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 over frequency-selective channels. Orthogonal frequency division multiplexing (OFDM) transmission is employed to resist the multipath effects. We focus on the time-domain (TD) BF due to the lower implementation complexity and less feedback requirement from the destination to perform BF. Our aim of the BF design is maximizing the minimum signal-to-noise-ratio (SNR) over all subcarriers at the destination, first under the total power constraint (TPC) and then under the per-relay power constraint (PPC). We show that the BF designs lead to non-convex problems generally. Three approaches to approximate these problems to convex problems are proposed. In the first approach, semidefinite relaxation (SDR) techniques with randomization methods is applied. This approach provides an upper bound of the optimum value of the design problem but with higher complexity. In the second approach, the existing iterative method for cooperative beamforming of multi-group multicasting (MGM) relay networks is extended to solve our problem. And the second approach is further improved by appropriately choosing the initial phase rotation in the third approach. Simulation results demonstrate that the third approach always outperforms the other two approaches. Moreover, the second approach performs closely to the first approach when the filter length is relatively small. When longer TD filter is employed, the second approach outperforms the first approach. Preprint submitted to Elsevier October 5, 2011