This paper studies the resource allocation for a multi-user two-way amplify-and-forward （AF） relay network over orthogonal frequency-division multiplexing （OFDM） technology, where all users communicate with their pre-assigned partners. Using convex optimization techniques, an optimal solution to minimize the total transmit power while satisfy each user-pair＇s data rate requirements is proposed. We divide the resource allocation problem into two subproblems： （1） power optimization within user-pair and relay in each subcarrier. （2） optimal subcarrier allocation and sum power assignment among N parallel OFDM subcarriers. Closed-form expressions of the power among user-pair and relay can be obtained in subproblem （1）, and so the proposed algorithm decreases the variable dimensionality of the objective function to reduce the complexity of this optimization problem. To solve it, a three-step suboptimal approach is proposed to assign the resources to user-pairs： Firstly, decompose each user-pair into two sub user-pairs which have one-way and two-way relaying transmission modes. Secondly, allocate the subcarriers to the new mode user-pairs and assign the transmit power to each carrier. Thirdly, distribute the assigned power to three nodes allocated in the subcarrier. Simulation results demonstrate the significant power is saved with the proposed solutions, as compared to a fixed subcarrier allocation.
