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The synchronous interference cancellation problem is addressed when training and working intervals are available, containing the desired signal and completely overlapping interference. A maximum likelihood (ML) approach is applied for estimation of the structured covariance matrices over both training and working intervals for a Gaussian data model. The special case is studied analytically, where the covariance matrix of the received signal is known a priori. This assumption corresponds to the practically important scenario of relatively large amount of information data in a burst compared to the amount of training data. It is shown that in this case the ML solution is equivalent to a regularized Least Square (LS) solution and the optimal regularization parameter is found. Furthermore, it is shown that the efficiency of the ML solution is close to the efficiency of the LS estimator, which means that the conventional training-based LS algorithm practically cannot be improved in the class of second-order semiblind techniques under the synchronous interference scenario.