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This paper studies the throughput enhancement in a wireless slotted ALOHA system via multi-user detection. For this aim, we focus on uplink access and propose an iterative receiver algorithm that can jointly detect the colliding packets for different users that share the same physical channel. This algorithm performs a spatial successive interference cancellation. We show that its performance can be improved with a good initialization. We evaluate the throughput of the system when we apply the iterative receiver for the detection of two and three colliding user packets. We show that our approach improves considerably the performance of the slotted ALOHA system since a packet can be received correctly, even if it collides with one or two other user packets.