destinations is through the common gateway which acts as a blind amplify and forward relay. Users are randomly distributed around the gateway and experience a Rayleigh or Nakagami-m fading channels. This paper develops a new accurate models for the multiple access interference at both the gateway and the destinations taking into account, in addition to the random number of the active users and their locations, the effects of fading and thermal noise at both the relay and the destinations. This leads to the derivation of new analytic expressions for the overall spectral efficiency which can be used to estimate the throughput of the aloha based gateways in Rayleigh and Nakagami-m fading channels and to study the impact of the different system parameters into their efficiency. The accuracy of the new mathematical results is confirmed by Monte Carlo simulation.