Frequency-Domain Approach to Relay Beamforming With Adaptive Decision Delay for Frequency-Selective Channels

In this paper, we consider a two-hop relay network on frequency-selective channels where multiple relays assist in the communication from a source to a destination. To combat the channel distortion, a new approach to relay beamforming is proposed where a filter-and-forward (FF) relay scheme is adopted at the relays. In view of the fact that the channel distortion is essentially ascribed to the frequency selectivity and is hence more convenient to be described in the frequency domain, we formulate the relay beamforming problem in the frequency domain and present conditions under which the equivalent channel from the source to the destination is able to achieve distortionless response. Subject to this distortionless constraint as well as a total relay transmit power budget, we provide a close-form solution to the relay beamforming problem which maximizes the received signal-to-interference-plus-noise-ratio (SINR). Furthermore, we also consider the problem of adaptively optimizing the decision delay at the destination for each channel realization. Since the decision delay factor is simply represented by a scalar parameter in the frequency-domain model, we propose an approach with low computational load to search for the optimal decision delay adaptively. Simulation results demonstrate that the proposed approach achieves a substantial performance improvement over the non-adaptive delay selection approaches.