Optimum/sub-optimum detectors for multi-branch dual-hop amplify-and-forward cooperative diversity networks with limited CSI

We study the optimum maximum-likelihood (ML) detection and sub-optimum detection for a multi-branch dual-hop cooperative diversity network with limited channel state information (CSI). Compared to the full CSI strategy, the signalling overhead at each relay involved with the limited CSI is reduced by 50%. We derive optimum ML detection with the limited CSI, which involves numerical integral evaluations. We also propose two closed-form sub-optimum detection rules of low complexity. It is shown that the first sub-optimum detection has almost identical performance to the optimum ML detection when Gaussianity in the added noise dominates, and the second sub-optimum detection has almost identical performance to the optimum ML detection when non-Gaussianity dominates. Finally, we propose a hybrid sub-optimum detection and demonstrate that its performance is almost identical to that of the optimum ML detection for general cases.