Maximum likelihood channel estimation for a full duplex relay is proposed, which estimates the residual self-interference (RSI) channel as well as the end-to-end channel of the relay system, aiming to cancel the RSI at the destination. The log-likelihood function is maximized through a quasi-Newton method, where alternative optimization and Euclidean projection are applied. The initial values of the quasi-Newton method are obtained from a minimum mean square error (MMSE) estimator to avoid local minima and increase the convergence speed. The Cramer-Rao bounds are derived to evaluate the accuracy of the estimates.
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