Exact Cramer–Rao Bounds for Semiblind Channel Estimation in Amplify-and-Forward Two-Way Relay Networks Employing Square QAM

In this paper, we derive the Cramer–Rao bound (CRB) for semiblind channel estimation in amplify-and-forward two-way relay networks employing square QAM, assuming flat-fading channel conditions. The derived bound is exact as it is based on the true likelihood function that takes into account the statistics of the transmitted data symbols. Using the new bound, we show that exploiting even a limited number of transmitted data symbols in addition to the pilot symbols leads to substantial estimation accuracy improvements over conventional pilot-based estimation. We also propose a semiblind expectation-maximization-based estimation algorithm that performs very close to the exact CRB at an affordable computational cost. The superior accuracy of the semiblind approach makes it possible to significantly reduce the training overhead for channel estimation, thus offering a higher throughput and a better tradeoff between accuracy and spectral efficiency. We also derive the modified CRB, which approximates the exact CRB at high SNR for low modulation orders.