The problem of random access (RA) in a wireless SIMO-OFDM system is addressed and a decentralized medium access control (MAC) strategy is proposed based on the so called random orthogonal frequency division multiple access (ROFDMA). By employing receive beamforming, the problem of packet collisions at the same subcarrier are solved by using random spatial division multiple access (RSDMA), which therefore provides a multipacket reception (MPR) capability. First, we study the optimal number of users allowed to transmit at the same subcarrier and the same slot to maximize the separable packets subject to their BER requirements. Then the transmission probability based on user's channel gain is designed to achieve the desired number of users with the highest probability. Finally, a MPR scheme under average transmit power constraint is proposed with modulation selection. The performance of the proposed scheme is analyzed analytically and evaluated through simulations
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