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With macro and micro base stations (BSs) of different transmission and processing capabilities jointly deployed, heterogeneous networks effectively extend the coverage and capacity of wireless networks and have been adopted as one of the key technologies in Fourth-Generation-Long-Term Evolution (4G-LTE). To fully exploit the benefits of heterogeneous networks, proper mobile association, interference management, and radio resource management schemes need to be developed. In this paper, we investigate radio resource allocation for heterogeneous networks with cooperative relays, where the relay nodes (RNs) with in-band backhaul act as micro BSs and are able to serve user equipment (UE) either independently or cooperatively with the BSs. In such a network, radio resource-allocation schemes need to decide for each resource block: 1) whether a UE is served by a BS or an RN, and 2) whether a UE should be cooperatively served or not. In making these decisions, radio resource consumption on RN's in-band backhaul links and fairness among the UEs should be taken into consideration, which further complicates the resource-allocation problem. In this paper, we propose a radio resource-allocation framework and derive a resource-allocation strategy that is asymptotically optimal on the proportional fairness metric. The derived resource-allocation scheme gives insights on the optimal radio resource allocation for the heterogeneous networks with cooperative RNs using in-band backhauls.