Sum-Rate Optimal Network Beamforming and Subcarrier Power Allocation for Multi-Carrier Asynchronous Two-Way Relay Networks

In this paper, we consider a multicarrier asynchronous bidirectional relay network, where different relay-transceiver links can cause different delays in the signals they convey, thereby producing inter-symbol-interference at the two transceivers. Such a two-way relay link can be modeled as a frequency selective channel with multiple taps, and thus, it can be equalized using orthogonal frequency division multiplexing (OFDM) transmission and reception schemes at the two transceivers, while the relays use simple amplify-and-forward relaying protocol. We prove rigorously that maximizing the sum-rate under a total power budget, through jointly optimal network beamforming at the relays and subcarrier power loading at the two transceivers, leads to a relay selection scheme, where only those relays which contribute to one tap of the end-to-end channel impulse response, have to be active and the remainder of the relays have to be switched off. The optimal tap can then be obtained using a simple search method. Moreover, we present semi-closed-form solutions for the optimal value of transceivers' subcarrier powers as well as for the relay beamforming weights.