In this paper, we explain how to implement differential modulation in multiple access channel (MAC) based uplink two-user multiple-input multiple-output (MIMO) communication system. It is assumed that the users cannot exchange their information and transmit data over uplink MAC channels simultaneously in the same frequency band and without any orthogonal signatures (no CDMA). We derive two types of differential decoders for two-user MIMO MAC system namely 1) Partial differential decoder, 2) Heuristic based differential decoders. The partial differential decoder is able to avoid the knowledge of the channel gains of one user at the receiver for joint decoding of the data of both users. Whereas, the heuristic differential decoders are obtained heuristically and work without any channel knowledge of both users. For the heuristic differential decoder to work properly, the data of one user must be rotated before transmission. An upper bound of the pairwise error probability (PEP) is derived for the proposed scheme. The upper bound of the PEP is minimized for obtaining an optimized value of the rotation angle.
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