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This paper discusses a general framework for evaluating the throughput performance of adaptive antenna arrays when the Slotted ALOHA protocol is employed as the random access mechanism for wireless packet transmission. A novel blind adaptive algorithm is presented and its performance is assessed by comparison with the minimum mean squared error (MMSE). Two propagation scenarios are considered: line of sight and Rayleigh fading. The results are obtained through a mix of analysis and simulation and it is shown that the proposed algorithm allows the antenna array to attain a high fraction of the optimal MMSE gains without resorting to training sequences.