The process of amplify-and-forward (AF) relaying is essential to the improvement of both current and future wireless communication standards. Nevertheless, significant performance loss may be posed by in-phase and quadrature imbalance (IQI) caused by defects in radio frequency components. Prior studies into this research problem were restricted to uncoded broadcasts, even though error-correcting codes are frequently used in real applications. To this purpose, we develop a novel approach applicable to the destination terminal for estimating and compensating for IQI that occurs at the source, relay, and destination terminals. The proposed approach is explored in the context of coded emissions of AF single-carrier frequency domain equalization (SC-FDE) systems. In contrast to other methods for mitigating this radio frequency deflection at each node, the proposed system estimates and compensates for all IQI parameters and channel impulse responses simultaneously. With the use of an iterative expectation–maximization (EM) process, a maximum-likelihood (ML) solution to the problem is computed. At each round, the soft information supplied by the channel decoder is employed to create the a posteriori expectations of the sent data symbols, which are then fed into the estimation process as if they were training symbols. In addition, we address how to use the estimated parameters to perform the task of data detection. The offered predictor and detector exchange soft information in a sequential process, boosting the overall system effectiveness. The simulation results show that the proposed method is not only practicable but superior to the established methods.