This paper presents a resource allocation scheme that fulfills the maximum possible aggregate rate of the capacity region by targeting the corner points of the multiple-input multiple-output multiple access channel. This corner points of the channel’s capacity region are attainable whenever each user’s transmission has minimum possible interference among other users. This work aims to investigate the non-singularity of such situations by the exploitation of users’ geographic location seeking the opportunity of getting users’ transmission spatially multiplexed. The developed model demonstrates that similar results can be achieved with partial channel state information knowledge under certain conditions throughout the operational signal to noise ratio range. The proposed resource allocation scheme is designed for a shotgun cellular system with a random distribution of users over a circular coverage area. The proposed model uses stochastic geometry to prove that when number of users grows up within the coverage area, the probability of achieving the corner points sum rate increases rapidly. The developed model was evaluated, and the results show that for a circular coverage area with a radius of 10 km, the probability of having users whose transmissions can be spatially multiplexed with minimum interference increases as the number of users grows to 300 users.