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A new packet-based, multiple access scheme for connectionless, uncoordinated random access is proposed using code-division multiple access (CDMA) as the typical access method. The new method uses a novel packet format with a common header with identical spreading codes for the data portion. The receiver operates in two stages: header detection using a conventional spread spectrum receiver and data detection using a multiuser detector to allow for decoding of overlapping active packets. The headers are spread with a large enough processing gain to allow detection even in severe interference. It is shown that this system is detector capability limited and that it can significantly outperform conventional ALOHA systems whose performance is limited by the collision mechanism. This system also experiences a much smaller packet retransmission rate and better spectral efficiency than conventional or spread ALOHA.