In this paper, we investigate the possibility of the cross-layer design of a distributed random access scheme with considering physical (PHY) and multiple access control (MAC) layers, which utilizes the interference cancellation technique. In this regard, we propose a new multiple access protocol, named carrier sense non-orthogonal multiple access (CSNOMA). We consider the spatially randomly distributed interferers to realistically capture the effect of interference. The proposed protocol shows better area spectral efficiency than carrier sense multiple access (CSMA), as the node density increases. We also present a practical signaling design compatible with IEEE 802.11 DCF mode.