Joint estimation of the channel and I/Q imbalance for two-way relay networks

In this work, we consider amplify-and-forward two-way relay networks operating under the imperfect conditions of in-phase and quadrature-phase (I/Q) imbalance. We propose novel, efficient solutions for the problem of joint channel and I/Q imbalance estimation and the related problem of optimal pilot design. Three different estimation algorithms are developed. The first is the pilot-based maximum-likelihood (ML) estimator. The second is a semi-blind estimator that employs the expectation–maximization (EM) strategy. The third is the semi-blind decision-directed (DD) estimator. As benchmarks on estimation performance, we obtain the analytical expressions for the Cramer–Rao bound (CRB) for pilot-based estimation, and the modified-CRB for semi-blind estimation. In addition to the estimation algorithms, we propose an optimal pilot design that minimizes the mean-squared estimation error. Using simulations, we show that both the pilot-based ML and the semi-blind EM converge to their respective exact CRBs. Importantly, it is shown that both the EM and the DD estimators offer substantially higher estimation accuracy than pilot-based estimation, as well as improved symbol-error-rate (by up to 1.8 dB), which is achieved at a low computational cost.