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Deep Neural Networks (DNNs) using convolutional layers are state-of-the-art in many tasks in communications. However, in other domains, like image classification, DNNs have been shown to be vulnerable to adversarial perturbations, which consist of imperceptible crafted noise that when added to the data fools the model into misclassification. This puts into question the security of using DNNs in communication tasks, and in particular in modulation recognition. We propose a novel framework to test the robustness of current state-of-the-art models. We show that they are susceptible to these perturbations. We use the constellation space to analyze these vulnerable models and found that they do not base their decisions on signal statistics that are important for the Bayes-optimal modulation recognition model, but spurious correlations in the training data. Our feature analysis and proposed framework can help in the task of finding better models for communication systems.