Pre-Channel Equalization and Distributed Beamforming in Asynchronous Single-Carrier Bi-Directional Relay Networks

We consider a single-carrier asynchronous two-way amplify-and-forward relay network, where two single-antenna transceivers exchange information with the help of several single-antenna relay nodes. We assume that the propagation delay of each relaying path, originating from one transceiver, going through a certain relay, and ending at the other transceiver, can be different from those of the other relaying paths. This assumption turns the end-to-end link into a multi-path channel, which produces inter-symbol-interference at the transceivers. In a block transmission/reception scheme, ISI results in inter-block-interference (IBI) between successive transmitted blocks. To combat IBI, cyclic prefix insertion and deletion as well as pre-channel block equalization are used at the two transceivers. Assuming a limited total transmit power budget, we minimize the total mean squared error between the transmitted and received signals at both transceivers by optimally obtaining the transceivers’ transmit powers and the relay beamforming weight vector as well as the pre-channel block equalizers at the transceivers. We prove that this optimization problem leads to a relay selection scheme, where only the relays contributing to one tap of the end-to-end channel impulse response, are turned on and the remaining relays are switched off. We present an efficient method to obtain the optimal values of the design parameters. Our simulation results show that compared to post-channel equalization, the proposed pre-channel equalization technique has the same performance as the post-channel equalization approach does, when the total available power is relatively low compared to the noise power at the transceivers, while offering receiver simplicity.