Cooperative beamforming for OFDM-based amplify-and-forward relay networks

In this paper, we investigate the cooperative beamforming (BF) design problem for amplify-and-forward relay networks that are operating over frequency-selective channels using Orthogonal frequency division multiplexing (OFDM) signaling. We focus on the time-domain (TD) BF due to the lower implementation complexity and lower feedback requirement from the destination. Our aim for the BF design is maximizing the minimum signal-to-noise-ratio (SNR) over all subcarriers at the destination. We show that the BF designs lead to non-convex problems generally. Three approaches to approximate these problems into convex problems are proposed. In the first approach, semidefinite relaxation (SDR) techniques with randomization methods are applied. In the second approach, an existing iterative method for cooperative beamforming of multi-group multicasting (MGM) relay networks is extended to solve our problem. The third approach consists of improving the second approach by appropriately choosing the initial phase rotation. Simulation results demonstrate that the third approach always outperforms the other two approaches. Moreover, the performance of the second approach is close to that of the first approach when the filter length is relatively small. When a longer TD filter is employed, the second approach outperforms the first approach.