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We consider cooperation in downlink non-orthogonal multiple access (NOMA) in a network supporting diverse communication modes. One user (UE2) exists as a potential relay between a base station (BS) and another user (UE1). With relaying the signal for UE1, UE2 obtains the opportunity for its own transmission to UE3 in D2D mode, meanwhile maintaining the transmission efficiency for UE1. On the basis of supporting different communication modes, we propose a NOMA-based cooperation scheme at UE2 to combine the relay message with its own. We derive achievable rate regions for two cases depending on the status of the Rayleigh fading channel of the UE2. We find solutions based on experiments through the transmit power allocation strategy at the UE2 and(/or) the BS. We show the impacts of our cooperative scheme and the corresponding user geometry on the achievable rates and the resource …