This paper explores multiuser multiple antenna systems as a means to enhance the spectral efficiency of aeronautical communications systems. To this end, the outage regime for a multiuser multiple antenna system is studied within a realistic geometry-based stochastic air-ground (AG) channel model. In this application, users (aircraft) transmit air traffic management data to the ground station at a predefined target rate. Due to the nature of the AG propagation, we argue that the relevant performance metric in this context is the information outage probability. We consider the outage probability under three decoding approaches. The first is based on successive interference cancellation (SIC). The second extends the first approach by considering joint group decoding. The third is a version of the second that limits the size of the jointly decoded user groups in order to lower the decoding complexity. The results show that joint group decoding, even in groups of only two, can significantly increase the spectral efficiency in the AG channel by allowing a large number of aircraft to transmit over a non-orthogonal channel with very low outage probabilities.