Deep learning (DL) based direction of arrival (DOA) estimation is an active research topic and currently represents the state-of-the-art. Usually, DL-based DOA estimators are trained with recorded data or computationally expensive generated data. Both data types require significant storage and excessive time to, respectively, record or generate. We propose a low complexity online data generation method to train DL models with a phase-based feature input. The data generation method models the phases of the microphone signals in the frequency domain by employing a deterministic model for the direct path and a statistical model for the late reverberation of the room transfer function. By an evaluation using data from measured room impulse responses, we demonstrate that a model trained with the proposed training data generation method performs comparably to models trained with data generated based on the source-image method.