Sum-rate maximization for asynchronous two-way relay networks

This paper is on sum-rate maximization, under a total transmit power budget, for an asynchronous single-carrier bidirectional (two-way) relay network. Considering a two-way relay network where two single-antenna transceivers exchange information through multiple single-antenna amplify-and-forward (AF) relays, we assume that different transceiver-relay links cause significantly different propagation delays in the signal they convey. This asynchronous bidirectional network is not amenable to a frequency flat end-to-end channel model, rather a multi- path end-to-end channel model with multiple taps appears to be more realistic. Such multi-path channel causes inter-symbol- interference (ISI) at the two transceivers. Such an ISI results in inter-block interference (IBI) in a block transmission/reception scheme which in turn can result in the loss of sum-rate, if it is not properly taken into account in the process of power allocation and network beamforming. Assuming the transceivers´ transmit powers as well as the relay beamforming weights as the design parameters, we rigorously prove that the sum-rate maximization problem of such a network leads to a relay selection scheme, where only those relays, which contribute to one of the taps of the end-to-end channel impulse response, are turned on and the rest of the relays are switched off. We present semi-closed-form solutions for the design parameters.