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The linear minimum mean-squared error (MSE) channel estimator for systems employing per-subcarrier transmit antenna selection is developed. Frequency domain correlations after the selection process are shown to be approximated well using a simple function, which makes near-optimal channel estimation practically possible. However, the resultant estimators are not robust to errors in the assumed model, in terms of the antenna-to-subcarrier assignment used at transmission, as we motivate both analytically and via simulations. This is an issue when the channels for conveying this information to the receiver are severely constrained. We present windowed channel estimations and new robust estimation algorithms, either individually or in combination, as solutions to counter this sensitivity. The robust estimators are developed based on the principles of 1) minimising the worst case MSE over the set of possible models and 2) minimising the expected MSE over the set of possible models. The latter estimator is preferred due to the lower implementation complexity and better MSE performance. We also prove theoretical asymptotic (in signal-to-noise ratio) performances of the two estimators used with the proposed correlation model. Simulation results illustrate the performance gains and improved robustness offered by the developed estimators.