Joint Power Allocation and Distributed Equalization Design for OFDM-Based Filter-and-Forward Two-Way Multi-Relay Networks

We consider multi-carrier two-way relaying networks consisting of two user transceivers and multiple filter-and-forward (FF) relays. The FF relaying technique along with the multi-carrier schemes at the transceivers are utilized to suppress the inter-symbol-interference caused by the frequency-selectivity of the end-to-end channel. We jointly optimize subcarrier power allocation at the transceivers and the FIR filters at the FF relays to minimize the total transmit power subject to two quality of service constraints measured by sum-rates at the transceivers. We propose two approaches to tackle this problem: a gradient steepest descent technique, and a semi-closed-form method, which enforces a new constraint on the optimization such that at the optimum, the frequency-selective end-to-end channel is turned into a frequency-flat one. Furthermore, we show that the second method can be used as an initial point for the gradient steepest descent technique. Aiming to evaluate the performance of the proposed methods with a benchmark, we obtain a lower bound for the minimum transmit power at the network. We show that the proposed techniques are within 3 dB of this lower bound. Our numerical results further show that the proposed methods outperform existing solutions for similar networks.