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In this paper, an efficient procedure for collision resolution in slotted ALOHA MIMO systems is proposed. We have proved in a previous work that packet collision resolution with spatial successive interference cancellation (SSIC) is a promising approach to improve the performance of slotted ALOHA protocol, when the colliding users' powers are different. However, it is not efficient for very close powers of collided packets. In this paper, we propose to solve this problem with a preliminary linear processing for its initialization. We evaluate the bit error rate and the throughput of the system using the proposed procedure. The simulation results show that we obtain an efficient random access method with high throughput for wireless transmission.