Distributed beamforming with compressed feedback in time-varying cooperative networks

In this paper, we investigate distributed beamforming with limited feedback for time varying cooperative network with multiple amplify-and-forward (AF) relays. With perfect channel state information, transmit beamforming has been shown to achieve significant diversity and coding gain in both MIMO or cooperative systems. However, it requires large amount of overhead for receiver to feed back channel information or beamforming coefficients, which makes it impractical. To perform transmit beamforming with limited feedback, the destination can choose the best codeword as beamforming vector from a predetermined codebook. In this work, we adopt the generalized Lloyd algorithm (GLA) to optimize codebook in terms of maximal average SNR. Furthermore, the feedback message can be compressed by exploiting temporal correlation of channel states. Specifically, We model channel states as a first-order finite-state Markov chain, and propose two compression methods according to the property of the transition probabilities among different channel states. Simulations show that distributed beamforming with compressed feedback performs closely to the case with infinite feedback.