Cooperative Amplify-and-Forward Beamforming for OFDM Systems with Multiple Relays

In this paper, we propose frequency-domain (FD) and time-domain (TD) beamforming (BF) schemes for cooperative orthogonal frequency division multiplexing (OFDM) networks with multiple amplify-and-forward relays. Whereas for FD-BF the BF weights are applied in the FD, for TD-BF cyclic BF filters (C-BFFs) are used on the TD signal avoiding discrete- time Fourier transform operations at the relays and drastically reducing the required amount of feedback from the receiver to the relays. Adopting the average mutual information (AMI) per sub-carrier as optimality criterion, we show that the direction of the optimal FD-BF weights can be obtained in closed-form and that the optimal sub-carrier power allocation (PA) problem is convex. For solution of the PA problem an interior point method and a bisectional search dual method are provide. Furthermore, for solution of the C-BFF optimization problem an efficient gradient algorithm is proposed. Simulation results for IEEE 802.11n channels show that TD-BF with short C-BFFs closely approaches the performance of FD-BF and outperforms direct transmission without relaying.